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The coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate of the original triangle's vertices).

To find the coordinates of the vertices of the dilated triangle A''B''C'' after two successive dilations, first with a scale factor of 4 and then with a scale factor of 3/4.

Firstly, Apply the first dilation with a scale factor of 4 to the original triangle ABC, with a center of dilation at the origin. This can be done by multiplying each coordinate of the original triangle by 4.

The coordinates of the dilated triangle A'B'C' after the first dilation would be;

A' = (4 × x-coordinate of A, 4 × y-coordinate of A)

B' = (4 × x-coordinate of B, 4 × y-coordinate of B)

C' = (4 × x-coordinate of C, 4 × y-coordinate of C)

Now, we apply the second dilation with a scale factor of 3/4 to the dilated triangle A'B'C', again with a center of dilation at the origin. This can be done by multiplying each coordinate of A'B'C' by 3/4.

The coordinates of the dilated triangle A''B''C'' after the second dilation would be;

A'' = ((3/4) × x-coordinate of A', (3/4) × y-coordinate of A')

B'' = ((3/4) × x-coordinate of B', (3/4) × y-coordinate of B')

C'' = ((3/4) × x-coordinate of C', (3/4) × y-coordinate of C')

Plugging in the values of A', B', C' obtained from the first dilation, we get;

A'' = ((3/4) × 4 × x-coordinate of A, (3/4) × 4 × y-coordinate of A)

B'' = ((3/4) × 4 × x-coordinate of B, (3/4) × 4 × y-coordinate of B)

C'' = ((3/4) × 4 × x-coordinate of C, (3/4) × 4 × y-coordinate of C)

Simplifying further, we get;

A'' = (3 × x-coordinate of A, 3 × y-coordinate of A)

B'' = (3 × x-coordinate of B, 3 × y-coordinate of B)

C'' = (3 × x-coordinate of C, 3 × y-coordinate of C)

Therefore, the  coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate.

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The answers are A = 46% and B = 20%.

Given that, a table of data, each cell in the table shows the number of cars in that category.

A) The probability that the car's total repair cost is less than $10000 =

86 / (86+35+67) x 100 = 86/188 x 100 = 46%

B) The probability that the car's purchase was more than $40,000 =

40 / (40+86+71) x 100 = 40/197 x 100 = 20%

Hence, the answers are A = 46% and B = 20%.

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Answer:

  y = -x +3

Step-by-step explanation:

You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

For the given equations, we can put them in this form to find the desired parameters.

  -3y = -9 +3x

  y = -x +3 . . . . . . . . . . divide both sides by -3

We observe that the y-intercept is +3, which we will need for our answer.

The slope-intercept form of the second equation is ...

  -2x -2y = -8

  x + y = 4 . . . . . . . . . . divide by -2

  y = -x +4 . . . . . . . . . . subtract x

We observe that the slope (coefficient of x) is -1, which we will need for our answer.

We want the equation of the line with slope -1 and y-intercept 3. It is ...

  y = -x +3 . . . . . . . . . . same as the equation of the first line

__

Additional comment

The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)

The value of the absolute difference can be expressed as | x - 2 | ≤ 0.01.

The tolerance for the ball bearing is given as 0.01 inches.

Let x = measured value of the diameter in inches

The absolute difference between x and the true diameter of 2 inches of the ball bearing must be less than or equal to the tolerance of 0.01 inches.

The value of the absolute difference can be expressed using absolute value notation as follows;

| x - 2 | ≤ 0.01

Thus, the inequality above, express the absolute value of the difference between x and 2, which is less than and equal to 0.01.

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The range of the function y=e⁴ˣ is y>0

The range of the function y=e⁴ˣ is the same as the range of any exponential function:

y > 0

The function can take on any positive value, but will never be 0 or negative.

It has a horizontal asymptote of y=0.

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Therefore, the answer is (B) 5 hours. We can start by finding out how long it takes Kylie to fill one 2-ounce container. we can get by forming equation .

what is equation ?

In mathematics, an equation is a statement that two expressions are equal. An equation can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots.

In the given question,

We can start by finding out how long it takes Kylie to fill one 2-ounce container. To do this, we can set up a proportion:

75 containers / 50 minutes = 1 container / x minutes

Solving for x, we get:

x = (50 minutes) / (75/1) = 0.67 minutes per container

Now we can use this information to find how long it will take Kylie to fill 450 containers:

450 containers × 0.67 minutes per container = 301.5 minutes

So it will take Kylie 301.5 minutes to make the slime and fill up 450 containers. We can convert this to hours by dividing by 60:

301.5 minutes / 60 minutes per hour = 5.025 hours

Rounding to the nearest hour, we get 5 hours.

Therefore, the answer is (B) 5 hours.

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Answer:

a) $299.60

b) $337.05

c) Nicole would pay more at the store

Step-by-step explanation:

a) 10% of $749 = $74.90

60% = ($74.90 x 6) = $449.40

$749 - $449.40 = $299.60

b) 10% = $74.90

50% = $374.50

$749 - $374.50 = $374.50

10% of $374.50 = $37.45

$374.50 - $37.45 = $337.05

The correct answer is to increase from left to right. The correct option is B.

To complete the table for the function [tex]y = 3^x - 3[/tex],

x y

-3 1/27

-2 1/3

-1 0

0 2

1 6

2 18

3 54

To graph the function, we can plot the points from the completed table on a coordinate plane and connect them with a smooth curve.

The graph of the function [tex]y = 3^x - 3[/tex]  looks like an exponential function that increases from left to right, passing through the point (0, 2) on the y-axis. The graph is concave up and approaches the x-axis but never touches it.

Therefore, the correct answer is to increase from left to right. The correct option is B.

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1) consumers are willing to buy more of a good at a lower price than at a higher price  Option B

2) All of these

3) All of these

An economic theory known as the law of demand states that, all other things being equal, if a good or service's price rises, consumers will demand fewer units of it, and vice versa.

Price and quantity demanded are inversely related, to put it another way. This is a fundamental concept in economics and plays a key role in shaping market behavior and pricing strategies.

The price system is a way of adjusting the balance between the forces of supply and demand. A key advantage of the corporate form of business organization is the ability to raise significant amounts of financial capital.

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Answer:

965.22%

Step-by-step explanation:

To write 9.6522 as a percentage, we can multiply it by 100 and add the percent symbol (%):

9.6522 * 100% = 965.22%

Therefore, 9.6522 is equal to 965.22% as a percentage.

Hope this helps!

Answer:

Step-by-step explanation:

41.67 is the answer brainlist and verifed  answer

The probability that she will hire a woman for the two positions is given as follows:

1/4.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the last node, the total number of outcomes is given as follows:

4.

The desired outcomes are Women on the first node and women on the second node, which is one outcome. (the last outcome).

Hence the probability is given as follows:

p = 1/4.

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It will take 2.48 hours for the number of bacteria to reach 3500.

In order to find number of hours to take for the number of bacteria to reach 3500, we can set the function equal to 3500 and solve for h.

The function given is P(h) = 2800e^(0.09h). So, plugging the values of 3500, we will get:

3500 = 2800e^(0.09h)

Dividing both sides by 2800, we get:

e^(0.09h) = 3500/2800

Taking the natural logarithm of both sides, we get:

0.09h = ln(3500/2800)

h = (ln(3500/2800))/0.09

h = 0.22314355131/0.09

h = 2.47937279233

h = 2.48 hours

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Here is a possible dataset with variables for which the central limit theorem could be applied:

A dataset of customer spending at different retail stores.

Variable for which CLT for mean could be applied:

Average monthly spending per customer. As the number of customers at each store increases, the sample mean spending will approach a normal distribution.

Variable for which CLT for proportions could be applied:

Proportion of customers who spend over $200 per month. Even with a small number of customers at each store, the proportion will be approximately normally distributed as the sample size increases due to the CLT for proportions.

The central limit theorem states that the sampling distribution of the sample mean and sample proportion will be normally distributed for large sample sizes, regardless of the original distribution. So these variables from the retail dataset would satisfy that condition. Please let me know if you would like any clarification or have a different dataset in mind. I can provide additional examples.

Step-by-step explanation:

2,36,53,58

Two place value system:

Twenty-three lakh, sixty-five thousand, three hundred and fifty-eight

Three place value system:

Two crore, thirty-six lakh, fifty-three thousand, three hundred and fifty-eight

3,42,82,627

Two place value system:

Thirty-four million, twenty-eight thousand, six hundred and twenty-seven

Three place value system:

Three crore, forty-two lakh, eighty-two thousand, six hundred and twenty-seven

8,70,13,569

Two place value system:

Eighty-seven million, thirteen thousand, five hundred and sixty-nine

Three place value system:

Eight crore, seventy-one lakh, thirty-five thousand, five hundred and sixty-nine

9,01,50,028

Two place value system:

Ninety million, one lakh, fifty thousand, twenty-eight

Three place value system:

Nine crore, one lakh, fifty thousand, twenty-eight

8,15,52,101

Two place value system:

Eighty-one million, five hundred and fifty-two thousand, one hundred and one

Three place value system:

Eight crore, fifteen lakh, fifty-two thousand, one hundred and one

9,91,60,001

Two place value system:

Ninety-nine million, one lakh, sixty thousand, one

Three place value system:

Nine crore, ninety-one lakh, sixty thousand, one

The probability that the student, who ran out of time on a multiple choice exam and randomly guessed the answers for two problems, answered both of the problems correctly is ⁹/₂₅.

Probability refers to the likelihood of an expected outcome occurring out of many possible outcomes.

Probability is computed as the quotient of expected outcome over total outcomes.

The number of questions left = 2

The number options of for each question = 5

Since there are 5 options for each question, 4 of which are wrong, the probability of getting both wrongs is:

⁴/₅ x ⁴/₅ = ¹⁶/₂₅ = 0.64 or 64%

Therefore, probability of getting both questions correct is 36% (1 - 64%) or ⁹/₂₅ (1 -  ¹⁶/₂₅).

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x = 12 times square root 2 (45 45 90 triangle)

y = 6 times square root 2 (30 60 90 triangle)

Answer:

A) (1, 0)

Step-by-step explanation:

The point (0, 0) lies on the x-axis and y-axis, so any point that lies on either axis will be collinear to it. Therefore, the answer is A) (1, 0).

Hope this helps!

When abraham was born his parents put 2000 into an account that yielded 1.2%, Abram will receive $2,213.10 on his 16th birthday.

To calculate how much Abram will receive on his 16th birthday, we need to use the compound interest formula:

A = [tex]P(1 + r/n)^{(nt)[/tex]

Where:

A = the amount Abram will receive

P = the principal amount (initial investment) = $2,000

r = the annual interest rate = 1.2% = 0.012

n = the number of times the interest is compounded per year = 2 (semi-annually)

t = the number of years = 16/2 = 8 (since interest is compounded twice a year)

Plugging in the values, we get:

A = $2,000(1 + 0.012/2)¹⁶

A = $2,000(1.006)¹⁶

A = $2,000(1.10655)

A = $2,213.10

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Complete question is:

When Abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi-annually. When he turns age 16, his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?

The volume is D) 84[tex]m^3[/tex].

What is volume?

The space taken up by any three-dimensional solid constitutes a  volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.

Here the given rectangular prism length = 7m , Width = 4m and Height = 3m.

Now using Volume of rectangular prism formula then,

V = lwh cubic unit.

=> V = 7×4×3

=> V = 84[tex]m^3[/tex]

Hence the volume is D) 84[tex]m^3[/tex].

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Sure, I'd be happy to help you calculate these percentages! Here are the solutions:

- 100% of 30 = 30

- 40% of 60 = 0.4 x 60 = 24

- 20% of 80 = 0.2 x 80 = 16

- 40% of 50 = 0.4 x 50 = 20

- 80% of 20 = 0.8 x 20 = 16

- 50% of 30 = 0.5 x 30 = 15

- 60% of 80 = 0.6 x 80 = 48

- 60% of 10 = 0.6 x 10 = 6

- 90% of 70 = 0.9 x 70 = 63

I hope that helps! Let me know if you have any other questions.

The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.

Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40

Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30

This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.

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Answer: long term

Step-by-step explanation: I got it right on the test

[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step

if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in  the set

if  [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set

if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.

Think about how to solve this problem in general. How can you assure that the sum [tex]a+b[/tex] is odd?

Think about this, what happens when you sum two even numbers? The result is even or odd?

[tex]2+6 = 8 \ \text{(even)}[/tex]

[tex]10+12 = 22 \ \text{(even)}[/tex]

And what happens when you sum two odd numbers ? The result will be even or odd?  Look

[tex]3+7 = 10 \ \text{(even)}[/tex]

[tex]5+11 = 16 \ \text{(even)}[/tex]

Therefore to assure that [tex]a+b[/tex] is odd, one of them has to be odd and one of them has to be even, that is why

[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step

if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in  the set

if  [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set

if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.

Answer:

8[tex]\frac{29}{40}[/tex]

Step-by-step explanation:

The least common multiply is 40

[tex]\frac{4}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{40}[/tex]

2 [tex]\frac{3}{10}[/tex] x [tex]\frac{4}{4}[/tex] = 2 [tex]\frac{12}{40}[/tex]

5 [tex]\frac{5}{8}[/tex] x [tex]\frac{5}{5}[/tex] = 5 [tex]\frac{25}{40}[/tex]

Now that we have a common denominator, add these numbers together

[tex]\frac{32}{40}[/tex] + 2 [tex]\frac{12}{40}[/tex] + 5 [tex]\frac{25}{40}[/tex]

7 [tex]\frac{69}{40}[/tex]

7 + [tex]\frac{40}{40}[/tex] + [tex]\frac{29}{40}[/tex]  I broke up [tex]\frac{69}{40}[/tex] because I know that [tex]\frac{40}{40}[/tex] equals 1

8 [tex]\frac{29}{40}[/tex]

Helping in the name of Jesus.

Factor of the equation are,

⇒ p (p + 2) - q (q + 6) - 8

We have to given that;

The expression is,

⇒ p² + 2p - 8 - q² - 6q

Now, We can factor as;

⇒ p² + 2p - 8 - q² - 6q

⇒ p (p + 2) - 8 - q (q + 6)

⇒ p (p + 2) - q (q + 6) - 8

Thus, Factor of the equation are,

⇒ p (p + 2) - q (q + 6) - 8

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Answer:

is a measure of the average absolute distance between each data value and the mean of a data set.

Using the laws of multiplication, we can find that after the 4th day the unicorn population of the park is 405.

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.

In the question,

Let the unicorn population be = x.

Now as per the question,

It triples every day.

The function will be = 3x.

The starting unicorn population is 5.

After the 1st day it will get tripled and become 3 × 5 = 15.

After the 2nd day the unicorn population will be 3 × 15 = 45.

After the 3rd day, 3 × 45 = 135.

Finally, after the 4th day, the unicorn population will be = 3 × 135 = 405.

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If one flyer is  3.0 × 10⁻³ inches thick, the stack of 1.25 × 10³ flyers has a thickness of 3.75 inches.

To find the thickness of a stack of flyers, we need to multiply the thickness of a single flyer by the number of flyers in the stack. In this case, the thickness of a single flyer is given as 3.0 × 10⁻³ inches, and the number of flyers in the stack is 1.25 × 10³.

So, the thickness of the stack can be calculated as:

Thickness of stack = Thickness of a single flyer x Number of flyers in the stack

Thickness of stack = 3.0 × 10⁻³ inches x 1.25 × 10³

Thickness of stack = (3.0 x 1.25) × (10⁻³ × 10³) inches

Thickness of stack = 3.75 inches

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The value of N in the algebraic equation is 600.

An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.

If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. We have:

(15/100 * 20/100 * 5N)  + (30/100 * 50/100 * 2N) = 270

0.15N + 0.3N = 270

0.45N = 270

N = 270/0.45

N = 600

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Question in English

If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. Calculate N.