On average, Americans consume 13.9 pounds of ice cream per person over an entire year. Ben loves ice cream, but limits himself to one 3-ounce (oz) serving each week. Find the difference between the amount of ice cream that Ben consumes compared to the national average. (1 pound equals to 16 ounces and there are 52 weeks in a year.)

The  approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant

The area and perimeter of a circle can be calculated using the formula

πr = πd, where r is the radius and d is the diameter of the circle

Area = πr² and

the perimeter is 2πr

r= 8 inch, π = 3.14

Area = 3.14 * 8 * 8

Area = 200.96 square inches

Area = 201 inch²

the perimeter is = 2*3.14*8

The perimeter is = 50.24 square inches

Perimeter = 50 inch

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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as:

C = 2πr

Where r is radius and π is constant pi ( π = 3.14 )

Given that the radius of the circle is 8 inches.

Substituting this value into the formula, we get:

A = πr²

A =  3.14 × ( 8 in )²

A =  3.14 × 64 in²

A = 200.96 in²

Next, we calculate the circumference:

C = 2πr

C = 2 × 3.14 × 8 in

C = 50.24 in

Therefore, the value of the circumference is 50.24 in.

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The surface area of the composite figure is 2,283 m².

option A.

The surface area of the composite figure is calculated as follows;

The composite figure is composed of a cube and a cuboid and their total surface area is calculated as follows;

Surface area of the cuboid = 2 (35 m x 9 m  +  35 m x 16 m   +  16 m x 9 m)

Surface area of the cuboid = 2038 m²

Surface area of a cube = 6L²

There is a surface of the cube on the cuboid, which is include in the surface area of the cuboid, so we will subtract that one surface.

Surface area of the cube = 6L² - L² = 5L²

= 5 x (7 m)²

= 245 m²

Total surface area =  2038 m² + 245 m²

Total surface area = 2,283 m²

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Step-by-step explanation:

the answer is 3

the answer is 3

Answer:

3

Step-by-step explanation:

explanation

f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7

Thus, we have:

(g/f ) (x) = g(x) / f(x) =  [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1

The conclusion can be determined from the dot plot is

The median of the data set is 10.

1. The number of observations is 10:

There are total 15 observations.

2. The median of the data set is 10.

From the dot plot the data is

9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12

Thus, the median is 10.

3. Mean = Sum of observation / Total Number of observation

Mean = (9+9+9+9+9+10+10+10+10+10+10+11+11+11+12) /15

Mean= 150/15=10

Thus, the Mean is 10.

4. Range = 12 - 9

Range = 3.

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The trigonometric ratio in terms p are

cos 200 = -p

- sin 70 = -p.

To express each of the given trigonometric values in terms of p:

Since the cosine of 0° is equal to 1, we can say that cos 0° = p.

cos 200°: Using the identity

cos(180° + θ) = -cos(θ), we can rewrite

cos 200° = -cos(180° + 20°).

Since cos 20° = p, we can express cos 200° as -p.

sin(-70°): Using the identity

sin(-θ) = -sin(θ), we can rewrite

sin(-70°) as -sin(70°)

=- sin (90- 20)

=  - cos 20

= -p

sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.

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The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.

To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:

CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

Where:

p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.

n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.

Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).

Given:

Michigan: p1 = 78/100 = 0.78, n1 = 100

New York: p2 = 58/120 = 0.4833, n2 = 120

Plugging in the values:

CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))

CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)

CI = 0.2967 ± 1.96 * sqrt(0.01053)

CI ≈ 0.2967 ± 1.96 * 0.1026

CI ≈ 0.2967 ± 0.201

The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.

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Answer:

5 and 6

Step-by-step explanation:

cause

The coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).

To rotate the points of a triangle 90 degrees clockwise, we can use the following formula for a 2D rotation:

x' = x cos(θ) + y  sin(θ)

y' = -x  sin(θ) + y  cos(θ)

Let's apply this formula to each point of the triangle ABC:

For point A(-6, 3):

x' = -6  cos(90°) + 3  sin(90°) = -6 (0) + 3(1) = 3

y' = -(-6)  sin(90°) + 3  cos(90°) = 6 (1) + 3 (0) = 6

So, point A' is (3, 6).

For point B(-2, 3):

x' = -2 cos(90°) + 3 sin(90°) = -2 .0 + 3. 1 = 3

y' = -(-2) sin(90°) + 3 cos(90°) = 2 .1 + 3 .0 = 2

So, point B' is (3, 2).

For point C(-4, 7):

x' = -4 cos(90°) + 7 sin(90°) = -4 .0 + 7 . 1 = 7

y' = -(-4) sin(90°) + 7 cos(90°) = 4.1 + 7 .0 = 4

So, point C' is (7, 4).

Therefore, the coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).

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To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.

Cost of gear per person:

Shoes: $10

Helmet: $3

Gloves: $2.50

Harness: $5.00

Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50

Total cost of gear for 3 people: $20.50 x 3 = $61.50

Cost of trainer: $15.00

Total bill (including gear and trainer): $70.25

Remaining amount for zip lining:

=  $70.25 - $61.50 - $15.00

= $-6.25

Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.

However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.

Approximate number of hours:

Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours

Approximate amount each person paid:

Amount each person paid

= Total bill / 3

= $70.25 / 3

≈ $23.42

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Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his Budget is less than R7200, then it would not be enough.

We are not provided with any information in the question, so we cannot answer it as is. However, we can use the formula provided to calculate the total floor area to be tiled:

Area of a rectangle = length x width

Let's say the length is L and the width is W. Then, the total floor area to be tiled is:

Total floor area = L x W

We are not given the values of L and W, so we cannot calculate the exact total floor area. However, we can assume that Tshego has already calculated the total floor area to be 32 m².

To determine how many boxes of tiles Tshego will need, we need to know the size of each box of tiles and the total area that one box can cover. Let's assume that each box of tiles covers an area of 1 m².

If the total floor area to be tiled is 32 m², and an extra 10% of the number of tiles must be added for cutting and breakages, then the total area to be covered with tiles would be:

Total area to be covered = 32 m² x 1.1 = 35.2 m²

Therefore, Tshego would need 36 boxes of tiles to cover the entire floor area.

To determine if Tshego's budget is enough to finish the tiling project, we need to know the cost of each box of tiles and the total cost of the project. Let's assume that each box of tiles costs R200.

The total cost of the project would be:

Total cost = Number of boxes x Cost per box

Total cost = 36 x R200 = R7200

If Tshego's budget is more than R7200, then it would be enough to finish the tiling project. If his budget is less than R7200, then it would not be enough.

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The correct answers are:

The explanation for each response can be given as:

a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.

b. Two reasons why the data may differ are:

  1. Variability in the patient's overall health and response to the treatment.

  2. Differences in the time of diagnosis and initiation of treatment among the patients.

c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.

d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.

e. The sampling method used by the first researcher, randomly selecting [tex]40[/tex] states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).

f. The second researcher used a non-random sampling method by choosing [tex]40[/tex] patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.

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The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)

Given data ,

The first sequence is add 10, then divide by 2 starting from 2

The second sequence is multiply by 3, then subtract 2 starting from 2

On simplifying , we get

Let the first number be 2

So , ( 2 + 10 )/2 = 6

Now , ( 2 x 3 ) - 2 = 4

And , the first ordered pair is ( 6 , 4 )

Now , ( 6 + 10 ) / 2 = 8

And , ( 4 x 3 ) - 2 = 10

So , the second ordered pair is ( 8 , 10 )

Now , ( 8 + 10 ) / 2 = 9

And , ( 10 x 3 ) - 2 = 28

So , the third ordered pair is ( 9 , 28 )

Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)

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The  recursive formula of g(n)  g(1) = -50 and g(n) = g(n-1) - 15

g(n) = g(n-1) - 15

Start with the given formula: G(n) = -50 - 15n

To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).

To do this, we can subtract 15 from both sides of the equation:

G(n) - 15 = -50 - 15n - 15

Simplifying the equation, we get:

G(n) - 15 = -65 - 15n

Rearranging the equation, we get:

G(n) = -65 - 15n + 15

Now, we can substitute g(n-1) for -65 - 15n:

G(n) = g(n-1) - 15

Finally, we can find the value of g(1) by substituting n = 1 into the original equation:

G(1) = -50 - 15(1)

G(1) = -50 - 15

G(1) = -65

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Complete question is also attached below:/

G(n)=−50−15n  complete the recursive formula of g(n)

g(1)=

g(n)=g(n−1) +=

A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.

Let us assume

the price of 1 kg strawberry taffy  = $x

And the price of 1kg banana taffy = $y

Then according to given information

the expression for Jon be,

4x + y = 23  ....(i)

the expression for Charlotte be,

5x + 2y = 34 ...(ii)

Now use elimination method

2x(i) - (ii) we get,

3x = 12

 x = 4

Plug it into (i) we get

y = 7

Hence, costs are:

1 kg strawberry taffy  = $4

1kg banana taffy = $7

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Answer: Range: 14 Interquartile:  5.5

Step-by-step explanation:

sec(theta) = 1/cos(theta)

I believe that is your option D

The height of the pyramid is 12 units

To find the height of the pyramid, we need to use the formula for the volume of a pyramid,

V = (1/3) * B * h,

where V is the volume, B is the area of the base, and h is the height of the pyramid.

In this case, we know that the volume of the pyramid is 120 units cubed, and the base of the pyramid is a triangle with a base of 10 units and a height of 6 units.

Therefore, the area of the base is,

(1/2) * 10 * 6 = 30 square units.

Plugging these values into the formula for the volume of a pyramid, we get:

120 = (1/3) * 30 * h

Multiplying both sides by 3, we get:

360 = 30 * h

Dividing both sides by 30, we get:

h = 12

Therefore, the height of the pyramid is 12 units.

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The variable a can take infinite many values (including 0)

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

-12a < -2a

This expression can be expressed as

-2a > -12a

Divide both sides by -2a

So, we have

1 < 6

The above expression is true

This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a

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Answer:

scienific scienific

Step-by-step explanation:

1) Equation for the parabola y = - x² + 36.

2) A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function.

The points of intersection will be: (0,36) and (4, 20)

Table of values for a linear function and the parabola

x        linear function      parabola y = - x² + 36

0        36                                  (0)² + 36 = 36

1        32                                  - (1)² + 36 = 35

2        28                                  - (2)² + 36 = 32

3        24                                   -3² + 36 = 27

4        20                                   -4² + 36 = 20

It is a linear function because the rate of change is constant: for each increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4

Remember to include the two points of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)

Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow?

Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.

The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6

The range is all the values between 0 and 36: 0 ≤ y ≤ 36

The domain represents the horizontal distance between the extremes of the rainbow at the ground.

The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.

The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.

The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.

Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.

The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.

The solutions were already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.

The probability of drawing 2 red marbles is 0.081 or 8.1%.

There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.

The probability of pulling a red marble on the first draw is 15/47.

If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.

So, the probability of pulling a second red marble is 14/46.

To find the probability of both events happening, we multiply the probabilities:

P(both red) = P(first red) × P(second red | first red)

P(both red) = (15/47) × (14/46)

P(both red) = 0.081 (rounded to 3 decimal places)

Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.

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Answer:

---------------

Let the number be n.

Set up an equation per the problem:

Distribute and solve for n:

The number is 10.

Answer:m-5n

Step-by-step explanation:

Answer:

7.6

Step-by-step explanation:

when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.

The measure of length c using the law of cosines is 11.79 units

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

The triangle (see attachment)

The measure of length c is calculated using the following law of cosines

c² = a² + b² - 2ab * cos(C)

So, we have

c² = 10² + 3² - 2 * 10 * 3 * cos(120)

Evaluate

c² = 139

Take the square root of both sides

This gives

c = 11.79

Hence, the value of c is 11.79

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It is found that x = -1/3 is the point of inflection again for function f(x) = 3x⁴ + 2x³ - 5x - 12.

Since the second variation of the function f(x) = 3x⁴ + 2x³ - 5x - 12 and then solving for the values of x where the second derivative equals zero

f'(x) = 12x³ + 6x² - 5

f''(x) = 36x² + 12x

We should discover the solutions to the equation f"(x) = 0 for x to determine the locations of inflection:

36x² + 12x = 0

12x(3x + 1) = 0

If x = 0 or x = -1/3, the equation is true.

Here F"(x) > 0 demonstrates that the graph of f(x) is concave if x 1/3.

Concavity in the curve of f(x) at -1/3 x 0 shows that f"(x) 0.

When x is greater than zero, then f"(x) is greater than zero, showing that f(x graph) is concave up.

When x = 0, the graph's concavity does not change, making x = 0 not an inflection point =only x = -1/3

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The word problem that exemplifies a linear function is

- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.

Option A is the correct answer.

We have,

A linear function is a mathematical model that represents a relationship between two variables that is a straight line.

In this problem,

The cost of Angie's swimming classes is a linear function of the number of months.

The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.

Thus,

The word problem that exemplifies a linear function is

- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.

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