The line plot (shown in the attached image) shows the prices of sunglasses at a department store.

a. Find the mean, median, and mode.
b. Which measure best describes the data? Why?
c. Which measure might be misleading in describing the average price of sunglasses? Explain your reasoning.

Please help!! show all work and be sure to give final responses in complete sentence form in context of the problem, and explain your reasoning.

Using it's formula, the present value of the amount is: $288.

The present value formula is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

In which the parameters are:

Considering quarterly compounding, the parameters for this problem are as follows:

R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.

Hence the present value is:

[tex]PV = \frac{R}{(1 + r)^n}[/tex]

[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]

PV = $288

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Answer:

8.

Step-by-step explanation:

P/Q = 3.125 = 3 1/8

- looks like the denominator Q could be 8.

It could not be any of the other choices.

25/8 = 3.125.

Answer:

33600 m²

Step-by-step explanation:

The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.

area of trapezoid = (a + b)h/2

where a and b are the lengths of the bases, and h is the height.

We need to find the height, BC.

Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.

DE + EC = DC

EC = AB = 360 m

DC = 600 m

DE + 360 m = 600 m

DE = 240 m

Use right triangle ADE to find AE. Then BC = AE.

DE² + AE² = AD²

DE² + 240² = 250²

DE² = 62500 - 57600

DE² = 4900

DE = √4900

DE = 70

BC = 70 = h

area = (a + b)h/2

area = (600 m + 360 m)(70 m)/2

area = 33600 m²

Answer:

33,600 m^2.

Step-by-step explanation:

This is a trapezium, so

Area = (h/2)(a + b)

=  (h/2) ( 360 + 600)

= 960h / 2

= 480h,

We find the value of h using Pythagoras:

250^2 = h^2  + (600-360)^2

h^2 =  250^2 - 240^2 = 4900

h = 70.

So the Area = 70 * 480

= 33,600 m^2

Answer:

1.857 pounds

Step-by-step explanation:

If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs

The slope intercept equation can be represented as follows:

y = 9 / 7 x + 1

y = 11 / 4 x - 8

y = 11 / 8 x + 6

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore,

The slope intercept equation can be represented as follows:

9x - 7y = - 7

7y = 9x + 7

y = 9 / 7 x + 1

11x - 4y = 32

4y = 11x - 32

y = 11 / 4 x - 8

11x - 8y = -48

8y = 11x + 48

y = 11 / 8 x + 6

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Answer:

x = 2

Step-by-step explanation:

To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".

f(x) = 2x + 1

g(x) = -x + 7

f(x) = g(x)                                              <----- Given equation

2x + 1 = -x + 7                                      <----- Insert functions

3x + 1 = 7                                             <----- Add "x" to both sides

3x = 6                                                  <----- Subtract 1 from both sides

x = 2                                                    <----- Divide both sides by 3

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

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Answer:

502.4 ft²

Step-by-step explanation:

To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.

Area (White Circle)

radius = 1/2 diameter

radius = (1/2) x 36 ft

radius = 18 ft

Area = πr²

Area = π(18 ft)²

Area = π(324 ft²)

Area = 1017.36 ft²

Area (White Circle + Ring)

radius = 1/2 diameter + width of ring

radius = (1/2 x 36 ft) + 4 ft

radius = 22 ft

Area = πr²

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft²

Area (Ring)

Area (Ring) = Area (White Circle + Ring) - Area (White Circle)

Area (Ring) = 1519.76 ft² - 1017.36 ft²

Area (Ring) = 502.4 ft²

The exponential equation that models this situation is:

[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the parameters are:

A(0) = 18000, r = 0.15.

Hence the equation for the value of the car over the next 5 years is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 18000(1 - 0.15)^t[/tex]

[tex]V(t) = 18000(0.85)^t, 0 \leq t \leq 5[/tex].

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The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Answer: 480

Step-by-step explanation:

20(12)(2) = 480

The probability that it willtake less than 34 minutes to complete the test is 0.1056

Given mean of 44 minutes and standard deviation of 8 minutes.

We have to find the probability that it will take less than 34 minutes to complete the test.

The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.

We are using z test to find the probability.

Z=X-μ/σ

Where μ is sample mean and

σ= standard deviation

Z is z value

First we will find the p value from 34 to 44.

Z=34-44/8

=-10/8

=-1.25

P value for X<34=P(Z<-1.25)

=0.5-0.3944

=0.1056.

Hence the probability that it will take less than 34 minutes is 0.1056.

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The surface area of the composite solid is 579.84 square feet

The composite solid that completes the question is added as an attachment

From the attached figure, we have the following figures:

The surface area of a rectangular prism is

A = 2(lw + lh + wh)

Using the dimensions of the prism, we have:

A = 2(6 * 11 + 6 * 8 + 8 * 11)

This gives

A = 404

The surface area of a cylinder is

A = 2πr^2 + 2πrh

Using the dimensions of the cylinder, we have:

A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5

Evaluate

A = 226.08

The area of the circle between both shapes is

A = πr^2

This gives

A = 3.14 * 4^2

A = 50.24

The surface area of the composite solid is then calculated as:

Surface area = Area of rectangular prism + Area of cylinder - Area of circle

This gives

Surface area = 404 + 226.08 - 50.24

Evaluate

Surface area = 579.84

Hence, the surface area of the composite solid is 579.84 square feet

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(a) The Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.

(b) The mean of the sample means from part (a) is 8/3.

(c) Yes, The mean of the sample distribution is always equal to the mean of the Population.

According to the questions,

Game number                          1      2        3      Total

Number of interceptions         1        2       5          8

a)   Element 1            Element 2

    1                              1

    2                            2

    5                            5

    1                             2

    1                            5

  2                             5

  2                              1

  5                               1

   5                              2

Sample mean of each sample is 1, 2, 5, 1.5, 3, 3.5, 3, 1.5,3,3.5.

b) The mean of the sample means from part a.

     (1+2+5+1.5+3+3.5+1.5+3+3.5)/9 = 8/3

The mean of the sample means from part (a) is 8/3

c) Mean of the populations = (1+2+5)/3 = 8/3

   The mean of the sample distribution from part b. is 8/3

Yes, The mean of the sample distribution is always equal to the mean of the Population

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Answer:

9/5

Step-by-step explanation:

First we have to find the constant k

m = k/(p-1)^2  (p-1)^ goes on the bottom of the fraction because of the inverse.

5 = k/(4-1)^2

5 = k/3^2

5 = k/9  Multiply both side by 9

45 = k  We know can use this constant to solve our problem

m = 45/(6-1)^2

m = 45/5^

m = 45/24

m = 9/5

the population of province is growing at the rate of 2.91%

the formula of the rate of growth of a population =

[(future population- initial population/initial population)*100]/time

population in 2016 = 4.2 milllion = 4200000

Population predicted in 20 years = 6.65 million = 6650000

so, initial population = 4200000

future population = 6650000

rate of growth = {(6650000- 4200000/4200000)*100]/20

                       = 58.33/20

                     = 2.91%

the population is growing at the rate of 2.91%

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The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

The given parameters are:

Initial = 5200

Rate = 5%

Because the population by 5% every year, then the situation is a geometric sequence.

The common ratio is then calculated as:

Ratio = 1 + Rate

This gives

Ratio = 1 + 5%

Evaluate

Ratio = 1.05

Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

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Answer:

You subtract 249 minus 5

The missing length in the right triangle as given in the task content is; 156.

It follows from the complete question that the triangle given is a right triangle and the missing length (longest side) can be evaluated by means of the Pythagoras theorem as follows;

x² = 144² + 60²

x² = 20736 + 3600

x² = 24,336

x = √24336

x = 156.

Remarks: The complete question involves a right triangle and the missing length is the longest side.

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3 roada andy to billy

5 road billy to willies

3×5 =15 it's the answer 15

The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.

Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.

We know that temperature is the intensity of the heat present around us.

We know that,

Maximum temperature=72 degrees,

Minimum temperature=62 degrees, which occurs at t=3 hours

Now we can write the equation as:

D(t)=A cos(ct)+B

Where A, c, B are constants.

We have a minimum at t=3 a minimum means cos(ct)=-1

then we have that D(3)=A cos(c*3)+B

=A*(-1)+b

=35°

Here we solve that ,

Cos(c*3)=-1

this means that

c*3=-1

c*3=π

c=π/3

We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1

D(t)=0=A(t)+B=72

With this we can find that values of A and b

-A+B=62

A+B=72

B=67

A=5

Equation will be D(t)=5 cos{(π/3)t}+67°.

Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..

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[tex]\large\bold\blue{ANSWER:-}[/tex]

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.

Answer: 23/26

Step-by-step explanation:

Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.

If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.

With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.

The total probability is 2,300/2,600, which simplifies to 23/26.

The given equation is (1/2)a + (2/3) b = 50

and b = 30

Substituting the given value of b is above the equation we get

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]

Therefore, a = 60 and b = 30 is a solution of the given equation.

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The rate at which she reads is 26 pages per hour

The given parameters are

Pages = 2 and 3/5

Time = 6 minutes

Convert the time from minutes to hour

Time = 6/60 hour

This gives

Time = 0.1 hour

The rate at which she reads is calculated as:

Rate = Page/Time

This gives

Rate = (2 and 3/5)/0.1 hour

Rewrite as:

Rate = 2.6 pages/0.1 hour

Divide

Rate = 26 pages per hour

Hence, the rate at which she reads is 26 pages per hour

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The rate at which Sean drank the slushy is 5 milliliters  per second.

The time it would take to drink all the slushy is 55 seconds.

In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.

Speed = slushy drank in 13 seconds / time

(275 - 210) / 13

65 / 13 = 5 milliliters  per second

Time it would take to drink all the slushy =total milliliters of the slushy / speed

275 / 5 = 55 seconds.

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The correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13

From the question, we are to determine the correct order of the numbers

The given numbers are

5/6, 12/13, and 0.8

Convert the fractions to decimals

5/6 = 0.8333

12/13 = 0.923

Thus, the numbers are

0.8333, 0.923, and 0.8

Order the numbers from the smallest to the largest

0.8 < 0.8333 < 0.923

≡ 0.8 < 5/6 < 12/13

Hence, the correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13

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The systems of linear equations have been matched with their respective solutions as shown in the image attached below.

A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.

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