Given that ΔA′B′C′ is a dilation of ΔABC, how are the angles and side lengths of the preimage and image related?
A. The angles are congruent and the side lengths are congruent.
B. The angles are congruent and the side lengths are proportional.
C. The angles are proportional and the side lengths are congruent.
D. The angles are proportional, and the side lengths are proportional.

Answer:

40

Step-by-step explanation:

All questions are worth the same, 1 point each.

80% of 50 = 0.8 × 50 = 40

Answer: 40

Answer:

40

Step-by-step explanation:

80/100*50 = 40

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Step-by-step explanation:

To calculate the monthly payment for a mortgage, you can use the formula for a fixed-rate mortgage:

Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Loan amount (in this case, the home cost minus the down payment)

r = Monthly interest rate (annual rate divided by 12 and converted to decimal)

n = Total number of payments (number of years multiplied by 12)

Given:

Home cost = $600,000

Down payment = 40% of the home cost = 0.4 * $600,000 = $240,000

Loan amount = Home cost - Down payment = $600,000 - $240,000 = $360,000

Annual interest rate = 3.00%

Loan term = 30 years

First, calculate the monthly interest rate:

Monthly interest rate = (Annual interest rate / 100) / 12 = (3.00 / 100) / 12 = 0.0025

Next, calculate the total number of payments:

Total number of payments = Loan term * 12 = 30 * 12 = 360

Now, substitute the values into the formula:

Monthly Payment = ($360,000 * 0.0025 * (1 + 0.0025)^360) / ((1 + 0.0025)^360 - 1)

After performing the calculations, the monthly payment for this mortgage is approximately $1,520.06.

I hope I was helpful

For the function  [tex]A(t)=4000e^0^.^0^4^t[/tex] the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

The given function is [tex]A(t)=4000e^0^.^0^4^t[/tex] gives the balance after t years.

The initial investment is 8000

4% is the compounded interest.

Now differentiate with respect to t

[tex]A'(t)=0.04(4000)e^0^.^0^4^t[/tex]

[tex]A'(t)=160e^0^.^0^4^t[/tex]

Now let us find the value of A'(8)

Plug in t as 8

[tex]A'(8)=160e^0^.^0^4^(^8^)[/tex]

A'(8)=220.3

Hence, the value of A'(8) is $220 and the value of [tex]A'(t)=160e^0^.^0^4^t[/tex]

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Answer:

90 minutos

Step-by-step explanation:

una hora es 60 minutos y media es 30 minutos.

The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.

5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;

D. 205.8 cm squared

A composite figure is a figure that is composed two or more regular figures.

The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.

The area of the unshaded semicircle = π × 24²/8 = 72·π

The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144

Area of the square = 24 × 24 = 576

Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8

The area of the shaded region ≈ 205.8 cm squared

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Answer: X = 8

Step-by-step explanation:

47 - 7 = 40

40 / 5 = 8

x = 8

Solving a simple equation, we can see that x = 35.

The 3 lines with an arrow that go to the left are parallel lines, thus, the relation between the sets of values in each of the sides must be the same ones.

Then we can take the quotients between the respective values, and these quotients must be equal, so we can write:

30/12 = x/14

And now we can solve that equation for x, we will get:

x = 14*(30/12)

x = 35

That is the value of x.

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Answer:

  53%

Step-by-step explanation:

You want to know the depreciation of car value after 5 years if it is 14% per year.

The multiplier of value each year is ...

  1 + growth rate = 1 + (-14%) = 0.86

When the value has been multiplied by that 5 times, it has been multiplied by ...

  0.86^5 ≈ 0.4704

This represents a change in value from the original value of ...

  0.4704 -1 = -0.5296 = -52.96% ≈ -53%

Zara's car has depreciated by 53% after 5 years.

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Every day, the number of people who receive the email grows by a factor of 3.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided above, an exponential function for the total number of people who received the email is given by;

[tex]P(t) = 4(3)^t[/tex]

By comparison, we have the following parameters;

Initial value, a = 4.

Growth rate, b = 3.

In conclusion, the number of people who receive the email from Elon every day grow by a factor of 3.

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After using ruler and following the steps described below

We get the standard position of 35 degree.

The given angle is = 35 degree

To draw standard position of angle:

We proceed it to draw by ruler

So, in order to get position,

Follow the following steps:

1: Draw a straight line with your ruler.

2: Place your protractor on the line and align the base of the protractor with the line.

3: Find the 35 degree mark on the protractor and make a small mark on the line at that point.

4: Move your protractor to the mark you just made.

5: Align the base of the protractor with the line and make another small mark on the line at the 35 degree mark.

6: Draw a straight line connecting the two points you just marked.

And there you have it! A 35 degree angle drawn on paper.

And after following these steps we get the standard potion angle 35 degree.

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If they both start riding at the same time and ride at their current rates, the time is that A. Amy will have to wait 0.5 minute for Sebastian.

Let v be the speed of Amy and Sebastian.

Option A states that Amy will have to wait 0.5 minutes for Sebastian. This implies that Sebastian is faster than Amy since he catches up to her within half a minute.

Therefore, Amy will have to wait 0.5 minute for Sebastian. This was calculated thus:

V = 3.0 - 2.5

v = 0.5

Therefore, Amy will have to wait 0.5 minute for Sebastian.

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The solution is : the value of P(2≤X≤5) is 0.50.

Here, we have,

given that,

The graph show the probability distribution of a random variable.

we know that,

The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.

so, we have,

P(2≤X≤5)

=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)

= 0.2+ 0.1 +0.05+0.15

= 0.50

Hence, The solution is : the value of P(2≤X≤5) is 0.50.

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Answer:

220 in²

Step-by-step explanation:

surface area = [area of the 4 vertical faces] + area of the base + area of top.

surface area = [2(4 X 10) + 2(5 X 10)] + (4 X 5) + (4 X 5)

= (80 + 100) + 20 +  20

= 220 in²

The maximum volume of the box is 864 cubic inches.

Let side length of the square cut from each corner is x inches.

After cutting the squares from each corner, the remaining dimensions of the sheet metal will be:

Length: 24 - 2x inches

Width: 24 - 2x inches

Height: x inches

So, the volume of the box

V = (24 - 2x) (24 - 2x)  x

V = x(24 - 2x)²

To find the maximum volume, we can take the derivative of V with respect to x, set it to zero, and solve for x:

dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0

4x² - 96x + 576 = 0

Solving the quadratic equation,

x = 6 and x = 12.

We can substitute x = 6 into the volume equation to find the maximum volume:

V = 6(24 - 2(6))²

V = 6(12)²

V = 6 x 144

V = 864 cubic inches

Therefore, the maximum volume of the box is 864 cubic inches.

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By evaluation, the values of the rational function are f(11) = - 1 / 12 and f(- 2) = 1, respectively.

In this problem we find the case of a rational function that must be evaluated at two different x-values: x = 11, x = - 2. The procedure is summarized below:

Now we proceed to present the complete procedure:

f(11) = 11 / (11 + 1) - 1

f(11) = 11 / 12 - 1

f(11) = 11 / 12 - 12 / 12

f(11) = (11 - 12) / 12

f(11) = - 1 / 12

f(- 2) = (- 2) / (- 2 + 1) - 1

f(- 2) = - 2 / (- 1) - 1

f(- 2) = 2 - 1

f(- 2) = 1

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If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.

The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).

To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.

The new coordinates of the vertices after the translation are:

A': (1, -2 - 5) = (1, -7)

B': (9, -2 - 5) = (9, -7)

C': (5, 2 - 5) = (5, -3)

Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

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The scatter plot shows a [positive linear] association.

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

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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Answer:

Danielle Stevenson receives $2,600 from selling the $160,000 house.

Step-by-step explanation:

To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:

Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.

Commission = 0.065 * $160,000 = $10,400.

Determine the broker's share: Broker Share = 0.5 * Commission.

Broker Share = 0.5 * $10,400 = $5,200.

Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.

Remaining Amount = $10,400 - $5,200 = $5,200.

Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.

Salesperson Share = 0.5 * $5,200 = $2,600.

Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.

Amount Danielle Receives = $5,200 - $2,600 = $2,600.

Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.

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Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

The minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

On the basis of the quantity of checks written, we can compare the overall costs of the two accounts.

Let's calculate the total cost for each account based on the given information:

First Account:

Monthly fee: $12

Per-check fee: $0.10

Total cost = Monthly fee + (Per-check fee * Number of checks)

Second Account:

Monthly fee: $9

Per-check fee: $0.25

Total cost = Monthly fee + (Per-check fee * Number of checks)

We must determine the point at which the first account's total cost is less than the second account's total cost. Let's construct the formula:

$12 + ($0.10 * Number of checks) < $9 + ($0.25 * Number of checks)

Simplifying the equation

$12 - $9 < ($0.25 - $0.10) * Number of checks

$3 < $0.15 * Number of checks

Dividing both sides by $0.15:

$3 / $0.15 < Number of checks

20 < Number of checks

Therefore, the minimum number of monthly checks Regina needs to write for the first account to be a better option is 21 or more. Answer C. 21 is one of the suggested choices.

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Answer:

2.5

Step-by-step explanation:

half of 10 is 10/2 = 5

so 50% of 5 is 2.5

The given function does not have an end behavior because it is not a polynomial function.

The end behavior of a function refers to how the function behaves or approaches as the input values (x-values) of the function become extremely large (approaching positive infinity) or extremely small (approaching negative infinity).The long term behavior of the function when x moves towards the ends of the coordinate plane can be predicted.

In a polynomial function, the leading coefficient and degree of the function often determine the polynomial function.

The given function is;

f(x) = 2x² - 5 / x² - 1

The end behavior of this function does not exist because this is not a polynomial.

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Answer:

27

Step-by-step explanation:

We can solve by using order of operations (PEMDAS), which shows us the order in which we're supposed to perform mathematical operations:

The / comes from the fact that you do these operations from left to right as multiplication and division have the same level of priority in an equation/operation.

Like multiplication/division, the / comes from the fact that you do these operations from left to right as addition and subtraction also have the same level of priority in an equation/operation.

Step 1:  Simplify inside the parentheses:

5 * 4 + (1 + 1) + 5

5 * 4 + 2 + 5

Step 2:  Multiply 5 and 4:

20 + 2 + 5

Step 3:  Add 20 and 2:

22 + 5

Step 4:  Add 22 and 5 to get your answer:

27

Thus, 5 *4 + (1 + 1) + 5 = 27

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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The likely population of the infected elk in the wildlife preserve is 840.

A sample is a smaller group of the population. A sample is a representation of the population.

The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.

Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve

(8/50) x 5250

= 0.16 x 5250 = 840

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The equivalent sine and cosine values are as follows:

The relationship between sine and cosine angles is:

sinθ = cos(90 - θ)

This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).

For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.

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a. Raina will have to pay a total of $2100 in interest.

b. The total repayment amount, including interest, will be $9100.

To calculate the total interest and total repayment amount, we can use the formula for simple interest:

Simple Interest = Principal * Rate * Time

(a) Total interest:

Principal = $7000

Rate = 6% per year

Time = 5 years

Total Interest = Principal * Rate * Time

= $7000 * 0.06 * 5

= $2100

(b) Total Repayment Amount = Principal + Total Interest

= $7000 + $2100

= $9100

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