According to a poll conducted by the gallup corporation in march 2011, the metropolitan areas with the highest and lowest proportions of obese adults were evansville, in-ky, and boulder, co, respectively. in evansville, for every 311 people who were not obese, there were 189 who were. in boulder, for every 16 obese people, there were 109 who were not obese. at that time, the estimated populations were 358,676 for evansville and 303,482 for boulder. how many more obese people were there in evansville than in boulder

The ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

The side length AB is given as:

AB = 8x

The area of the white square is calculated as

White = (AB)²

This gives

White = (8x)²

Evaluate

White = 64x²

The side length AB represents the diameter of the black circle.

So, the radius is:

r =AB/2

This gives

r = 8x/2 = 4x

The area is then calculated as:

Circle = πr²

This gives

Circle = π(4x)²

Evaluate

Circle = 16πx²

Next, calculate AW and AZ using:

AZ = AW = AB/2

Evaluate

AZ = AW = 8x/2 = 4x

Calculate WZ using the following Pythagoras theorem

WZ² = AW² + AZ²

This gives

WZ² = (4x)² + (4x)²

Evaluate

WZ² = 2(4x)²

Take the square root of both sides

WZ = 4x√2

The area of the gray square is:

Gray = WZ²

This gives

Gray = 2(4x)²

Evaluate

Gray = 32x²

At this point, the areas are:

The ratio is then represented as:

Ratio = Circle : White : Gray

This gives

Ratio = 16πx² : 64x² : 32x²

Divide through by 16x²

Ratio = π : 4 : 2

Hence, the ratio of the area of the black circle to the area of the white square to the area of the gray square is π : 4 : 2

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Answer:

3rd Option    -     3(x-4) = 6x

Step-by-step explanation:

To remove the fractions we escalate them up to the other side. So to remove the x under 3 we do the following :

[tex]\frac{3}{x} = \frac{6}{x-4}[/tex]   ----->  [tex]{3}= \frac{6x}{x-4}[/tex] (As you can see the x now goes to the numerator of the right side)

Now to remove x-4 under 6x we do the following :

[tex]{3}= \frac{6x}{x-4}[/tex]   ------> [tex]3(x-4)= {6x[/tex]

Therefore giving our answer as the 3rd option.

Hope this helped and have a good day

The recursive formula will be equal to f(n + 1) = –2 f(n).

The complete question is given below:-

Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?

3, –6, 12, –24, 48, …

f (n + 1) = –3 f(n )

f (n + 1) = 3 f(n )

f (n + 1) = –2 f(n )

f (n + 1) = 2 f(n)

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The recursive formula for this sequence is calculated as we will put the different values of n to find the values of the function in the series.

n  =  1

f(n) = 3

n = 2

f(2) = -2 (3) = -6

n = 3

f(3) = -2 (-6) = 12 and so on

Therefore the recursive formula will be equal to f(n + 1) = –2 f(n).

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Answer:

3.5 gallons of punch

Step-by-step explanation:

There are 4 quarts in 1 gallon.

Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.

Elijah made 3.5 gallons of punch.

Answer x= 30

M angle A = 85

M angle C = 45

Reason - see picture for the math

Answer:

see attached

Step-by-step explanation:

Morning:

12, 19, 19, 21, 23, 25, 27, 31, 36, 39

Min value: 12

Lower quartile (Q1): 19

Median (Q2): 24

Upper Quartile (Q3): 31

Max value: 39

Afternoon:

8, 8, 11, 15, 16, 27, 34, 39, 43, 51

Min value: 8

Lower quartile (Q1): 11

Median (Q2): 21.5

Upper Quartile (Q3): 39

Max value: 51

Answer:

7.  AM IQR: 12   PM: IQR: 28  8. see below in explanation

Step-by-step explanation:

7. 31-19=12

    39-11= 28

You subtract Q1 from Q3 to get the IQR.

8. I believe the morning group of dogs would be easier to walk as one group because the group has a closer range of weights (12-39) compared to the afternoon group of (8-51). Walking a large group of dogs with similar weights would be easier than walking a group of very small and very large dogs at the same time because their pace of walking would be so different.

The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.

We need the answer in cubic centimeters. So let's convert 350 cubic inches to cubic centimeters. We will do it unit conversion way (the long way).

We will write cubic inches as three inches side-by-side

350 in^3

This way, we can multiply this by the ratio of centimeters to inches [2.54 cm = 1 inch], so that the units cancel and we have cubic centimeters (what we desire).

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in

So, we can cancel the three inches top and bottom thus we have the answer in centimeters cubed. And the value is

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in.

350 in^3*3.54cm/1in*3.54cm/1in*3.54cm/1in=5735.47.

So 350 cubic inches is approximately 5735.5 cubic centimeters (rounded to 1 decimal place).

This is larger than a 5500 cubic centimeters engine.

5735.5-5500=235.5cubic centimeters.

The bigger engine is about 235.5 cubic centimeters larger than the smaller engine.

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A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.

It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.

Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

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Cindy gets (12-c) amount while others get 12 cookies.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

From the question, we are informed that Grandma baked 96 cookies

And there are 8 grandchildren available

To calculate the number of cookies each of them gets we have,

= 96 /8

= 12 cookies

This means each gets 12 cookies

But Cindy received fewer cookies with less C amount.

Therefore Cindy gets (12-c) amount while others get 12 cookies.

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Answer:

D. 3

Step-by-step explanation:

Answer:

it's 9

Step-by-step explanation:

type it in a calculater

Answer:3,5,7,9

Step-by-step explanation:I’m pretty sure all the inputs are the domains

Choices B, C, and D are correct. Nice work.

Further explanation:

Answer:

Step-by-step explanation:

Area of the sector :

[tex]Area (sector) = \pi r^{2} \times \frac{\theta}{360^{o}}[/tex]

Finding the area given r = 30 ft. and θ = 60° :

⇒ Area = π × (30)² × 60/360

⇒ Area = π × 900/6

⇒ Area = 150π ft²

===========================================================

Length of the arc :

[tex]Length (arc) =2 \pi r} \times \frac{\theta}{360^{o}}[/tex]

Finding the arc length given r = 30 ft. and θ = 60° :

⇒ Arc Length = 2 × π × 30 × 60/360

⇒ Arc Length = 60/6 × π

⇒ Arc Length = 10π ft.

Answer:

1. 150π ft²

2. 10π ft²

Step-by-step explanation:

Hello there!

Here is how we solve the given problem:

L = ∆°/360° ×2πr

From our problem,

∆ = 60°, r = 30ft

Lets substitute the values

1. A = (∆°/360°) × πr²

= 60°/360° × π × 30²

= 150π ft²

2. L = ∆°/360° × 2πr

= (60/360) × 2 × 30 × π

= 10π ft²

NOTE:

Use the formulas given below to be on a save side;

I hope this helps.

Have a nice studies. :)

well, we know the discount is 4975 - 3781 = 1194.

if we take 4975 to be the 100%, what is 1194 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 4975 & 100\\ 1194& x \end{array} \implies \cfrac{4975}{1194}~~=~~\cfrac{100}{x}\implies \cfrac{26}{6}=\cfrac{100}{x} \\\\\\ 26x = 600\implies x=\cfrac{600}{26}\implies x\approx 23.08[/tex]

Answer:

0.76

Step-by-step explanation:

4975 × 0.76 = 3781

the discount percent given is .76%

The expression that represents the width of the patio is (x+3) feet

From the question, we are to determine the width of the patio

The area of the patio = Length of the patio × Width of the patio

From the given information,

Length of the patio = (x+11) feet

Area of the patio = x^2+14x+33 = x²+14x+33

Putting the parameters into the formula,

x²+14x+33 = (x+11)  × Width of the patio

∴ Width of the patio = (x²+14x+33) / (x+11)

First, we will factor x²+14x+33

x²+14x+33

x²+11x+3x+33

x(x+11) +3(x+11)

(x+3)(x+11)

Thus,

Width of the patio = [(x+3)(x+11)] / (x+11)

∴ Width of the patio = (x+3) feet

Hence, the expression that represents the width of the patio is (x+3) feet

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Its 48

33+15

Step-by-step explanation:11+11+11+15= Perimeter

33+15 = Perimeter

48 = Perimeter

The length of the given golden rectangle is; 1.618 units

We are told that, for the golden rectangle;

Length = x units,

Width = (x - 1) units,

Area = 1 unit².

The area of this rectangle will have the formula;

A = x(x - 1)

Thus;

x(x - 1) = 1

Expanding gives;

x² - x - 1 = 0

Using online quadratic equation calculator, we have;

x = 1.618 or -0.618.

Length has to be positive and so we choose x = 1.618

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Answer:

1,290.6 in3                                                                                                                                                  

nut.

Answer:

3 I think.

Step-by-step explanation:

5 would be broken up to 2 groups of 2 and 1 group of 1.

In 20 different ways 5 dessert courses can be arranged taken 2 at a time.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, There are 5 dessert courses in a restaurant and they will be presented two at a time in an order.

Here we have to use permutation as order matters.

Now, the permutation of 5 different things taken 2 at a time is,

= [tex]^5P_2[/tex].

= 5!/(5 - 2)!.

= 5!/3!.

= 5 × 4.

= 20 different ways.

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Answer: y = -8

Step-by-step explanation:

Lines that have a slope of Zero means that the line is horizontal and y is always the same. So your equation is y = -8

Answer:

y = - 8

Step-by-step explanation:

A line with a slope of 0 is a horizontal line parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (0, - 8 ) with y- coordinate - 8 , then

y = - 8 ← equation of line

The English phrase can be written as the fraction:

   [tex]\frac{m}{n + p}[/tex]

Remember that the quotient between two numbers gives a fraction.

Now, we have the sentence:

"the quotient of m and the sum of n and p."

Then we know that the numerator is m, and the denominator is (n + p) (the sum of n and p).

So the expression will just be the fraction:

[tex]\frac{m}{n + p}[/tex]

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Answer:

2 solutions   x = 3 y = -2.

Step-by-step explanation:

x + 2y = –1

2x + 3y = 0

Multiply first equation by -2:

-2x - 4y = 2      Adding this to second equation:

       - y = 2

y = -2.

Plug this into first equation:

x - 4 = -1

x = 3.

Answer:

This system of equations has one real solution, (2, 8).

Step-by-step explanation:

Given:

y = x² + 4

y = 4x

1. Substitute the given value of y into y = x² + 4:

⇒ 4x = x² + 4

2. Solve for x (by factoring):

⇒ 4x = x² + 4

⇒ 0 = x² - 4x + 4

⇒ 0 = (x - 2)² [perfect square rule: a² -2ab + b² = (a - b)²]

⇒ 0 = (x - 2)² [take the square root of both sides]

⇒ [tex]\sqrt{0} = \sqrt{(x - 2)^2}[/tex]

⇒ 0 = x - 2 [add 2 to both sides]

⇒ 0 + 2 = x - 2 + 2

⇒ 2 = x

3. Find the value of y by substituting the given value of x into y = 4x:

⇒ y = 4(2)

⇒ y = 8

4. Check your work:

⇒ y = x² + 4          and          ⇒ y = 4x

⇒ 8 = 2² + 4         and          ⇒ 8 = 4(2)

⇒ 8 = 4 + 4          and           ⇒ 8 = 8 ✔

⇒ 8 = 8 ✔

Solution: (x, y) ⇒ (2, 8)

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The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Using the sine rule, the measurement of the angle of opposite the side measuring 11 inches can be done. Therefore, the measure can be written as,

8/ Sin(30°) = 11/ Sin(θ)

Sin(θ) = [11 × Sin(30°)]/8

Sin(θ) = 0.6875

θ = Sin⁻¹ (0.6875)

θ = 43.4325° ≈ 43°

Hence, The angle opposite the side measuring 11 inches has one solution of approximately 43°. Thus, the correct option is B.

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The equation of the line with Slope = −6 and passing through (-5,−9) is y +9 = -6(x+5)

The equation of a line in pint slope form is expressed as:

y - y1 = m(x-x1)

where

m is the slope = -6

(x1, y1)  is the point = (-5, -9 )

Substitute into the formula

y - (-9) = -6(x -(-5))

y +9 = -6(x+5)

Hence the equation of the line with Slope = −6 and passing through (-5,−9) is y +9 = -6(x+5)

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Answer:

height = 7

Step-by-step explanation:

[tex]2\cdot\frac{42}{8.7 + 3.3} = 7[/tex]