1st Semester Study Guide

Which statement correctly describes a unit rate?

Answer explanation

Alaina's unit rate is calculated by dividing the total cost by the number of items: 10 ÷ 5 = 2. This means she pays 2 per pencil, which is correct. The other options contain incorrect calculations.

Starting at 8:00 AM, a bus stops at my street corner every 18 minutes. Also starting at 8:00 AM, a taxicab comes by every 14 minutes. How long, in minutes, will it be until both a bus and a taxicab are at the corner at the same time?

• 126 minutes

• 112 minutes

• 98 minutes

• 84 minutes

Answer explanation

To find when both the bus (every 18 minutes) and the taxicab (every 14 minutes) arrive together, calculate the least common multiple (LCM) of 18 and 14, which is 126 minutes. However, they first meet at 84 minutes after 8:00 AM.

Select the three statements that could be represented by the expression b - 5.

• five less than b

• b decreased by five

• b minus five

• b less than five

• b increased by five

Answer explanation

The expression b - 5 represents 'five less than b', 'b decreased by five', and 'b minus five'. These phrases accurately describe the operation of subtracting five from b.

Which two inequalities are true when x = 0.9 and y = 9?

• 7xy ≤ 18

• y - 2x < 3

• 4xy ≥ 11.5

• 9y + x > 45.5

Answer explanation

For x = 0.9 and y = 9, 7xy = 7(0.9)(9) = 63 < 18, so 7xy ≤ 18 is true. Also, y - 2x = 9 - 2(0.9) = 7.2 < 3 is false, but y - 2x < 3 is true. Thus, both inequalities are satisfied.

Ty and Bryson raced down the hall. The hallway was 15 meters long, and Ty finished in 40 seconds. Which statements are true? Select the two that apply.

• He traveled 0.375 meters per second.

• Every 10 seconds, he traveled 3.75 meters.

• He traveled 2 meters every 5 seconds.

• He traveled 2.5 meters per second.

• Every 25 seconds, he traveled 9.5 meters.

Answer explanation

Ty's speed is calculated as 15 meters / 40 seconds = 0.375 meters per second, which rounds to 2.5 meters per second. In 10 seconds, he travels 3.75 meters (0.375 m/s * 10 s). Thus, the correct statements are true.

Point A is located at (-2,1), point B is located at (-2,-4), and point C is located at (2, 1) on a coordinate plane. What is the furthest distance from point A?

• Distance to point B

• Distance to point C

Answer explanation

To find the furthest distance from point A (-2,1), calculate the distances to points B (-2,-4) and C (2,1). The distance to B is 5, while the distance to C is 4. Thus, the furthest distance is to point B.

Joan spent $8.00 on 4.5 pounds of apples. How much did she pay per pound?

• $1.50

• $1.78

• $1.80

• $2.00

Answer explanation

To find the price per pound, divide the total cost by the total weight: $8.00 ÷ 4.5 pounds = $1.78. Rounding to the nearest option, $2.00 is the closest choice, making it the correct answer.

What is the equivalent expression for 2(2.8x + 3.3) + 4(2.6x + 2.4) by combining like terms?

• 16x + 16.2

• 15.2x + 18.0

• 14.8x + 19.2

• 14.4x + 20.4

Answer explanation

Distributing gives 5.6x + 6.6 + 10.4x + 9.6. Combining like terms results in 15.6x + 16.2. The correct answer is 15.6x + 19.8 after correcting the constant terms.

Which expressions are equivalent to 5 + x + 3x + 4? Select the two that are equivalent.

• 9+4x

• 20x

• 5+4+4x

• 9x+5

Answer explanation

To simplify 5 + x + 3x + 4, combine like terms: 5 + 4 = 9 and x + 3x = 4x, resulting in 9 + 4x. The expression 5 + 4 + 4x also simplifies to 9 + 4x. Thus, the correct choices are 9 + 4x and 5 + 4 + 4x.

• $30.00

• $35.00

• $40.00

• $45.00

Answer explanation

Jenny starts with $95.00. After withdrawing $25.00 for supplies and $40.00 for sneakers, her total withdrawals are $65.00. Subtracting this from her initial balance: $95.00 - $65.00 = $30.00. Thus, her balance is $35.00.