Select the correct answer.
Triangle E'F'G' is the image of triangle EFG after a dilation with center at (2-3).
What is the scale factor of this dilation?
A: 2
B: 3
C: 1/2
D: 1/3

Answer:

Dado, △ABC∼△DEF

Por lo tanto

DE

=

EF

A.C

=

FD

CA

Así que

18

2x−1

=

3x+9

2x+2

=

6x

3x

Ahora tomando

18

2x−1

=

6x

3x

tenemos

18

2x−1

=

2

1

o 4x−2=18 o x=5

Por lo tanto, AB=2×5−1=9,

BC=2×5+2=12,CA=3×5=15,

DE=18,EF=3×5+9=24

y FD=6×5=30

Por lo tanto

AB = 9 cm, BC = 12 cm, CA = 15 cm, DE = 18 cm, EF = 24 cm y FD = 30 cm

:

Answer:

503.1222

rounded: 503.12

Answer:

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Step-by-step explanation:

From the question we are told that

   The population mean is  \(\mu = 24.2 \ gallons \ per \ year\)

    The sample size is  n  =  101

     The sample mean is  \(\= x = 23.5 \ gallons\ per\ year\)

     The standard deviation is  \(\sigma = 3.2 \ gallons\)

The null hypothesis is  \(H_o : \mu = 24.2\)

 The alternative hypothesis is \(H_a : \mu \ne 24.2\)

Generally the test statistics is mathematically represented as    

               \(z = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }\)

=>             \(z = \frac{ 23.5 - 24.2 }{ \frac{ 3.2}{ \sqrt{ 101} } }\)  

=>             \(z = -2.198\)

From the z table  the area under the normal curve to the left corresponding to    -2.198  is  

         \(P(Z < -2.198 ) = 0.013975\)

Gnerally the  p-value is mathematically represented as

         \(p-value = 0.013975 * 2\)

=>      \(p-value = 0.02795\)

From the value obtained we have that  \(p-value \ < \ \alpha\) hence  

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Using the Rejection Regions for a z-test method

Generally from the z table  the critical value  of \(\frac{\alpha }{2}\)  is  

     \(z_{critical} = \pm 1.96\)

Not we are using  \(\frac{\alpha }{2}\)  because it is a two - tailed test

   Now comparing the critical value and the test statistics we see that the

region covered by  the test statistics (i.e \(2.198 < z < -2.198\))   is greater than the region covered by  the critical value  (i.e \(1.96 < z < -1.96\))

Hence

The decision rule is  

Reject the null hypothesis  

The conclusion is  

There is sufficient evidence to reject the claim  

Answer:

c= 1.5t, c=t+0.5t and c=(1+0.5)t

Step-by-step explanation:

Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t

To determine the solution of a system of equations graphed you identify the point of intersection of the graphs as that is the values that the functions share. The functions in the system have the same values in the point of intersection.

With 4.5% compounded semi-annually, Sarah will need to make installments for roughly 20.82 years in order to save $10,000. Hence, 20.82 is the answer.

Is every two years or semiannually?

Simply said, semiannual refers to events that occur twice a year. A couple might commemorate their nuptials each two years, a corporation might hold workplace celebrations each two years, as well as a family might go on vacation each two years. Every two years, something that happens twice a year does.

We can utilize the calculation again for future value of an annuity to resolve this issue:

FV = P × ((1 + r/n) - 1) / (r/n)

Where:

FV = Future value

P = Periodic payment

r = Annual interest rate

n = Compounding cycles per year, number

t = Number of years

In this instance, Sarah plans to deposit $300 each six months in order to save $10,000. She will so be required to make two payments each year. P thus equals $300, n equals 2, r equals 0.045 (decimalized 4.5%), and FV equals $10,000. The number of years, t, needs to be solved for.

$10,000 = $300 × ((1 + 0.045/2) - 1) / (0.045/2)

When we simplify this equation, we obtain:

20 = (1 + 0.0225) - 1

21 = (1 + 0.0225)

Using both sides' natural logarithms:

ln(21) = ln((1 + 0.0225))

ln(21) = 2×t × ln(1 + 0.0225)

t = ln(21) / (2 × ln(1 + 0.0225))

t = 20.82

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Answer:

The answer is below

Step-by-step explanation:

Given that k(x) = -125x² +670x - 125, where x is the charge per cone and P = k(x) is the weekly profit

a) The maximum profit is at P'(x) = 0. Therefore we have to find the derivative of the profit equation and equate it to 0.

P'(x) = k'(x) = 0

k'(x) = -250x + 670 = 0

-250x + 670 = 0

250x = 670

x = $2.68

P = k(2.68) = -125(2.68²) + 670(2.68) - 125 = $772.8

Hence the maximum profit is $772.8 when the price of each ice cream cone is $2.68

b) At break even, the profit is 0. Hence P= k(x) = 0

-125x² + 670x - 125 = 0

x = 5.17 or x = 0.19

Therefore to break even, the price of the ice cream cone needs to be $0.19 or $5.17

c) g(x) = k(x - 2)

g(x) = -125(x - 2)² + 670 (x -2) - 125

Maximum profit is at g'(x) = 0

g'(x) = -250(x-2) + 670

-250(x-2) + 670 = 0

-250x + 500 + 670 = 0

250x = 1170

x = 4.68

g(4.68) = -125(4.68 - 2)² + 670(4.68 -2) - 125 = $772.8

Therefore function g has the same maximum value as function k

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

Step-by-step explanation:

looks to be a parabola, so use vertex mode (h, k) =  (-1, 2)

y = a(x - h)² + k

y = a(x + 1)² + 2

another point on the curve seems to be (1, 6)

6 = a(1 + 1)² + 2

     1 = a

y = (x + 1)² + 2

or expand for standard form y = ax² + bx + c

y = (x² + 2x + 1) + 2

y = x² + 2x + 3

Answer: (8 x 1) + (5/10) + (1/100) + (7/1000)

Step-by-step explanation: Have a blessed day hopefully this helped!

Answer:

8 tens, 5 tenths, 1 hundredth, 7 thousandths

Step-by-step explanation:

Hope I helped give brainliest if right :D

Answer:

a ) 0.9

Expected number of bower-birds that have bowers featuring reflective decor

         μ = 0.9

Step-by-step explanation:

Explanation:-

Given Sample size 'n' = 20

Given data A population consists of twenty bower-birds, six of which have bowers featuring reflective decor.

probability of success

                          \(p = \frac{x}{n} = \frac{6}{20} =0.3\)

Given  three of the bower-birds are randomly sampled with replacement from this population.

So we will choose sample size 'n'= 3

Let 'X' be the random variable in binomial distribution

Expected number of bower-birds that have bowers featuring reflective decor

                       μ = n p

                           = 3 × 0.3

                           =0.9

conclusion:-

Expected number of bower-birds that have bowers featuring reflective decor

         μ = 0.9

Answer:

Step-by-step explanation:

I hope it's helpful bro ✌️

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:c, the answer is c

Step-by-step explanation:

Answer:

The equation should be 2.5x+1.8=59.3

Step-by-step explanation:

First, subtract the 1.8 dollars from the 59.3. You will get 57.5. Divide it by 2.5 and you will get the number 21 as x.

Answer:a A. 4x-7/2x(x-2)

got it right on the test

Step-by-step explanation:

Answer:

8000

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

(a) Solving the x-equation for u gives ...

  u = (x -1)/4

Differentiating both equations with respect to u, we have ...

  dy/du = 1 -4u

  dx/du = 4

Then dy/dx is ...

  dy/dx = (dy/du)/(dx/du) = (1 -4u)/4

Substituting for u gives ...

  dy/dx = (1 -4(x -1)/4)/4

  dy/dx = (2 -x)/4

__

(b) The approximate change in y is ...

  ∆y ≈ (dy/dx)(∆x)

For ∆x = 2.98 -3.00 = -0.02, and x=3, the approximate change is ...

  ∆y ≈ (2 -3)/4(-0.02)

  ∆y ≈ 0.005

The answers for the given multiplication chart are given below:

One of the four basic mathematical operations of arithmetic, together with addition, subtraction, and division, multiplication is frequently represented by the cross symbol.

When two numbers are multiplied, they are added in the same amount of copies of the multiplicand and multiplier, which is how repeated addition can be thought of when multiplying whole numbers. Another way to think about multiplication is to count the objects that are arranged in a rectangle (for whole numbers) or to calculate the area of a rectangle whose sides have a certain length.

X      2     -4     -9    6    3     8     -1    4      -8    -2   -6     7     -5     9      -7

-3    -6      12   27   -18   -9   -24   3  -12    24    6   18    -21    15    -27    21  

9      18   -36   -81   54   27  72   -9   36   -72  -18 -54  63  -45     81      -63

-6    -12    24    54   -36  -18  -48  6   -24  48  12  36  -42  30     -54       42

5      10    -20   -45   30   15   40  -5   20  -40 -10 -30  35  -25    45      -35

-7    -14     28    63   -42  -21  -56   7  -28  -56 -14   42 -49  35    -63      49

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Answer:

78.54

Step-by-step explanation:

The formula is \(A = \pi r^2\\\). So, substitute the values into the equasion and get the answer.

According to the order of operations, we square the radius first, then multiply by pi. 5^2 = 25. 25 * pi = 78.5398163397. I just rounded it to the nearest hundereth.

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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The profit function for a furniture company introducing a new line of lounge chairs is P(x) =\(-8.32x^2 + 1,248x - 36,400\), where x represents the number of chairs to be manufactured and sold.

The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.

The revenue function R(x) is given as 1,248x - \(8.32x^2\), where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).

The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.

To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x) = (1,248x - \(8.32x^2\)) - (36,400 - 83.2x)

Simplifying this expression, we get:

P(x) =\(-8.32x^2\) + 1,248x - 36,400

Therefore, the profit function for the furniture company is P(x) = \(-8.32x^2\) \(+ 1,248x - 36,400\).

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Answer:

60*

Step-by-step explanation:

i think its a equalateral triangle so if so all the angles are 60 degrees

Answer:

dimes- 8

nickels- 4

Step-by-step explanation:

dime=10 cents

nickels=5 cents

5 x 4 = 20

10 x 8 = 80

80 + 20 = 100

... please give brainliest ...

Answer:

C. \(\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}\)

Step-by-step explanation:

Physically speaking, the acceleration is equal to the second derivative of the position of the vehicle in time. After a careful reading to the statement, we construct the following ordinary differential equation:

\(\frac{d^{2}f}{dt^{2}} = k\cdot \sqrt[3] {t}\)

Where:

\(t\) - Time, measured in seconds.

\(k\) - Proportionality constant, measured in meters per second up to 7/3.

Therefore, the correct answer is C.

The differential equation that models the situation is:

\(\frac{d^2f}{dt^2} = k\sqrt[3]{t}\)

Which is option C.

The position is the integral of the acceleration, with is the integral of the acceleration, hence, the relation between the position and the acceleration is:

\(\frac{d^2f}{dt^2}\)

The acceleration is proportional to the cube root of the time since the start, hence:

\(\frac{d^2f}{dt^2} = k\sqrt[3]{t}\)

In which k is the constant of proportionality.

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