Rectangles ABCD and PQRS are similar to each other. If AB= 25 units, PQ =
5 units, AD = 20 units, find the measure of PS.

Answer:

B) 110.92 u²

Step-by-step explanation:

to find the surface area, find the area of each side and add them together.

here are all 6 sides:

4.5 * 6.8

4.5 * 6.8

4.5 * 2.2

4.5 * 2.2

2.2 * 6.8

2.2 * 6.8

4.5 * 6.8 = 30.6

4.5 * 6.8 = 30.6

4.5 * 2.2 = 9.9

4.5 * 2.2 = 9.9

2.2 * 6.8 = 14.96

2.2 * 6.8 = 14.96

30.6 + 30.6 + 9.9 + 9.9 + 14.96 + 14.96

110.92

#hopefully that helps :)

Answer:

I love the blank question,it seems glitched

Step-by-step explanation:

Answer:

The third one

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

7=2x-7

-2x-7-7

-2x=-14

x=-14÷2

x=-7

1. The number of sides of the polygon is of: 12 sides.

2. The missing exterior angles are of: α = 48.5º.

3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.

A regular polygon is a polygon in which all the sides have the same length.

The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:

Measure of each angle = 360º/number of sides.

For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:

24º = 360º/number of sides.

24n = 360

n = 360/24

n = 12 sides.

The sum of the measures of the external angles of a polygon is always of 360º.

Hence, for item 2, the missing angles are obtained as follows:

2α + 90 + 55 + 40 + 78 = 360

2α + 263 = 360

2α = 97

α = 97/2

α = 48.5º.

An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:

Exterior angle = 180º - 160º = 20º.

Then the number of sides of  the polygon is obtained as follows:

20n = 360

n = 360/20

n = 18 sides.

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The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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Answer:26

Step-by-step explanation:

Answer:

4921/90

Step-by-step explanation:

Answer:

bce

on edg

Step-by-step explanation:

Answer: I will try my best, but if this answer is incorrect you will have to elaboarate a little more. Check explanation.

Step-by-step explanation: 1. A negative number using the minus sign right next to the number to show it is negative. Negative numbers are less than 0. 2. I don't understand what you mean, could you please clarify?

The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The B option is correct.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

A number is -906,060.

The equivalent number of the given number.

We know the number is -906,060.

It can be represented as \(\rm -906,060 = -9.0606 \ times\ 10^5\).

Thus, the B option is correct.

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Answer:

y = 6.08871x + 63.9274

Step-by-step explanation:

You can use Desmos a free graphing calculator to do this.  

Answer:

I would say 5 hours

Step-by-step explanation:

she worked 28 hours for 4 days of work. If she works two hours every morning for 4 days I would multiply those numbers together and get 8 so that leaves me with 20 hours. I would then divide 20 by 4 and that would leave me with 5 hours.

therefore she has been working 5 hours each afternoon.

hope this helps :)

Answer:

72

Step-by-step explanation:

First, you will multiply 150 times 48. Then, you would divide the answer, 7200, by 100 to get 72. I hope this helps :)

Answer:

She can swin 3.6 km in 1 hour using freestyle.

Step-by-step explanation:

If she can swin 0.3 kilometers in 10 minutes or 1/6 hours using backstroke, then her speed on that style is:

\(v_{backstroke} = \frac{0.3}{\frac{1}{6}} = 0.3*6 = 1.8 \text{ } \frac{\text{km}}{\text{h}}\)

If she can swim twice the distance in the same time for freestyle, then her speed on that is twice the one in backstroke. Therefore, her speed on freestyle is:

\(v_{freestyle} = 2*v_{backstroke} = 2*1.8 = 3.6 \text{ } \frac{\text{km}}{\text{h}}\)

Since her speed in freestyle is 3.6 km per hour, this means that she can swim a total of 3.6 km in one hour.

Answer:

C: 24 = \(w^{2}\) + 3 (the yellow option)

Step-by-step explanation:

We can see that 24 obviously represents our total area, we are told that the rug is 3 feet LONGER THAN it is wide, suggesting that addition will be involved.

In conclusion the most logical answer would be C: 24 = \(w^{2}\) + 3

If two groups of numbers have the same mean, then other measures of location need not be same. The Sample Mean is always smaller than the mean of the population from which the sample was taken.

Mean: It is the most commonly used measure of central tendency. It actually represents the average of the given collection of data. It is applicable for both continuous and discrete data.

Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:

If two groups of numbers have same mean that does not imply they will have same std deviation, median and mode. Even if two groups have same mean other measures may not be same because one group might be more or less scattered than the other group and though they may have same mean.

So the correct answer is option A.

Other measures of location need not be same.

2. Here, the correct option is option d. This is because when we calculate mean we basically take the average of each and every value in the given sample, which is bound to lie between the maximum and minimum value.

A mean can be zero if it has equal positive and negative numbers and a mean can be negative if it has more negative numbers. Again the mean of the sample is not always necessarily smaller than the mean of the population of which the sample is a part. Hence the first three options are incorrect

Therefore,  the correct option is option d. Mean is always smaller than the mean of the population from which the sample was taken.

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When x = 11, the value of y is approximately 8.276. We are given that the relationship between x and y is given by \(y = Ax^n\)where A and n are constants.

We are also given the values of A and n:

\(A = e^0.5\)

n = 3/8

We can substitute these values into the equation to get:

\(y = e^0.5 x^(3/8)\)

Now, we are asked to find the value of y when x = 11. To do this, we substitute x = 11 into the equation:

\(y = e^0.5 x^(3/8)\)

\(y = e^0.5 (11)^(3/8)\)

We can use a calculator to evaluate this

First, we evaluate the exponent (3/8) using the exponent rules:

\((11)^(3/8) = (11^(1/8))^3 = 1.706\)

Next, we substitute this value back into the equation:

\(y = e^0.5 x^(3/8)\)

\(y = e^0.5 (11)^(3/8)\)

\(y = e^0.5 (1.706)\)

Using a calculator, we can evaluate this expression to get:

y ≈ 8.276

Therefore, when x = 11, the value of y is approximately 8.276.

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We can conclude that after 75 years, the town will have 53.3 acres of conservation land.

Given that a town has 10 acres of conservation land and plans to increase the amount of conservation land by 11.5% every 5 years, we can calculate the amount of conservation land there will be after 75 years.

To determine the increase in conservation land over 5 years, we use the formula:

Increase = (11.5/100) × 10 = 1.15 acres

The conservation land after 5 years would be:

10 + 1.15 = 11.15 acres

Continuing this pattern, we can find the conservation land after 10 years, 15 years, and so on:

Conservation land after 10 years = 11.15 + 1.15 = 12.3 acres

Conservation land after 15 years = 12.3 + 1.15 = 13.45 acres

We can continue this calculation for each 5-year interval up to 75 years, as follows:

Conservation land after 20 years = 16.3 acres

Conservation land after 25 years = 18.05 acres

Conservation land after 30 years = 19.97 acres

Conservation land after 35 years = 22.13 acres

Conservation land after 40 years = 24.56 acres

Conservation land after 45 years = 27.3 acres

Conservation land after 50 years = 30.4 acres

Conservation land after 55 years = 34.0 acres

Conservation land after 60 years = 38.0 acres

Conservation land after 65 years = 42.4 acres

Conservation land after 70 years = 47.5 acres

Conservation land after 75 years = 53.3 acres

Therefore, after 75 years, the town will have approximately 53.3 acres of conservation land.

Applying the above calculations, we can conclude that after 75 years, the town will have 53.3 acres of conservation land.

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The answer is as follows:f'(0,0) = A = $\begin{pmatrix}-1 & 0 \\ 0 & 2\end{pmatrix}$, and the limit exists and is zero. Therefore, $f$ is differentiable at the origin.

Let's compute f(x, y) - f(0,0). We get: $f(x, y) - f(0,0) = ((2 - x + 3y + y^2) - 2, (3x - 2y - xy) - (-2)) = (-x + 3y + y^2, 3x - 2y - xy + 2)$.Now we need to use the definition of derivative:$$f'(0,0) = \lim_{(x,y)\to (0,0)} \frac{f(x, y) - f(0,0) - A(x, y)}{\sqrt{x^2 + y^2}},$$where A is the linear map $\mathbb{R}^2\to\mathbb{R}^2$ such that $A(x,y) = (-x, 2y)$. We need to show that the limit exists and find A such that it works.

Let's plug in the values:$\frac{f(x, y) - f(0,0) - A(x, y)}{\sqrt{x^2 + y^2}} = \frac{(-x + 3y + y^2 + x, 3x - 2y - xy + 2 - 2y)}{\sqrt{x^2 + y^2}} = \frac{(3y + y^2, 3x - xy + 2)}{\sqrt{x^2 + y^2}}.$It's enough to show that $\frac{(3y + y^2, 3x - xy + 2)}{\sqrt{x^2 + y^2}}$ converges to zero as $(x,y)\to (0,0)$.

We can use the Cauchy-Schwarz inequality:$$|3y + y^2| + |3x - xy + 2| \leq \sqrt{(1^2 + 3^2)(y^2 + (y+3)^2)} + \sqrt{(3^2 + (-1)^2)(x^2 + (-x+2)^2)}.$$This is less than $M\sqrt{x^2 + y^2}$ for some constant M, so the limit exists and is zero. Therefore $f$ is differentiable at the origin and $f'(0,0) = A = \begin{pmatrix}-1 & 0 \\ 0 & 2\end{pmatrix}$.

Thus, the answer is as follows:f'(0,0) = A = $\begin{pmatrix}-1 & 0 \\ 0 & 2\end{pmatrix}$, and the limit exists and is zero. Therefore, $f$ is differentiable at the origin.

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Answer:

x = 9.

Step-by-step explanation:

If you meant (x + 13) = 24, then we first must subtract 24 by 13.

24 - 13 = 9

Now, check your work by replacing the "x" with 9.

(9+ 13) = 24

24 = 24 <----- This is a true statement.

Therefore, x = 9.

Hope this helps! :D

Based on the information provided, the number of guests was 8 guests and the equation to represent this situation is 3/8 x + 2 = 5.

The first step to get to know the number of guests is to write an equation, this will help us discover the number of x  or guests. To write the equation, let's include the variable and values given:

3/8 x + 2 = 5

Now, let's solve this equation:

0.375x + 2 = 5

x = 5 -2/ 0.375

x = 3 / 0.375

x = 8 guests

Based on the above, it can be concluded that the number of guests, in this case, was 8.

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Which quantity is unknown?

the number of guest

_____________________________________

Write an equation that represents the situation.

3/8g + 2 = 5

_____________________________________

How many guests does David have?

g = 8

Answer:

Step-by-step explanation:

Answer:

B, A, C, D

Step-by-step explanation:

rise over run

slope: the ratio of the change in the dependent values (outputs) to the change in the independent values (inputs) between two points on a line

One bagel costs 155 cents.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question.

Let x = cost of one bagel

y = cost of one toast

z = cost of one muffin

If two pieces of toast and a bagel costs $3.15, then 2y + x = 3.15.

2y + x = 3.15   ⇒   x = 3.15 - 2y     (equation 1)

If a bagel and a muffin costs $3.30, then x + z = 3.30.

x + z = 3.30     (equation 2)

Substitute equation 1 to equation 2.

x + z = 3.30     (equation 2)

3.15 - 2y + z = 3.30   ⇒   z = 0.15 + 2y      (equation 3)

If a piece of toast, two bagels, and three muffins costs $9.15, then

y + 2x + 3z = 9.15     (equation 4)

Substitute equations 1 and 3 to equation 4.

y + 2x + 3z = 9.15     (equation 4)

y + 2(3.15 - 2y) + 3(0.15 + 2y) = 9.15

y + 6.30 - 4y + 0.45 + 6y = 9.15

3y = 2.4

y = 0.8

Substitute the value of y to equation 1.

x = 3.15 - 2y     (equation 1)

x = 3.15 - 2(0.8)

x = 1.55

Hence, the cost of one bagel is $1.55 or 155 cents.

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(a) To determine the radius and height of a cone with a given surface area and maximal volume, we need to find the critical points by differentiating the volume formula with respect to the variables, setting the derivatives equal to zero, and solving the resulting equations.

(b) To find the ratio for a cone with a given volume and minimal surface area, we follow a similar approach.

(c) A cone with a given volume and maximal surface area does not exist. This is because the surface area and volume of a cone are inversely proportional to each other.

Let's denote the radius of the cone as r and the height as h. The surface area of a cone is given by: A = πr(r + l), where l represents the slant height.

The volume of a cone is given by: V = (1/3)πr²h.

To maximize the volume while keeping the surface area constant, we can use the method of Lagrange multipliers.

The equation to maximize is V subject to the constraint A = constant.

By setting up the Lagrange equation, we have:

(1/3)πr²h - λ(πr(r + l)) = 0

πr²h - λπr(r + l) = 0

Differentiating both equations with respect to r, h, and λ, and setting the derivatives equal to zero, we can solve for the critical values of r, h, and λ.

(b) To find the ratio for a cone with a given volume and minimal surface area, we follow a similar approach. We set up the Lagrange equation to minimize the surface area while keeping the volume constant. By differentiating and solving, we can determine the critical values and calculate the ratio.

(c) A cone with a given volume and maximal surface area does not exist. This is because the surface area and volume of a cone are inversely proportional to each other. When one is maximized, the other is minimized. So, if we maximize the surface area, the volume will be minimized, and vice versa. Therefore, it is not possible to have both the maximum surface area and maximum volume simultaneously for a cone with given values.

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The solutions to the trigonometric function \(2\sin{\theta} = -\sqrt{2}\) on the first lap of the trigonometric circle are given as follows:

The trigonometric function in the context of this problem is defined as follows:

\(2\sin{\theta} = -\sqrt{2}\)

We must isolate the desired variable, hence:

\(\sin{\theta} = -\frac{\sqrt{2}}{2}\)

Then we must apply the arcsine function, which is the inverse cosine, hence:

\(\theta = \arcsin{\left(-\frac{\sqrt{2}}{2}\right)}\)

Using a calculator, the angles are given as follows:

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Answer:

x=31/14

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−4x+1=−9x−16+9x+16

−4x+1=−9x+−16+9x+16

−4x+1=(−9x+9x)+(−16+16)(Combine Like Terms)

−4x+1=0

−4x+1=0

Step 2: Subtract 1 from both sides.

−4x+1−1=0−1

−4x=−1

Step 3: Divide both sides by -4.

−4x−4=−1/-4

x=1/4