A liquid has a density of $1.25 \text{ g/cm}^3$. What is its density in $\text{kg/m}^3$?
An item's cost price was $\$80$. The owner marked the price up. Later, the item was sold with a $20\%$ discount, but the owner still realized a $10\%$ profit on the original cost. What was the price before the $20\%$ discount?
Evaluate the following expression using the order of operations: $\frac{0.4 \times (1.5)^2 + 2 \div \frac{1}{4}}{\sqrt{0.81} - 0.5}$.
Calculate $\frac{(5.1 \times 10^{-4}) \times (2.0 \times 10^{7})}{6.0 \times 10^{-3}}$. Express the answer in standard scientific notation.
A complex calculation yields the result $450,912.18$. Round this value to three significant figures.
A television priced at $\$900$ is subjected to two consecutive discounts: first $20\%$ off, and then an additional $15\%$ off the discounted price. What is the final selling price?
Which of the following operations involving irrational numbers results in a rational number?
In a survey of $300$ students, $180$ are male. $70\%$ of the female students prefer math, and $105$ males also prefer math. What is the simplified ratio of female students who prefer math to male students who prefer math?
Evaluate: $\left( 3 \frac{1}{2} - 1.25 \right) \div \left( \frac{5}{6} + 0.5 \right)$.
An investment earned $\$350$ in simple interest over $2.5$ years. If the principal amount was $\$2800$, what was the annual interest rate?
A calculator shows the exact product $18.61 \times 3.09 = 57.5149$. If the calculation is estimated using $19 \times 3$, what is the percentage error of the estimation relative to the exact value? (Round the percentage to two decimal places.)
Container A contains liquid X and liquid Y in the ratio $3:2$. Container B contains X and Y in the ratio $5:1$. If $10$ liters from A is mixed with $12$ liters from B, what is the resulting ratio of X to Y in the final mixture?
A country's GDP was $\$1.5 \text{ trillion}$ in 2010 and $\$2.1 \text{ trillion}$ in 2020. What was the percentage increase in GDP over this decade?
Evaluate using order of operations and exponent rules: $100 \times (5^{-2}) + 8^{\frac{2}{3}} - 6^0$.
A pump moves water at a rate of $24 \text{ gallons per minute}$. If $1 \text{ gallon} \approx 3.785 \text{ liters}$, what is the flow rate in $\text{Liters per second}$? (Round to two decimal places.)
Calculate $(4.5 \times 10^5) + (3.1 \times 10^4)$ and express the result in standard scientific notation.
If $x$ is a non-zero rational number and $y$ is an irrational number, which expression must always result in an irrational number?
A company decreases its product price by $10\%$. By what percentage must the sales volume increase to maintain the same total revenue? (Round to two decimal places.)
Three chemicals, X, Y, and Z, are mixed in a ratio of $X:Y:Z = \frac{1}{3} : 0.5 : \frac{1}{6}$. If the total volume of the mixture is $1.8$ liters, how much more volume of chemical Y is there than chemical X?
A commodity's price increased by $20\%$ on Monday. On Tuesday, the price dropped by $25\%$ of the Monday closing price. If the final price on Tuesday was $\$90.00$, what was the original price of the commodity before Monday's increase?
A satellite is traveling at a constant speed of $18,000$ miles per hour. Given that $1$ mile $\approx 1.609$ kilometers, convert the satellite's speed to meters per second, rounded to three significant figures.
Machine A processes $15$ units in $2.5$ hours. Machine B processes $1.25$ times the number of units Machine A processes in the same amount of time. If both machines work together, how many hours will it take to process a total order of $99$ units?
A retailer sold a custom-made jacket for $\$770$, realizing a profit equal to $\frac{2}{9}$ of the original cost price. To maximize revenue, the retailer wishes to adjust the price such that the profit is exactly $25\%$ of the *new selling price*. What should the new selling price be?
The line $y = 2x + k$ intersects the parabola $y = x^2 - 4x + 7$ at exactly one point. Determine the distance from this unique intersection point to the origin $(0, 0)$.
A right trapezoid has height $h=12$ and its non-perpendicular side $c$ is $15$. The length of the shorter base $b$ and the longer base $a$ satisfy the relationship $2a - 3b = 11$. Find the area of the trapezoid.