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#### If a truck travels 360 kilometers in 5 hours, how far will it travel in 9 hours if the same speed is maintained?

Correct! Wrong!

First, determine distance the car travels in one hour:
360 km ÷ 5 hours = 72 km per hour

Then multiply this number by the total number of hours traveled:
9 hours × 72 km per hour = 648 km

It is important to note that the final calculation produces the correct units; this helps to confirm that the calculation is correct.

#### What is equivalent to 3x(2 + 5y)?

Correct! Wrong!

Begin by taking note of the format in which the answer options are written. As there is no parenthetical expression in any of the answer choices, begin by distributing the 3x through the parentheses. Multiply each of the term inside the parentheses three times and combine any similar terms:

3x(2 + 5y)
= 3x(2) + 3x(5y)
= 6x + 15xy

#### A box contains four yellow marbles and eight blue marbles. What is the probability that Emma will choose a yellow marble at random from the box?

Correct! Wrong!

The probability of a successful event is defined as the ratio of successful events to total events. A successful event in this case is selecting a yellow marble from the box. The number of events equals the number of marbles in the box:
P(Yellow) = Yellow Marbles/Total Marbles

P(Yellow) = 4/12
P(Yellow) = 1/3

#### Jennie wants to paint a room's walls. She is aware that each can of paint holds one gallon. A half gallon of paint will completely cover a 55 square foot wall. The room's four walls are each 10 feet tall. Two of the walls are 10 feet wide, while the other two are 15 feet wide. How many 1-gallon buckets of paint does Jennie need to paint the entire room?

Correct! Wrong!

The total number of buckets required will be determined by dividing the total area of the walls by the total area covered by each bucket. First, determine the size of the walls Jennie intends to paint. Two of the walls are 10 × 10 and the other two are 10 × 15:

2 (10 × 10) = 200 sq. ft.
2 (10 × 15) = 300 sq. ft.
As a result, the total area of the walls is 500 square feet.

If a half gallon of paint covers 55 square feet, each gallon covers 2 × 55 = 110 square feet. Four gallons can only cover 440 square feet. Five gallons will cover 550 square feet, which is enough to cover the entire wall area.

#### What was Jelly's tip percentage if she left a \$10.16 tip on a breakfast that cost \$86.89?

Correct! Wrong!

To find out what percentage A is of B, divide A by B and multiply the result by 100 percent:
10.16 ÷ 86.89 = 0.1169 × 100% = 11.69%
This is approximately 12%.

#### Factor: 4y(3x + 2) − 2(3x + 2)

Correct! Wrong!

Correct answer: (4y − 2)(3x + 2)

Any part of an expression that is shared by all of its terms can be factored out. (3x + 2) is a common term in this case and can be factored out of both parts of the expression:
4y(3x + 2) − 2(3x + 2) = (3x + 2)[4y − 2]

See that distributing (3x + 2) through [4y − 2] yields the original expression, which validates the answer.

#### Robert makes \$8.10 per hour and works 40 hours per week. John's hourly wage is \$10.80. How many hours would John have to work to earn the same as Robert over 40 hours?

Correct! Wrong!

To begin, compute Robert's total earnings after 40 hours: 40 hours × \$8.10 per hour = \$324
Then, divide this total by John's hourly rate to determine how many hours John would need to work:
\$324 ÷ \$10.80 per hour = 30 hours

#### Angel was three times Brian's age five years ago. How old is Angel now that Brian is 10 years old?

Correct! Wrong!

To keep things organized, create a table that compares the situation five years ago to the situation today.

Five years ago Today
Brian 10 - 5 = 5 10
Angel 3 x 5 = 15 15 + 5 = 20

Brian is now 10 years old, so he was 5 years old five years ago.
Angel was 3 times Brian's age five years ago, so Angel must have been 15 at the time.

To calculate Angel's current age, add 5 years to her age five years ago. Angel is now 15 + 5 = 20 years old.

#### How many outfit combinations are possible with six shirts, three slacks, and five ties?

Correct! Wrong!

Multiply the number of options for each factor to determine the number of possible outfit combinations:
6×3×5=90

#### Ruby has set a \$300 budget for her holiday spending. She makes the decision to purchase a pair of shoes for each of her grandchildren. Which of the following inequalities represents Ruby's budget constraint if each pair costs c dollars and she has 7 grandchildren?

Correct! Wrong!

Ruby pays 7c if she buys 7 pairs of shoes at \$c each. Given that she has only \$300 to spend, 7c must be less than or equal to \$300:
7c ≤ 300

#### What is the 181.5% of 18?

Correct! Wrong!

The key word ‘of,' indicates that the percentage has been multiplied by the value. To begin, convert the fraction to a decimal by shifting the decimal point two places to the left, yielding 1.815. Then multiply this figure by 18.

1.815 × 18 = 32.67

#### Find x: 3(x + 1) = 5(x − 2) + 7

Correct! Wrong!

Begin by distributing the 3 and 5 within their respective parentheses, then combine like terms on either side of the equal sign:
3(x + 1) = 5(x − 2) + 7
3x + 3 = 5x − 10 + 7
3x + 3 = 5x − 3

To maintain equality, add 3 to both sides:
3x + 6 = 5x

Subtract 3x from both sides, then divide the resulting equation by 2 to find x:
6 = 2x
3 = x
Remember that whenever a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and seeing if it yields a true statement.

#### Consider the following: 2, 2, 3, 5, 9, 11, 17, 21 Which measurement will NOT change if the number 23 is added to the list?

Correct! Wrong!

The mode will remain unchanged. The mode is the most frequently occurring number; in this case, it is 2. The following measures will be modified:

The mean is the average, and it will rise in this case because a number greater than the current average is added to the list.

The median is the number in the middle, and it will change rapidly between 7 and 9.
The range is the difference between the highest and lowest numbers, and it will change from 19 to 21 due to the addition of a new maximum value (21 2 = 19 and 23 2 = 21).

#### Triangle ABC has the coordinates (−2,7), (−3,6), and (4,5) in a coordinate plane. What are the coordinates of the new image if triangle ABC is reflected along the y-axis?

Correct! Wrong!

One solution is to draw the figure and then count how many units each point is from the y-axis, and then count the same number of units in the opposite direction. A more efficient method is to recognize that reflecting over the y-axis changes the sign of the x-value but has no effect on the y-value of the point.

Reflecting (−2,7), (−3,6), (4,5) across the y-axis yields the points (2,7), (3,6), (−4,5), according to the second method.

#### Group trips are available from a river rafting guide. She charges \$250 for two people and an additional \$40 for each additional person. How much will each person pay if 5 friends split the cost of a trip equally?

Correct! Wrong!

First, compute the total cost of the trip. Begin with \$250 for the first two people, then add \$40 for each of the remaining three: 250 + 40 + 40 + 40 = \$370

Then divide this total by 5 to determine how much each person will pay:
\$370 ÷ 5 = \$74

#### It takes 10 people 5 days to paint a building. How much of the building could 7 people paint in 5 days if each person paints as quickly as the others?

Correct! Wrong!

In 5 days, 10 people can paint a building. In 5 days, each person paints 1/10 of the building.
In 5 days, 7 people would paint 7 × 1/10 of the building.
In 5 days, 7 people would paint 7/10 of the building.

#### In the metric system of units: 1 meter = 100 centimeters and 1 meter: 1 foot = 3.25:1 What is the length of 21 feet in meters?

Correct! Wrong!

3.25 feet = 1 meter
1 foot = 1÷3.25 meters
21 feet = 21×1÷3.25 = 6.4615 meters

#### What is the value of x that y = 15 - 3x and y = 0?

Correct! Wrong!

y =15 - 3x and y = 0
Hence 15 - 3x = 0
Substitute 5 for x.
15 - 3(5) = 0
x=5

#### The sides of an isosceles triangle are equal. What is the perimeter of a triangle if two of its sides are 5 inches and 2 inches long?

Correct! Wrong!

The other side must be 5 inches long or the two shorter sides will not be able to meet.
The perimeter is the distance around the outside of the triangle, so 5 + 5 + 2 = 12.

#### Find the value of x: 4(𝑥+1)=6(𝑥−4)+20

Correct! Wrong!

Simplify:
4(𝑥+1)=6(𝑥−4)+20
4𝑥+4=6𝑥−24+20
4𝑥+4=6𝑥–4

Subtract 4𝑥 from both sides:
4=2𝑥–4

8=2𝑥

4=𝑥

#### What is the 2.5% of 1,200?

Correct! Wrong!

2.5% of 1,200=0.025×1200=30

#### Which of the following expressions represents 2x(4+2y)?

Correct! Wrong!

Make use of the distributive property:
2𝑥(4+2𝑦)=8𝑥+4𝑥𝑦=4𝑥𝑦+8𝑥

Correct! Wrong!

11×36+6×12+4=472

#### The answer is 83, which is 5 less than twice a positive integer. What is the integer?

Correct! Wrong!

Assume x is an integer. Then:
2𝑥–5=83
2x=88 if you add 5 on both sides.
Divide both sides by 2 to get x=44.

Correct! Wrong!