Consider a circle whose size can vary. The circumference of the circle is always 2π times as large as its radius. Let r represent the radius of the circle (in feet) and let C represent the circumference of the circle (in feet).

a. Write a formula that expresses C in terms of r.
b. Use your formula from part (a) to determine the circumference of a circle whose radius is 6 feet feet
c. Write a formula that expresses r in terms of C.
d. Use your formula from part (c) to determine the radius of a circle whose circumference is 37

Answer:there are 42 students in the club.

Step-by-step explanation:

Let s represent the number of students in the club.

Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum. This means that

8(s - 5) = 296

8s - 40 = 296

8s = 296 + 40 = 336

s = 336/8

s = 42

Answer:

5/3 pounds

Step-by-step explanation:

Five pounds of candy that is 20% chocolate is combined with a candy that is 40% chocolate

Let x be the pounds of candy that is added with 40% of chocolate

5 pounds that is 20%. 20% = 0.2

x pounds that is 40%. 40% = 0.4

mixture is x+5 pounds that is 25%. 25%= 0.25

[tex]0.2(5)+0.4x=0.25(x+5)[/tex]

[tex]1+0.4x=0.25x+1.25[/tex]

Subtract .25x from both sides

[tex]1+0.15x=+1.25[/tex]

Subtract 1 from both sides

[tex]0.15x=0.25[/tex]

divide both sides byu 0.15

x=5/3 pounds

Question: John drove to a distant city in 5 hours.

When he returned, there was less traffic and the trip took only 3 hours.

If John averaged 26 mph faster on the return trip, how fast did he drive each way

Answer:

For the first trip he drove at a speed of 39 mph

For the second trip he drove at a speed of 65 mph

Step-by-step explanation:

Let the distance for both journey be Z because they are equal.

Let the speed for the first journey be X

Let the speed of the second journey be Y

Formula for speed = distance ÷ time

For the first journey the speed X = Z ÷ 5

For the second journey the speed Y = Z ÷ 3

Since John averaged 26 mph faster in the second trip than the first trip due to traffic, it means that the difference in speed between the first & second trip is 26 mph

Difference in speed = (Z÷3) - (Z÷5) = 26

subtracting both results to  (5Z-3Z) ÷ 15 = 26

Upon cross multiplication

2Z = 390

Z = 390÷2 = 195 miles

Therefore speed for first journey = 195 ÷ 5 = 39 mph

Speed for second journey = 195 ÷ 3 = 65 mph

To verify, 65 - 39 = 26 mph

Answer:

D

Step-by-step explanation:

y=a(1-r)^n

a is the initial cost of the vehicle

r is the percentage decrease in decimal

n is the number of years.

so y as the final cost is computed as:

8500(1-0.047)^6

we get $6367.61

Answer:

9.17% of racers did not complete the marathon.

Step-by-step explanation:

Consider the provided information.

Out of 229 racers who started the Eugene marathon.

208 completed the race, 17 gave up 4 disqualified .

Then total racers who could not complete the marathon  is

229-208=21

Now calculate the percentage:

[tex]Percentage=\frac{21}{229}\times 100\\\\Percentage=\frac{2100}{229}\\\\Percentage\approx9.17[/tex]

Hence, 9.17% of racers did not complete the marathon.

The discount amount of exercise machine is $ 102

The sales price of machine is $ 748

Solution:

Given that,

Original price of machine is $ 850

Discount rate = 12 %

To find: discount amount and sales price of machine

Given that discount rate is 12 % , which means 12 % of original price of machine

Discount amount = 12 % of original price of machine

Discount amount = 12 % of 850

[tex]Discount\ Amount = 12 \% \times 850\\\\Discount\ Amount = \frac{12}{100} \times 850\\\\Discount\ Amount = 0.12 \times 850 = 102[/tex]

Thus the discount amount is $ 102

Sales price = Original price - Discount amount

[tex]Sales\ Price = 850 - 102\\\\Sales\ Price = 748[/tex]

Thus the sales price of machine is $ 748

t = 9 + s is the expression for number of pages in terry's essay

Solution:

Given that, Terry's essay has 9 more pages than stacey's essay

Let "s" be the number of pages in Stacey essay

Let "t" be the number of pages in terry essay

To find: Expression for the number of pages in terry's essay

From given statement,

Terry's essay has 9 more pages than stacey's essay

Which means, number of pages in terry essay is 9 more than number of pages in Stacey essay

Therefore,

Number of pages in terry essay = 9 + number of pages in Stacey essay

[tex]t = 9 + s[/tex]

Thus the expression for number of pages in terry's essay is found

Answer: the correct option is D

Step-by-step explanation:

Note: the chapter summary can be found in chapter 22 of the Pearson Education,Inc. (PDF format).

In the chapter, a single slit aperture diffraction and a circle aperture diffraction was discussed.

A circle aperture diffraction occurs when light pass through a tiny hole or aperture to produce a circular disc image. This disc is called Airy's disc.

To calculate the aperture diameter,d we can use the formula below;

d= m× λ/ sin θ. ------------------------------------------------------------------------------(1).

The single slit aperture diffraction is when light pass through a single slit to produce. The wavelength, λ is greater than the width of the aperture.

Answer:without the discount, it would have cost her $497

Step-by-step explanation:

Let x represent the amount that the gravel would have cost her without the discount.

Her brother works for the gravel company and got her a 28% discount. The value of the discount would be

28/100 × x = 0.28 × x = 0.28x

It mans that the amount that she paid for the gravel is

x - 0.28x = 0.72x

If Jamie paid $357.83 for the gravel (without tax), it means that

0.72x = 357.83

x = 357.83/0.72

x = 496.99

Approximately $497

Answer:$78

Step-by-step explanation:

The two events,i.e request for full fare and the request for discounted fare ar mutually exclusive ,i.e if one happens the other cannot and vice versa .

The representation via set diagram will show a disjointed subset while P(AnB)^° is 1- (P(A)+P(B))=0.1.

Where A is the probability of full fare request while B is the probability of discounted request.

Probability (AUB)=P(A)+ P(B)=0.5×100+0.4×70=78.

Answer:

When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.

Step-by-step explanation:

Consider the provided information.

It is given that the value of variable x increase, and value of variable y also increase.

A positive relationship is when the values increase together or we can say that the value both variable tends to move in same direction. If the value of x  increase then the value of y is also increase.

A Negative relationship is when one value decreases as the other increases.  Or we can say that the value of x increase the value of y decrease.

Hence, the provided relationship is positive as both values moves in same direction.

When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.

Answer:

Square pyramid cup is better deal then Cone cup.

Step-by-step explanation:

Diagram is missing in the question we have attached diagram for your reference.

Given:

height of square pyramid = 20 cm

height of cone = 20 cm

Base of square pyramid = 12 cm

diameter of cone = 12 cm

radius of cone is half of diameter.

radius of cone = [tex]\frac{diameter}{2}=\frac{12}{2} = 6\ cm[/tex]

We need to find the which cup is the better deal.

Solution:

We will first find the volume of both cups and then we can say the the one which has greater volume is the better deal in buying.

Volume of square pyramid is calculated by one third times square of the base times height.

framing in equation form we get;

Volume of square pyramid  = [tex]\frac{1}{3}\times 12^2\times20= 960\ cm^3[/tex]

Now we know that;

Volume of cone is calculated by one third times square of the radius times height times π.

framing in equation form we get;

Volume of cone = [tex]\frac{1}{3}\pi r^2h= \frac{1}{3}\pi\times 6^2\times 20 \approx 754cm^3[/tex]

Now we can see that;

Volume of square pyramid cup which [tex]960\ cm^3[/tex] is greater than Volume of cone cup [tex]754\ cm^3[/tex]

Hence Amount of popcorn will be more in square pyramid cup then in cone cup.

Hence Square pyramid cup is better deal then Cone cup.

Answer:

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one student ticket.

On the first day of ticket sales the school sold 24 adult tickets and 3 student tickets for a total of $223.00. This means that

24x + 3y = 223 - - - - - - - - - - - -1

The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. This means that

7x + 6y = 152 - - - - - - - - - - - - - -2

Multiplying equation 1 by 6 and equation 2 by 3, it becomes

144x + 18y = 1338

21x + 18y = 456

Subtracting, it becomes

123x = 882

x = 882/123

x = 7.17

Substituting x = 7.17 into equation 2, it becomes

7 × 7.17 + 6y = 152

50.19 + 6y = 152

6y = 152 - 50.19 = 101.81

y = 101.81/6 = 16.97

Answer:

a) 0.54

Step-by-step explanation:

The correlation coefficient can be found by taking square root of R-squared value and the sign of correlation coefficient can be assessed by considering the sign of slope value. So,

r²=28.8%=28.8/100=0.288

r=[tex]\sqrt{r^{2} }[/tex]=[tex]\sqrt{0.288}[/tex]=0.5367

By rounding to two decimal places the correlation coefficient

r=0.54

We can see that slope=0.4845 has positive sign so, the correlation coefficient contains the positive sign.

Hence the correlation coefficient r=0.54.

The answer is x equal -11

Answer: x = -11

Step-by-step explanation: First distribute or multiply through the parentheses on the left side of the equation.

When we do this, we get 3x + 15 = x - 7.

Then subtract x to get 2x + 15 = -7.

Then subtract 15 to get 2x = -22.

Then divide both sides of the equation by 2 and we find that x = -11.

Answer:

Step-by-step explanation:

A nickel is worth 5 cents. Converting to dollars, it becomes

5/100 = $0.05

A dime is worth 10 cents. Converting to dollars, it becomes

10/100 = $0.1

Let x represent the number if nickels.

Let y represent the number of dimes.

He has no more than 19 coins. This means that

x + y ≤ 19

He has no less than $1.30 combined. This means that

0.05x + 0.1y ≥ 1.3

If Nolan has 5 nickels, then, substituting x = 5 into x + y ≤ 19, it becomes

5 + y ≤ 19

y ≤ 19 - 5

y ≤ 14

substituting x = 5 into 0.05x + 0.1y ≥ 1.3, it becomes

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 1.05/0.1

y ≥ 10.5

Therefore, all possible values for the number of dimes that he could have would be

10.5 ≤ y ≤ 14

Answer:

The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.

Step-by-step explanation:

let S be the sample space for the inspection of the light bulbs.

Therefore, n(s) = 800

let ' A ' be the event of no defects bulbs.

Therefore, n(A) = 796

Now the Experiment probability for a light bulb chosen has no defects will be given by,

[tex]P(A)=\dfrac{n(A)}{n(S)}[/tex]

Substituting the values we get

[tex]P(A)=\dfrac{796}{800}=0.995[/tex]

The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.

Answer:

95%

Step-by-step explanation:

We are asked to find the percentage of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.

We will use Empirical rule of normal distribution to answer our given problem.

Empirical rule of normal distribution states that 68% of data falls within the first standard deviation from the mean. 95% of data fall within two standard deviations. 99.7% of data fall within three standard deviations.

Therefore, 95% of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.

David should buy Car A because it covers more miles in one gallon than Car B

Step-by-step explanation:

Given

Distance traveled by Car A = [tex]d_A = 702\ miles[/tex]

Gallons used by Car A = [tex]g_A = 12[/tex]

Distance traveled by Car B = [tex]d_B = 873\ miles[/tex]

Gallons used by Car B = [tex]g_B = 15[/tex]

In order to find the distance traveled on one gallon, we will divide the total distance by number of gallons

So,

Distance traveled by Car A in one gallon = [tex]\frac{702}{12} =58.5\ miles\ per\ gallon[/tex]

Distance traveled by Car B in one gallon = [tex]\frac{873}{15} = 58.2\ miles\ per\ gallon[/tex]

We can see that Car A travels more distance in one gallon that is 58.5 miles per gallon

So,

David should buy Car A because it covers more miles in one gallon than Car B

Keywords: Fractions, Unit rate

Learn more about unit rate at:

#LearnwithBrainly

Car A gets 58.5 miles per gallon, Car B gets 58.2 miles per gallon. David should buy Car A.

Car A: Travels 702 miles on 12 gallons = 702 miles/12 gallons = 58.5 miles per gallon

Car B: Travels 873 miles on 15 gallons = 873 miles/15 gallons = 58.2 miles per gallon

David should buy Car A as it has a slightly higher fuel efficiency of 58.5 miles per gallon compared to 58.2 miles per gallon for Car B.

Answer: the cost of riding the taxi for 8 miles is $9

Step-by-step explanation:

The taxi company charges a flat fee of 3.00 for using the taxi and 0.75 per mile. This means that the total cost of using the taxi and travelling x miles would be

3 + 0.75x

This is the equation representing the situation.

To find the cost of riding the taxi for 8 miles, we would substitute x = 8 in our equation. It becomes

Therefore, the total cost of riding the taxi for 8 miles would be

3 + 0.75 × 8

= 3 + 6 = $9

Answer:

100/240/260 will be the combination.

Step-by-step explanation:

In a right angle triangle JKL,

∠JKL = 90° and side JL is the hypotenuse of the triangle.

By Pythagoras theorem,

JK² + KL² = JL²

Since JL = 260

Therefore, (JK)² + (KL)²= (260)² = 67600

In the given options, square of two numbers total becomes 67600.

And the possible numbers will be 100 and 240.

(100)² + (240)² = 10000 + 57600 = 67600

Since side JK > side KL

Therefore, measure of JK = 240 cm, KL = 100 cm and JL = 240 cm could be the combination among all values.

Answer:

34.8

Step-by-step explanation:

1. Convert percent to decimal

40.00/100=.4

2.Multiply decimal by subtotal

87*.4=34.8

Peter will save $34.80 on the coat.

Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is often denoted by the symbol "%".

If the coat is on sale for 40% off, Peter will only need to pay 60% of the original price.

60% of $87 can be calculated as follows:

= 60/100 x $87

= $52.20

Therefore, the amount that Peter will save on the coat is:

= $87 - $52.20

= $34.80

So, Peter will save $34.80 on the coat.

Learn more about Percentage here:

https://brainly.com/question/29306119

#SPJ2

Answer:

C 5/7

Step-by-step explanation:

you have to split the 5 oranges between the 7 brothers, so you would do 5/7

5 split between 7 is the same as 5/7

Answer:5/7

Step-by-step explanation:

If you take each orange and cut them into 7 pieces then you could pass out one piece of each 1/7 of the oranges to each brother. You would do this 5 times until each brother had 5/7 and all the oranges would be passed out to the brothers.

Answer:

The answer to your question is a) y = x - 1  b) the point is not on the line

Step-by-step explanation:

Data

A ( -1, -2)

B (4, 3)

C ( 3, 1)

Process

1.- Find the slope of the line (m)

Formula

 m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Substitution

m = [tex]\frac{3 + 2}{4 + 1} = \frac{5}{5} = 1[/tex]

2.- Find the equation of the line

Formula

    y - y1 = m(x - x1)

Substitution

    y + 2 = 1(x + 1)

Solve for y

   y = x + 1 - 2

   y = x - 1

- Prove that the point (3, 1) is on the line

  1 = 3 - 1

  1 = 2

The point is not on the line because  1 ≠ 2

Answer:

For this case we don't have any problems for the conditions 1) and 3), but we have a problem with condition 2) since is not satisfied.

We just need to find a counterexample to show that the statement is False. If we find two elements in the subset provided S, and we show that the sum is not in S, then we have the counter example.

Let's say that we have two elements [tex] a^m +1 , -a^m +1 \in S[/tex] so both elements are in S, and if we apply the condition for the addition closed we got:

[tex] (a^m +1) +(-a^m +1) = a^m -a^m +1+1 = 2[/tex]

And by definition of S, 2 is not in S so then since we can't satisfy the closed addition property then S can't be a subsapce

Step-by-step explanation:

For this case the answer would be no.

It can't be a subspace because we not satisfy the condition of closed under addition.

We need to remember that a subset U of V is a subspace of V if and only if U satisfies the following 3 conditions

1) Additive identity [tex] 0 \in U[/tex]

2) Closed under addition [tex] u,v \in U \Rightarrow u+x \in U[/tex]

3) Cloases under scalar multiplication [tex] a \in F, u \in U \Rightarrow au \in U[/tex]

Proof

For this case we don't have any problems for the conditions 1) and 3), but we have a problem with condition 2) since is not satisfied.

We just need to find a counterexample to show that the statement is False. If we find two elements in the subset provided S, and we show that the sum is not in S, then we have the counter example.

Let's say that we have two elements [tex] a^m +1 , -a^m +1 \in S[/tex] so both elements are in S, and if we apply the condition for the addition closed we got:

[tex] (a^m +1) +(-a^m +1) = a^m -a^m +1+1 = 2[/tex]

And by definition of S, 2 is not in S so then since we can't satisfy the closed addition property then S can't be a subsapce

Answer:

Italian style = 19,000 packages

French style = 13,000 packages

Oriental style = 53,000 packages

Step-by-step explanation:

let the number of packages of Italian style = x

let the number of packages of French style = y

let the number of packages of Oriental style = z

See the attached table which summarize the problem

Using the table we can get the following system of equations:

0.4x + 0 * y + 0.2z = 18,200

0.3x + 0.5y + 0.3z = 28,100

0.3x + 0.5y + 0.5z = 38,700

Solving the 3 equations together to find x , y and z

Using the calculator

x = 19,000

y = 13,000

z = 53,000

To determine the width of the frame, subtract twice the frame width from the length and width of the outer rectangle and set up an equation based on the perimeter.

To determine the width of the frame, we need to first find the dimensions of the inner rectangle formed by the painting. If we subtract twice the frame width from the length and width of the outer rectangle, we get the length and width of the inner rectangle. Let's call the width of the frame 'x'.

The length of the inner rectangle is 15 inches - 2 inches, and the width of the inner rectangle is 18 inches - 2 inches. The perimeter of the inner rectangle is the sum of its four sides, which can be calculated using the

formula P = 2l + 2w. We know that the perimeter of the inner rectangle is 90 inches, so we can set up the equation:

90 = 2(15 - 2x) + 2(18 - 2x)

Solving this equation will give us the value of 'x', which represents the width of the frame.

https://brainly.com/question/32613996

#SPJ3

Answer:

Russia gets 267 baseball cards in a year.

Step-by-step explanation:

Given:

Number of packs given per month = 2

Number of cards in each pack = 11

Number of cards given on his birthday = 3

Now, we know that, there are 12 months in a year.

Using unitary method, the total number of packs given in year and total cards can be calculated. So,

Packs given in 1 month = 2

∴ Packs given in 12 months = 2 × 12 = 24

Number of cards in 1 pack = 11

∴ Number of cards in 24 packs = 11 × 24 = 264

Now, his birthday will come once in a year. So, additional cards received by him will be 3 only. So,

Total number of cards = Number of cards in 24 packs + Additional cards

Total number of cards = 264 + 3 = 267

Therefore, Russia gets 267 baseball cards in a year.

Answer:

Option A) Whether or not a subject graduates high school      

Step-by-step explanation:

We are given the following experiment in the question:

Experiment:  if preschool attendance is associated with high school graduation for low-income students.

Independent variable: preschool attendance

The children were divided into two groups, one group will attend preschool program, the second group will not attend preschool.

The response variable is another term for dependent variable.

Here,

Dependent variable: whether or not children will graduate from high school.

Because this is dependent on the variable whether the child attends the preschool or not.

Option A) Whether or not a subject graduates high school

Final answer:

The response variable in the study is A) Whether or not a subject graduates high school. This measures the outcome of the treatment, which is preschool attendance for low-income children.

Explanation:

In this study, the response variable is the outcome that the researcher is trying to measure as a result of manipulating the experimental conditions. The experimental condition in this case is whether the child attends preschool or not. Hence, the response variable would be A) Whether or not a subject graduates high school. The preschool attendance (C) is the independent variable or treatment variable, as it is what the researcher manipulates and controls. The variables of the length of time it takes to graduate (B), and the income status of the children (D) are not the focus of the measurement for the direct effect of preschool attendance.

Low-income children have been observed to have various educational disadvantages compared to their wealthier peers, such as lower standardized test scores, lower graduation rates, and higher dropout rates. The study aims to investigate if attending preschool can help bridge the educational achievement gap that starts before children even enter formal schooling. By assigning low-income children randomly to either attend preschool or not, the researcher can control for other variables and focus on the impact of preschool attendance on high school graduation.

Answer:

heres your answers

Step-by-step explanation:

George Washington  was defeated  when he went to fight the French in the Ohio River Valley.

The British then sent a trained army to attack the French Fort Duquesne.

The British suffered a defeat in the first battle of the French Indian War.