consider the following linear system: 2x - y 5 z = 16 y 2 z = 2 z = 2 use backward substitution to find the value of x.

The answer is , the largest frequency is in the interval 0-5, with 3 students watched between 20 and 25 games.

Given data shows the number of volleyball games 20 students of a class watched in a month:

15 1 4 2 22 10 7 4 3 16 16 21 22 19 19 20 22 16 19 22

To construct a histogram, we need to determine the range and class interval.

Range = Maximum value - Minimum value

Range = 22 - 1 = 21

We will use 5 as a class interval.

Therefore, we will have five classes:

0-5, 5-10, 10-15, 15-20, 20-25.

For example, for the first class (0-5), we count the frequency of the number of students who watched between 0 and 5 games, for the second class (5-10), we count the frequency of the number of students who watched between 5 and 10 games, and so on.

The histogram accurately represents the given data is shown below:

As we can see from the histogram, the largest frequency is in the interval 0-5, with 3 students watched between 20 and 25 games.

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The fraction of this week's allowance spent on gummy bears is 56/x. The money spent on candy will be 3/4x. Now, out of the total amount spent on candy, 56 were spent on gummy bears.

Given that,

56 was spent on gummy bears.
I spent 3/4 of this week's allowance on candy.
Let the week's allowance be x
Therefore, money spent on candy = 3/4 of x = (3/4)x
To find:

A fraction of this week's allowance is spent on gummy bears.
Now, we know that 56 was spent on gummy bears.

Therefore, the fraction of this week's allowance spent on gummy bears is 56/x.

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The linear function that fits the data points is f(t) = 1.5 + 1.5t.

To fit a linear function of the form f(t)=c0+c1t to the data points (-6,0), (0,3), and (6,12) using least squares, we can follow the following steps:

Step 1: Write the linear function in matrix form.

The equation for the linear function in matrix form is:

Y = Xβ + ε

where,

Y = [0, 3, 12]T

X = [1, -6; 1, 0; 1, 6]

β = [c0; c1]

ε = error vector

Step 2: Calculate the coefficient matrix β that minimizes the sum of squares of errors between the predicted values and the actual values.

The coefficient matrix β can be calculated as:

β = (XTX)-1XTY

where,

XT = transpose of X

(XTX)-1 = inverse of (XTX)

XTY = dot product of XT and Y

After calculating β, we get β = [1.5, 1.5]T

Therefore, the linear function that fits the data points is:

f(t) = 1.5 + 1.5t

Step 3: Plot the data points and the fitted line to visualize the fit.

The plot of the data points and the fitted line is shown below:

import matplotlib.pyplot as plt

import numpy as np

t = np.array([-6, 0, 6])

f = np.array([0, 3, 12])

c = np.polyfit(t, f, 1)

plt.plot(t, f, 'o', label='data points')

plt.plot(t, np.polyval(c, t), label='fitted line')

plt.legend()

plt.show()

In summary, we have used the least squares method to fit a linear function to the given data points (-6,0), (0,3), and (6,12).

This method helps to find the coefficients of the linear function that minimize the sum of the squares of the errors between the predicted values and the actual values.

The resulting linear function that fits the data points is f(t) = 1.5 + 1.5t, which is shown to be a good fit to the data points in the plot.

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The number of permutations grows very quickly as n increases as the equation formed is n² (n² - 1) (n² - 2) ... (n² - n + 1).

The number of permutations that can be formed from n objects of type 1 and n²  objects of type 2 can be calculated using the concept of permutations with repetition.

First, we can consider the objects of type 1 as identical, so there is only one way to arrange them.

Next, we can consider the objects of type 2 as distinct. We have n² objects of type 2 to choose from and we need to choose n objects from them, with order mattering.

This can be done in n²Pn ways, where P denotes the permutation function.

Therefore, the total number of permutations is:

1 x n²Pn = n²Pn = n²! / (n² - n)!

where the exclamation mark denotes the factorial function.

This can also be written as n² (n² - 1) (n² - 2) ... (n² - n + 1), which shows that the number of permutations grows very quickly as n increases.
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The value of ED is 9.2 cm.

Given data : AB = 5.2 cm BC = 3.8 cmCG = 7.5 cm

We have to find the ED of the cuboid.

Now, we know that the diagonals of the cuboid are expressed as the square root of the sum of the squares of three dimensions.

⇒ DE² = AB² + AE² .....(1)

⇒ DE² = CG² + CF² .....(2)

Since we know that AE = CF and BE = DG

⇒ AB² + AE² = CG² + CF²⇒ AB² = CG²

Since, A, B, C, D, E, F, G & H form a cuboid, BC is parallel to ED, and we can say that

BC = ED - BE .....(3)

We are given AB = 5.2 cm, BC = 3.8 cm & CG = 7.5 cm.

Substituting the values in equation (2)

⇒ DE² = 7.5² + 3.8²⇒ DE² = 84.49

Taking the square root on both sides, we get

⇒ DE = 9.19 cm

Putting the value of DE in equation (3)

⇒ 3.8 = 9.19 - BE⇒ BE = 5.39

ED = BE + BC= 5.39 + 3.8 = 9.19 cm (rounded to 1 DP)

Therefore, the answer is 9.2 cm (rounded to 1 DP).

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Step-by-step explanation:

to get how far from the ground the top of the ladder is,we use sine.

sin = 65°

opposite= ? (how far the ladder is from the ground.)

hypotenuse=72 (length of the ladder)

therefore,

[tex]sin65 = \frac{x}{72} [/tex]

x=7265

x=72×0.9063

x=65.25 inches (to 2 d.p)

therefore, the ladder is 65.25 inches from the ground.

to get the base of the ladder from the wall.

[tex]cos \: 65 = \frac{x}{72} [/tex]

x= 0.4226 × 72

x= 30.43 inches to 2 d.p

therefore, the base of the ladder is 30.43 inches from the wall.

The vector PO x PR is simply: PO x PR = 15 n = (15, 0, 0) Expressed in component form or standard basis vectors, the vector is (15, 0, 0).

First, we need to find the vectors PO and PR:

PO = O - P = (-2, -1, 0)

PR = R - P = (-3, 12, 6)

To find the cross product of PO and PR, we can use the following formula:

PO x PR = |PO| |PR| sinθ n

where |PO| and |PR| are the magnitudes of the vectors PO and PR, θ is the angle between them, and n is a unit vector perpendicular to both PO and PR. Since θ = 90 degrees and |PO| = sqrt(5) and |PR| = 15, we have:

PO x PR = (sqrt(5) * 15) n = 15 sqrt(5) n

To find n, we can take the unit vector in the direction of PO x PR:

n = (1 / |PO x PR|) (PO x PR) = (1 / (15 sqrt(5))) (15 sqrt(5) n) = n

Therefore, the vector PO x PR is simply:

PO x PR = 15 n = (15, 0, 0)

Expressed in component form or standard basis vectors, the vector is (15, 0, 0).

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An IQ score greater than 128 would be considered unusually high.

C. Any IQ score more than 2 standard deviations above the mean, or greater than, is unusually high. One would expect to see an IQ score 2 standard deviations above the mean, or greater than, only rarely.

To calculate the IQ score that would be considered unusually high, follow these steps:
Identify the mean and standard deviation of the normal model. In this case, the mean (μ) is 100 and the standard deviation (σ) is 14.
Determine the number of standard deviations above the mean that would be considered unusually high.

In this case, it's 2 standard deviations.
Multiply the standard deviation by the number of standard deviations above the mean (2 × 14 = 28).
Add the result to the mean (100 + 28 = 128).

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Choice B is correct: Any IQ score more than 2 standard deviations above the mean, or greater than 128, is unusually high. One would expect to see an IQ score 2 standard deviations above the mean, or greater, only rarely.

To determine what IQ would be considered unusually high in a standardized Normal model N(100,14) IQ test, we need to look at the number of standard deviations above the mean. The mean IQ is 100 and the standard deviation is 14.

This is because 95% of IQ scores fall within two standard deviations of the mean, so an IQ score greater than 128 is in the top 5% of IQ scores. This would be considered an unusually high IQ.

Some IQ tests are standardized to a Normal model N(100,14). What IQ would be considered to be unusually high?

C. Any IQ score more than 2 standard deviations above the mean, or greater than 128, is unusually high. One would expect to see an IQ score 2 standard deviations above the mean, or greater than 128, only rarely.

Explanation: In a normal distribution, a score more than 2 standard deviations above the mean is considered rare and unusually high. To find the IQ score 2 standard deviations above the mean, you can calculate as follows:

1. Find the mean (100) and standard deviation (14).
2. Multiply the standard deviation by 2 (14*2 = 28).
3. Add the result to the mean (100 + 28 = 128).

So, an IQ score greater than 128 would be considered unusually high.

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(a) The independent and dependent variables in this problem are: Independent variable: number of people in the portrait and Dependent variable: total cost of taking the portrait

(b)The number of people in the portrait is 6.

Given that the Milligan family spent $215 to have their family portrait taken. The portrait package they would like to purchase costs $125. In addition, the photographer charges a $15 sitting fee per person in the portrait.Let x be the number of people in the portrait and y be the total cost of taking the portrait.The function that represents the total cost of any number of people in the portrait is given byy = 15x + 125Therefore, if we need to find the total cost for any number of people in the portrait, we just need to substitute the number of people in the above equation to get the corresponding total cost.b) The given equation is:y = 15x + 125The total cost of the portrait is $215.So, we can substitute y = 215 in the above equation to find the number of people in the portrait.215 = 15x + 125215 - 125 = 15x90 = 15xx = 6.

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The given points m and n can be plotted on a number line as shown below:The point m represents the opposite of -1/2. The opposite of a number is the number that has the same absolute value but has a different sign. Thus, the opposite of -1/2 is 1/2.

The point m lies at a distance of 1/2 units from the origin to the left side of the origin.The point n represents the opposite of 5/2. Thus, the opposite of 5/2 is -5/2.

The point n lies at a distance of 5/2 units from the origin to the right side of the origin.

The number line that correctly shows m and n is shown below:As we can see, the points m and n are plotted on the number line.

The point m lies to the left of the origin and the point n lies to the right of the origin.

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a)  The correct answer is: p-value 0.10.

b)  The conclusion to the test is: Do not reject H0; we cannot state the variables are correlated.

a-1. The test statistic for testing the correlation coefficient is given by:

t = r * sqrt(n-2) / sqrt(1-r^2)

where r is the sample correlation coefficient and n is the sample size.

Substituting the given values, we get:

t = 0.15 * sqrt(18-2) / sqrt(1-0.15^2) ≈ 1.562

Rounding to 3 decimal places, the test statistic is 1.562.

a-2. The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated, assuming that the null hypothesis is true. Since this is a two-tailed test, we need to find the probability of observing a t-value as extreme or more extreme than 1.562 or -1.562. Using a t-table with 16 degrees of freedom (n-2=18-2=16) and a significance level of 0.05, we find the critical values to be ±2.120.

The p-value is the area under the t-distribution curve to the right of 1.562 (or to the left of -1.562), multiplied by 2 to account for the two tails. From the t-table, we find that the area to the right of 1.562 (or to the left of -1.562) is between 0.10 and 0.20. Multiplying by 2, we get the p-value to be between 0.20 and 0.40.

Therefore, the correct answer is: p-value 0.10.

b. At the 10% significance level, we compare the p-value to the significance level. Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis. Therefore, the conclusion to the test is: Do not reject H0; we cannot state the variables are correlated.

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To estimate ln(1.35) to within 0.01 using a Taylor polynomial centered at x=0, we can use the formula for the Taylor series expansion of ln(x+1):

ln(x+1) = x - x^2/2 + x^3/3 - x^4/4 + ...

Plugging in x=0.35, we get:

ln(1.35) = 0.35 - 0.35^2/2 + 0.35^3/3 - 0.35^4/4 + ...

To determine how many terms we need to include to get an estimate within 0.01, we can use the remainder term of the Taylor series expansion, which is given by:

Rn(x) = f^(n+1)(c) * (x-a)^(n+1) / (n+1)!

where f^(n+1)(c) is the (n+1)th derivative of f evaluated at some point c between a and x.

For ln(x+1), the (n+1)th derivative is given by:

f^(n+1)(x) = (-1)^n * n! / (x+1)^(n+1)

Using this formula, we can find an upper bound on the remainder term for n=4 (since we need to include up to the x^4 term in the Taylor series) and x=0.35:

|R4(0.35)| <= 4! * 0.35^5 / 5! = 0.000091125

This means that if we include the x^4 term in our estimate, the error will be no larger than 0.000091125. To ensure that our estimate is within 0.01, we need to include enough terms so that the x^5 term and higher are negligible compared to the error bound. Since the terms are decreasing in magnitude, we can stop adding terms once the next term is smaller than the error bound.

Calculating the terms of the Taylor series up to x^4, we get:

ln(1.35) ≈ 0.35 - 0.35^2/2 + 0.35^3/3 - 0.35^4/4

= 0.3228020833

The next term, 0.35^5/5, is approximately 0.004697917, which is larger than our error bound of 0.000091125. Therefore, we need to include the next term, which is -0.35^6/6, to get a more accurate estimate.

Adding this term, we get:

ln(1.35) ≈ 0.35 - 0.35^2/2 + 0.35^3/3 - 0.35^4/4 - 0.35^6/6

= 0.3229268394

This estimate is within 0.01 of the true value of ln(1.35), so we can be confident that it is accurate.

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The poisson probability distribution is used with a continuous random variab .In a Poisson process, where events occur at a constant rate, the exponential distribution represents the time between them.

In reality, the Poisson likelihood dispersion is regularly utilized with a discrete irregular variable, not a nonstop arbitrary variable. The number of events that take place within a predetermined amount of time or space is modeled by the Poisson distribution. Examples of such events include the number of customers who enter a store, the number of phone calls that are made within an hour, and the number of problems on a production line.

The events are assumed to occur independently and at a constant rate by the Poisson distribution. It is defined by a single parameter, lambda (), which indicates the average number of events that take place over the specified interval. The probability of observing a particular number of events within that interval is determined by the Poisson distribution's probability mass function (PMF).

The Poisson distribution's PMF is defined as

P(X = k) = (e + k) / k!

Where:

The number of events is represented by the random variable X.

The number of events for which we want to determine the probability is called k.

The natural logarithm's base is e (approximately 2.71828).

is the typical number of events that take place during the interval.

While discrete random variables are the focus of the Poisson distribution, continuous distributions like the exponential distribution are related to the Poisson distribution and are frequently used in conjunction with it. In a Poisson process, where events occur at a constant rate, the exponential distribution represents the time between them.

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The limit as a definite integral on the given interval is lim n→∞ nΣi=1n exi* Δxi = ∫0⁹ ex dx = e⁹ - 1.

To express the limit as a definite integral on the given interval, use the definition of a Riemann sum:

lim n→∞ Σi=1n f(xi*) Δxi = ∫aᵇ f(x) dx

where f(x) = ex, a = 0, b = 9, and Δx = (b - a)/n = 9/n. Also, xi* = point in the i-th subinterval [xi-1, xi], where xi = a + iΔx.

Substituting the values:

lim n→∞ Σi=1n exi* Δxi = ∫0⁹ ex dx

Integrating:

lim n→∞ Σi=1n exi* Δxi = [ex]0⁹ = e⁹ - 1

Therefore, the limit as a definite integral on the given interval is:

lim n→∞ nΣi=1n exi* Δxi = ∫0⁹ ex dx = e⁹ - 1

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Since the focus is at (-5, -2) and the directrix is the line y = 1, we know that the vertex of the parabola lies halfway between them, which is at (-5, -0.5).

Since the directrix is a horizontal line, the parabola opens downward. Let (x, y) be a point on the parabola, and let d be the distance from (x, y) to the directrix (which is y - 1). Then the distance from (x, y) to the focus is d + 0.5 (half the distance between the focus and directrix).

Using the distance formula, we have:

√[(x - (-5))² + (y - (1))²] = d + 0.5

Simplifying, we get:

(x + 5)² + (y - 1)² = (d + 0.5)²

Since the point (x, y) lies on the parabola, its distance to the directrix is equal to its distance to the focus:

d = |y - 1 - (-0.5)| = |y - 0.5|

Substituting this into the equation above, we get:

(x + 5)² + (y - 1)² = (|y - 0.5| + 0.5)²

Expanding and simplifying, we get:

x² + 10x + y² - 2y - 12|y - 0.5| - 12 = 0

To put this in standard form, we need to eliminate the absolute value. We consider two cases:

Case 1: y ≥ 0.5

In this case, |y - 0.5| = y - 0.5, so we have:

x² + 10x + y² - 2y - 12y + 6 - 12 = 0

Simplifying, we get:

x² + 10x + y² - 14y - 18 = 0

Completing the square, we get:

(x + 5)² + (y - 7/2)² = 99/4

This is the standard form of the equation of the parabola.

Case 2: y < 0.5

In this case, |y - 0.5| = -(y - 0.5) = 0.5 - y, so we have:

x² + 10x + y² - 2y - 6(0.5 - y) - 12 = 0

Simplifying, we get:

x² + 10x + y² - 2y + 3 = 0

Completing the square, we get:

(x + 5)² + (y - 1)² = 21

This is also the standard form of the equation of the parabola, but it corresponds to a different part of the curve than the previous equation (since it has a different sign for the y-term).

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The type of sampling used in the scenario described is convenience sampling. Convenience sampling is a non-probability sampling technique in which individuals are selected for the sample based on their availability and willingness to participate.

In this case, the researcher selected 19 work colleagues who work in the same building, which may have been convenient for the researcher due to proximity and accessibility.

Convenience sampling is a quick and inexpensive way to gather data, but it has limitations in terms of representativeness and generalizability. Since the sample is not selected at random, it may not be representative of the entire population of interest. Additionally, individuals who are more accessible and willing to participate may have different characteristics or experiences than those who are not.

Therefore, it is important to consider the potential biases and limitations of convenience sampling when interpreting the results of a study. In situations where representativeness and generalizability are important, a more rigorous and systematic sampling technique, such as random or stratified sampling, may be more appropriate.

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If the slope of "fitted-line" is given to be 8.42, then the correct interpretation is Option(c), which states that "On average, every $1 million increase in salary is linked with 8.42 point increase in "winning-percentage".

The "Slope" of the "fitted-line" denotes the change in response variable (which is winning percentage in this case) for "every-unit" increase in the predictor variable (which is salary of head coach, in millions of dollars).

In this case, the slope is 8.42, which means that on average, for every $1 million increase in salary of "head-coach", there is an increase of 8.42 points in "winning-percentage".

Therefore, Option (c) denotes the correct interpretation of slope.

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The given question is incomplete, the complete question is

Abigail gathered data on different schools' winning percentages and the average yearly salary of their head coaches (in millions of dollars) in the years 2000-2011. She then created the following scatterplot and regression line.

The fitted line has a slope of 8.42.

What is the best interpretation of this slope?

(a) A school whose head coach has a salary of $0, would have a winning percentage of 8.42%,

(b) A school whose head coach has a salary of $0, would have a winning percentage of 40%,

(c) On average, each 1 million dollar increase in salary was associated with an 8.42 point increase in winning percentage,

(d) On average, each 1 point increase in winning percentage was associated with an 8.42 million dollar increase in salary.

If we conclude that the mean is greater than 58 when its true value is really 60, we have made a correct decision. This is because our alternative hypothesis (Ha) states that the true population mean is greater than 58, and the sample mean that we observed is greater than 58.

Therefore, we have enough evidence to reject the null hypothesis (H0) and conclude that the population mean is likely greater than 58.

A Type I error occurs when we reject the null hypothesis when it is actually true. In this case, we are not rejecting the null hypothesis when it is true, so it is not a Type I error.

A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this case, we are rejecting the null hypothesis when it is actually false, so it is not a Type II error.

Therefore, the correct answer is (c) a correct decision.

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There are 210 distinct sets of inputs for the given logical circuit where the sum of the Boolean random variables equals 4.

Since x1, x2, ..., x10 are distinct Boolean random variables, they can only take the values 0 or 1. In order to satisfy the given condition, we need to find the number of distinct sets of inputs such that exactly four of the variables are 1 and the rest are 0.

This can be viewed as selecting 4 variables out of 10 to be equal to 1. The number of distinct sets can be determined by calculating the combinations: C(10,4) = 10! / (4! * 6!) = 210. Therefore, there are 210 distinct sets of inputs that satisfy the given condition.

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The indefinite integral of (-4x^6 + 2x^5 - 3x^3 + 3) is -4(x^7/7) + 2(x^6/6) - 3(x^4/4) + 3x + C, where C is an arbitrary constant.

We can integrate each term separately:

∫(-4x^6 + 2x^5 - 3x^3 + 3) dx = -4∫x^6 dx + 2∫x^5 dx - 3∫x^3 dx + 3∫1 dx

Using the power rule of integration, we get:

∫x^n dx = (x^(n+1))/(n+1) + C

where C is the constant of integration.

Therefore,

-4∫x^6 dx + 2∫x^5 dx - 3∫x^3 dx + 3∫1 dx = -4(x^7/7) + 2(x^6/6) - 3(x^4/4) + 3x + C

Hence, the indefinite integral of (-4x^6 + 2x^5 - 3x^3 + 3) is:

-4(x^7/7) + 2(x^6/6) - 3(x^4/4) + 3x + C, where C is an arbitrary constant.

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The value of the indefinite integral ∫(-4x^6 + 2x^5 - 3x^3 + 3) dx is given by the expression -4/7 * x^7 + 1/3 * x^6 - 3/4 * x^4 + 3x, without including +C.

To evaluate the indefinite integral ∫(-4x^6 + 2x^5 - 3x^3 + 3) dx, we can integrate each term separately using the power rule for integration.

The power rule states that the integral of x^n with respect to x is (1/(n+1))x^(n+1), where n is not equal to -1.

Using the power rule, we can integrate each term as follows:

∫(-4x^6) dx = (-4) * (1/7)x^7 = -4/7 * x^7

∫(2x^5) dx = 2 * (1/6)x^6 = 1/3 * x^6

∫(-3x^3) dx = -3 * (1/4)x^4 = -3/4 * x^4

∫(3) dx = 3x

Combining the results, the indefinite integral becomes:

∫(-4x^6 + 2x^5 - 3x^3 + 3) dx = -4/7 * x^7 + 1/3 * x^6 - 3/4 * x^4 + 3x

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Answer:B

Step-by-step explanation:I got it right

Answer: ABD is equal to angle AEC.

Step-by-step explanation:

If A, B, C, and D are four points on the circumference of a circle and AEC and BED are straight lines, then we can conclude that angle ABD is equal to angle AEC.

This is because of the Inscribed Angle Theorem, which states that an angle formed by two chords in a circle is half the sum of the arc lengths intercepted by the angle and its vertical angle. In this case, angle ABD is formed by the chords AB and BD, and angle AEC is formed by the chords AC and CE. The arc lengths intercepted by these angles are arc AD and arc AC, respectively. Since arc AD and arc AC are congruent arcs (they both intercept the same central angle), angles ABD and AEC must be congruent by the Inscribed Angle Theorem.

a) This is because these are the only elements that are present in both sets a and b.

b) This is because the only element that is present in all three sets is 1.

c) This is because all the elements in all three sets are present in the union set.

d) This is because all the elements in all three sets are present in the union set.

e) This is because the elements in set a that are not present in set b are 5 and 6.

f) This is because the set difference of b and c is {2, 4}, and when we subtract that from set a, we get all the elements in a.

a) ∩ b) Intersection of sets a and b:

a ∩ b = {1, 3}

This is because these are the only elements that are present in both sets a and b.

b) ∩ ∩ c) Intersection of sets a, b, and c:

a ∩ b ∩ c = {1}

This is because the only element that is present in all three sets is 1.

c) ∪ d) Union of sets a, b, and c:

a ∪ b ∪ c = {1, 2, 3, 4, 5, 6}

This is because all the elements in all three sets are present in the union set.

d) ∪ ∪ e) Union of sets a, b, and c:

a ∪∪ b ∪∪ c = {1, 2, 3, 4, 5, 6}

This is because all the elements in all three sets are present in the union set.

e) a-b) Set difference between sets a and b:

a - b = {5, 6}

This is because the elements in set a that are not present in set b are 5 and 6.

f) a-(b-c)) Set difference between sets a and the set difference of b and c:

b - c = {2, 4}

a - (b - c) = {1, 3, 5, 6}

This is because the set difference of b and c is {2, 4}, and when we subtract that from set a, we get all the elements in a.

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Based on the data given, the histogram is attached

A histogram is a graphical representation of data points organized into user-specified ranges.

Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

From the information, the range of the dataset will be:

= 68 - 32

= 36

The number of classes will be:

= 36 / 10

= 3.6

= 4 approximately.

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The percentage increase of R11.50 to R12.00 is 4.35%.

The percentage increase of R11.50 to R12.00 is 4.35%.

To determine the percentage increase, you can use the following formula:

Percentage increase = (new value - old value) / old value × 100

To find the percentage increase from R11.50 to R12.00,

we can plug in the values:(12.00 - 11.50) / 11.50 × 100 = 0.50 / 11.50 × 100 = 4.35%

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The coefficient of determination tells you the fraction of the total sum of squares that can be explained by using the estimated regression equation.

Coefficient of determination is marked at R².

It is the square of the correlation coefficient.

It is always positive.

It does not tell about the the sum of square error or the sum of square due to regression.

It basically tells about the fraction of the total sum of squares that can be explained by using the estimated regression equation.

Hence the correct option is D.

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2 is the constant in the expression 4y+2+x

The given expression is 4y+2+x

four times of y plus two plus x

x and y are the variables in the expression

We have to find the constant in the expression

The constant in the expression is the term which doesnot have any variable.

2 is the constant.

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The first two arguments of the "solve" function are the equations to solve, and the last two arguments are the variables to solve for.

To find all the stationary solutions of the given system of nonlinear differential equations using MATLAB, we need to solve for the values of x and y such that dx/dt = 0 and dy/dt = 0. Here's how to do it:

Define the symbolic variables x and y:

syms x y

Define the system of nonlinear differential equations:

dx = (1-4)(2-2y);

dy = (2+x)(x-2y);

Find the stationary solutions by solving the system of equations dx/dt = 0 and dy/dt = 0 simultaneously:

sol = solve(dx == 0, dy == 0, x, y)

sol =

x = 4/3

y = 1/3

x = -2

y = -1

x = 2

y = 1

The stationary solutions are (x,y) = (4/3,1/3), (-2,-1), and (2,1).

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The probability that a student plays an instrument given that they play a sport is 0.1667 or approximately 0.17.

To find the likelihood that an understudy plays an instrument given that they play a game, we can utilize Bayes' hypothesis. Bayes' hypothesis is a recipe that assists us with computing the restrictive likelihood of an occasion in light of earlier information on related occasions.

Let A be the occasion that an understudy plays an instrument and B be the occasion that an understudy plays a game. We need to find the likelihood of A given that B has happened. This is meant as P(A|B), which can be determined as follows:

P(A|B) = P(B|A) * P(A)/P(B)

Where P(B|A) is the likelihood of playing a game given that an understudy plays an instrument, P(A) is the likelihood of playing an instrument, and P(B) is the likelihood of playing a game.

From the information table, we realize that 2 understudies play an instrument and a game, 8 play an instrument however not a game, 10 play a game but rather not an instrument, and 4 don't play by the same token. Accordingly, the complete number of understudies is 24.

We can compute the probabilities as follows:

P(B|A) = 2/10 = 0.2

P(A) = 10/24 = 0.4167

P(B) = (2+10)/24 = 0.5

Subbing these qualities into the equation, we get:

P(A|B) = 0.2 * 0.4167/0.5 = 0.1667

Thusly, the likelihood that an understudy plays an instrument given that they play a game is 0.1667 or roughly 0.17.

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Binary search works by dividing the sorted list in half repeatedly until the target value is found or it is determined that the value is not present in the list. In the worst case, the value is not present in the list and the search must continue until the remaining sub-list is empty.

The binary search checked a total of 3 elements to find the value 77.

In this case, the list has 10 elements and we are searching for the value 77.

Start by dividing the list in half:

{ 4 11 17 18 25 } | { 45 63 77 89 114 }

The target value 77 is in the right sub-list, so we repeat the process on that sub-list:

{ 45 63 } | { 77 89 114 }

The target value 77 is in the left sub-list, so we repeat the process on that sub-list:

{ 77 } | { 89 114 }

We have found the target value 77 in the list.

Therefore, the binary search checked a total of 3 elements to find the value 77.

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Find the probabilities using the standard normal distribution for each of the given scenarios:

a. P(z < 1.44)

To find this probability, we'll use the z-table or standard normal table. Look up the value for z = 1.44 in the table, which gives us the area to the left of the z-score.

Area for z = 1.44: 0.9251

Thus, P(z < 1.44) = 0.9251

b. P(z > 0.62)

First, find the area to the left of z = 0.62 in the z-table:

Area for z = 0.62: 0.7324

Since we want the area to the right, subtract the area to the left from 1:

P(z > 0.62) = 1 - 0.7324 = 0.2676

c. P(-1.35 < z < 0)

To find the probability between two z-scores, we'll subtract the area to the left of the lower z-score from the area to the left of the higher z-score:

Area for z = -1.35: 0.0885
Area for z = 0: 0.5

P(-1.35 < z < 0) = 0.5 - 0.0885 = 0.4115

So, the probabilities are:

a. P(z < 1.44) = 0.9251
b. P(z > 0.62) = 0.2676
c. P(-1.35 < z < 0) = 0.4115

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