Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= xUse the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(a) P(X %u2264 1)(b) P(0.5 %u2264 X %u2264 1)(c) P(X > 1.5)(d) The median checkout duration [solve 0.5 = F(mew)](e) Use F'(x) to obtain the density function f(x)(f) Calculate E(X)(g) Calculate V(X) and %u03C3x(h) If the borrower is charged an amount h(X) = X2 when checkout duration is X, compute the expected charge E[h(X)].

Answer:

The exact value of the given trigonometric expression is undefined.

Step-by-step explanation:

Given trigonometric expression:

[tex]\dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)[/tex]

To find the exact value of the given  trigonometric expression, begin by finding the exact values of each of the trigonometric functions in the expression

The exact value of cos(2π/3) is:

[tex]\implies \cos\left(\dfrac{2 \pi}{3}\right)=-\dfrac{1}{2}[/tex]

The exact value of tan(-7π/4) is:

[tex]\implies \tan\left(-\dfrac{7 \pi}{4}\right)=1[/tex]

Since the cosecant function is the reciprocal of the sine function, the exact value of csc(π) is:

[tex]\implies \csc (\pi)=\dfrac{1}{\sin(\pi)}=\dfrac{1}{0}=\textsf{unde\:\!fined}[/tex]

Therefore:

[tex]\begin{aligned}\implies \dfrac{\cos\left(\dfrac{2 \pi}{3}\right)}{\tan\left(-\dfrac{7 \pi}{4}\right)}+\csc(\pi)&=\dfrac{-\dfrac{1}{2}}{1}+\dfrac{1}{0}\\&=-\dfrac{1}{2}+\dfrac{1}{0}\\\\&=\textsf{unde\:\!fined}\end{aligned}[/tex]

The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).

A) The 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).Explanation:Given,Sample size, n = 123Average surgery time, μ = 136.9 minutesStandard deviation, σ = 24.1 minutesWe know that for a sample of size n, the 95% confidence interval is given by,  (Formula1)Where, z is the z-score, α/2 = 0.05/2 = 0.025  is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula1), we get the 95% confidence interval as(130.82, 142.98)Thus, the 95% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (130.82, 142.98).B) The 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).Explanation:We know that for a sample of size n, the 99.5% confidence interval is given by, (Formula2)Where, z is the z-score, α/2 = 0.005/2 = 0.0025 is the level of significance and n - 1 = 122 degrees of freedom.Now, substituting the given values in (Formula2), we get the 99.5% confidence interval as (127.93, 145.87).Thus, the 99.5% confidence interval for a sample of 123 hip surgeries of a certain type with an average surgery time of 136.9 minutes and a standard deviation of 24.1 minutes is (127.93, 145.87).C) The surgeon's claim that the mean surgery time is between 133.71 and 140.09 minutes is equivalent to the confidence interval (133.71, 140.09). The surgeon's claim falls inside the 95% confidence interval, (130.82, 142.98), therefore we can say that the surgeon's claim can be made with 95% confidence.D) The formula to find the minimum sample size for a 95% confidence interval that will specify the mean to within ±3 minutes is given by (Formula3)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula3), we get the minimum sample size as 424.15.The minimum sample size required to get a 95% confidence interval that will specify the mean to within ±3 minutes is 425 (Rounded up to the nearest integer).F) The formula to find the minimum sample size for a 99% confidence interval that will specify the mean to within ±3 minutes is given by (Formula4)Where, n is the sample size and σ is the standard deviation.Now, substituting the given values in (Formula4), we get the minimum sample size as 596.73.The minimum sample size required to get a 99% confidence interval that will specify the mean to within ±3 minutes is 597 (Rounded up to the nearest integer).

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Answer:

0.999

Step-by-step explanation:

If the driver wore a seat belt, that is the only column we have to look at.

The chance the driver survived is number survived / number total.

Plugging in, we get 412,042/412,493, or about 0.999.

Hope this helps!

It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

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In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,

we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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If a random variable is normally distributed, and has a mean of 228 and

a standard deviation of 16. If a sample of size 12 is taken, then the shape

of the sampling distribution for the sample mean is normally distributed

since the variable is normally distributed. Hence, option B is correct.

A normal distribution is a type of probability distribution in which the

value of the mean, standard deviation, and random variables are well

known. Sampling distribution refers to the probability distribution of the

statistics that have been derived from a sample taken from a population.

As per the Central Limit Theorem, if the sample size is large enough,

then the sampling distribution of the sample means will be normally

distributed, no matter how the population looks. If the random variable is

normally distributed, then the sampling distribution of the sample mean

will also be normally distributed, no matter what the size of the sample is.

Hence, option B is the correct answer as the sampling distribution of the

sample mean is normally distributed since the variable is normally distributed.

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1. The number of hours which Sidra did on homework is 12 hours

2. The total number of hours which Sally's friends spend on homework per month is 64 hours.

Sidra does 3 keys worth of homework, and since a key equals 4 hours, she does:

= 3 keys x 4 hours/key

= 12 hours of homework.

To find the total number of hours that Sally's friends spend on homework per month, we need to add up the hours of homework done by each of her friends:

Tim: 5 keys x 4 hours/key = 20 hours

Mary: 2 1/2 keys x 4 hours/key = 10 hours

Keith: 5 1/2 keys x 4 hours/key = 22 hours

Sidra: 3 keys x 4 hours/key = 12 hours

Total hours of homework per month:

= 20 + 10 + 22 + 12

= 64 hours.

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The sampling distribution is approximately normal.

The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.

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The center, 6,  is less frequent than the neighbor values, but the single dot that best represents the data still is 6.

Each point on the dot plot over each number represents the amount of times that we have that value in the data set.

Here the center is 6, and we can see that we have only one point in 6, while in the neighbors we can see more points, then we can see that the center is less populated than the neighbor values.

Now, what single dot would best represent the data?

To answer that we need to get the mean of the data set,

Counting the values in the graph, and dividing by the number of points, we have:

mean = (3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8+ 8+ 9)/12 = 6.16

Which we can round to 6.

So that is the single dot that best represents the data.

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Answer:

adjacent = cos(angle) x hypotenuse

The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.

If the education level is 14 years,

To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.

This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.

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To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.

Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.

Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.

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Answer:

Step-by-step explanation:

C(1,2), radius=6

Equation using  [tex](x-h)^2+(y-k)^2=r^2[/tex]:

   [tex](x-1)^2+(y-2)^2=36[/tex]

You answer would be mate it would be x=66

Answer:

To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.

So the perimeter P is:

P = (2v-5) + (4v+5) + (2v-5) + (8v-7)

Simplifying and combining like terms, we get:

P = 16v - 12

Therefore, the perimeter is 16v - 12.

The sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest.

Tο sοlve fοr x in the equatiοn [tex]x^2 + 3x - 4 = 0[/tex], we can use the quadratic fοrmula:

[tex]x= \frac{(-b+\sqrt{b^{2} -4ac} )}{2a} \\[/tex]

where a, b, and c are the cοefficients οf the quadratic equatiοn[tex]ax^2 + bx + c = 0.[/tex]

In this case, a = 1, b = 3, and c = -4. Substituting these values intο the quadratic fοrmula, we get:

[tex]x = (-3\± \sqrt{(3^2 - 4(1)(-4)))} / 2(1)\\\\x = (-3 \± \sqrt{(25))} / 2\\\\x = (-3 \± 5) / 2[/tex]

This gives twο pοssible sοlutiοns:

x1 = (-3 - 5) / 2 = -4

x2 = (-3 + 5) / 2 = 1

Therefοre, the sοlutiοns in οrder frοm least tο greatest are:

Lesser x = -4

Greater x = 1

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Answer:

If the value of Mike's car decreased by 30%, we can calculate the new value of the car as follows:

New value = Original value - (Percentage decrease × Original value)

Percentage decrease = 30%

Original value = 12000

New value = 12000 - (0.30 × 12000)

New value = 12000 - 3600

New value = 8400

Therefore, at the end of the decrease, the value of Mike's car was 8400.

Answer:

Step-by-step explanation:

Kind of like rema from the song calm down calm down!!

you an find it on youtub

Answer:

Step-by-step explanation:

An important math tool is graphing. It can be a straightforward method for introducing more general concepts like most and least, greater than, or less than. It can also be a great way to get your child interested in math and get them excited about it. Using graphs and charts, you can break down a lot of information into easy-to-understand formats that quickly and clearly convey key points.

Given equation 2x + y = 6 we can drive from this equation that at x = 0 y will be 6 and y =0 x will be 3 hence we have two points of the line (0,6) and (3,0)

From the Given equation (2) 6X + 3Y = 12 we can drive from this equation that at x = 0 y will be 4 and y =0 x will be 2 hence we have two points of the line (0,4) and (2,0).

Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).

lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).

Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.

Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.

In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point

To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]

Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)

Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)

To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.

(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.

Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).

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In the following question, among the conditions given, There must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.

The arm wrestler had at least 75 matches and no more than 125 total matches. This means that the arm wrestler had a maximum of 50 matches in any consecutive period of 75 hours. Therefore, there must be a period of consecutive hours during which the arm wrestler had exactly 24 matches.

To show this, let us consider the following: in the 75-hour period, there must have been at least 3 periods of consecutive 24-hour periods (24 matches per period). If we subtract 3 x 24 matches from the total of 75 matches, we are left with 3 matches. Therefore, there must have been at least one 24-hour period in the 75-hour period in which the arm wrestler had exactly 24 matches.

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Step-by-step explanation:

Since it is equilateral the angle at the top is 60 °

for right triangles   sin (angle ) =  opposite leg / hypotenuse

                                 sin (60) = sqrt 6/ x

                                        x = sqrt 6 / sin (60) = sqrt 6 / sqrt(3)/2 =

                                                2 sqrt 2    = 2.83

Answer: 3/5

hope this helped you. Please brainliest! :D

Step-by-step explanation: If I am wrong tell me :D

Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.

In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.

The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:

[tex]nCk = n! / (k! *(n-k)!)[/tex]

where n! denotes the factorial of n, i.e., the product of all positive integers up to n.

by the question.

Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:

[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]

Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]

Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).

Since a_i >= 4 for i=1, we have:

[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]

Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:

[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]

This gives us:

[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]

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The value of μV is 40 cm³.

Given,The area of bottom of cylindrical container = 10 cm²The height of container = h = Mean height = 4 cm Standard deviation of height = σ = 0.2 cm We are supposed to find the mean volume of fluid in the container.In order to calculate the mean volume, first we need to calculate the volume of fluid in the container.Volume of a cylindrical container = πr²h Where, r is the radius of the base of the container.So, we need to calculate the value of r.The area of the bottom of the container is given as 10 cm².

We know that the area of the base of a cylinder is given as:Area of base of cylinder = πr² We are given that area of the base is 10 cm². So,10 = πr²r² = 10/πr = √(10/π) We can find the volume of fluid using the values we have.Volume of fluid = πr²h = π(√(10/π))² x 4 = 40 cm³We know that mean volume, μV is given as:μV = πr²μh So, we need to calculate the value of μh. We know that standard deviation σh is given as:σh = 0.2 cm So,μh = h = 4 cm So,μV = πr²μh = π(√(10/π))² x 4 = 40 cm³

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Answer:

12 large boxes, 9 small boxes

Step-by-step explanation:

Let s = number of small boxes

l = number of large boxes

We set up and solve this system of equations:

s + l = 21------->3s + 3l = 63

3s + 5l = 87------>3s + 5l = 87

----------------

2l = 24

l = 12, s = 9

From the given information provided, the solution to the given trigonometric inequality is (π/4, 5π/4).

To solve the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians, we can use the following steps:

Rewrite the inequality in terms of tangent:

Divide both sides by cos(x) to get:

tan(x) > 1

Find the solutions of the equation tan(x) = 1:

tan(x) = 1 when x = π/4 or x = 5π/4.

Check the sign of tangent in the intervals between the solutions:

We need to check the sign of tan(x) for x values in the following intervals:

(0, π/4), (π/4, 5π/4), and (5π/4, 2π).

In the interval (0, π/4), tan(x) is positive and less than 1.

In the interval (π/4, 5π/4), tan(x) is positive and greater than 1.

In the interval (5π/4, 2π), tan(x) is negative and less than -1.

Determine the solution set:

Since we are looking for x values that satisfy tan(x) > 1, the only interval that contains such values is (π/4, 5π/4). Therefore, the solution to the inequality sin(x) > cos(x) over the interval 0 ≤ x ≤ 2π radians is:

π/4 < x < 5π/4

In interval notation, we can write:

(π/4, 5π/4)

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The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.

The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.

The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.

ADEF and AABC are not in the same location, even if they are the same height and shape.

The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.

A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.

Therefore, A reflection across the y-axis and a translation 2 units down.

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The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).

In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.

Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.

A (-3, 0)

B (-1, 2)

C (2, 2)

D (3, -1)

E (1, -2)

The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:

A' = (-3 * 5, 0 * 5) = (-15, 0)

B' = (-1 * 5, 2 * 5) = (-5, 10)

C' = (2 * 5, 2 * 5) = (10, 10)

D' = (3 * 5, -1 * 5) = (15, -5)

E' = (1 * 5, -2 * 5) = (5, -10)

The coordinates of the dilated figure are:

A' (-15, 0)

B' (-5, 10)

C' (10, 10)

D' (15, -5)

E' (5, -10)

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