For the following problems, are they similar? if so why? (AA~, SAS~, SSS~)

As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC.

How very much larger (as well as smaller) any item becomes following the transformation is indicated by the dilation factor.

Given data:

A'B'C' is the dilation of triangle ABC.

Scale factor = 1/2  = 0.5

As, the scale factor is less than 1 . So, the dilation is the reduction for the image of triangle ABC

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The 100th permutation in the list is 75931, which starts with the digit 7 and is the 4th permutation starting with 7.

To find the 100th permutation, we can use the formula for the total number of permutations of n distinct objects, which is n! (n factorial).

In this case, there are 5 digits, so there are 5! = 120 permutations in total. Since the permutations are listed in numerical order, we can divide the total number of permutations by 5 to find the number of permutations starting with each digit.

120 ÷ 5 = 24

This tells us that there are 24 permutations starting with each digit. To find the 100th permutation, we need to determine which digit it starts with. We can do this by dividing 100 by 24 and taking the quotient and remainder:

100 ÷ 24 = 4 with a remainder of 4

This tells us that the 100th permutation starts with the fourth digit in the sequence: 7. We now need to find the 4th permutation starting with 7. To do this, we can list all the permutations starting with 7 in numerical order:

7 _ _ _ _ (4! = 24 permutations)

7 1 _ _ _

7 3 _ _ _

7 5 _ _ _

7 9 _ _ _

The 4th permutation starting with 7 is 75_9_, which is the 100th permutation in the list.

Therefore, the 100th permutation in the list is 75931.

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To  draw the image of triangle △ABC under a dilation with center C and scale factor 2, we need to draw the original triangle, draw lines from C to each vertex,

To draw the image of triangle △ABC under a dilation with center C and a scale factor of 2, we need to follow a few steps. Firstly, we need to draw the original triangle △ABC. Then, we need to draw a straight line from the center of dilation C to each vertex of the triangle. These lines will act as our guides for where the new vertices will be located.

Next, we need to use the scale factor of 2 to determine the distance between the original vertices and the new vertices. This means that we need to multiply the distance between each vertex and the center of dilation by 2. We can then plot the new vertices along the lines we drew in the previous step.

Finally, we can connect the new vertices to form the image of the triangle under the dilation. This image will be twice as large as the original triangle and will be located in the same direction as the lines we drew from the center of dilation to each vertex.

use the scale factor to determine the new vertex locations, and finally connect the new vertices to form the image.

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The linear regression equation that represents this set of data is y=12x-860

Linear regression is a statistical method used to model the relationship between two variables by fitting a linear equation to the observed data. The goal of linear regression is to find the best-fitting straight line that represents the relationship between the two variables.

the linear regression equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

Putting the initial values,

x=77

y=64

64=77m+c.......Equation1

Taking second values, we get

x=76

y=76

76=76m+c.......Equation2

Subtracting the Equation 1 from 2, we get

12=m

Putting the value of m=12 in equation 1, we get

c=-860

Hence, The linear regression is y=12x-860

Now, Test grade, x=69

Homework grade, y=12x-860

69=12x-860

69+860=12x

x=77.4

Using this equation, estimate the homework grade is 77.4 for r a student with a test grade of 69.

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Answer:

155.5 square feet

Step-by-step explanation:

A = (1/2)(10)(8.6 + 6.3 + 8.6 + 7.6)

= 5(31.1)

= 155.5 square feet

Kayden has 5 dimes and 15 quarters because he has three times as many quarters as dimes, and their total value of coins is 425 cents.

Let's use algebra to solve the problem.

Let x be the number of dimes that Kayden has.

Then the number of quarters he has is 3x (since he has 3 times as many quarters as dimes).

The value of x dimes is 10x cents, and the value of 3x quarters is 75x cents (since a quarter is worth 25 cents).

According to the problem, the total value of the coins is 425 cents. So we can write the equation:

10x + 75x = 425

Simplifying and solving for x, we get:

85x = 425

x = 5

Therefore, Kayden has 5 dimes and 3x = 15 quarters.

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Answer:

Step-by-step explanation:

200 Items were sold

For A total of $130

The Items sold were 0.50

and 0.75.

130 Cans of soda were sold

86 Bags Of popcorn were sold.

Answer:

put 23  

and be my freind pleas i only have 2

The fourth Arithmetic mean is -4.

To find the fourth arithmetic mean between -24 and 16, first calculate the common difference between the terms. The formula for this is:

Common difference (d) = (Final term - Initial term) / (Number of means + 1)

In this case, the initial term (a) is -24, the final term (b) is 16, and the number of arithmetic means (n) is 7.

d = (16 - (-24)) / (7 + 1)

d = (16 + 24) / 8

d = 40 / 8

d = 5

Now, you can find the fourth arithmetic mean (a_4) using the formula:

a_4 = a + 4d

a_4 = -24 + 4(5)

a_4 = -24 + 20

a_4 = -4

So, the fourth arithmetic mean is -4.

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Solving for q will give us the optimal quantity that maximizes the profit,  a function that gives the total profit earned can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

Assuming that the revenue and cost are functions of the quantity sold (q), the total profit can be calculated as follows:

Profit(q) = Revenue(q) - Cost(q)

To find the quantity which maximizes the profit, we can take the derivative of the profit function with respect to q and set it equal to zero, and then solve for q:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the quantity that maximizes the profit. However, without knowing the specific forms of the revenue and cost functions, we cannot write a specific profit function or find the quantity that maximizes the profit.

In general, the profit function can be written as:

Profit(q) = (Revenue per item - Cost per item) * q

where the revenue per item and cost per item are functions of q. To find the quantity that maximizes the profit, we need to differentiate the profit function with respect to q and set it equal to zero:

Profit'(q) = Revenue'(q) - Cost'(q) = 0

Solving for q will give us the optimal quantity that maximizes the profit.

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Answer: 3 minutes and 30 seconds, or 3.5 minutes

The equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74[/tex]

The standard equation of a circle is given by: (x-h)2 + (y-k)2 = r2 Where (h,k) is the coordinates of center of the circle and r is the radius.

To determine the equation of the circle, we need to find the radius first. Since the center of the circle is (5,5), we can use the distance formula to find the distance between the center and the given point (0,-2):

[tex]distance = \sqrt{[(x2 - x1)^2 + (y2 - y1)^2]}\\distance = \sqrt{[(0 - 5)^2 + (-2 - 5)^2]}\\distance = \sqrt{[(-5)^2 + (-7)^2]}\\distance = \sqrt{[25 + 49]}\\distance = \sqrt{[74]}[/tex]

Therefore, the radius of the circle is sqrt[74].

Now, we can use the standard form of the equation of a circle to find the equation of the circle:

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

where (h,k) is the center of the circle, and r is the radius.

Plugging in the values we have:

[tex](x - 5)^2 + (y - 5)^2 = (\sqrt{[74]})^2[/tex]

Simplifying the equation:

[tex](x - 5)^2 + (y - 5)^2 = 74[/tex]

Therefore, the equation of the circle with center (5,5) containing the point (0,-2) is [tex](x - 5)^2 + (y - 5)^2 = 74.[/tex]

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The p-value for this hypothesis test is 0.263.

In this case, the null and alternative hypotheses for a hypothesis test of the difference in two population proportions are:

null hypothesis: p1 = p2

alternative hypothesis: p1 > p2

Notice that the alternative hypothesis is a one-tailed test.

Suppose proportions z test method from stats models is used to perform the test and the output is (1.13, 0.263).

To find the p-value for this hypothesis test, we need to use the output from the statsmodels function.

The second number in the output is the p-value.

Therefore, the p-value for this hypothesis test is 0.263.

The first number in the output is the z-value, which is not relevant to finding the p-value. Therefore, we can ignore it. Answer: 0.263

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Answer:

-46

Step-by-step explanation:

-7×-7= 49

3-49= -46

-46 is the answer

Answer: The full price was 275

the equation of the circle with center (0,-3) containing the point (√32,-2) is x² + (y + 3)² = 33.

How to solve an equation?

To determine the equation of a circle, we need to know the coordinates of its center and the radius. The formula for the equation of a circle is (x - a)² + (y - b)² = r², where (a, b) represents the center of the circle and r represents its radius.

In this case, the center of the circle is given as (0,-3), so we can substitute these values into the formula: (x - 0)² + (y - (-3))² = r²

To find the value of r, we need to use the fact that the circle contains the point (√32,-2). We know that any point on the circle will be a distance r away from the center, so we can use the distance formula to find r.

The distance between the center (0,-3) and the point (√32,-2) is:

sqrt[(√32 - 0)² + (-2 - (-3))²] = sqrt[32 + 1] = sqrt(33)

Therefore, the radius r is sqrt(33).

Substituting this value into the equation of the circle, we get:

(x - 0)² + (y - (-3))² = (sqrt(33))²

Simplifying this equation, we get:

x² + (y + 3)² = 33

So the equation of the circle with center (0,-3) containing the point (√32,-2) is x² + (y + 3)² = 33.

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The recursive and explicit formulae of the given arithmetic expression are:

Recursive formular = [tex]a_{n+1} = a_{n-5}[/tex]

Explicit formular is Tn = 68 - 53n

You can determine the value of any term in a series using an explicit formula. A subset of integers are the natural numbers, which are 1, 2, 3, 4, etc. If you know the value of the (n-1)th term in a series and have access to its recursive formula, you can use it to determine the value of the nth term. The primary distinction between recursive and explicit formulas is that the former provides the value of a particular phrase based on the preceding term, while the latter provides the value of a particular term based on the position.

Given:

a1 = 63

a2 = 67 = 63 - 5 = a1 - 5

Recursive formular = [tex]a_{n+1} = a_{n-5}[/tex]

a = 63, d = -5

F(11) = a + (n - 1)d = 63 + (n - 1)-5 = 63 - 5n + 5 = 68 - 53n

Explicit formular is Tn = 68 - 53n

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The difference between the median high temperature and median low temperature is 22.5°F

The data set has an odd number of values, the median is the middle value when the data is arranged in numerical order.

Hence Median of the data is given by

Median = value at position (n + 1) / 2,

where n is the number of data points.

Here we have

The weather forecast is shown.

High 84°F 90°F 82°F  79°F  83°F  92°F  82°F

Low  56°F 63°F 60°F  52°F  60°F  61°F  53°F  

To find the difference between the median high temperature and the median low temperature, Calculate the median temperatures for both high and low temperatures.

To find the median, we need to first arrange the temperatures in ascending order  

For the high temperatures, we have:

79°F, 82°F, 82°F, 83°F, 84°F, 90°F, 92°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of high temparature = 83°F

For the low temperatures, we have:

52°F, 53°F, 56°F, 60°F, 60°F, 61°F, 63°F

Here median = 4th term [ Since the number of terms 7 is an odd number ]

The median of low temparature = 60°F

The difference between the median high temperature and median low temperature is:

83°F - 60.5°F = 22.5°F

Therefore,

The difference between the median high temperature and median low temperature is 22.5°F

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Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

To find the expected number of automobiles lined up at the opening time, we can use the following  formula is used

Expected value = Σ (number of automobiles * probability)

Using the probability distribution provided in the question, we have:

Expected value = (10.20) + (20.20) + (30.40) + (40.20)

Expected value = 0.20 + 0.40 + 1.20 + 0.80

Expected value = 2.6

Therefore, on a typical day, Lakeside Olds can expect around 2.6 automobiles to be lined up at the opening time for service.

Note that since the expected value is not a whole number, it is an estimate and may not represent the actual number of automobiles on any given day.

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Answer:

x=-2

Step-by-step explanation:

Let's call the amount of pure acid in the original 10cc solution A.

A = 0.3(10cc) = 3cc

Let's also call the amount of pure water we need to add to dilute the solution by x cc.

So after we add x cc of water, we have a new solution with a total volume of (10 + x) cc, and the amount of pure acid in the new solution is still 3cc.

To have a 6% acid solution, we know that:

3cc / (10 + x) cc = 0.06

Solving for x:

3cc = 0.06(10 + x)cc

3cc = 0.6 + 0.06x cc

2.4cc = 0.06x cc

x = 40cc

So we need to add 40cc of pure water to dilute the 10cc 30% acid solution to a 6% acid solution.

Answer:

2.083 yards

Step-by-step explanation:

1 inch ≈ 0.0278 yard

75 inches ≈ 2.083 yards

So, 75 inches is about 2.083 yards.

Answer:

75/36 or 2.083

Step-by-step explanation:

We know that there are 36 inches in a yard so just take 75 inches and divide by 36 and you get 2.083

The family will have approximately $13,444.03 in the account at the end of 15 years.

To find the value of the account at the end of 15 years, we'll use the formula for compound interest, which is:
A = P * (1 + r)^n
Where A is the final amount,

P is the principal amount (the initial deposit),

r is the annual interest rate (as a decimal), and n is the number of years.
In this case, P = $500,

r = 7% (0.07),

and n = 15.
Step 1: Convert the interest rate to a decimal:

7% = 0.07
Step 2: Add 1 to the interest rate: 1 + 0.07 = 1.07
Step 3: Raise the result from Step 2 to the power of the number of years:

[tex](1.07)^15[/tex]≈ 2.7591
Step 4: Multiply the principal amount by the result from Step 3:

$500 * 2.7591 ≈ $1377.55.

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The measures of the angles x and y are:

m∠y =  = 148°

m∠x  = 153°

Remember that:

The sum of two adjacent angles is always 180°

The sym of the interior angles of a triangle is always 180°

With the first rule, we know that:

m∠a + m∠y = 180°

And we know that m∠a = 32°, then:

32° +  m∠y = 180°

m∠y = 180° - 32° = 148°

Now, the angle at b is 59°, then the top angle of the triangle is:

180° - 59° = 121°

And the left angle in the triangle is A, such that:

A + 121° + 32° = 180°

A = 180° - 32° - 121° = 27°

And that angle plus the measure of x must be 180°, then:

m∠x + 27° = 180°

m∠x = 180° - 27° = 153°

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Answer:

y = x^2 + 8x + 19

Step-by-step explanation:

y=(x+4)²+3

First expand the parentheses:

y = x^2 + 4x + 4x + 16 + 3

y = x^2 + 8x + 19

The probability that the sampling distribution of sample proportions is less than 91% is very low, approximately 0.0000025.

The sample size is n = 81 and the population proportion is p = 0.95. The mean of the sampling distribution of sample proportions is equal to the population proportion, which is 0.95. The standard deviation of the sampling distribution of sample proportions is given by the formula sqrt(p*(1-p)/n), which is approximately 0.03. Thus, the z-score corresponding to a sample proportion of 0.91 is (0.91 - 0.95)/0.03 = -1.33. The probability that the sampling distribution of sample proportions is less than 91% is the same as the probability that a standard normal variable is less than -1.33, which is approximately 0.0000025 (using a standard normal distribution table or calculator). This indicates that it is very unlikely to obtain a sample proportion less than 91% if the true population proportion is 95%.

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The probability that the student will get exactly four correct answers is approximately 0.1706

To solve this problem, we can use the binomial distribution, which gives the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, each question has three possible answers, only one of which is correct. So the probability of getting a correct answer by guessing is 1/3.

Let X be the number of correct answers out of 8. Then X follows a binomial distribution with n=8 and p=1/3.

To get exactly four correct answers, we need to get four successes and four failures in any order. The number of ways to choose four questions to answer correctly is 8 choose 4 (written as 8C4), which is equal to 70. The probability of getting four successes and four failures is therefore

P(X=4) = (8C4) × (1/3)^4 × (2/3)^4

= 70 × 1/81 × 16/81

= 1120/6561

≈ 0.1706

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Answer:

the only correct statement is B: the upper quartile value is 96.

Step-by-step explanation:

First, let's put the temperatures in order: 76, 80, 82, 89, 89, 91, 96, 98, 98, 100.

A. To find the median, we need to find the middle value in the ordered set of data. Since there are an even number of values, we take the average of the two middle values. The two middle values are 89 and 91, so the median is (89+91)/2 = 90. Therefore, statement A is false.

B. To find the upper quartile, we need to find the value that separates the highest 25% of the data from the rest. Since there are 10 values, the upper quartile is the 7th value when the data is ordered. The 7th value is 96, so statement B is true.

C. To find the lower quartile, we need to find the value that separates the lowest 25% of the data from the rest. Since there are 10 values, the lower quartile is the 3rd value when the data is ordered. The 3rd value is 82, so statement C is false.

D. The interquartile range is the difference between the upper quartile and the lower quartile. From our previous calculations, we know that the upper quartile is 96 and the lower quartile is 82. Therefore, the interquartile range is 96-82 = 14. Statement D is false.

Therefore, the only correct statement is B: the upper quartile value is 96.

The prove that a WXYZ is a parallelogram and WXYZ is a rectangle is given based on the image attached.

To be able to prove that the parallelogram WXYZ is a rectangle, one need to show that it has all the properties of a rectangle. An example of the properties of a rectangle is that it is one that has four right angles.

Hence

From the question, WXYZ is a parallelogram, and ZX = WY.

So to Prove: WXYZ is a rectangle

Therefore, based on the properties listed above, one can prove that the parallelogram is a rectangle.

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In the frequency table, we can see that the most common reason for taking a gap year is travel, with a frequency of 5.

To draw up a frequency table for the given question, we can use the following : List down the reasons:

List down the five different reasons for taking a gap year.

Count the frequency of each reason:

Tally the number of times each reason appears in the data.

Let's say we have the following data:

Reasons for taking a gap year:

Travel Work Experience Family Medical Total Tally

the number of times each reason appears in the data:

Reasons for taking a gap year Tally Frequency Travel Work Experience Family Medical Total

Draw the frequency table:

Draw the frequency table by filling in the tally and frequency columns.

The final frequency table should look like this:

Frequency Table Reasons for taking a gap year Tally Frequency Travel [tex]||||5Work|||3Experience||||4Family||2Medical|1|2| Total5 3 4 2 2 16[/tex]

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