Practice Test 8 - Pre Algebra

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

Emma needs to understand what $\frac{7}{9}$ means when her teacher says it represents "7 divided by 9." If Emma has 7 identical candy bars to share equally among 9 friends, and she also has 14 identical candy bars to share equally among 18 different friends, what can she conclude?
Simplify: $\frac{4^5 \cdot 4^3}{4^6} \cdot 4^2$
A teacher analyzes the relationship between class attendance rate and final exam scores. The scatter plot reveals that while students with very low attendance (below 60%) consistently score poorly, students with attendance above 60% show no clear pattern between attendance and exam performance. What type of association does this represent?
A scientist measures the thickness of a cell membrane as $0.000000847$ meters. When this measurement is rounded to the nearest hundred-millionth, the result can be written in the form $a \times 10^{-7}$ where $a$ is a whole number. What is the value of $a$ ?
The formula for the circumference of a circle is $C = 2\pi r$ , where $r$ is the radius. A circular track has a circumference that is 24 meters more than 4 times the radius. What is the radius of the track in meters?
A company's profit $P$ (in thousands of dollars) satisfies $P \leq 50$ or $P \geq 80$ . If the profit must also satisfy $P > 30$ , which compound inequality represents all possible profit values?
Which of the following numbers, when written in scientific notation, has the smallest coefficient (the number before the power of 10)?
A regular hexagon is divided into 6 congruent triangular sections. If each triangular section has an area of 15.6 square centimeters, and a circular hole with radius 2 cm is cut from the center of the hexagon, what is the area of the remaining figure? (Use π ≈ 3.14)
Which of the following represents the solution set for $\frac{x}{-3} > 4$ when graphed on a number line?
The formula $P = 2l + 2w$ gives the perimeter of a rectangle. A rectangular garden has a perimeter of $84$ feet and a length that is $6$ feet more than twice the width. What is the width of the garden?
Triangle ABC is isosceles with AB = AC. If the measure of angle B is $(5x - 15)°$ and the measure of angle A is $(2x + 20)°$ , what is the measure of angle C?
The concentration of a chemical solution is $6.4 \times 10^{-2}$ grams per liter. If you need to dilute this solution to a concentration of $1.6 \times 10^{-3}$ grams per liter, what is the dilution factor?
A scientist measures the change in a chemical solution's pH level during an experiment. The pH starts at $7.5$ , decreases by $2.25$ , then increases by $0.75$ , decreases by $1.5$ , and finally increases by $3.25$ . If a solution is considered acidic when pH < 7, basic when pH > 7, and neutral when pH = 7, what type of solution resulted, and by how much did the pH change from the starting point?
An inequality has the solution set $x \geq -3$ . A student claims this means 'x can be any number except those smaller than -3.' Which part of this interpretation needs correction?
Sarah is solving a multi-step equation and gets stuck. She writes: " $2(x+3) - 5 = 3x - 7$ . I distributed and got $2x + 6 - 5 = 3x - 7$ , then $2x + 1 = 3x - 7$ . Now I have $2x - 3x = -7 - 1$ , so $-x = -8$ , which means $x = 8$ ." When she checks her answer, it doesn't work. What should she do next to fix her error?
An inequality has solution set $-4 \leq x < 1$ . A student tests three boundary-related values: $x = -4$ , $x = 1$ , and $x = 0$ . If the original inequality is $2x + 3 \geq -5$ and $x < 1$ , which verification results should the student expect?
A recipe calls for 3 cups of flour to make 18 muffins. Sarah wants to make 42 muffins but only has 6.5 cups of flour available. Based on the recipe's unit rate, how much additional flour does she need?
Jamie is comparing two fractions: $\frac{11}{16}$ and $0.6875$ . She converts the first fraction to a decimal and notices something interesting about the relationship between these two numbers. What is the value of $\frac{11}{16} - 0.6875$ ?
If $5^{2x-1} = 125^{x-2}$ , what is the value of $x$ ?
A student is comparing the effectiveness of different study methods by tracking test scores before and after using each method. She has data for 15 students across 4 different methods. To determine which method shows the greatest improvement AND which method has the most consistent results, which analytical approach would be most appropriate?

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