The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 35 feet and a width of 45 feet. The length of the new space is 42 feet. Find the perimeter of the space used for the new playground. Perimeter: feet

The table which represents a linear function is answer B. By calculating the slope between any two points on the table.

A linear function is a mathematical function that produces a straight line when graphed. It is a type of function where the input variable (x) and output variable (y) are related in a way that can be represented by a straight line.

To determine which table represents a linear function, we need to check whether the change in the output variable (y) is proportional to the change in the input variable (x) for any two points on the table.

Answer A:

When we compare the difference between each value of y, we see that each subsequent value of y is multiplied by 2. For example, 2 x 2 = 4, 4 x 2 = 8, and so on. This means that there is a constant rate of change between each pair of x and y values, but the rate of change is not constant. Therefore, the function is not linear.

Answer B:

When we compare the difference between each value of y and x, we see that the difference between any two values of y is proportional to the difference between the corresponding x values. Specifically, when x increases by 1, y increases by 1, except for the first two values. This means that the rate of change between each pair of x and y values is constant, and the function is linear.

Answer C:

When we compare the difference between each value of y, we see that the difference between any two values of y is not proportional to the difference between the corresponding x values. Specifically, the rate of change is not constant. Therefore, the function is not linear.

Answer D:

When we compare the difference between each value of y, we see that the rate of change is not constant. Specifically, the rate of change from x = 1 to x = 2 is different from the rate of change from x = 2 to x = 3. The function is not linear.

Therefore, only answer B represents a linear function.

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The volume of the box is a function of x, given by:[tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

What is volume ?

Volume is a physical quantity that measures the amount of three-dimensional space that a substance or object occupies. It is usually measured in cubic units, such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

To construct the box, we start with a square piece of cardboard that is 8 inches by 8 inches. We will cut out squares from each corner with side length x inches. This will leave us with a rectangular piece of cardboard with dimensions 8-2x by 8-2x, and we can fold up the sides to form the open box.

The height of the box will be x inches, and the length and width of the base of the box will be 8-2x inches. Therefore, the volume of the box will be:

Volume = Length x Width x Height

Volume = (8-2x) x (8-2x) x x

[tex]Volume = x(64-32x+4x^2)[/tex]

Therefore, the volume of the box is a function of x, given by: [tex]V(x) = 4x^3 - 32x^2 + 64x[/tex]

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Answer:

20 units

Step-by-step explanation:

six puls six plus four plus four is twenty

The 1-dimensional space can be identified using the point x= 3, that is the x-coordinate of the point. This depicts the complexity of the space in 1-dimension.

The link between the number of dimensions and the complexity of the space is shown by the fact that just one integer is required to identify a specific location in a 1-dimensional space. The complexity of the space increases as the number of coordinates required to identify a point increases in higher dimensions.

Hence, the 1-dimensional space can be identified using the point x= 3, that is the x-coordinate of the point. This depicts the complexity of the space in 1-dimension.

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The cost of Shai's haircut is $25 and the cost of his shave is $30, so the subtotal before tax and tip is:

$25 + $30 = $55

The sales tax is 8.25%, so the tax amount is:

$55 * 0.0825 = $4.54

The total cost before tip is:

$55 + $4.54 = $59.54

If Shai tips 25% on the subtotal, the tip amount is:

$55 * 0.25 = $13.75

So the total cost including tax and tip is:

$59.54 + $13.75 = $73.29

Therefore, Shai must pay a total of $73.29 if he gets his hair cut and beard shaved and he tips the barber 25%. The answer is option (B).

Answer:

B, C

Step-by-step explanation:

360 - 90 - 15 = 255

-90 - 15 = -105

Answer:

Last choice

Step-by-step explanation:

the 'w-axis intercept' occurs when d = 0  ( puppy is just born day 0)

 and is equal to 4.25 ounces

On using unit conversion the value for 31.5 inches is obtained as 80.01 centimeters.

What is unit conversion?

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.

To convert inches to centimeters, we can multiply the number of inches by 2.54.

So to convert a 31.5 inch board to centimeters, use the arithmetic operation of multiplication.

We can multiply 31.5 by 2.54 -

31.5 inches × 2.54 centimeters/inch = 80.01 centimeters

Therefore, the board is 80.01 centimeters long.

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Part a: Compounded Semiannually: A = 20,771.75.

Part b: Compounded quarterly: A = 20817.66.

Part c: Compounded monthly: A = 20848.76

Part d: Compounded continuously :A = 407,538.49

Compound interest formula:

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

And

A = P[tex]e^{rt}[/tex]

Principal P : $15,000

Time t = 6 years

Rate of interest r = 5.5%

number of time compounded - n

Part a: Compounded Semiannually:

r --> r/2

n = 2

A = 15,000[tex](1 + \frac{0.055}{2} )^{2*6}[/tex]

A = 20,771.75

Part b: Compounded quarterly:

r --> r/4

n = 4

A = 15,000[tex](1 + \frac{0.055}{4} )^{4*6}[/tex]

A = 20817.66

Part c: Compounded monthly:

r --> r/12

n = 12

A = 15,000[tex](1 + \frac{0.055}{12} )^{12*6}[/tex]

A = 20848.76

Part d: Compounded continuously

A = Pe∧(rt)

A = 15,000(2.72)∧(0.55*6)

A = 407,538.49

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The value of a is given as follows:

a = 2.4.

Similar polygons are polygons that share these two features presented as follows:

As the two polygons are similar for this problem, the proportional relationship for the lengths is given as follows:

3/5 = a/4 = (b - 6)/2.

Hence the value of a is obtained as follows:

3/5 = a/4

5a = 12

a = 12/5

a = 2.4.

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Using the method of undetermined coefficients, the particular solution is:

[tex]\mathrm{y_p(t) = 6e^{2t} \times cos(9t) + 3^{2t} \times sin(9t)}[/tex]

To use the method of undetermined coefficients, we assume that the particular solution has the same form as the forcing term, but with undetermined coefficients.

Let's start by finding a particular solution for the equation:

y′′ − 4y′ + 81y = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the forcing term contains both exponential and trigonometric functions, we'll assume that the particular solution is of the form:

[tex]y_p[/tex](t) = A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

where A, B, and C are undetermined coefficients that we need to determine.

Let's find the first and second derivatives of [tex]y_p[/tex](t):

[tex]y'_p[/tex](t) = (2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

[tex]y''_p[/tex](t) = (4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex])

Substituting these expressions into the differential equation, we get:

(4A - 81B)*[tex]e^{2t}[/tex]*cos(9t) + (4B + 81A)*[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]

4[(2A + 9B)*[tex]e^{2t}[/tex]*sin(9t) + (2B - 9A)*[tex]e^{2t}[/tex]*cos(9t) - C[tex]e^{(-t)[/tex]

81[A*[tex]e^{2t}[/tex]cos(9t) + B[tex]e^{2t}[/tex]*sin(9t) + C[tex]e^{(-t)[/tex]]

= 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Simplifying and grouping terms, we get:

[(4A + 18B)cos(9t) + (18A - 4B)sin(9t)][tex]e^{2t}[/tex]+ (81C + 3)[tex]e^{(-t)[/tex] = 48[tex]e^{2t}[/tex]cos(9t) + 80[tex]e^{2t}[/tex]sin(9t) + 3[tex]e^{(-t)[/tex]

Since the two sides of the equation must be equal for all values of t, we can equate the coefficients of the exponential and trigonometric functions on both sides:

4A + 18B = 48 => A = 6

18A - 4B = 80 => B = 3

81C + 3 = 3 => C = 0

Therefore, the particular solution is:

[tex]y_p[/tex](t) = 6[tex]e^{2t}[/tex]*cos(9t) + 3[tex]e^{2t}[/tex]*sin(9t)

Thus, the general solution of the differential equation is:

[tex]\mathrm{y(t) = y_h(t) + y_p(t)}[/tex]

where [tex]y_h[/tex](t) is the complementary solution. Since the characteristic equation of the differential equation is r² - 4r + 81 = 0, it has two complex conjugate roots: r = 2 ± 9i. Therefore, the complementary solution is:

[tex]y_h[/tex](t) = [tex]c_1[/tex]*[tex]e^{2t}[/tex]cos(9t) + [tex]c_2[/tex][tex]e^{2t}[/tex]*sin(9t).

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The area of the complex figure is 178 square meters.

Option (A) is correct.

What is an area?

In geometry, area is the measure of the amount of surface enclosed by a two-dimensional shape or a planar figure. It is typically measured in square units such as square centimeters, square inches, or square meters.

To find the area of a rectangle, we can multiply its length by its width.

Given width = 8 m and length = 16 m, the area of the rectangle is:

Area = length x width = 16 m x 8 m
Area = 128 cm^2 ------(I)

To find the area of a rectangle, we can multiply its length by its width.

Given width = 5 m and length = 6 m, the area of the rectangle is:

Area = length x width = 6 m x 5 m
Area = 30 m^2 -----(II)

The area of a triangle is given by the formula A = 1/2 x b x h, where A is the area, b is the base of the triangle, and h is its height.

Given that the height of the triangle is 8 m and its base is 5 m, the area of the triangle is:

A = 1/2 x b x h = 1/2 x 5 m x 8 m
Area = 20 square m  ---------(III)

Adding (I), (II) and (III), we get

Area = 128 + 30 + 20

Area = 178 sq.m

Hence, the area of the complex figure is 178 square meters.

Option (A) is correct.

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Answer:

The area of the complex figure is 178 square meters. Thus, Option (A) is correct.

The area of the canvas is 8 1/8 square units.

The area of a canvas with dimensions of 2 1/2 x 3 1/4 can be calculated by multiplying the length by the breadth.

2 1/2 and 3 1/4 must first be converted into improper fractions:

2 1/2 = (2 x 2 + 1) / 2 = 5/2

3 1/4 = (3 x 4 + 1) / 4 = 13/4

The area may now be calculated by multiplying the two fractions:

(5/2) x (13/4) = (5 x 13) / (2 x 4) = 65/8

The canvas's surface area is 65/8 square units as a result. This can be expressed as a mixed number as well:

65/8 = 8 1/8

Hence, the canvas has an area of 8 1/8 square units.

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Answer:

the last one

Step-by-step explanation:

it passes through the most points

Answer:

Side PQ is the same as RQ

Angle QRS is the same as QPS

Step-by-step explanation:

For the given rectangle, the ordered pair that represents the location of point Z is (11,6).

What is a rectangle?

The internal angles of a rectangle, which has four sides, are all precisely 90 degrees. The two sides come together at a straight angle at each corner or vertex. The rectangle differs from a square because its two opposite sides are of equal length. Also, it is known as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. A rectangle's diagonals cut each other in half. It has four right angles and is a parallelogram. The complete distance that the rectangle's outside boundary covers is referred to as its perimeter. The area a two-dimensional form occupies in a plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.

The rectangle should have opposite sides of equal length.

Here,

XY = WZ

XW = YZ

From the graph, we can write the coordinates as:

X = (7,11)

Y = (11,11)

W = (7,6)

Point Z should lie directly below Y so that it is in a straight vertical line.

Then it should have the same x coordinate as Y.

It should also lie in the same horizontal line that passes through W.

So it will have the same y coordinate as W.

Therefore for the given rectangle, the ordered pair that represents the location of point Z is (11,6).

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The sample space will be 243, 743, 1243, 1743, 2243, 2743, 3243, 3743, 4243, and 4743.

A sample space is the collection of all potential results of a random experiment or process in probability theory. It's represented by the symbol (the uppercase Greek letter omega).

For instance, if we flip a fair coin, the sample space is H, T, where H stands for the outcome of a heads result and T stands for a tails result. The sample space on a normal six-sided dice is 1, 2, 3, 4, 5, and 6.

No matter how likely they are, all outcomes are included in the sample area. In order to accurately estimate the probability of an event, the sample space must be defined.

Now,

To choose a systematic sample of size n = 10 from a town with 5000 people, we will use a systematic sampling technique. Here are the steps to follow:

Determine the sampling interval: The sampling interval is the number of people in the population divided by the desired sample size. In this case, the sampling interval is 5000/10 = 500.

Select a random starting point: To ensure the sample is representative of the population, we need to select a random starting point between 1 and 500.

We can use a random number generator to choose a starting point. Suppose we choose the number 243 as our starting point.

Select every nth person: Starting from the chosen starting point, we will select every 500th person until we reach a sample size of 10.

So, we will select people with the following index numbers: 243, 743, 1243, 1743, 2243, 2743, 3243, 3743, 4243, and 4743.

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The length of the diagonals will be WZ = XZ = 11 units.

A diagonal in geometry is a line segment that connects two polygonal or polyhedral vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.

The length of the two diagonals of the rectangle is equal. The value of x will be calculated as,

6x - 7 = 3x + 2

3x = 9

x = 3

WZ = 6x - 7

WZ = 6 x 3 - 7

WZ = 18 - 7

WZ = 11

XZ = 3x + 2

XZ = 3 x 3 + 2

XZ = 11

Therefore, the length of the diagonals will be WZ = XZ = 11 units.

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Answer:

14.4 - proofs attached to answer

Step-by-step explanation:

proofs attached to answer

Answer: 57.50$

Step-by-step explanation:

if you have more questions like this there are good commission calculators id recommend look them up

15% of 50 is 7.50

add them together and you get

57.50$

hope this helps

Answer:

7

Step-by-step explanation:

Using Simple interest, savings account for her needed to deposit $1,842.82 each year.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

t can also be computed using the annuity factor of 5% for 17 years to divide the total sum of $50,000.

The 529 plan, according to available data, is a tax-advantaged or tax-qualified savings plan designed to encourage individuals to save for future education costs of their relations or for themselves.

Data and Calculations:

N (number of intervals) = 17 years

Interest every year is equal to 5%.

Present Value = $0 PV

FV (Future Value) = $50,000 ($31,327.88 + $18,672.12)

Results: PMT = $1,842.82

Sum of all periodic payments = $31,327.88 ($1,842.82 x 17)

Total Interest = $18,672.12

Hence, in order to save $50,000 in 17 years at a 5% return for his granddaughter, the man who wanted to open a 529 college savings account for her needed to deposit $1,842.82 each year.

Hence the interest the bank will collect will be $117.53.

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Survey is a method used to collect the information from the group by asking  relevant questions.

It is simply how  likely the event can be occurred or in other words it is a likelihood of an event occurring

Let the events be:

A----Cooked food P(A)=10

B----washed dishes P(B)=13

C----- operated the cash register.

P(C)=25

P(A∩B)=5

(cooked + washed dishes)

P(A∩C)=5

(cooked & operated the cash register)

P(B∩C)=8

(washed dishes and operated the cash register)

P(A∩B∩C)=3 did All three jobs

P(A∩B∩C)'=3 did none of these jobs

P(AUBUC) = P(A) + P(B) + P(C) - P(A∩B)-P(A∩C)-P(B∩C) + P(A∩B∩C).

A.) How many employees were surveyed?

=P(A) + P(B) + P(C) - P(A∩B)-P(B∩C)-P(C∩A) + P(A∩B∩C)

=(10+13+25)-(5-5-8)+3

=48-(-8)+3

= 48 + 8 + 3

= 59

= 59+ 3 (members who did none of the jobs)

=62

62 employees were surveyed

x=A∩B∩C

=3

ab= A∩B-x

=5-3

=2

bc=B∩C-x

=8-3

=5

ca=A∩C-x

5-3

=2

b) only cooked food:

=A-(ab+x+ca)

= 10-(2+3+2)

=10-7

=3

3 employees only cooked food

c)only operated the cash register:

=C-(bc+x+ca)

=25-(5+3+2)

=25-10

=15

15 employees only operated the cash register

d) employees cooked food or operated the cash register:

P(A or C)=P(A)+P(C)

=10+25

=35

e) washed dishes or operated the cash register

P(B or C)= P(B)+P(C)

=13+25

=38

f)only washed dishes:

=B - P(bc+x+ab)

=13-(5+3+2)

=13-10

=3

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this question is incomplete

The complete question is:

In a survey of employees at a fast food​ restaurant, it was determined that 10 cooked​ food, 13 washed​ dishes, 25 operated the cash​ register, 5 cooked food and washed​ dishes, 5 cooked food and operated the cash​ register, 8 washed dishes and operated the cash​ register, 3 did all three​ jobs, and 3 did none of these jobs. Complete parts A) through F) below,

A.) How many employees were surveyed?

B.) How many of the employees only cooked food?

C.) How many of the employees only operated the cash register?

D.) How many of the employees washed dishes or operated the cash register?

E.) How many of the employees washed dishes or operated the cash register ?

F.) How many of the employees only washed dishes?

Answer:42

Step-by-step explanation:took the quiz

Step-by-step explanation:

The sum of the given numbers is:

15 + 17 + x + 28 + 39 = 99 + x

To find the missing value, we can use the formula for the mean (average):

mean = (sum of numbers) / (number of numbers)

Substituting the given values:

23 = (15 + 17 + x + 28 + 39) / 5

Multiplying both sides by 5:

115 = 15 + 17 + x + 28 + 39

Simplifying:

x + 99 = 115

x = 16

Therefore, the missing value is 16.

Answer:

Step-by-step explanation:

i think so

The solution of the inequality is x > -4. In the interval notation is (-4,∞).

What is inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equal. But various inequalities are used to compare the values, whether it is less than or greater than.

An inequality exists when two real numbers or algebraic expressions are connected by the symbols “>”, “<”, “≥”, “≤”.

The given inequality is:

6x + 8 > - 16

Subtract 8 from both sides:

6x + 8 - 8 > - 16 - 8

6x  > - 24

Divide both sides by 6:

x > -24/6

x > -3

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The domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

A coordinate plane is a two-dimensional graph that is used to locate points in a given space. The two axes intersect at a point called the origin, which is located at the coordinates (0, 0). Points on the coordinate plane can be labeled using their x and y coordinates, which are written in the form (x, y).

The graph below shows a function in the coordinate plane, which is made up of a curved line that begins at the point (1, -2) and rises as it moves to the right. The domain of the function is all x-values, or inputs, which are greater than or equal to 1. The range of the function is all y-values, or outputs, which are greater than or equal to -2.

When determining the domain and range of a function, it is important to remember that the domain is the set of all possible inputs, while the range is the set of all possible outputs. In the case of the graph below, the domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

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Answer: Let's use variables to represent the three digits of the number. We can use d1 for the first digit, d2 for the second digit, and d3 for the third digit. Based on the given information, we can write the following equations:

d1 > d2 + 4 (the first digit is greater than the second by 4)

d3 > d1 + 2 (the third digit is greater than the first by 2)

We also know that the three digits combine to form a three-digit number. We can write this number as:

100d1 + 10d2 + d3

To solve for the digits, we can use the information we have to write expressions for d1, d2, and d3 in terms of a single variable, and then use that to find the digits. Let's start with the first equation:

d1 > d2 + 4

Subtracting 4 from both sides, we get:

d1 - 4 > d2

Now we can substitute this expression for d2 in the second equation:

d3 > d1 + 2

d3 > (d1 - 4) + 2

d3 > d1 - 2

So we have the following inequalities:

d1 > d2 + 4

d3 > d1 - 2

We can use these to write expressions for d1, d2, and d3 in terms of a single variable, say x:

d1 = x + 4

d2 = x

d3 = x + 2 + 4 = x + 6

Now we can substitute these expressions into the equation for the three-digit number:

100d1 + 10d2 + d3 = 100(x+4) + 10x + (x+6) = 111x + 406

So the three-digit number can be written as 111x + 406. To find the digits, we need to choose a value of x that satisfies the inequalities we derived. Let's start with the first inequality:

d1 > d2 + 4

x + 4 > x + 4

x > 0

So x must be greater than 0. Now let's check the second inequality:

d3 > d1 - 2

x + 6 > x + 2

6 > 2

This inequality is always true, so we don't need to worry about it. Therefore, any value of x greater than 0 will satisfy the given conditions. For example, if we choose x = 1, then the digits are:

d1 = 5

d2 = 1

d3 = 7

And the three-digit number is:

100d1 + 10d2 + d3 = 500 + 10 + 7 = 517

So the number is 517.

Step-by-step explanation:

The value of probability that they have pulse rates with mean less than 78 beats per min would be; 0.5948

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Given that If 16 female are randomly selected the Mean is 75 beats per min And, Standard deviation is, 12.5

Hence, We get;

z = (78 - 75) / 12.5

z = 3/12.5

z = 0.24

Hence, The probability is, 0.5948

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