Evaluate the expression $P = -3x^2 - (2x - y)$ when $x = -2$ and $y = 5$.
Simplify the expression using exponent rules: $\left( \frac{15x^{-3}y^4}{5x^2y^{-1}} \right)^{-2}$.
Solve for $x$: $\frac{2}{3}(6x - 9) - 5 = \frac{1}{2}x + 1$.
Solve the compound inequality: $-1 < \frac{3x - 5}{2} \le 5$.
Solve the linear inequality and determine which statement about the solution set is FALSE: $-4(x - 3) + 2x > 20$.
Determine the domain of the function $f(x) = \frac{\sqrt{x - 3}}{x - 7}$.
Determine the range of the function $g(x) = -2|x + 1| + 5$.
What is the $y$-intercept of the line $5x - 3y = 15$?
Which equation represents the line perpendicular to $y = -\frac{2}{5}x + 8$ and passing through the point $(-4, 1)$?
The line passing through $(3, k)$ and $(-1, 5)$ has a slope $m = -\frac{3}{4}$. Find the value of $k$.
Solve the system of equations using elimination: $3x + 4y = 1$ and $5x - 2y = -7$.
Solve the system of equations using substitution: $y = 3x - 10$ and $2x + 5y = 1$.
Calculate the value of $\frac{6.3 \times 10^{-4}}{9.0 \times 10^{3}}$ and express the result in scientific notation.
Simplify the expression assuming $a \ne 0$ and $b \ne 0$: $\left( \frac{a^0 b^{-3}}{a^2 b^1} \right)^{-3}$.
Simplify the polynomial expression: $(5x^2 - 3xy + 7y^2) - (2x^2 + 5xy - y^2)$.
Expand the product of the polynomials: $(x - 3)(2x^2 + 5x - 1)$.
Factor the trinomial completely: $6x^2 - 17x + 5$.
Factor the expression completely: $4x^3 - 36x$.
The inequality $y > -\frac{1}{2}x + 3$ is graphed. Which description of the graph is correct?
Solve the literal equation $A = P + Prt$ for the variable $r$.
Three times a number decreased by 5 is 16. If $x$ represents the number, which equation models this relationship, and what is the value of $x$?
The sum of two consecutive odd integers is 52. What is the value of the smaller integer?
The length of a rectangular garden is 4 meters more than its width. If the perimeter of the garden is 48 meters, what is the width of the garden?
A train traveled 450 km at a constant speed for 6 hours. What was the average speed of the train?
A chemist has 30 L of a solution that is $20\%$ acid. How many liters of pure acid are contained in the solution?
A cash register contains 20 coins, consisting only of nickels (\$0.05) and dimes (\$0.10). If the total value of the coins is \$1.65, how many dimes are there?
Sarah is currently 5 years older than Tom. In 3 years, the sum of their ages will be 41. How old is Tom currently?
Calculate the simple interest earned on a principal of \$8000 invested at an annual rate of $5\%$ for 4 years.
To receive an 'A' grade, a student needs a test average of at least 90. If their first three test scores are 85, 92, and 88, what is the minimum score $x$ they need on the fourth test to achieve an 'A'?
The ratio of red marbles to blue marbles in a bag is $4:7$. If there are 33 total marbles, how many blue marbles are in the bag?
A chemist has $10 \text{ L}$ of a $40\%$ acid solution. How many liters of a $70\%$ acid solution must be added to obtain a final solution that is $50\%$ acid?
A boat travels $60 \text{ km}$ upstream in the same amount of time it travels $90 \text{ km}$ downstream. If the speed of the current is $5 \text{ km/h}$, what is the speed of the boat in still water?
A farmer has $100 \text{ meters}$ of fencing and wants to enclose a rectangular garden bordered on one side by a long barn (no fence needed on that side). What is the maximum area that can be enclosed?
Pipe A can fill a tank in $6$ hours, and Pipe B can fill it in $8$ hours. Pipe C can empty the tank in $4$ hours. If the tank is initially half full and all three pipes are opened simultaneously, how long will it take to reach full capacity?
The side lengths of a right-angled triangle form an arithmetic progression. If the hypotenuse is $15 \text{ cm}$, what is the length of the shortest side?
Sarah is $5$ years older than twice John's age. In $10$ years, Sarah's age will be $3$ years less than three times John's current age. How old is John now?
Determine the next term in the sequence: $2, 6, 12, 20, 30, \dots$
A rectangle has a perimeter of $34 \text{ cm}$. If the length is increased by $3 \text{ cm}$ and the width is decreased by $1 \text{ cm}$, the area remains unchanged. What is the original area of the rectangle?
The cost $C$ (in dollars) of producing $x$ units of a specialized product is modeled by the function $C(x) = 0.5x^2 - 60x + 2000$. What is the minimum production cost?
Pump A takes $3$ hours longer than Pump B to drain a pool alone. Working together, they can drain the entire pool in $2$ hours. How long does Pump A take to drain the pool alone?
A box-and-whisker plot displays a dataset where the median ($Q_2$) is located very close to the first quartile ($Q_1$), and the right whisker (from $Q_3$ to the maximum) is significantly longer than the left whisker. Which statement best describes the distribution of the data?
Given two events $A$ and $B$, $P(A) = 0.6$, $P(B) = 0.5$, and $P(A \cup B) = 0.9$. Using set notation, determine $P((A \cup B)')$, the probability that neither $A$ nor $B$ occurs.
A security code requires 5 digits. The first digit cannot be 0 or 1. The last digit must be an even number (0, 2, 4, 6, 8). Repetition of digits is allowed. How many distinct codes are possible?
A biased coin is tossed 150 times, resulting in 95 heads. Based on this experimental data, if the coin is tossed an additional 300 times, what is the best prediction for the total number of times it will land on tails across all 450 tosses?
A researcher calculated the summary statistics for a dataset and found that the third quartile ($Q_3$) is $85$. If the Interquartile Range ($IQR$) is $15$, what is the value of the first quartile ($Q_1$)?
In a large college cohort, $70\%$ of students passed Math ($M$), and $60\%$ passed Science ($S$). If $20\%$ of the students failed both subjects, what percentage of students passed only Math? (Use $P(M \cup S) = P(M) + P(S) - P(M \cap S)$)
How many distinct ways can the letters of the word MISSISSIPPI be arranged if the arrangement must begin and end with the letter 'S'?
A spinner with four equally sized sectors (1, 2, 3, 4) is spun 100 times. The results are: 1 (20 times), 2 (38 times), 3 (15 times), 4 (27 times). Which number exhibits the largest magnitude of difference between its theoretical probability and its experimental probability?
Given two events $A$ and $B$, $P(A') = 0.4$, $P(B') = 0.3$, and $P(A' \cap B') = 0.1$. Are events $A$ and $B$ independent?
Experiment 1: A standard six-sided die is rolled 50 times, yielding a '4' 12 times. Experiment 2: A different standard six-sided die is rolled 100 times, yielding a '4' 18 times. If both experiments are combined, what is the combined experimental probability of rolling a '4'?