Rectangle W X Y Z is cut diagonally into 2 equal triangles. Angle Y X Z is 26 degrees and angle X Z W is x degrees. Angles Y and W are right angles.
The angle relationship for triangle XYZ is
26° + 90° + m∠YZX = 180°.
Therefore, m∠YZX = 64°.
Also, m∠YZX + m∠WZX = 90°.
So, x =

Answers

Answer 1

The value of x is 0 degrees.

To find the value of angle XZW (denoted by x), we can use the information provided in the problem.

We know that angle YXZ is 26 degrees and angle Y and angle W are right angles, which means they are 90 degrees each.

In triangle XYZ, the sum of the angles is 180 degrees. Therefore, we can write the equation: angle YZX + angle YXZ + angle ZXY = 180 degrees.

Substituting the given values, we have: 64 degrees + 26 degrees + angle ZXY = 180 degrees.

Simplifying the equation, we get: angle ZXY = 90 degrees.

Now, we can look at triangle ZWX. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can write the equation: angle ZWX + angle WXZ + angle XZW = 180 degrees.

Substituting the known values, we have: angle ZWX + 90 degrees + x degrees = 180 degrees.

Simplifying the equation, we get: angle ZWX + x degrees = 90 degrees.

Since we know that angle ZWX is 90 degrees (from the previous calculation), we can substitute it into the equation: 90 degrees + x degrees = 90 degrees.

Simplifying further, we have: x degrees = 0 degrees.

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Answer 2

Answer:

x=26 degrees

Step-by-step explanation:


Related Questions

Score 3. (Each question Score 15, Total Score 15) Use elementary transformation to transform the matrix A into standard form. 03 -62 A -78 -1 -9 12 1 =

Answers

By using elementary transformation, the matrix A can be transformed into standard form.

To transform the matrix A into standard form, we will use the elementary transformation method. Firstly, we can interchange the first row with the second row of matrix A. This gives us the new matrix A':-62 03 -78 -1 -9 12 1.Next, we can add 2 times the first row to the second row of matrix A'.

This gives us the new matrix

A'':-62 03 -78 -1 -9 12 1 -65 -06 -57.

Now, we can add 13 times the first row to the third row of matrix A''. This gives us the new matrix

A''':-62 03 -78 -1 -9 12 1 -65 -06 -57 149 40 -67.

Finally, we can add 9 times the first row to the fourth row of matrix A'''. This gives us the final matrix A in standard form:-

62 03 -78 -1 -9 12 1 -65 -06 -57 149 40 -67 551 186 139.

Note: The standard form of matrix A is a matrix in row echelon form where each leading entry of a row is 1 and each leading entry of a row is in a column to the right of the leading entry of the previous row.

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lim z->0 2^x - 64 / x - 6 represents the derivative of the function f(x) = _____at the number α = ________

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The derivative of the function f(x) = 2^x at the number α = 6 is given by the expression lim z->0 (2^x - 64) / (x - 6).

To find the derivative of the function f(x) = 2^x at α = 6, we use the definition of the derivative, which involves taking the limit of the difference quotient as x approaches α.

In this case, the expression lim z->0 (2^x - 64) / (x - 6) represents the difference quotient, where z is a small number that approaches zero. By substituting α = 6 into the expression, we have:

lim z->0 (2^6 - 64) / (6 - 6)

= (2^6 - 64) / 0

Here, we encounter an indeterminate form of division by zero. To determine the derivative, we need to apply a mathematical technique called L'Hôpital's rule, which allows us to evaluate limits involving indeterminate forms.

By differentiating the numerator and the denominator separately and taking the limit again, we can find the derivative of the function:

lim z->0 (2^x - 64) / (x - 6)

= lim z->0 (ln(2) * 2^x) / 1

= ln(2) * 2^6

= ln(2) * 64

Therefore, the derivative of the function f(x) = 2^x at α = 6 is ln(2) times 64, or simply 64ln(2).

In summary, the derivative of the function f(x) = 2^x at the number α = 6 is 64ln(2).

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A tank contains 1560 L of pure water: Solution that contains 0.09 kg of sugar per liter enters the tank at the rate 9 LJmin, and is thoroughly mixed into it: The new solution drains out of the tank at the same rate

(a) How much sugar is in the tank at the begining? y(0) = ___ (kg)
(b) Find the amount of sugar after t minutes y(t) = ___ (kg)
(c) As t becomes large, what value is y(t) approaching In other words, calculate the following limit lim y(t) = ___ (kg)
t --->[infinity]

Answers

To find the amount of sugar in the tank at the beginning (y(0)), we multiply the initial volume of water (1560 L) by the concentration of sugar (0.09 kg/L): y(0) = 1560 L * 0.09 kg/L = 140.4 kg.

Tank initially containing 1560 L of pure water. A solution with a concentration of 0.09 kg of sugar per liter enters tank at a rate of 9 L/min and mixes .The mixed solution drains out of tank at same rate.

We need to determine the amount of sugar in the tank at the beginning (y(0)), the amount of sugar after t minutes (y(t)), and the value that y(t) approaches as t becomes large.

(a) To find the amount of sugar in the tank at the beginning (y(0)), we multiply the initial volume of water (1560 L) by the concentration of sugar (0.09 kg/L): y(0) = 1560 L * 0.09 kg/L = 140.4 kg.

(b) The amount of sugar after t minutes (y(t)) can be calculated using the rate of sugar entering and leaving the tank. Since the solution entering the tank has a concentration of 0.09 kg/L and enters at a rate of 9 L/min, the rate of sugar entering the tank is 0.09 kg/L * 9 L/min = 0.81 kg/min. Since the solution is thoroughly mixed, the rate of sugar leaving the tank is also 0.81 kg/min. Therefore, the amount of sugar after t minutes is given by y(t) = y(0) + (rate of sugar entering - rate of sugar leaving) * t = 140.4 kg + (0.81 kg/min - 0.81 kg/min) * t = 140.4 kg.

(c) As t becomes large, the amount of sugar in the tank will not change because the rate of sugar entering and leaving the tank is equal. Therefore, the limit of y(t) as t approaches infinity is equal to the initial amount of sugar in the tank, which is 140.4 kg.

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1.1 Find the Fourier series of the odd-periodic extension of the function f(x) = 3. for x € (-2,0) (7 ) 1.2 Find the Fourier series of the even-periodic extension of the function f(x) = 1+ 2x. for x
"

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The Fourier series of the odd-periodic extension of  the Fourier series of the even-periodic extension of the function[tex]f(x) = 1+ 2x[/tex]. for x Here, we have[tex]f(x) = 1+ 2x for x€ (0, 2)[/tex] We are going to find the Fourier series of the even periodic extension.

Determine the fundamental period of[tex]f(x)T = 4[/tex] Step 2: Determine the coefficients of the Fourier series. The Fourier series of the even-periodic extension of[tex]f(x) = 1+ 2x.[/tex] for x is given by: The Fourier series representation is unique.

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For the given following functions, find the corresponding inverse Laplace transforms. (You can use Laplace table or any Laplace properties) s²+1
(a) F (s) = s^2+1/ (s-2) (s-1) s (s+1)
(b) F (s) = e^-s/(s− 1) (s² + 4s+8)
(c) F (s) = 2s^2+3s-1/(s-1)^3 e^(-3s+2)

Answers

(a) To find the inverse Laplace transform of F(s) = (s²+1) / [(s-2)(s-1)s(s+1)], we can use partial fraction decomposition.

First, factorize the denominator: (s-2)(s-1)s(s+1) = s^4 - 2s^3 - s^2 + 2s^3 - 4s^2 + 2s + s^2 - 2s - s + 1 = s^4 - 4s^2 + 1.

Now, we can rewrite F(s) as: F(s) = (s²+1) / (s^4 - 4s^2 + 1).

Next, we need to express F(s) in terms of partial fractions. Let's assume the decomposition is: F(s) = A/(s-2) + B/(s-1) + C/s + D/(s+1).

By equating the numerators, we can solve for the unknown coefficients A, B, C, and D.

Once we have the partial fraction decomposition, we can use the Laplace transform table to find the inverse Laplace transform of each term.

(b) For F(s) = e^-s / [(s-1)(s² + 4s + 8)], we can also use partial fraction decomposition.

First, factorize the denominator: (s-1)(s² + 4s + 8) = s³ + 4s² + 8s - s² - 4s - 8 = s³ + 3s² + 4s - 8.

Now, we can rewrite F(s) as: F(s) = e^-s / (s³ + 3s² + 4s - 8).

Next, express F(s) in terms of partial fractions: F(s) = A/(s-1) + (Bs + C)/(s² + 4s - 8).

By equating the numerators, solve for the unknown coefficients A, B, and C.

Then, use the Laplace transform table to find the inverse Laplace transform of each term.

(c) For F(s) = (2s² + 3s - 1) / [(s-1)³ e^(-3s+2)], we can use the properties of Laplace transforms.

First, apply the shifting property of the Laplace transform to the denominator: F(s) = (2s² + 3s - 1) / (s-1)³ e^(-3s) e^2.

Now, we have F(s) = (2s² + 3s - 1) / (s-1)³ e^(-3s) e^2.

We can use the Laplace transform table to find the inverse Laplace transform of each term separately, considering the shifting property and the transforms of powers of s.

Overall, the process involves decomposing the functions into partial fractions, applying the shifting property if necessary, and utilizing the Laplace transform table to find the inverse Laplace transforms of each term.

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10.Has atmospheric methane (CH4 concentration increased significantly in the past 30 years? To answer this question,you take a sample of 100 CH4 concentration measurements from 1988-the sample mean is 1693 parts per billion (ppb).You also take a sample of 144 CH4 concentration measurements from 2018-the sample mean is 1857 ppb.Assume that the population standard deviation of CH4 concentrations has remained constant at approximately 240 ppb. a. (10 points) Construct a 95% confidence interval estimate of the mean CH4 concentration in 1988

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The 95% confidence interval estimate of the mean CH4 concentration in 1988 and in 2018 is (1639.43 ppb, 1746.57 ppb) and (1821.13 ppb, 1892.87 ppb) respectively.

By graphing the confidence intervals on a single number line, we can observe whether the intervals overlap or not. If the intervals do not overlap, it indicates a statistically significant difference between the mean CH4 concentrations in 1988 and 2018.

In order to construct the confidence intervals, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

For part (a), using the sample mean of 1693 ppb, a population standard deviation of 240 ppb, and a sample size of 100, we calculate the critical value and standard error to obtain the confidence interval.

For part (b), using the sample mean of 1857 ppb, a population standard deviation of 240 ppb, and a sample size of 144, we calculate the critical value and standard error to obtain the confidence interval.

By graphing the confidence intervals on a single number line, we can visually compare the intervals and determine if there is a significant change in the CH4 concentration between the two time periods. If the intervals overlap, it suggests that the difference is not statistically significant, while non-overlapping intervals indicate a significant difference.

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By the least square method, find the coefficients of the polynomial g(x)= Ax - Bx? that provides the best approximation for the given data (xi,yi): (-3, 3), (0,1),(4,3).

Answers

The polynomial that provides the best approximation is

g(x) = a0 + a1x

= -B + Ax

= -7/16 + 13/32 x.

We have to find the coefficients of the polynomial g(x) = Ax - Bx that gives the best approximation for the given data (-3, 3), (0, 1), (4, 3) using the least square method.

Least Square Method: The least square method is the method used to find the best-fit line or curve for a given set of data by minimizing the sum of the squares of the differences between the observed dependent variable and its predicted value, the fitted value.

The equation for the best approximation polynomial g(x) of the given data is

g(x) = Ax - BxAs a polynomial of first degree, we can write

g(x) = Ax - Bx = a0 + a1xi

where a0 = -B and a1 = A.

Therefore, we need to find the values of A and B that make the approximation the best.

The equation to minimize isΣ (yi - g(xi))^2 = Σ (yi - a0 - a1xi)^2i = 1, 2, 3

We can express this equation in matrix notation as

Y = Xa whereY = [3, 1, 3]T, X = [1 -3; 1 0; 1 4], and a = [a0, a1]T.

Then the coefficients a that minimize the sum of the squares of the differences are given by

a = (XTX)-1 XTY

where XTX and XTY are calculated as

XTX = [3 1 3; -3 1 -3] [1 -3; 1 0; 1 4]

= [3 2; 2 26]XTY

= [3 1 3; -3 1 -3] [3; 1; 3]

= [-3; 1]

Now we have

a = (XTX)-1 XTY

= [3 2; 2 26]-1 [-3; 1]

= [-7/16; 13/32]

Therefore, the polynomial that provides the best approximation is

g(x) = a0 + a1x

= -B + Ax

= -7/16 + 13/32 x.

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Use limits to find the horizontal and vertical asymptotes of the graph of the function 3x³ f(x)= √16x6+1, if any.

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To find the horizontal and vertical asymptotes of the function [tex]\(f(x) = \sqrt{16x^6 + 1}\)[/tex], we need to examine the behavior of the function as  [tex]\(x\)[/tex]approaches positive or negative infinity.

Let's start by finding the horizontal asymptote. We can determine this by evaluating the limit as [tex]\(x\)[/tex] approaches infinity and negative infinity.

As [tex]\(x\)[/tex] approaches infinity:

[tex]\[\lim_{x \to \infty} f(x) = \lim_{x \to \infty} \sqrt{16x^6 + 1}\][/tex]

To simplify the expression, we can ignore the constant term within the square root as it becomes negligible compared to [tex]\(x^6\)[/tex] as [tex]\(x\)[/tex] approaches infinity.

[tex]\[\lim_{x \to \infty} f(x) \approx \lim_{x \to \infty} \sqrt{16x^6} = \lim_{x \to \infty} 4x^3 = \infty\][/tex]

Since the limit as [tex]\(x\)[/tex] approaches infinity is infinity, there is no horizontal asymptote.

Next, let's consider the vertical asymptotes. To find these, we need to determine if there are any values of [tex]\(x\)[/tex] that make the function undefined. In this case, since [tex]\(f(x)\)[/tex] involves a square root, we should look for values of [tex]\(x\)[/tex] that make the expression inside the square root negative or zero.

Setting [tex]\(16x^6 + 1\)[/tex] less than or equal to zero:

[tex]\[16x^6 + 1 \leq 0\][/tex]

This equation has no real solutions since the expression [tex]\(16x^6 + 1\)[/tex] is always positive.

Therefore, the function [tex]\(f(x) = \sqrt{16x^6 + 1}\)[/tex] does not have any vertical asymptotes.

In summary:

- There is no horizontal asymptote.

- There are no vertical asymptotes.

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Use the information in this problem to answer questions 18 and 19. 18. Factor completely. 18x³ + 3x² - 6x A. 6x²+x-2 B. x(3x + 2)(2x - 1) C. 3x(3x-2)(2x + 1) D. 3x(3x + 2)(2x - 1)

Answers

The completely factored form of the expression 18x³ + 3x² - 6x is 3x(3x - 2)(2x + 1). Therefore, the correct option is C. 3x(3x - 2)(2x + 1).

To factor the expression 18x³ + 3x² - 6x completely, we can factor out the greatest common factor, which is 3x:

18x³ + 3x² - 6x = 3x(6x² + x - 2)

Now, we can factor the quadratic expression inside the parentheses:

6x² + x - 2 = (3x - 2)(2x + 1)

Putting it all together, we have:

18x³ + 3x² - 6x = 3x(6x² + x - 2) = 3x(3x - 2)(2x + 1)

Therefore, the correct choice is:

C. 3x(3x - 2)(2x + 1)

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consider a binary response variable y and a predictor variable x that varies between 0 and 5. The linear model is estimated as yhat = -2.90 + 0.65x. What is the estimated probability for x = 5?

a. 0.35

b. 6.15

c. 0.65

d. -6.15

Answers

The estimated probability for x = 5 in the given linear model is 0.65.

In a binary logistic regression model, the predicted probability of the binary response variable (y) can be estimated using the logistic function, which takes the form of the sigmoid curve. The equation for the logistic function is:

P(y = 1) = 1 / (1 + e^(-z))

where z is the linear combination of the predictors and their corresponding coefficients.

In the given linear model yhat = -2.90 + 0.65x, the coefficient 0.65 represents the effect of the predictor variable x on the log-odds of y being 1. To estimate the probability for a specific value of x, we substitute that value into the linear model equation.

For x = 5, the estimated probability is:

P(y = 1) = 1 / (1 + e^(-(-2.90 + 0.65 * 5)))

= 1 / (1 + e^(-2.90 + 3.25))

= 1 / (1 + e^(0.35))

≈ 0.65

Therefore, the estimated probability for x = 5 is approximately 0.65. Option (c) is the correct answer.

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For each eigenvalue problem, verify that the given eigenfunctions are correct. Then, use the eigenfunctions to obtain the generalized Fourier series for each of the indicated functions f(x).

y = 0, y(0) = 0, y (4) = 0 2)

Answers

The eigenfunctions for the given eigenvalue problem y = 0, y(0) = 0, y(4) = 0 are verified to be y_n(x) = B_n*sin((nπ/2)*x), where n is an integer. Since the function f(x) = 0, the generalized Fourier series representation of f(x) yields all Fourier coefficients c_n to be zero.

To verify the correctness of the eigenfunctions, we solve the eigenvalue problem by assuming a second-order linear homogeneous differential equation y'' + λy = 0. The general solution is y(x) = Acos(sqrt(λ)x) + Bsin(sqrt(λ)x). Applying the boundary condition y(0) = 0, A = 0. Thus, y(x) = Bsin(sqrt(λ)x). With y(4) = 0, we find sin(2sqrt(λ)) = 0, which leads to λ = (nπ/2)^2. The eigenfunctions are y_n(x) = B_nsin((nπ/2)*x), where B_n is a constant. For f(x) = 0, the Fourier series representation yields c_n = 0, except for n = m, where c_n = 0.

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In the figure shown, the small circle is tangent to the large circle and passes through the center of the large circle. If the area of the shaded region is 1, what is the diameter of the small circle? 01/03/ O 3x 2x

Answers

2.04

To find the diameter of the small circle, we can set up an equation based on the given information.

Let's denote the diameter of the small circle as "d." Since the small circle is tangent to the large circle and passes through its center, the radius of the large circle is equal to half the diameter of the small circle, which is "d/2."

The area of the shaded region consists of the small circle subtracted from the large circle. The area of a circle can be calculated using the formula A = πr², where A is the area and r is the radius.

The area of the large circle is π(d/2)² = π(d²/4), and the area of the small circle is π(d/2)²/4 = π(d²/16).

Given that the area of the shaded region is 1, we can set up the following equation:

π(d²/4) - π(d²/16) = 1

Simplifying the equation:

(4πd² - πd²)/16 = 1

(3πd²)/16 = 1

Now, we can solve for d:

3πd² = 16

d² = 16/(3π)

d = √(16/(3π))

Calculating the value, we find that the diameter of the small circle is approximately 2.04.

To find the diameter of the small circle in the given scenario, where it is tangent to the larger circle and passes through its center, we can use the concept of the Pythagorean theorem.

Let's denote the radius of the large circle as R and the radius of the small circle as r. Since the small circle passes through the center of the large circle, the diameter of the large circle is equal to twice its radius, so the diameter of the large circle is 2R.

Considering the configuration of the circles, we can observe that the radius of the large circle (R) forms the hypotenuse of a right triangle, with the diameter of the small circle (2r) and the radius of the small circle (r) as the other two sides.

Using the Pythagorean theorem, we can write the equation:

(2R)^2 = (2r)^2 + r^2

Simplifying this equation, we get:

4R^2 = 4r^2 + r^2

3R^2 = 5r^2

From the given information, we know that the area of the shaded region is 1. This shaded region consists of the space between the large and small circles. The area of this shaded region can be calculated as:

Area = π(R^2 - r^2) = 1

From here, we can substitute the value of R^2 from the previous equation:

Area = π(3R^2/5) = 1

Solving this equation, we can find the value of R^2 and subsequently the value of R. Once we have the value of R, we can calculate the diameter of the small circle (2r) using the equation 3R^2 = 5r^2.

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Prove that in an undirected graph G = (V, E), if |E| > (V-¹), then G is connected.

Answers

In an undirected graph G = (V, E), if the number of edges |E| is greater than the number of vertices minus one (V-1), then the graph G is connected.

This means that there exists a path between every pair of vertices in G.To prove that the graph G is connected when |E| > (V-1), we can use a proof by contradiction. Assume that G is not connected, meaning there exists a pair of vertices u and v that are not connected by any path.

Since G is not connected, the maximum number of edges possible in G is given by the sum of the degrees of u and v, which is (deg(u) + deg(v)). However, the sum of the degrees of all vertices in G is equal to twice the number of edges, i.e., 2|E|.

Therefore, we have (deg(u) + deg(v)) ≤ 2|E|. Substituting the value of deg(u) + deg(v) = 2|E| - (V-2), we get (2|E| - (V-2)) ≤ 2|E|.

Simplifying the inequality, we have -(V-2) ≤ 0, which implies V-2 ≥ 0, or V ≥ 2.

Since V ≥ 2, it contradicts our assumption that G is not connected. Hence, G must be connected when |E| > (V-1).

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The function y(t) satisfies the differential equation y' (t)-cos(t)y(t)=-2 cos(t)e subject to the initial conditiony (5)+ where is a real constant Given that y(-5)-y (5), find the value c Enter your answer with up to one place after the decimal point of your answer is an integer, do not enter a decimal pome. For example, your rower in √51414 14 your ar 2 sin The function y(t) satisfies the differential equation y' (t)- cos (t) y(t) = -2 cos(t)en(e) subject to the initial condition y()=e+ where c is a real constant. Given that y (-) = y(), find the value c.

Answers

To find the value of c, we can use the given information that y(-5) = y(5).

Let's solve the differential equation and find the expression for y(t) first.

The given differential equation is: y'(t) - cos(t) * y(t) = -2 * cos(t) * e^(-c)

To solve this linear first-order ordinary differential equation, we can use an integrating factor. The integrating factor is e^(-∫cos(t)dt) = e^(-sin(t)).

Multiplying both sides of the equation by the integrating factor, we get:

e^(-sin(t)) * y'(t) - cos(t) * e^(-sin(t)) * y(t) = -2 * cos(t) * e^(-sin(t)) * e^(-c)

Now, we can rewrite the left-hand side using the product rule for differentiation:

(d/dt)(e^(-sin(t)) * y(t)) = -2 * cos(t) * e^(-sin(t)) * e^(-c)

Integrating both sides with respect to t, we have:

∫(d/dt)(e^(-sin(t)) * y(t)) dt = ∫(-2 * cos(t) * e^(-sin(t)) * e^(-c)) dt

e^(-sin(t)) * y(t) = -2 * ∫(cos(t) * e^(-sin(t)) * e^(-c)) dt

Now, let's integrate the right-hand side. Note that the integral of e^(-sin(t)) * cos(t) is not an elementary function and requires special functions to express.

e^(-sin(t)) * y(t) = -2 * F(t) + k

where F(t) represents the antiderivative of (cos(t) * e^(-sin(t)) * e^(-c)) and k is the constant of integration.

To determine the value of k, we can use the initial condition y(5) = e^5 + c:

e^(-sin(5)) * (e^5 + c) = -2 * F(5) + k

Now, we can substitute y(-5) = y(5) into the equation:

e^(-sin(-5)) * (e^(-5) + c) = -2 * F(-5) + k

Using the fact that e^(-sin(-5)) = e^sin(5), we have:

e^sin(5) * (e^(-5) + c) = -2 * F(-5) + k

Since y(-5) = y(5), we can equate the two expressions:

e^(-sin(5)) * (e^5 + c) = e^sin(5) * (e^(-5) + c)

Now, we can solve for c:

e^(-sin(5)) * e^5 + e^(-sin(5)) * c = e^sin(5) * e^(-5) + e^sin(5) * c

Simplifying the equation, we get:

e^(5 - sin(5)) + e^(-sin(5)) * c = e^(-5 + sin(5)) + e^sin(5) * c

e^(-sin(5)) * c - e^sin(5) * c = e^(-5 + sin(5)) - e^(5 - sin(5))

c * (e^(-sin(5)) - e^sin(5)) = e^(-5 + sin(5)) - e^(5 - sin(5))

c = (e^(-5 + sin(5)) - e^(5 - sin(5))) / (e^(-sin(5)) - e^sin(5))

Calculating this expression numerically, we find:

c ≈ -2.027

Therefore, the value of c is approximately -2.027.

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Learning Outcomes Assessed: 1. Interpret graphs, charts, and tables following correct paragraph structures and using appropriate vocabulary and grammar. 2. Produce appropriate graphs and charts to illustrate statistical data. Hours Per Week Playing Sports Gender Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Boys 4 6 7 10 9 Girls 3 5 7 8 7 The table above shows the number of hours per week boys and girls spend playing sports. Look at the information in the table above then: 1. Illustrate the information in an appropriate chart/graph 2. Identify two trends in the chart and write a complete paragraph for each one summarizing the information by selecting and reporting the main features and making comparisons. Each paragraph must contain: • an introductory sentence . a topic sentence at least three supporting sentences; and

Answers

The provided table displays the number of hours per week spent playing sports based on gender and grade level. It includes data for grades 3 to 8 and differentiates between boys and girls.

To interpret the table, we observe that each row corresponds to a specific grade level, while the columns represent the gender categories. The numbers within the cells indicate the average hours per week spent playing sports. For example, in grade 3, boys spend 4 hours per week, while girls spend 3 hours per week.

To visually represent this data, a suitable graph would be a grouped bar chart. The x-axis would indicate the grade levels, while the y-axis would represent the number of hours per week. Separate bars would be used for boys and girls, and the height of each bar would correspond to the average number of hours spent playing sports for the respective grade and gender category.

By creating such a chart, we can easily compare the average hours spent playing sports between different grade levels and genders, enabling a visual understanding of the data patterns and potential differences in sports participation.

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2. (a)
People often over-/under-estimate event probabilities. Explain,
with the help of examples, the manner in which people
over-/under-estimate probabilities because of the (i) availability,
(ii) re

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People often overestimate and underestimate event probabilities because of the availability and representativeness heuristics.

Here are some examples to illustrate how these heuristics influence our thinking: Availability heuristic: This heuristic causes people to judge the likelihood of an event based on how easily it comes to mind. If something is easily recalled, it is assumed to be more likely to occur. For example, a person might believe that shark attacks are common because they have heard about them on the news, despite the fact that the likelihood of being attacked by a shark is actually quite low. Similarly, people might think that terrorism is a major threat, even though the actual risk is quite low. Representativeness heuristic: This heuristic is based on how well an event or object matches a particular prototype. For example, if someone is described as quiet and introverted, we might assume that they are a librarian rather than a salesperson, because the former matches our prototype of a librarian more closely. This heuristic can lead to people overestimating the likelihood of rare events because they match a particular prototype. For example, people might assume that all serial killers are male because most of the ones they have heard about are male. However,

this assumption ignores the fact that female serial killers do exist.people tend to overestimate or underestimate probabilities because of the availability and representativeness heuristics. These heuristics can lead to faulty thinking and can cause people to make incorrect judgments.

By being aware of these heuristics, people can learn to make better decisions and avoid making mistakes that could be costly in the long run.

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Find the solution to the initial value problem. z''(x) + z(x)= 4 c 7X, Z(0) = 0, z'(0) = 0 O) 0( 7x V The solution is z(x)=0

Answers

Solving the characteristic equation z² + 1 = 0 We get,[tex]z = ±i[/tex]As the roots are imaginary and distinct, general solution is given as z(x) = c₁ cos x + c₂ sin x

The solution to the initial value problem Solution: We have z''(x) + z(x) = 4c7x .....(1)

We need to find the particular solution Now, let us assume the particular solution to be of the form z = ax + b Substituting the value of z in equation (1) and solving for a and b, we geta = -2/7 and b = 0Therefore, the general solution of the differential equation is

z(x) = c₁ cos x + c₂ sin x - 2/7

x Putting the initial conditions

z(0) = 0 and z'(0) = 0 in the above equation,

we get c₁ = 0 and c₂ = 0

Therefore, the solution to the initial value problem is z(x) = 0

Hence, option (a) is the correct solution.

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II. x if x > 0 Let (x)={-1 ifr=0 1x if x < 0 1. Graph /(x) 2. Is /(x) continuous at x=0?

Answers

The given function is {(x)= 1 if x<0; x if x>0; -1 if x=0} and we need to find the followingGraph of /(x):To graph the function we use the following table;x-20+2-2-20+/-(x)1-1-1+1+1We then plot the points in a Cartesian plane and connect the points with a curve, as shown below;The graph shows that the function is continuous except at x=0.

A function is said to be continuous at a point c if the following conditions are met;f(c) is defined,i.e., c is in the domain of the function.The limit of the function at c exists,i.e., andThe limit of the function at c equals f(c).To determine if /(x) is continuous at x=0, we need to check if the three conditions are met as follows;Condition 1: f(c) is definedSince x=0 is in the domain of the function, i.e., we can say that f(c) is defined, and this condition is met.

Condition 2:  The limit of the function at c existsi.e., $\underset{x\to 0}{\mathop{\lim }}\,(x)$ existWhen x<0, the limit of the function is 1, i.e.,$\underset{x\to 0}{\mathop{\lim }}\,(x)=1$When x>0, the limit of the function is 0, i.e.,$\underset{x\to 0}{\mathop{\lim }}\,(x)=0$However, when x=0, the limit does not exist, i.e., the left and right limits are not equal. Thus this condition is not met.Condition 3: The limit of the function at c equals f(c)We have already seen that the limit at x=0 does not exist. Thus, this condition is not met, and the function is not continuous at x=0.In summary, /(x) is not continuous at x=0.

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What is the Fourier transform of f(t) = 8(x − vt) + 8(x+vt)? ƒ(k) = f e¹kt f(t)dt =
a) 2 cos(kx/v)
b) 2 cos(kx/v)/v
c) 2 cos(kx)
d) 2 cos(kx)/v

Answers

The correct answer is (d) 2 cos(kx)/v.

The Fourier transform of f(t) = 8(x − vt) + 8(x+vt) is given by:

ƒ(k) = ∫f(t)e^(-ikt)dt

= ∫[8(x-vt)+8(x+vt)]e^(-ikt)dt

= 8∫[x-vt]e^(-ikt)dt + 8∫[x+vt]e^(-ikt)dt

= 8e^(-ikvt)∫xe^(ikt)dt + 8e^(ikvt)∫xe^(-ikt)dt

Using integration by parts, we get:

∫xe^(ikt)dt = (xe^(ikt))/(ik) - (1/(ik))^2 e^(ikt)

Substituting the limits of integration and simplifying, we get:

∫xe^(ikt)dt = (1/ik^2)[e^(ik(x-vt)) - e^(ik(x+vt))]

Similarly, ∫xe^(-ikt)dt = (1/ik^2)[e^(-ik(x-vt)) - e^(-ik(x+vt))]

Substituting these values in the expression for ƒ(k), we get:

ƒ(k) = (8/ik^2)[e^(-ikvt)(e^(ikx) - e^(-ikx)) + e^(ikvt)(e^(-ikx) - e^(ikx))]

Simplifying further, we get:

ƒ(k) = (16i/k^2v)sin(kx)

Using Euler's formula, we can write:

sin(kx) = (1/2i)(e^(ikx) - e^(-ikx))

Substituting this value in the expression for ƒ(k), we get:

ƒ(k) = 8(e^(-ikvt) - e^(ikvt))/kv

= 16i/k^2v sin(kx)/2i

= 2cos(kx)/v

Therefore, the correct answer is (d) 2 cos(kx)/v.

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Suppose that the random variable X is the time taken by a garage to service a car: These times are distributed between 0 and 10 hours with a cumulative distribution function given by: Flc) 0.36065 1n(32 + 2)-0.25 for 0 < € < 10. What is the probability that a repair job takes no more than 0.5 hours? Select one: a. 0 b. 0.5 0.7982 d.0.2018 Check

Answers

The correct option is a. 0.  F(0.5) - F(0)F(0.5) = 0.36065 ln(0.5 + 2) - 0.25 = 0.4699F(0) = 0Now, P(Y ≤ 0.5) = F(0.5) - F(0) = 0.4699 - 0 = 0.4699The probability that a repair job takes no more than 0.5 hours is 0.

which is the first option. Solution: Given, the random variable X is the time taken by a garage to service a car: These times are distributed between 0 and 10 hours with a cumulative distribution function given by :F(x) = 0.36065 ln(x + 2) - 0.25 for 0 < x < 10. We need to find the probability that a repair job takes no more than 0.5 hours. Let Y represent the time taken by a garage to service a car. Now, for Y ≤ 0.5,Y ∈ [0, 0.5].Therefore, 0 < x + 2 ≤ 2.5 or -2 > x or x > -2. Now, the probability that Y ≤ 0.5

given the cumulative distribution function (CDF) of X:

F(x) = 0.36065 * ln(32 + 2x) - 0.25 for 0 < x < 10

To find the probability that X is less than or equal to 0.5, we substitute x = 0.5 into the CDF:

F(0.5) = 0.36065 * ln(32 + 2(0.5)) - 0.25

Calculating this expression:

F(0.5) = 0.36065 * ln(33) - 0.25

Using a calculator or software, we can evaluate this expression:

F(0.5) ≈ 0.498

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Given that the random variable X is the time taken by a garage to service a car. These times are distributed between 0 and 10 hours with a cumulative distribution function given by:F(x) = 0.36065 ln(x+2)-0.25 for 0 < x < 10

To find: What is the probability that a repair job takes no more than 0.5 hours?

Solution:We are given, F(x) = 0.36065 ln(x+2)-0.25 0 < x < 10

For a random variable X, the probability that x ≤ X ≤ x + δx is approximately δF(x)

Therefore, the probability that 0 ≤ X ≤ x is F(x)

The probability that a repair job takes no more than 0.5 hours is P(X ≤ 0.5)P(X ≤ 0.5) = F(0.5) = 0.36065 ln(0.5+2)-0.25 = 0.2018

Therefore, the correct option is d. 0.2018.

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You develop a research hypothesis that people with at least a Bachelor's degree are more likely to identify and behave as a feminist (measured as an interval-ratio index variable) than people without a Bachelor's degree. You collect a large, random and unbiased sample on 438 adults. For an alpha of .05, what is the critical value for the appropriately tailed test? a. 1.65 b. 1.96 c. 2.58 d. 2.33

Answers

A research hypothesis is an initial assumption or a preconceived belief that people have about a relationship between variables. Such hypotheses are subjected to empirical validation through an experimental or survey research.

In this context, the research hypothesis is that people with at least a Bachelor's degree are more likely to identify and behave as a feminist (measured as an interval-ratio index variable) than people without a Bachelor's degree. In testing research hypotheses, statistical methods are used to determine if the differences or associations between variables are statistically significant or due to chance. The level of statistical significance is determined by alpha, the level of probability at which the null hypothesis will be rejected. A commonly used alpha level is .05, which means that there is only a 5% probability that the differences or associations are due to chance. Since the research hypothesis is directional (one-tailed), the critical value is +1.65 (option A).Therefore, the answer is option A (1.65).

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Let S :U →V and T :V →W be linear transformations. Prove that Im (TS) – Im (T)

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Im (TS) - Im (T) is a linear transformation.

Let S : U → V and T : V → W be linear transformations. To prove that Im(TS) - Im(T) is a linear transformation, we need to show that it satisfies the conditions of a linear transformation.

Im (TS) - Im (T) can be represented as follows:

Im (TS) - Im (T) = {z ϵ W : z = TS(x) - T(y), where x ϵ U, y ϵ V}

We must show that Im (TS) - Im (T) is a linear transformation.

Therefore, we must show that the following two properties hold:

Additivity:

If z1, z2 ϵ Im (TS) - Im (T), then z1 + z2 also belongs to Im (TS) - Im (T). Homogeneity: If z ϵ Im (TS) - Im (T), and c is any scalar, then cz also belongs to Im (TS) - Im (T).

Let's show that Im (TS) - Im (T) satisfies the above two conditions:

Additivity:If z1, z2 ϵ Im (TS) - Im (T), thenz1 = TS(x1) - T(y1)z2 = TS(x2) - T(y2)for some x1, x2 ϵ U and y1, y2 ϵ V.

Then, their sum can be written as:(z1 + z2) = TS(x1) + TS(x2) - T(y1) - T(y2) = TS(x1 + x2) - T(y1 + y2)Therefore, z1 + z2 also belongs to Im (TS) - Im (T).

Homogeneity:If z ϵ Im (TS) - Im (T), and c is any scalar, thenz = TS(x) - T(y)for some x ϵ U and y ϵ V.

Then,cz = cTS(x) - cT(y) = T(cS(x) - y)

Therefore, cz also belongs to Im (TS) - Im (T).

Hence, Im (TS) - Im (T) is a linear transformation.

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Find the current in an LRC series circuit at t = 0.01s when L = 0.2H, R = 80, C = 12.5 x 10-³F, E(t) = 100sin10tV, q(0) = 5C, and i(0) = 0A.
Q.2 Verify that u = sinkctcoskx satisfies a2u/at2=c2 a2u/ax2

Answers

The total current at any given time t is the sum of the natural and forced response components, i(t) = i_n(t) + i_f(t). By evaluating i(t) at t = 0.01s, we can find the current in the LRC series circuit at that time.

The given differential equation for the LRC series circuit is a second-order linear ordinary differential equation. By solving this equation using the given initial conditions, we can determine the current at t = 0.01s. The solution to the differential equation involves finding the natural response and forced response components.

To obtain the natural response, we assume the form of the solution as i(t) = A e^(-αt) sin(ωt + φ), where A, α, ω, and φ are constants to be determined. By substituting this assumed solution into the differential equation and solving for the constants, we can determine the natural response component of the current.

Next, we consider the forced response component, which is determined by the applied voltage E(t). In this case, E(t) = 100 sin(10t)V. By substituting the forced response form i(t) = B sin(10t + φ') into the differential equation and solving for B and φ', we can determine the forced response component of the current.

The total current at any given time t is the sum of the natural and forced response components, i(t) = i_n(t) + i_f(t). By evaluating i(t) at t = 0.01s, we can find the current in the LRC series circuit at that time.

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The voltage of an AC electrical source can be modelled by the equation V = a sin(bt + c), where a is the maximum voltage (amplitude). Two AC sources are combined, one with a maximum voltage of 40V and the other with a maximum voltage of 20V. a. Write 40 sin (0.125t-1) +20 sin(0.125t + 5) in the form A sin(0.125t + B), where A > 0,-

Answers

40 sin (0.125t-1) +20 sin(0.125t + 5) in the form A sin(0.125t + B) can be written as 60 sin(0.125t + 5) - 20 sin(0.125t - 1), where A = 60 and B = 5.

To write the expression 40 sin(0.125t - 1) + 20 sin(0.125t + 5) in the form A sin(0.125t + B), we can use the properties of trigonometric identities and simplify the expression.

Let's start by expanding the expression:

40 sin(0.125t - 1) + 20 sin(0.125t + 5)

= 40 sin(0.125t)cos(1) - 40 cos(0.125t)sin(1) + 20 sin(0.125t)cos(5) + 20 cos(0.125t)sin(5)

Now, let's rearrange the terms:

= (40 sin(0.125t)cos(1) + 20 sin(0.125t)cos(5)) - (40 cos(0.125t)sin(1) - 20 cos(0.125t)sin(5))

Using the identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can simplify further:

= (40 sin(0.125t + 5) + 20 sin(0.125t - 1)) - (40 sin(0.125t - 1) - 20 sin(0.125t + 5))

Now, we can combine the like terms:

= 40 sin(0.125t + 5) + 20 sin(0.125t - 1) - 40 sin(0.125t - 1) + 20 sin(0.125t + 5)

Simplifying:

= 60 sin(0.125t + 5) - 20 sin(0.125t - 1)

Therefore, the given expression 40 sin(0.125t - 1) + 20 sin(0.125t + 5) can be written in the form A sin(0.125t + B) as:

60 sin(0.125t + 5) - 20 sin(0.125t - 1), where A = 60 and B = 5.

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can select 4 books from 14 different books in a box. In how many ways can the winner select the 4 books? (1 mark) b. In how many ways can the winner select the 4 books and then arrange them on a shelf? (1 mark) c. Explain why the answers to part a. and part b. above, are not the same. (1 mark)

Answers

a. The winner can select 4 books from 14 in 1,001 ways (using combinations).

b. The winner can select and arrange the 4 books on a shelf in 24 ways (using permutations).

c. Part a. counts combinations without considering order, while part b. counts permutations with order included, leading to different results.

a. To determine the number of ways the winner can select 4 books from 14 different books in a box, we can use the concept of combinations. The number of ways to choose 4 books out of 14 is given by the binomial coefficient:

C(14, 4) = 14! / (4! * (14 - 4)!) = 14! / (4! * 10!)

Simplifying further:

C(14, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) = 1001

Therefore, the winner can select the 4 books in 1,001 different ways.

b. To calculate the number of ways the winner can select the 4 books and arrange them on a shelf, we need to consider the concept of permutations. Once the 4 books are selected, they can be arranged on the shelf in different orders. The number of ways to arrange 4 books can be calculated as:

P(4) = 4!

P(4) = 4 * 3 * 2 * 1 = 24

Therefore, the winner can select the 4 books and arrange them on a shelf in 24 different ways.

c. The answers to part a. and part b. are not the same because they involve different concepts. Part a. calculates the number of ways to choose a combination of 4 books from 14 without considering the order, while part b. calculates the number of ways to arrange the selected 4 books on a shelf, taking the order into account. In other words, part a. focuses on selecting a subset of books, whereas part b. considers the arrangement of the selected books.

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3. Given the function f: [-1, 1] → R defined by f(x) = e-*- x², prove that there exists a point ro € [-1, 1] such that f(zo) = 0. (NOTE: You are not asked to determine the point xo). [6]

Answers

For the given function there exists a point ro ∈ [-1, 1] such that f(zo) = 0.

To prove that there exists a point ro ∈ [-1, 1] such that f(zo) = 0, we can make use of the Intermediate Value Theorem.

The Intermediate Value Theorem states that if a function f is continuous on a closed interval [a, b] and takes on two different values, c and d, then for any value between c and d, there exists at least one point in the interval where the function takes on that value.

In this case, we have the function f(x) = e^(-x²), defined on the closed interval [-1, 1].

The function f(x) is continuous on this interval.

Let's consider the values c = 1 and d = e^(-1), which are both in the range of the function f(x).

Since f(x) is continuous, by the Intermediate Value Theorem, there exists a point ro ∈ [-1, 1] such that f(ro) = 0.

Therefore, we have proven that there exists a point ro ∈ [-1, 1] such that f(zo) = 0.

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In APQR, the measure of /R=90°, QP = 85, RQ = 84, and PR = 13. What ratio
represents the sine of ZP?

Answers

The ratio of that represents the sine of angle P is 4/5

What is trigonometric ratio?

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Trigonometric ratios are the ratios of the length of sides of a triangle.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

Since angle R is the 90° , them QP is the hypotenuse of the triangle and taking angle P as reference, QR is the opposite and PR is the hypotenuse.

sinP = 84/85

therefore, the ratio that represents the sine of angle P is 84/85.

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The scores and their percent of the final grade for a statistics student are given. What is the student's weighted mean score?

Answers

The student's weighted mean score is 84.87.

To find out the student's weighted mean score, you need to multiply each score by its corresponding weight, add the products, and divide the result by the sum of the weights.

Here are the steps to calculate the weighted mean score:

Step 1: Write out the scores and their corresponding weights

Score Weight: 905%807%806%706%605%504%

Step 2: Multiply each score by its corresponding weight.

To make calculations easier, divide the weights by 100 and multiply them by the scores.

Score Weight Adjusted Score

905% 0.90 81.5807% 0.07 5.606% 0.06 4.206% 0.06 4.206% 0.05 3.055% 0.05 2.5

Step 3: Add the adjusted scores together.

81.5 + 5.6 + 4.2 + 4.2 + 3.0 + 2.5 = 101.0

Step 4: Add the weights together.0.90 + 0.07 + 0.06 + 0.06 + 0.05 + 0.05 = 1.19

Step 5: Divide the sum of the adjusted scores by the sum of the weights.101.0 ÷ 1.19 = 84.87

Therefore, the student's weighted mean score is 84.87.

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Given the following information for sample sizes of two independent samples, determine the number of degrees of freedom for the pooled t-test.
n_1 = 26, n_2 = 15
a. 25
b. 38
c. 39
d. 14

Answers

The correct option is  c.The formula for calculating the degrees of freedom for the pooled t-test is as follows:

df = (n1 - 1) + (n2 - 1) Where

n1 is the sample size of the first sample and n2 is the sample size of the second sample.

Using the given information, we have:

n1 = 26, n2 = 15

Substituting these values into the formula, we get:

df = (26 - 1) + (15 - 1)

df = 25 + 14

df = 39

Therefore, the number of degrees of freedom for the pooled t-test is 39. The correct option is letter c.

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Solve the given initial-value problem. *-()x+(). xc0;-) :-1-3 X -3 -2 X X() = X(t)
"

Answers

The solution of the given initial-value problem is: `x(t) = e^(2t) - 2e^t`

Given the differential equation is: `(d^2x)/(dt^2) - 3(dx)/(dt) - 2x = 0`

The given initial value is: `x(0) = -1` and

`(dx)/(dt)|_(t=0) = -3`

To solve the given initial-value problem, we assume that the solution is of the form

`x(t) = e^(rt)`

Such that the auxiliary equation can be written as:

`r^2 - 3r - 2 = 0`

By solving the quadratic equation, we get the roots as:

`r = 2, 1`

Therefore, the general solution of the given differential equation is:

`x(t) = c_1e^(2t) + c_2e^t`

Now, applying the initial condition `x(0) = -1`, we get:

`-1 = c_1 + c_2`....(1)

Also, applying the initial condition `(dx)/(dt)|_(t=0) = -3`,

we get:

`(dx)/(dt)|_(t=0) = 2c_1 + c_2 = -3`....(2)

Solving equations (1) and (2), we get: `c_1 = 1` and `c_2 = -2`

Therefore, the solution of the given initial-value problem is:

`x(t) = e^(2t) - 2e^t`.

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If you are in the 20.5 percent federal tax bracket, how much will you save in taxes What is the balance after 4 years on $2000 at 4% Assume that an agribusiness firm uses an average of 40 boxes of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $30 a year per box, and it costs approximately $60 to order and receive a shipment of paper.What order size would minimize the sum of annual ordering and carrying costs? (2)Compute the total annual cost using your order size from part a. (3)The office manager is currently using an order size of 200 boxes. The partners of the firm expect the office to be managed "in a cost-efficient manner." Would you recommend that the office manager use the optimal order size instead of 200 boxes? Justify your answer. (2 marks) (b) Given a certain confidence of 95.56% for temperature measurements in the interval between 88 and 92, what is the mean, , and what is the standard deviation, o, when N=200 measurement are taken? Please describe one way to determine the presence of an enzyme (i.e. tyrosinase) without using a Western Blot or running an activity gel. Give a brief synopsis on how this process takes place. the single value of a sample statistic that we assign to the population parameter is a property taxes are an example of a (n): select one: a. discretionary variable cost. b. discretionary fixed cost. c. committed fixed cost. d. committed jordan carpets is considering expanding from the united states to spain. what problems may be faced by american supervisors relocating to spain? a) Calculate the tangent vector to the curve C1 at the point(/2),b) Parametricize curve C2 to find its binormal vector at thepoint (0,1,3). "1) The thicknesses of glass sheets made using process A and process B are recorded in the table below Process Sample Size Sample Mean (mm) Sample Standard Deviation (mm) 41 3.04 0.124 41 3.12 0.137a) Does the sample information provide sufficient evidence to conclude that the two processes produce glass sheets that do not have equal thicknesses on average? Use a=0.01. b) What is the P-value for the test in part a? c) What is the power of the test in part a for a true difference in means of 0.1? d) Assuming equal sample sizes, what sample sizes are required to ensure that B=.1 if the true difference in means is 0.1? Assume a=0.01. e) Construct a confidence interval on the difference in means H1 - H2. What is the practical meaning of this interval? monopolists are guaranteed to earn a positive economic profit because they are the only seller in their industry. T/F ? All of the supervisors at Genius Company Ltd. are quite busy since they have to complete their subordinates' bi-annual appraisal reviews. The supervisors cite the following five ratings from the review report: A stands for Excellent, B for Good, C for Fair, D for Pass, and F for Fail.Sharon, Kit, Janice, and Anna are all great pals. They have spent the last five years at Genius Company Ltd. They are having lunch one afternoon and discussing their appraisal results.Sharon: My boss is an angel who treats everyone on my team with kindness. Even though our performance was adequate, we all received an A on our appraisal reports.Kit: I'm envious of your success! My boss never acknowledges our efforts. Despite the fact that I have been the department's top salesperson for four consecutive quarters, my supervisor consistently gives me a D in all appraisals!Janice: You are not alone, Kit. I am recognized as a trustworthy and helpful employee. Last month, I requested a week of sick leave, and my appraisal graded me a D in the category of 'Quality of work.'Anna: Our supervisor is quite pleasant. Our team is thrilled since no one suffers because she merely gives us a "C" average.The HR Manager has overheard their conversation. She is worried about the gossip may affect the morale of the employees, so she is thinking of a solution.Question:The HR manager would like to invite more parties to evaluate employees performance. Name THREE parties who can provide performance management feedback for the employees. estimate the change in enthalpy and entropy when liquid ammonia at 270 k is compressed from its saturation pressure of 381 kpa to 1200 kpa. for saturated liquid ammonia at 270 k, vl = 1.551 103 m3 Determine which of the following sets are countable and which are uncountable. a)The set of negative rationals p)b) {r + : r Qn N} c){x R x is a solution to ax+bx+c = 0 for some a, b, c = Q} Which survey question could have been asked to produce this data display? Responses How many bags of dog food do you buy each month? How many bags of dog food do you buy each month? How many times do you feed your dog each day? How many times do you feed your dog each day? How much does your dog weigh? How much does your dog weigh? How much does your bag of dog food weigh? How much does your bag of dog food weigh? testing 110 people in a driving simulator to find the average reaction time to hit the brakes when an object is seen in the view ahead. Particulars Account Balances Dec. 312019 2018Assets. $. $Cash. 75,000 35,000Accounts Receivable 90,000. 98,000MerchandiseInventory 120,000. 87,000Long-term Investment. 10,000. 15,000Land. 30,000 20,000325,000 255,000Liabilities and Shareholders ' EquityAccounts Payable 45,000 50,000Notes Payable (short term) 35,000. 20,000Notes Payable (Due Dec. 2007) 20,000 -Share Capital 150,000 125,000Retained, Earnings 75,000 60,000325, 000 255,000Requirement:s prepare statement showing Changes in Working Capital and Statement of Sources and Uses of funds