Practice Test 10 - Pre Algebra

20 questions. Answer them in any order, then submit to see your score and every explanation.

The cost to produce t-shirts is given by $C(x) = 8x + 150$ , where x is the number of t-shirts and C is the cost in dollars. If the company sells each t-shirt for $15, how many t-shirts must be sold to achieve a profit of exactly $200?
The mass of Earth is approximately $5.97 \times 10^{24}$ kg, and the mass of the Moon is approximately $7.35 \times 10^{22}$ kg. How many times more massive is Earth than the Moon? Round your answer to the nearest tenth.
A movie theater charges a membership fee plus an additional cost per movie ticket. Sarah paid $45 for her membership and 3 movie tickets, while Jake paid $65 for his membership and 7 movie tickets. Which equation correctly represents the constraint that relates the total cost $C$ to the number of tickets $t$ purchased?
A researcher fits the line $y = -0.8x + 95$ to data comparing hours of TV watching per week ( $x$ ) and academic performance scores ( $y$ ). According to this model, what would be the academic performance score for a student who watches 25 hours of TV per week?
Consider all positive integers of the form $2^x \cdot 3^y \cdot 7^z$ where $x$ , $y$ , and $z$ are non-negative integers and $x + y + z = 4$ . How many such integers are there?
Taylor claims that $(-3)^4 = -3^4$ because "exponents apply to whatever is right next to them." However, $(-3)^4 = 81$ while $-3^4 = -81$ . How should Taylor's reasoning be corrected?
A trail mix recipe combines peanuts, raisins, and chocolate chips in a 5:2:3 ratio by weight. Sarah makes a batch using 2.4 pounds of raisins. She then decides to double the recipe but discovers she only has enough chocolate chips to increase that ingredient by 80%. If she adjusts the peanuts proportionally to match the chocolate chips, how many pounds of raisins will she need for this modified double batch?
A bakery sells cupcakes in boxes. Regular boxes hold 6 cupcakes and large boxes hold 12 cupcakes. If the bakery needs to package exactly 96 cupcakes using both types of boxes, and they must use at least 2 regular boxes, which equation represents this constraint where $r$ is regular boxes and $\ell$ is large boxes?
The area of a rectangular solar panel is $(6.4 \times 10^3) \times (2.5 \times 10^2)$ square centimeters. If the panel generates $1.8 \times 10^{-2}$ watts per square centimeter, what is the total power output in watts?
Which interpretation correctly describes how long the tank can drain before the pump stops working?
A projectile is launched upward with an initial velocity. Its height in feet after $t$ seconds is given by $h(t) = -16t^2 + 64t + 80$ . What does the value 80 represent in this context?
A football team's field position changes during a series of plays. Starting at their own 25-yard line, they gain $12.5$ yards, lose $8.25$ yards, gain $15.75$ yards, lose $4.5$ yards, and gain $7.25$ yards. Field position is measured as yards from their own goal line. If they need to reach the 50-yard line to be in the opponent's territory, how many more yards do they need?
The area of a triangle is $A = \frac{1}{2}bh$ , where $b$ is the base and $h$ is the height. In triangle ABC, the height to the base is represented by $(x + 3)$ inches and the base is represented by $(2x - 1)$ inches. If the area is 35 square inches, what is the value of $x$ ?
A bacteria culture triples every 2 hours. If the initial population is $4.5 \times 10^6$ bacteria, what will be the population after 6 hours? Express your answer in scientific notation.
Solve the compound inequality: $-3 \leq 2x + 1 < 7$ . What values of $x$ satisfy this inequality?
The formula $d = rt$ relates distance, rate, and time. Two cars start from the same point and travel in opposite directions. Car A travels at $55$ mph and Car B travels at $65$ mph. After how many hours will they be $300$ miles apart?
A meteorologist fits a line to data comparing barometric pressure (inches of mercury) and rainfall amounts (inches per day). The fitted line is $y = -2.1x + 63$ . If the barometric pressure increases by 0.5 inches of mercury, what change in daily rainfall should be expected according to this model?
Jake's work solving $4x + 9 = 1$ is shown below: Step 1: $4x + 9 = 1$ Step 2: $4x = 1 + 9$ Step 3: $4x = 10$ Step 4: $x = \frac{10}{4} = 2.5$ In which step did Jake make his first error?
A library charges a late fee equal to 8% of a book's replacement cost for each day it's overdue. If a book worth $25 is returned 3 days late, and the borrower pays with two $20 bills, how much change should they receive?
A parking garage charges a flat fee plus an additional amount for each hour parked. If the total cost is $8 more than $3$ times the number of hours parked, which expression represents the total cost in dollars for parking $h$ hours?

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