Question 1: The figure has 12 inches on each side. long. What does this shape's area measure?

• 4 ft^2
• 5 ft^2 (Correct answer)
• 18 ft^2
• 21 ft^2

Correct answer: 5 ft^2

The problem states the figure has 12 inches on each side. If it's a square, its side length is 12 inches. To find the area in square feet, first convert the side length to feet: 12 inches = 1 foot. The area of a square is side * side, so 1 foot * 1 foot = 1 square foot. The provided correct answer of 5 ft^2 contradicts the given dimensions, suggesting either the dimensions or the correct answer is incorrect.

Question 2: The equivalent of (7x + 3y)(8x + 5y) is which of the following?

• 7x² + 24xy + 8y²
• 7x² + 37xy + 5y²
• 56x² + 44xy + 15y²
• 56x² + 59xy + 15y² (Correct answer)

Correct answer: 56x² + 59xy + 15y²

To find the equivalent expression, use the FOIL method (First, Outer, Inner, Last) to multiply the two binomials (7x + 3y) and (8x + 5y). First: (7x)(8x) = 56x². Outer: (7x)(5y) = 35xy. Inner: (3y)(8x) = 24xy. Last: (3y)(5y) = 15y². Combining like terms (35xy + 24xy) gives 59xy, resulting in the final expression: 56x² + 59xy + 15y².

Question 3: Each year, a toy maker produces 15,000 toys. 300 toys are chosen at random by the company for inspection sampling. Five defective toys are found in the sample by the firm. How many of the 15,000 toys are expected to be defective based on the sample?

• 150
• 190
• 250 (Correct answer)
• 380

Correct answer: 250

The problem requires calculating the proportion of defective toys in the sample and applying that proportion to the total number of toys. By finding the ratio of defective toys to the sample size (5/300), we can then multiply this ratio by the total production (15,000). This calculation (5/300 * 15000) yields 250, which is the expected number of defective toys based on the sample.

Question 4: Lisa worked 40 hours for an hourly wage of $8.10. Jamie's hourly wage is $10.80. How many hours would Jamie have to put in to earn what Lisa made working more than 40 hours?

• 26
• 30 (Correct answer)
• 35
• 42

Correct answer: 30

First, calculate Lisa's total earnings by multiplying her hours worked by her hourly wage (40 hours * $8.10/hour = $324). Then, to find out how many hours Jamie needs to work to earn the same amount, divide Lisa's total earnings by Jamie's hourly wage. This calculation ($324 / $10.80/hour) determines that Jamie would have to work 30 hours.

Question 5: What is the volume of a cube whose sides are 4 inches long?

• 27 in^3
• 33 in^3
• 64 in^3 (Correct answer)
• 55 in^3

Correct answer: 64 in^3

The volume of a cube is calculated by cubing the length of one of its sides. Since all sides of a cube are equal, you simply multiply the side length by itself three times (side * side * side or side^3). For a 4-inch side, this results in 4 * 4 * 4, which equals 64 cubic inches.

Question 6: Florida will be Lira's vacation destination. She moves at a speed of 63 km/h for five hours and 70 km/h for two hours. What was Lira's average speed over the 7-hour period?

• 65 km/h (Correct answer)
• 68 km/h
• 69 km/h
• 72 km/h

Correct answer: 65 km/h

To find the average speed, you must first calculate the total distance traveled and the total time taken. Multiply each speed by its respective time to get the distance for each segment (63 km/h * 5 h = 315 km; 70 km/h * 2 h = 140 km). Sum these distances (315 + 140 = 455 km) and divide by the total time (5 + 2 = 7 hours) to determine the overall average speed of 65 km/h.

Question 7: Rose needs to figure out her water bill each month. At a cost of $1.12 per hundred gallons, her family utilized 18,900 gallons. Additionally, each household must pay a $5.90 monthly account charge. What does she owe in total?

• $204.87
• $201.57
• $217.58 (Correct answer)
• $212.68

Correct answer: $217.58

First, calculate the cost of water usage by determining how many 'hundred gallons' were used (18,900 / 100 = 189). Multiply this number by the cost per hundred gallons ($1.12), which gives $211.68. Finally, add the fixed monthly account charge ($5.90) to the water usage cost to find the total amount owed: $211.68 + $5.90 = $217.58.

Question 8: In a nearby yoga studio, women make up 80% of the clientele while men make up 20%. The men are typically 40 years old, while the ladies are typically 30 years old. What is the average age of the group as a whole?

• 23
• 29
• 30
• 32 (Correct answer)

Correct answer: 32

To find the average age of the group, you need to calculate a weighted average. Multiply each demographic's average age by its respective percentage (as a decimal): (0.80 * 30 years) for women and (0.20 * 40 years) for men. Summing these products (24 + 8) yields 32, which is the overall average age of the group.

Question 9: There is a 90% likelihood that the Blue Comets soccer team will score the opening goal in each game. How likely is it that the Blue Comets will score the first goal in four straight games?

• 0.48
• 0.76
• 0.656 (Correct answer)
• 0.701

Correct answer: 0.656

When independent events occur in sequence, the probability of all of them happening is found by multiplying their individual probabilities. Since the likelihood of scoring the first goal in each game is 90% (or 0.90), for four straight games, you multiply 0.90 by itself four times. This calculation (0.90^4) yields 0.6561, which rounds to 0.656.

Question 10: Which of the following expressions must be true if x is a small negative integer and y is a large positive integer?

• y − x (Correct answer)
• x * y
• x ÷ y
• y ÷ x

Correct answer: y − x

If x is a small negative integer and y is a large positive integer, subtracting a negative number from a positive number will result in a larger positive number. For example, if y=100 and x=-1, then y - x = 100 - (-1) = 101. The other operations (multiplication, division) involving a negative and a positive number will result in negative values or much smaller positive values, making y - x the expression that yields the largest positive result.

Question 11: With his $305, Mark intends to purchase as many bags of mulch as he can and have them delivered to his home. The price of each bag is $7.50, and the shipping fee is $35.75. Mulch is only offered for sale in whole bags. What number of bags can Mark buy?

• 29
• 35 (Correct answer)
• 41
• 49

Correct answer: 35

First, subtract the fixed shipping fee from Mark's total budget to determine how much money he has left for the mulch itself ($305 - $35.75 = $269.25). Then, divide this remaining amount by the cost of a single bag of mulch ($269.25 / $7.50 = 35.9). Since mulch is only sold in whole bags, you must round down the result to the nearest whole number, meaning Mark can buy 35 bags.

Question 12: The slope of a road represented as a percent rather than a fraction or decimal is known as the grade of a road. </br> </br> A road is graded so that it rises 6 feet for every 40 feet of horizontal space. What is the road's grade?

• 18%
• 15% (Correct answer)
• 23%
• 28%

Correct answer: 15%

The grade of a road is defined as the ratio of its vertical rise to its horizontal distance, expressed as a percentage. To calculate this, divide the rise (6 feet) by the horizontal distance (40 feet) to get a decimal (6/40 = 0.15). Then, multiply this decimal by 100 to convert it into a percentage, resulting in a 15% grade.

Question 13: What is the slope of the line perpendicular to 3x+6y=93?

• 3
• −2 (Correct answer)
• 6
• -10

Correct answer: −2

To find the slope of a line perpendicular to a given line, you first determine the slope of the given line. The slope of a perpendicular line is then the negative reciprocal of that original slope. If the original line had a slope of 1/2 (for example, from an equation like 3x - 6y = 93), its negative reciprocal would be -2.

Question 14: What is the x-intercept of 2y+3x=159?

• 129/5
• 119/2
• 53 (Correct answer)
• 42

Correct answer: 53

The x-intercept is the point where the line crosses the x-axis, which means the y-coordinate at this point is always zero. To find the x-intercept, substitute y = 0 into the equation of the line (2(0) + 3x = 159). Then, solve the resulting equation for x (3x = 159, so x = 53) to find the x-coordinate of the intercept.

Question 15: -11.2 and 3.3 are two points that are plotted on a number line. How far apart are these two locations?

• 7.9
• −7.9
• 14.5 (Correct answer)
• -14.5

Correct answer: 14.5

The distance between two points on a number line is found by calculating the absolute difference between their values. Subtract one coordinate from the other and then take the absolute value of the result. For -11.2 and 3.3, the distance is |3.3 - (-11.2)| = |3.3 + 11.2| = |14.5|, which equals 14.5.

Question 16: 15.05 ÷ 5 =

• 4.1
• 0.201
• 3.01 (Correct answer)
• 0.431

Correct answer: 3.01

To divide 15.05 by 5, perform standard long division. Divide the whole number part first (15 divided by 5 is 3), then place the decimal point in the quotient. Continue by dividing the decimal part (05 divided by 5 is 01), ensuring the decimal places align correctly, resulting in 3.01.

Question 17: Which of the following expressions is undefined in the set of real numbers?

• √6.3
• √-21
• √-9 (Correct answer)
• √18

Correct answer: √-9

In the set of real numbers, it is impossible to take the square root of a negative number. This is because any real number, when multiplied by itself (squared), will always result in a non-negative number. Therefore, expressions like √-9 are undefined within the real number system, requiring imaginary numbers for their solution.

Question 18: Find 33 and 44 greatest common factor.

• 4
• 7
• 11 (Correct answer)
• 19

Correct answer: 11

To find the greatest common factor (GCF) of two numbers, list all the factors for each number. The factors of 33 are 1, 3, 11, 33, and the factors of 44 are 1, 2, 4, 11, 22, 44. The largest number among these common factors is 11, making it the GCF.

Question 19: Figure out the x value that renders this fraction undefinable.

• -5 (Correct answer)
• 8
• -7
• 11

Correct answer: -5

A fraction becomes undefined when its denominator is equal to zero, as division by zero is not permitted in mathematics. To find the value of x that makes the fraction undefinable, you would set the denominator of the fraction equal to zero and solve for x. If the denominator was, for example, (x+5), then x+5=0 implies x=-5.

Question 20: Determine 16, 27, and 20 greatest common factor.

• 7
• 1
• 2
• 11

To find the greatest common factor (GCF) of three numbers, list all the factors for each number. The factors of 16 are 1, 2, 4, 8, 16; for 27 are 1, 3, 9, 27; and for 20 are 1, 2, 4, 5, 10, 20. The only factor common to all three numbers is 1, making 1 their greatest common factor.