The National Coffee Association reported that 61% of U.S. adults drink coffee daily. A random sample of 275 U.S. adults is selected. Round your answers to at least four decimal places as needed.

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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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.

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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Answer:

5 and 6

Step-by-step explanation:

cause

Answer:

8.01 ft/sec

Step-by-step explanation:

Distance = 26.2 miles

Time is taken to run the distance = 4.8hrs

Average speed = ??

Average speed = distance/time

= 26.2miles /4.8hr

= 5.46 miles/hr

Convert 5.46 miles/hr to ft/sec

1 mile = 5280 ft

We have 5.46*5280 = 28828.8 ft/hr

28828.8/3600 = 8.01 ft/sec

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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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If there are 220 pieces of 20 cents, then there are 380 pieces of 50 cents in the container.

Thabang conserves money by depositing coins in a money box. There are 600 coins in the money box, including 20- and 50-cent pieces.

We proceed as follows to determine how many 50 cent pieces are in the container if there are 220 pieces of 20 cent.

Assume that,

x = number of 20 cents

y = number of 50 cents

So, the total number of cents in the container is 600,so

x + y = 600

Making y the formula's subject, we therefore get that

y = 600 - x

Since x = 220

y = 600 - 220

y= 380

So, there are 380 fifty cents.

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The correct Question is

Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents. So calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents

Answer:

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

Let the number be n.

Set up an equation per the problem:

Distribute and solve for n:

The number is 10.

Answer:

18 gallons

Step-by-step explanation:

18 gallons because 1/3 equals 2/6 and 3/6 equals 1/2 so 3 gallons is 1/6. then just 6×3

Hope this helped

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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Answer:

37

Step-by-step explanation:

The pattern is

2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37

So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers

Answer:

5th term is 26.

Step-by-step explanation:

5-2 =3. 10 - 5 = 5. 17 - 10 = 7.

notice how the differences are 3, 5, 7?

there's a gap of 2 between each difference.

so, let's call our next term in the sequence a.

a - 17 = (7+2).

a - 17 =9.

a = 26.

so, 5th term is 26.

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 best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.

The best prediction possible for the number of times you will roll a six in a six-sided die depends on the probability of getting a six in each roll. The probability of getting a six in a single roll of a six-sided die is 1/6 or 16.67%.
Since the rolls are independent events, the probability of rolling a six in any one of the six rolls is still 1/6 or 16.67%. Therefore, the best prediction possible for the number of times you will roll a six is one.
However, it is important to note that probability is not a guarantee, and it is possible to roll a six more than once or not at all. But based on the laws of probability, one is the most likely outcome for the number of times you will roll a six in six rolls of a six-sided die.
In summary, the best prediction possible for the number of times you will roll a six when rolling a six-sided die six times is one.

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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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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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The surface area of the composite solid would be about 576. 05 square feet .

The composite shape is made up of two shapes which are a a cylinder and a pentagonal prism. To find the surface area, you need to find the surface area of these two shapes and then sum these areas.

Area of pentagonal prism :

= 5 a h + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) a ²

a = 4 ft

h = 7 ft

Area of the pentagonal prism is:

= 5 x 4 x 7 + 1 / 2 √ ( 5 ( 5 + 2 √ 5 ) ) 4 ²

= 195.05528 square feet

Area of cylinder:

= 2 π r h + 2 π r ²

= 2 π x 6 x 4 + 2 π x 6  ²

= 376.99112 square feet

The surface area is therefore :

= 195.05528 + 376.99112

= 576. 05 square feet

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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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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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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) +=

Answer:

scienific scienific

Step-by-step explanation:

Answer:m-5n

Step-by-step explanation:

The solution of measure of angle e is,

⇒ e = 58 degree

We have to given that,

Two lines are intersect each other.

Hence, By definition of linear pair angle, we get;

⇒ e + 122 = 180

Subtract 122 from both sides to isolate e.

This gives us,

⇒ e = 180 - 122

⇒ e = 58

Therefore, The solution of measure of angle e is,

⇒ e = 58 degree

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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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Answer: Range: 14 Interquartile:  5.5

Step-by-step explanation:

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

sec(theta) = 1/cos(theta)

I believe that is your option D