The school is planning to add 2 new playgrounds. Each playground will be in the shape of a square that measures by 24m by 24m.What will be the area of the​ playgrounds?

Answer:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)

Step-by-step explanation:

To rotate a point $(x,y)$ by $270^{\circ}$ clockwise, we first swap the $x$ and $y$ coordinates and then negate the new $y$ coordinate.

Using this, we can find the image vertices of the given polygon as follows:

For vertex K(0, 0), we have $(0,0) \rightarrow (0,0)$. So K′ is at the origin.

For vertex L(5, 2), we have $(5,2) \rightarrow (2,-5)$. So L′ is at (-2, 5).

For vertex M(5, -5), we have $(5,-5) \rightarrow (5,5)$. So M′ is at (5, 5).

For vertex N(0, -3), we have $(0,-3) \rightarrow (-3,0)$. So N′ is at (-3, 0).

Therefore, the image vertices of the polygon KLMN after a $270^{\circ}$ clockwise rotation are K′(0, 0), L′(−2, 5), M′(5, 5), and N′(−3, 0).

Thus, the correct option is:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(−3, 0)

The fractional part of 70/28 is 35/14 i.e., 2.5

Percentage:

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100

28 of 70 can be written as:

=> [tex]\frac{28}{70}[/tex]

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

[tex]\frac{28}{70}[/tex] × [tex]\frac{100}{100}[/tex]

=> (28 × 100) /70 ×[tex]\frac{1}{100}[/tex]

=> 40/100

Therefore, the answer is 40%

The fractional part of 70/28 is 35/14 i.e., 2.5

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Answer:

The volume of the display case in cubic inches is 10,328 1/16 in.

Answer:

They would have gotten 2 full apples each. There would be 4 left over. If they decided to split those 4 apples, they would have gotten 2 1/2 apples each.

Step-by-step explanation:

20 ÷ 8 = 16 R 4

16 ÷ 8 = 2 (the full apples they got each_)

4 x 2 = 8 (split the 4 apples in half to make 8)

Therefore, each student would have gotten 2 full apples and 1/2 of an apple.

The total distance traveled by the car between t = 0 and t = 3 is given as follows:

c. 15 mi.

The velocity function is given as follows:

v(t) = 20 - 10t.

The distance function is the integral of the velocity function, hence it is given as follows:

d(t) = 20t - 5t².

The distance at t = 0 is given as follows:

d(0) = 20(0) - 5(0)²

d(0) = 0.

The distance at t = 3 is given as follows:

d(3) = 20(3) - 5(3)²

d(3) = 15.

Hence the total distance is given as follows:

15 - 0 = 15 mi.

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The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

For the transformation 1, we have a reflection, which keeps both the side lengths and the angle measure constant, just changing the orientation of the figure.

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We can see here that the statements that are true are:

B. The symbol should be used because (8, 13, 22, 36) is a set and none of the elements in - 13 is a set.

C. The ∉ symbol should be used because ∉ is not an element of the set.

F. The ∈ symbol should be used because ∉ is not an element of the set.

A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.

Numbers, letters, words, forms, persons, and other mathematical things can all be included in a set.

We can see here that -13 ∉  (8, 13, 22, 36).

These statements are true because -13 is not actually an element of (8, 13, 22, 36). Thus, in the given set of data, -13 is not seen in the given set.

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Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

Okay, let's break this down step-by-step:

* The spinner has 5 equal sections, numbered 1 through 5.

* Each section represents a 1 in 5 chance of landing on a particular number.

* The spinner has a 3 section.

* Jashon will spin the spinner 150 times.

So, to calculate the expected number of times a 3 will come up:

* There is 1 section for the number 3 out of the 5 total sections.

* So the probability of landing on the 3 section is 1/5 = 0.2

* In 150 spins, the probability of landing on 3 will be 0.2 multiplied by 150 spins.

* So 0.2 * 150 = 30

Therefore, if Jashon spins the spinner 150 times, he can expect the number 3 to come up approximately 30 times.

Let me know if you have any other questions!

The graph of the function f(x) with vertex (1, 2) and another point (0, 2) is shown below.

Consider a function f(x) = 3x² - 6x + 2

We know that the graph of quadratic function is a parabola.

We graph the function f(x)

The graph of function f(x) is shown below.

From the graph of f(x), we can observe that the vertex of parabola is (1, 2)

For x = 0 the value of the function f(x) would be,

f(x) = 3x² - 6x + 2

f(0) = 3(0)² - 6(0) + 2

f(0) = 0 - 0 + 2

f(0) = 2

This means that the y-intercept of f(x) is (0, 2)

Therefore, the reuired graph of the function f(x) is shown below.

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Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

We can write the quadratic in standard form as:

y = x² -18x - 1053

For a quadratic equation whose solutions are:

x = x₁

x = x₂

We can write it as:

y = (x - x₁)*(x - x₂)

Here the solutions are:

x = 9 + 9√13

x = 9 - 9√13

Then we can write the quadratic as:

y = (x - 9 - 9√13)*(x - 9 + 9√13)

Expanding that:

y = x² -18x - 81*13

y = x² -18x - 1053

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The overall mean of data set is 49.57. Option D

The overall mean is all the sums of the means divided by the total number of set in the table.

All the mean in the table are 42. 75 + 51. 75 + 50.00 + 49.50 + 51.25 + 47.25 + 50.75 + 47.75 + 56.50 + 47.50 + 38.75 + 49.25 + 57.00 + 48.75 + 54.75 = 743.5

We see that there are 15 data set.

mean = 743.5/ 15

Overall mean = 49.57

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Monique gave away a greater fraction of cake than Chris.

We can represent the fraction of cake Chris gave away as 3/8, and the fraction of cake Monique gave away as 4/8 (which can be simplified to 1/2)

3/8 ______ 1/2

In order to compare the fractions, we can convert them to have a common denominator. The smallest common multiple of 8 and 2 is 8, so we can write:

3/8 = 3/8

1/2 = 4/8

Now we can fill in the symbol to complete the comparison:

3/8 < 1/2

Therefore, Monique gave away a greater fraction of cake than Chris.

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Answer:

[tex] \frac{210}{360} = \frac{7}{12} [/tex]

This figure represents 7/12 of the circle.

Answer:

Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.

22/32 x 100 = 68.75%

Lana has completed 68.75% of the puzzles in her book.

Answer:

Lana has completed 68.75% of the puzzles in her puzzle book.

Step-by-step explanation:

Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%

percentage = 0.6875 x 100%

percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.

Answer: x^2+2x-63

Step-by-step explanation:

Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)

                                =x^2-(7-9)+(7*(-9))

                                =x^2+2x-63

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Answer: x ≥ 3

Step-by-step explanation:

The equation can be y = 3x + 7, evaluating it in x = 16 we will get:

y = 55

We can write a linear equation, which is the simplest type of equations.

For example, let's define:

y = 3x + 7

Now the evaluation.

We want to find the value of y when x = 16. To do so, we need to evaluate the equation in x = 16, that means replacing the variable x by the number, then we will get.

y = 3*16 + 7

y = 55

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Answer:

To represent each part of Alexi's circle as a fraction, we need to determine the total number of parts in the circle and the number of parts represented by each tile.

Adding up the number of tiles, we get:

1 + 2 + 5 + 6 + 8 = 22

So there are a total of 22 parts in Alexi's circle.

To find the fraction represented by each tile, we can divide the number of parts represented by the tile by the total number of parts in the circle.

Starting with the first tile, which represents 1 part, the fraction it represents is:

1/22

Moving to the second tile, which represents 2 parts, the fraction it represents is:

2/22 = 1/11

Continuing in the same way for the remaining tiles, we get:

So the fractions represented by each part of Alexi's circle are

Using the model to estimate f(x) when x = 5 and x = 10, the vaues are 18.33 and 17.78

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

f(x) = -0.11x + 18.88

Also, we have

x = 5 and x = 10

Substitute the known values in the above equation, so, we have the following representation

f(5) = -0.11 * 5 + 18.88 = 18.33

f(10) = -0.11 * 10 + 18.88 = 17.78

Hence, the values are 18.33 and 17.78

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Complete question

Question: A statistician calculated the following linear model to describe the data: f(x) = – 0.11x + 18.88 Use the model to estimate f(x) when x = 5

Answer:

Table B is proportional since y = 1.5x:

4.5 ÷ 3 = 1.5

7.5 ÷ 5 = 1.5

10.5 ÷ 7 = 1.5

The relative frequency of a person having the flu and testing positive for the flu is 0.1053/0.901 = 0.117, or approximately 11.7%. The relative frequency table is given below.

To get the relative frequencies, we divide each cell value by the total frequency of the table.

This is how we construct relative frequency table.

To construct a relative frequency table, we need to determine the different possible outcomes and their corresponding frequencies based on the given information.

Let's define the following events:

A: a person has the flu

B: a person tests positive for the flu

Then, using the information given in the problem, we can construct the following relative frequency table:

                   A (has the flu)   not A (does not have the flu) Total

B              0.13*0.81 = 0.1053          0.08*0.87 = 0.0696              0.1749

not B       0.19*0.81 = 0.1540           0.63*0.87 = 0.5471               0.7011

To                   0.2843                                 0.6171                         0.901

In this table, the values in the cells represent the product of the probability of the row event and the probability of the column event. For example, the value 0.1053 in the top left cell represents the probability of a person having the flu (event A) and testing positive for the flu (event B), which is calculated as 0.13 x 0.81.

The total frequency for each row and column is calculated by summing the values in that row or column. The total frequency for the entire table is the sum of all the values, which is 0.901 in this case.

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[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]

[tex] = 7 {x}^{2} - 5x + 49[/tex]

The probability that a student has a dog given that they have a cat is 2/5.

To find the probability that a student has a dog given that they have a cat, we need to use conditional probability. We can use the formula:

P(Dog | Cat) = P(Dog and Cat) / P(Cat)

where P(Dog and Cat) is the probability that a student has both a dog and a cat, and P(Cat) is the probability that a student has a cat.

From the given data table, we can see that there are a total of 25 students in the class, and 15 of them have a cat. Of the 15 students with a cat, 6 also have a dog. Therefore, P(Dog and Cat) = 6/25 and P(Cat) = 15/25.

Substituting these values into the formula, we get:

P(Dog | Cat) = (6/25) / (15/25) = 6/15 = 2/5

Therefore, the probability that a student has a dog given that they have a cat is 2/5 or 0.4.

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The statement The product of p is and -8 is less than 24 as an expression is -8p <  24

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

The statement represented as

The product of p is and -8 is less than 24

Less than is represented using the symbol <

So, we have

The product of p is and -8 is less than 24: The product of p is and -8 is <  24

Represent products as *

So, we have

The product of p is and -8 is less than 24: -8p <  24

Hence, the expression is -8p <  24

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Answer:

$1,000.

Step-by-step explanation:

200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.

i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0

To use a graph to find the value of x for the given values of y in the equation y=-|x-2|+2, we can follow these steps:

i) When y<0:

The graph of y=-|x-2|+2 is below the x-axis when y<0. Therefore, there is no solution for x when y<0, because there is no point on the graph that has a negative y-coordinate.

ii) When y>0:

The graph of y=-|x-2|+2 intersects the x-axis at two points when y>0. To find the x-coordinates of these points, we can set y=0 in the equation y=-|x-2|+2 and solve for x, as shown in the previous answer.

The x-intercepts are at (4,0) and (0,0), which means that the graph crosses the x-axis at x=4 and x=0 when y>0.

iii) When y=0:

To find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (i.e., where y=0), we can look at the x-intercepts that we found in part ii) above. The x-coordinate(s) of the point(s) where the graph intersects the x-axis are x=4 and x=0, so the solutions for x when y=0 are x=4 and x=0.

Therefore, i) There is no solution for x when y<0.

ii) When y>0, the solutions for x are x=4 and x=0.

iii) When y=0, the solutions for x are x=4 and x=0 (the x-intercepts).

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The couple needs to deposit about $554.49 each month end until they retire to reach their goal.

To find the monthly deposit needed, we'll use the future value of an ordinary annuity formula:

FV = PMT * [((1 + r)^n - 1) / r]

We already know the future value (FV) as $953,776.53, and we want to solve for PMT, the monthly deposit:

PMT = FV / [((1 + r)^n - 1) / r]

We'll use the same r (0.08/12) and a new n (35 * 12) for the 35 years until retirement:

PMT = 953776.53 / [((1 + 0.08/12)^(35*12) - 1) / (0.08/12)]

PMT ≈ 554.49

Thus, the couple needs to deposit about $554.49 each month end until they retire to reach their goal.

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Answer:

I think it's 3

Step-by-step explanation:

it's skipping 2 after every three