**A circle has an area of 169 π in2. Which of the following is the circumference of the circle in terms of pi ( )?**

13 π in

26 π in

7.5 π in

20 π in

*Correct Answer : B*

We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then

Substituting 169*π* in place of area

* *

Dividing both sides by pi and taking square root on both sides yields

The radius of the circle from the given area is 13 in. and the circumference of the circle is given by the relation:

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Related Questions

### Correct Answer is B

#### Explanation

We need to find the radius of the circle in order to find circumference of the circle. If we let r to be radius of the circle, then

Substituting 169*π* in place of area

* *

Dividing both sides by pi and taking square root on both sides yields

The radius of the circle from the given area is 13 in. and the circumference of the circle is given by the relation:

### Correct Answer is B

#### Explanation

we find the value of x by applying the absolute conditions to the given equation.

First, add 2 to both sides of equation

The absolute conditions are:

If * * , a>0, then u=a or u=-a

In this case a=10, which is greater 0.

The first condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

The second condition becomes

Add 2 to both sides of the equation

Divide both sides by 4

Then, the value of x is 3 or -2.

### Correct Answer is B

#### Explanation

We are asked to determine Japheth’s uncle’s age relating to Japheth’s age.

First, express Japheth’s uncle’s age in terms of Japheth’s age as follows

Japheth’s age=k

Japheth’s uncle’s age, u = 3k-10.

Thus, the relationship between Japheth’s uncle’s age to that of Japheth is u=3k-10.

### Correct Answer is D

#### Explanation

Percentages are fractions with denominator equal to 100. To convert a percent to decimal form, divide the value by 100.

The decimal form of 98.2% is 0.982.

### Correct Answer is A

#### Explanation

we are asked to find the number of gallons a full tank can hold. A full tank is equivalent to 1.

Convert the mixed fraction into proper fraction as follows

(2frac{2}{5}=frac{left(2ast5 ight)+2}{5}=frac{10+2}{5}=frac{12}{5})

If we let x be the number of gallons in full tank, and setting up the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

(frac{x gallons}{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

Cross-multiply to find the value of x.

(frac{x }{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

(x astfrac{4}{7}full tank=frac{12}{5} gallonsast1 full tank)

(x =frac{frac{12}{5} gallonsast1 full tank}{frac{4}{7}full tank}=frac{12}{5}divfrac{4}{7} gallons=frac{12}{5}astfrac{7}{4}gallons=frac{21}{5}gallons)

Converting 21/5 to a mixed fraction is 4 1/5. Thus, when the tank is full, it holds 4 1/5 gallons of water.

### Correct Answer is D

#### Explanation

We are asked to find the number of cups of flour that will be used to make 90 cookies.

First, we convert 2 ¼ into improper fraction as:

Letting x to be the number of cups of flour, we set up a proportion equation with number of cookies on numerator and number of cups of flour on the denominator becomes:

Solve the value of x by cross-products

Dividing both sides by 60, the above equation result to

Thus, the number of cups of flour needed to make 90 cookies is 81/16 cups, which is equal to 5 1/16 cups.

### Correct Answer is A

#### Explanation

Using a calculator to evaluate 15*÷*27 results in 0.5555555556. To two decimal places, the answer becomes 0.56.

Thus, 0.56 is the decimal equivalent of 15/27.

### Correct Answer is A

#### Explanation

To find the cheapest option, we find the amount the consume will spend for each option given.:

- 2 packs of Orange and 1 pack of Cream Soda will cost $16+$5= $21
- 3 Packs of Orange will cost $16+$12=$28
- 2 packs of Root Beer and 1 pack of Cream Soda will cost 2($15)+$7=$37
- 5 packs of cream Soda will cost 5($7)=$35

From the above evaluation, the cheapest option will cost the consumer $21. Thus, buying 2 packs of Orange and 1 pack of Cream Soda will be cheaper to purchase compared to other options.

### Correct Answer is B

#### Explanation

A histogram is used to visualize the frequency of a one variable over the other while a line graph is used to compare two variables.

A scatter plot used to show the correlation between two variables.

A pie chart is used to show the proportion of the given information in circle, with each section of a circle representing a given fraction of a whole.

From the given information, a pie chart is an appropriate tool show the frequency of the students choosing their favorite color.

### Correct Answer is D

#### Explanation

To find the area of the room, we form an equation of find an equation relating the length and width of the rectangle. If we let the width of the room to be w, then** **

Width of the rectangle= w

Length of rectangle=(w+5)

Area of the rectangle, A= Length*width=(w+5)*w

A=w(w+5)

Thus, the area of the rectangular room is w(w+5).

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