Write [tex]\frac{x^{2} - 5 }{x} + \frac{x + 8}{x-1}[/tex] as a single fraction.

a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 500 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/500

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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If the exam is quite easy then the shape of the histogram would be negatively skewed.

What is a histogram?

A histogram is a statistical information display that uses rectangles to show the frequency of data items in equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most common form of a histogram.

a) If the exam is quite easy, it is expected that the majority of the students score well on the test, and since most of the data is closer to the maximum value rather than the minimum, the histogram has a negatively skewed shape.

Hence, if the exam is quite easy then the shape of the histogram would be negatively skewed.

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it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated

A Measurement process is biased if it systematically overstates or understates the true value of the measurement

Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.

Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated

but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false

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The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given statement is "7-radical 7 over10+radical 3".

Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]

Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

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Answer:

15 is a composite number.

In basic Mathematics, the numbers that have more than two factors are known as composite numbers. For example, factors of 6 are 1, 2, 3 and 6. Thus, there are four factors in total, and 6 is a composite number. The first ten composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. To understand better, have a look at the following examples.

Therefore, your answer is 15

The null hypothesis and the alternate hypothesis for the set of elementary school children is given by H₀ :  μ₁ = 2 and H₁ : μ₂  ≠ 0 and the p-value is 0.136 .

Given x₁ = 74 , x₂ = 72

s₁ = 9 , s₂ = 11 (standard deviation)

n₁ = 50 ,n₂ = 50

Let μ₁ be the true mean for x₁

Let μ₂ be the true mean for x₂

null and alternate hypothesis:

H₀ :  μ₁ - μ₂  = 0

H₁ : μ₁ - μ₂  ≠ 0

Test statistic ,

Z = (x₁ - x₂ - D₀ ) / (√σˣ₁² /n₁ + √σˣ₂² /n₂ )

Now we will substitute the values to calculate the the test statistic.

D₀ = μ₁ - μ₂

hence Z₀ = (74 - 72) / √(81/80+121/50)

or,  Z₀ = 1.49256..

or,  Z₀ ≈ 1.49

Now we will calculate the p-value using the z-score.

p-value:

= 2P(Z > Z₀)

= 2P(Z>1.49)

= 2 {1-0.93189}

= 0.1362...

≈ 0.136

Hence the p-value is 0.136 .

A hypothesis is presented as a theory to explain a certain phenomenon. A hypothesis cannot be said to as a scientific hypothesis if it cannot be tested using the scientific process.

History-based observations that can't currently be fully explained by existing bodies of knowledge are typically where science starts. A hypothesis is a theory put out to explain an observed occurrence or a proven assertion regarding the relationship between two or more variables in a scientific field.

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An important measure of location for categorical data is the mode.

While the mean and median can only be determined for numeric data, the mode can be used to describe categorical variables. The mode's principal benefit as a gauge of central tendency is this. When continuous or discrete variables are expressed as intervals, it is also helpful.

The mode represents the value that occurs most often in a dataset.

A dataset can have no mode (if no value repeats), one mode, or multiple modes.

A set of data values' mode is the value that appears the most frequently. The value x (i.e., X = x) at which the probability mass function takes its maximum value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.

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Answer: One solution

Step-by-step explanation:

6x+16=2x+30

4x=14

x=7/2

(C) The standard deviation is 100 and the mean is 22.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

So, using the concepts of expected value and variance of random variables, this issue can be resolved.

By the expected value principle:

E(Y) = E(2+4X) = E(2) + E(4X) = 2 + 4E(X) = 2 + 4(5) = 22

[tex]\mathrm{E}(\mathrm{Y})=\mathrm{E}(2+4 \mathrm{X})=\mathrm{E}(2)+\mathrm{E}(4 \mathrm{X})=2+4 \mathrm{E}(\mathrm{X})=2+4(5)=22[/tex]

Then, μy = 22

In terms of variance concept:
Var(Y) = Var(2 + 4x) = Var(2) + Var(4x) + 2Cov(2, 4x)

Cov(2, 4x) = 0

Var(2) = 0

Hence:
Var(Y) = Var(4x) = 4²Var(X) = 16σ²ₓ = 16(25²) = 10000

Standard deviation(Y) = √10000 = 100

Therefore, (C) the standard deviation is 100 and the mean is 22.

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Complete question:
The random variable X is normally distributed with a mean of 5 and a standard deviation of 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y? The mean is 20 and the standard deviation is 102.

A) The mean is 20 and the standard deviation is 50.

B) The mean is 22 and the standard deviation is 102.

C) The mean is 22 and the standard deviation is 100.

D) The mean is 22 and the standard deviation is 50.

The statements that correctly describes the points of discontinuity of the function include the following;

A. There is an infinite discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

E. There is a jump discontinuity at x = 1.

In Mathematics, there are three (3) main types of discontinuity in a function and these include the following:

A jump discontinuity can be defined as a point on the graph of a function at which the left-hand limit [tex]\lim_{x \to x^-_0} f(x) = A_2[/tex] and right-hand limits [tex]\lim_{x \to x^+_0} f(x) = A_2[/tex] are not equal (A₁ ≠ A₂).

By critically observing the graph representing this function, we can logically deduce that there is a jump discontinuity at x is equal to 1 (x = 1).

A removable discontinuity can be defined as a point on the graph of a function at which it is not connected. This ultimately implies that, a removable discontinuity refers to a point on the graph of a function that is considered to be undefined or doesn't accurately fit the other part of a graph.

By critically observing the graph representing this function, we can logically deduce that there is a removable discontinuity at x is equal to negative 1 (x = -1) while there is an infinite discontinuity on the vertical asymptote at negative 2 (x = -2).

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Complete Question:

Which correctly describes the points of discontinuity of the function? Select all that apply.

A. There is an infinite discontinuity at x = -2.

B. There is a jump discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

D. There is an infinite discontinuity at x = 1.

E. There is a jump discontinuity at x = 1

True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.

The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.

The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.

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The figure H''B''G''P'' created following the transformations applied to HBGP such that HBGP is larger than  H''B''G''P'', inverted and on the other side of the y-axis indicates;

The completed table is presented as follows;

[tex]\begin{array}{|c|c|c|c|c|\pi \pi }\text{Preimage} &\text{Side Length} & \text{Image} &\text{Side Length}&\text{Ratio of Preimage to Image Lengths } \\GB & 5 &G''P'' &2.5&2:1 \\PH &3 & P''H'' &1.5&2:1 \\HB & 5 & H''B'' &2.5&2:1 \\BG &3 & B''G'' & 1.5& 2:1 \\\end{vmatrix}[/tex]

A geometric transformation involves making changes to a geometric figure.

The coordinates if the vertices of the quadrilateral HBGP are;

H(-1, -2), B(-6, -2), G(-6, 1), and P(-1, 1)

The approximate coordinates of the vertices of the quadrilateral H''B''G''P'' are;

H''(0.5, 1), B''(3, 1), G''(3, -0.5), P''(0.5, -0.5)

The length of the side GP in quadrilateral HBGP = -1 - (-6_) = -1 + 6 = 5

Length of the side PH in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

Length of the side HB in quadrilateral HBGP = -1 - (-6) = -1 + 6 = 5

Length of the side BG in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

The possible transformations applied to HBGP to create H''B''G''P'' includes;

A dilation, a rotation of 180° and a translation

The length of the side G''P'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side P''H'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

The length of the side H''B'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side B''G'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

Ratio of the side length of GP to the side length of G''P'' = 5:2.5 = 2:1

Ratio of the side length of PH to the side length of P''H'' = 3:1.5 = 2:1

Ratio of the side length of HB to the side length of H''B'' = 5:2.5 = 2:1

Ratio of the side length of BG to the side length of B''G'' = 3:1.5 = 2:1

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The p-value will be 0.9457

Sample size = 49

Meantime = 19 minutes

Standard deviation = 3.9 mins

Calculating the z-score for test statistic -

z = (x - μ) / (s / √n)

z = (19 - 18) / (3.9 / √49)

= 1 / 0.63

= 1.58

To find the p-value, we can use a standard normal table to find area under the normal curve of the z-score.

The p-value will be the area under the curve to the right of 1.58.

This value is 0.9457, which means that there is a 94.57% chance.

Now,

Since the p-value is greater than the significance level (0.9457 > 0.05),  the null hypothesis can not be rejected. Therefore, the mean time parents spend posting pictures of their children per week is not significantly different from 18 minutes at the 5% significance level.

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The table of values and the linear equations indicates

4. Andy is correct, the equation of the table of values is; y = 2·x + 4

5. The Three equations are the same

A linear equation is an equation that produces a straight line graph, when plotted on the coordinate plane and can be expressed in the form; y = m·x + c

Where;

m = The slope of the straight line graph of the equation

c = The y-intercept

4. The values in the table indicate that the difference between consecutive terms in the x-values and the first difference in the y-value is constant, therefore, the values represent a linear relationship.

The slope, m, of the linear relationship is constant and it can be found using any two pair of points as follows;

m = (4 - 2)/(0 - (-1))  = 2

The equation is therefore;

y - 2 = 2·(x - (-1)) = 2·(x + 1) = 2·x + 2

y = 2·x + 2 + 2 = 2·x + 4

The equation, y = 2·x + 4 is in the form y = m·x + c, therefore;

Andy is correct

5. The slope-intercept form of the equation of a straight line is; y = m·x + c

Therefore;

y + 1 = 2·x -3

y + 1 - 1 = 2·x - 3 - 1 (subtraction property)

y = 2·x - 4

The equation, y = 2·x - 4, is in the form, y = m·x + c

2·x - 3 = y + 1

2·x - 3 - 1 = y + 1 - 1 (subtraction property)

2·x - 4 = y

y = 2·x - 4 (symmetric property)

The equation, y = 2·x - 4 is in the form, y = m·x + c, which is the same as the first equation

2·y + 2 = 4·x - 6

2·y + 2 - 2 = 4·x - 6 - 2 (subtraction property of equality)

2·y = 4·x - 8

2·y ÷ 2 = (4·x - 8) ÷ 2 (division property)

y = 2·x - 4

The above equation is the same as the first two equations, therefore, the equations are the same

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The triple integral f(x, y, z)dV for the following function f is 256π(256 - x - y)² as an iterated integral in cylindrical coordinates.

In two-dimensional space R2, a point with rectangular coordinates (x, y) can be identified with (r, θ) in polar coordinates and vice versa, where x=rcosθ, y=rsinθ, r2=x2+y2 and tanθ=(y.x) are the relationships between the variables.

In three-dimensional space R3, a point with rectangular coordinates (x, y, z) can be identified with cylindrical coordinates (r,θ,z) and vice versa. We can use these same conversion relationships, adding z as the vertical distance to the point from the x y-plane

According to the question:

The integrated integral in cylindrical coordinates is given by:

∫∫∫f(ρ, θ, z)dV = ∫∫∫xρcos(θ)ρsin(θ)zdρdθdz

Evaluating the integral yields:

∫∫∫f(ρ, θ, z)dV = 256π∫zdz

= 256πz²

= 256π(256 - x - y)²

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The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.

Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question

the charge for tuition = $32000

Charge deduced from tuition per year = $2300

So we assume the tuition cost as y and the number of years as x.

The regression equation will be

y = 34000 - 2300x

where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.

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Answer: B. Angle Bisector

Why: the line from D to be is intersecting or bisecting the 90 degree angle

Answer:

40

Step-by-step explanation:

280 divided by 7

Answer:

3(n+6)

Step-by-step explanation:

3n+18= 3(n+6)

The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  [tex]\int\limits_e {x^2} \, dx[/tex].

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]

[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]

[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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Answer:

22

Step-by-step explanation:

The measure of the given sides and angles are,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given: ΔXYZ ≅ ΔEGF

Because the triangles are assumed to be congruent, their corresponding angles and sides must have similar measurements and lengths.

a. ZX = _ in

ZX's length is the same as FE's length. Therefore, the length should be 1.3 inches.

b. EG = _ in

EG's length is the same as XY's length. The figure indicates that the answer should be 3.0 in.

c. m ∠X = _ °

Angle E and angle x should both have the same measure. This is stated to be 48 degrees.

d. m ∠G

Angle Z's measurement is the same as angle F's measurement.

In that case, 107° should be the value assigned to angle F.

Angle E in the triangle to the right measures 48°, while angle F measures 107°.

the sum of these angles is subtracted from 180°.

The angle G's measure, which is equal to 25°.

Hence,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

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Complete question:

Complete question is attached below.

After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

Here, we are given that a sheet of paper is cut into 6 ​same-size parts. Each of the parts is then cut into 6 ​same-size parts and so on.

Thus, after one cut we will have 6 pieces

After second cut, we will have 6*6 = 36 pieces

After the third cut, we will have 36*6 = 216 pieces

After the fourth cut, we will have 216*6 = 1,296 pieces

Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.

Thus, after the nth cut, the number of pieces will be-

a[tex]r^{n-1}[/tex]

where a = first term which is 6

and r = common ratio which is also 6

⇒ 6*[tex]6^{n-1}[/tex]

= [tex]6^{n}[/tex]

Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

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Answer:

43.152

Step-by-step explanation:

6/5*35.96=43.152

Answer:

cheese is cheese

Given surd [tex]\frac{7}{\sqrt{7} }[/tex] after rationalization we get it as [tex]\sqrt{7}[/tex]

The process of rationalization can be thought of as the removal of a radical or an imaginary number from the denominator of an algebraic fraction. In other words, eliminate the radicals from a fraction so that the denominator is solely composed of rational numbers.

Here we use the Rationalization technique

Given surds,

[tex]\frac{7}{\sqrt{7} }[/tex]

Multiplying Numerator and Denominator [tex]\sqrt{7}[/tex]

Then,

[tex]\frac{7}{\sqrt{7} }[/tex] × [tex]\frac{\sqrt[]{7} }{\sqrt{7} }[/tex]

We get the result as [tex]\frac{7\sqrt{7} }{7}[/tex] which is equal to √7

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The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, [tex]Z_{0.005/2}=1.96[/tex]

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]

Thus, the margin of error for the population mean is 5.601

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Why you lie you say 30 but give a 15