Browse Math problems in the Studdy Learning Bank!

Problem 5601

Find two standard form equations with the same solutions as $4x - 5y = 10$ .

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Problem 5602

Determine which of the given expressions are real numbers: $(-1024)^{1 / 5}$ , $(-256)^{1 / 8}$ , $(-531441)^{1 / 12}$ , $(-131072)^{1 / 17}$ .

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Problem 5603

Who is right about the GCF of $16$ and $12$ ? Explain the correct GCF.

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Problem 5604

Convert $4.74$ imperial gallons to cubic feet, rounded to the nearest whole number.

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Problem 5605

A patient takes $\$7\$ days to recover from a surgical procedure with a mean recovery time of$ \ $4.9\$ days and a standard deviation of$ \ $2.1\$ days. Find the patient's$ z$-score. (Round to two decimal places.)

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Problem 5606

Approximate $e$ by substituting large $n$ into $\left(1+\frac{1}{n}\right)^{n}$ .

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Problem 5607

Find the value of $y$ given the equation $y-4=\frac{3}{7}$ . Write the answer as a fraction or rounded to two decimal places.

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Problem 5608

Find the product of two linear functions $g(x) = 2x - 1$ and $h(x) = 3x + 4$ .

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Problem 5609

Convert 9 feet 10 inches to inches. Given: 1 foot = 12 inches, find the length of the board in inches.

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Problem 5610

Expand $(1-2x)^{1/2}$ as a power series in $x$ up to and including $x^3$ , simplifying coefficients, where $-1/2<x<1/2$ .

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Problem 5611

Write a proportion for the statement: $7$ is to $35$ as $4$ is to $20$ .

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Problem 5612

Contractor needs nails for house. Small boxes have 200 nails, large 400. Bought 3 times more large boxes. Solve $3y + x = 28$ and $2x + 3y = 14$ to find small boxes $x$ and large boxes $y$ .

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Problem 5613

Find the number of chickens ( $x$ ) and cows ( $y$ ) if the total number of legs is 18, where $2x + 4y = 18$ .

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Problem 5614

Find the value of $z$ given $x=59$ , $\mu=43$ , and $\sigma=6.2$ . (Round your answer to two decimal places.)

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Problem 5615

(a) The most obese countries have obesity rates ranging from $11.4\%$ to $74.6\%$ . Estimate the average obesity percentage. (Round to 2 decimal places)
(b) The US obesity rate is $33.9\%$ . Is this above or below average? above average below average
(c) The US has an obesity rate higher than at least $\%$ of the countries in the data set.

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Problem 5616

Find the first two approximations of the root of $f(x) = x^2 - 2x - 8$ using Newton's method, given $x_0 = 3$ .

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Problem 5617

Find the final coordinates after moving left 2 units and down 1 unit from the starting point $(4,2)$ .

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Problem 5618

Complete the table for $y=-6x+19$ and graph the function.

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Problem 5619

Rafael took a taxi, paid $\$ 46$ and gave a $15\%$ tip. (a) Create a proportion to find the tip amount $x$ . (b) Use the proportion to find the tip amount without rounding. Amount of tip: $\$ x$

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Problem 5620

The number of a company's video stores can be approximated by $y=-266x+4887$ , where $x$ is years after 2005. a. Graph the linear equation. b. The missing coordinate is $(8, -2009)$ . c. The company will have 400 video stores in 2013. d. The $y$ -coordinate of the $y$ -intercept is 4887. e. The $x$ -intercept represents the year when the company had 0 video stores.

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Problem 5621

Find the product of two $2 \times 2$ matrices: $\left[\begin{array}{cc}-2 & 0\\0 & -4\\0 & 3\\-2 & 0\end{array}\right]$ and $\left[\begin{array}{cc}-1 & -1\\3 & -1\end{array}\right]$ .

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Problem 5622

Complete the equation and identify the property used. Determine the value of the underlined expression. $8 \times(14+7)=84+(8 \times 7)$ $7+(8+12)=\underline{47}+12$

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Problem 5623

Find the probability that event A occurs given that event B occurs, given that the probabilities of A, B, and A and B occurring are $\frac{5}{8}$ , $\frac{4}{5}$ , and $\frac{5}{9}$ respectively.

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Problem 5624

Find the sum of the first 12 terms of an arithmetic progression with first term $15$ and common difference $13$ .

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Problem 5625

Solve the equation $-2.9 x - 3.1 = 5.6$ and check the result.

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Problem 5626

Find the probability of selecting 3 women as officers from a club with 8 men and 7 women.

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Problem 5627

Solve the equation $y - 5 = 3$ .

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Problem 5628

Simplify the expression $4^{2} + 2 \div 2 + \sqrt{36}$ and select the correct answer from the given options.

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Problem 5629

Solve for $x$ in the equation $y = \frac{9x-7}{7x+5}$ .

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Problem 5630

Solve for $b$ in the equation $\frac{2 A}{b} = h$ .

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Problem 5631

Solve the equation $9^x + 2 \cdot 3^{x+1} = 1$ for the value of $x$ .

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Problem 5632

Dr. Potter gave $60$ vaccinations with a total of $184$ doses. Each polio vaccination has $4$ doses, and each measles vaccination has $2$ doses. Find the number of polio and measles vaccinations given.

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Problem 5633

Find the $T_F$ - and $T_C$ -intercepts of the linear equation $T_F = \frac{9}{5}T_C + 32$ (rounded to the nearest integer).

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Problem 5634

If a line on a graph is horizontal, it has a $\textbf{zero slope}$ .

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Problem 5635

Find the number of signatures each person has, given that Victor has 50 more signatures than Marsha and they have a total of 280 signatures.
Let $s$ be the number of signatures Marsha has. Then, Victor has $s+50$ signatures. The total number of signatures is $s + (s+50) = 280$ .

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Problem 5636

Find the solution to the system of linear inequalities $x \geq -4, x + 2y < 10, 3x + 6y \geq 9$ . Determine if the point $(3,0)$ satisfies the system.

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Problem 5637

Match each $(x,y)$ pair with the corresponding linear function $y = mx + b$ .

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Problem 5638

Determine which points $(x, y)$ satisfy the system of inequalities: $x \geq -4$ , $x + 2y < 10$ , $3x + 6y \geq 9$ . Explain why each of the given points $(-1, 1)$ , $(3, 0)$ , $(-5, -5)$ , and $(0, 5)$ is or is not a solution.

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Problem 5639

Simplify the expression: $\sqrt{5}+\frac{\sqrt{5}}{10}(\sqrt{32}-5)$ .

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Problem 5640

Find the real numbers $x$ that satisfy the equation $3^{8-x}=27^{x}$ .

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Problem 5641

Find the coordinates of the vertex $A'$ after rotating triangle $ABC$ with vertices $A(1,5), B(5,2)$ , and $C(-1,2)$ by $90^{\circ}$ .

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Problem 5642

Find the exact value of $x$ given the equation $5 \cdot 8^{4 x}=376$ .

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Problem 5643

Solve the quadratic equation $4a^2 = 1 - 16a$ for the variable $a$ .

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Problem 5644

Determine if $0$ is a perfect square and justify your answer.

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Problem 5645

Find the probability of rolling a 2 or 7 on a number cube. Express the answer as a decimal or simplified fraction.
$P(2 \text{ or } 7) = \frac{2}{6}$

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Problem 5646

Find the solution set for the absolute value equation $12-|m-4|=8$ .

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Problem 5647

Solve for $x$ in the linear equation $\frac{-3x+y}{6}=1$ , then evaluate the function at $x=2$ .

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Problem 5648

Find the length of AC given that AB=7 ft, BD=2 ft, and DC=4.5 ft. Round the final answer to 2 decimal places.

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Problem 5649

Which paper towel product offers the better value? Product A: $\$ 5.16$ for 6 rolls, or Product B: $\$ 7.04$ for 8 rolls?

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Problem 5650

Solve $3x^2=15$ and find the $x$ -intercepts of $f(x)=3x^2-15$ . The solution(s) is/are $x=\pm\sqrt{5}$ .

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Problem 5651

Find the rate of boxes of spaghetti to ounces. Jacob uses $14$ boxes of spaghetti weighing $168$ ounces total.

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Problem 5652

Solve the equation $11r + 9 + 2r = 9$ , simplifying and finding the value of $r$ .

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Problem 5653

Find the rental cost for each movie and video game given that Lisa rented 3 movies, 2 games for $18, and 8 movies, 4 games for$ 41.

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Problem 5654

Find the least common denominator for $4/5 + 18/100$ .

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Problem 5655

Solve the equation $2(y-1.1)+0.5=-0.5$ and verify the solution.

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Problem 5656

Graph the rational function $f(x)=\frac{-3}{-x-2}$ .

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Problem 5657

Solve for $f$ in the equation $-10+f=10-5j+4$ .

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Problem 5658

Find the probability of not being dealt a queen from a standard 52-card deck. The probability is $\frac{48}{52}$ .

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Problem 5659

Find the value of $\cot 80^{\circ}$ rounded to the nearest thousandth.

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Problem 5660

Find the sum of squared differences between $x_k$ and $y_k$ values from the given table, rounded to 4 decimal places.
$\sum_{k=1}^{4}\left(x_{k}-y_{k}\right)^{2}$

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Problem 5661

Simplify $(5 x)^{2}$ and verify using a graphing calculator.

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Problem 5662

Find the percentage of 22 in 40 and calculate 65% of 60.

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Problem 5663

Sketch the graph of $y=x^{4}-8x^{3}+16x^{2}-2$ and summarize key points in a table.

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Problem 5664

Solve for $x$ and round to nearest whole number in the equation $-12(2 x+12)=-6$ .

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Problem 5665

Simplify the expression $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ and select the correct answer.

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Problem 5666

A car worth $\$ 42,000$ depreciates by $\$ 6000$ per year. The model is $y=-6000 x+42,000$ . Find the missing coordinate $(4, ?)$ and interpret the $y$ -intercept. What does the $x$ -intercept represent?

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Problem 5667

Find the value of a number if $150\%$ of it is 50.

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Problem 5668

A virus infects 1 in 400 people. A test is positive 80% if infected and 10% if not infected. Find the probability a person has the virus given a positive test, and the probability a person doesn't have the virus given a negative test, rounded to the nearest tenth of a percent.
$P(A \mid B) = 95.2\%$ $P(A' \mid B') = 99.8\%$

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Problem 5669

Rewrite the quadratic equation $y = -(x - 1)^2$ in standard form.

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Problem 5670

Is $8,397$ divisible by $9$ ? If so, express it as $9 \times$ another factor. If not, explain.

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Problem 5671

Find the number that is 40% of 13. Translate to an equation: $x = 0.4 \times 13$ . Solve for $x$ .

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Problem 5672

Convert $0.\overline{72}$ to a rational number in simplest form.

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Problem 5673

Solve the linear equation $2(x-4)=16$ for the value of $x$ .

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Problem 5674

Solve for $x$ in the equation $-14x = \frac{-9}{2}$ . Express the final answer as a decimal rounded to 2 decimal places.

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Problem 5675

Find the value of $a$ if $7^{a}=\sqrt[8]{7^{3}}$ .

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Problem 5676

Solve for $g$ in the equation $6.5g + 6 = 3.5g + 18$ . Find the value of $g$ and explain how to check the solution.

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Problem 5677

Find the value of $y$ when $x$ is 11, given the equation $y=|x|+8$ .

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Problem 5678

Solve for $g$ : $-4.9g + 13.5 + 3.2g = 5.7 + 2g$

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Problem 5679

Find the range of values for $x$ that satisfy the inequality $9 x - 6 < 21$ .

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Problem 5680

Find the number of $x$ -intercepts of a parabola $a x^{2} + b x + c = 0$ given $b^{2} - 4 a c = -4$ .

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Problem 5681

Solve the quadratic equation $x^{2} + 9x + 27 = 7$ for $x$ .

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Problem 5682

Encuentre el punto de intersección de dos líneas con ecuaciones $y=-\frac{4}{3}x+2$ y $y=\frac{1}{3}x+2$ .

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Problem 5683

Express the product of 6 and the difference between 5 and $x$ .

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Problem 5684

Analyze and persevere to write a numerical expression with at least 3 operations that equals $5 + (8 - 4) \div 2 + 3$ . Justify your answer.

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Problem 5685

Find the value of $x$ in the equation $6x = x - 1,680$ .

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Problem 5686

Find the grid width and vertical axis scale to best plot the distance data over time. The data shows the distance (km) at various time points (minutes).

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Problem 5687

Find the equation(s) with $a = -6$ as a possible solution. $a^2 = 36$ or $a^3 = 216$ ?

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Problem 5688

Rewrite rotation formulas to eliminate $x'y'$ -term in equation $x^2 + 16xy + y^2 - 3 = 0$ .

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Problem 5689

Solve the equation $5(x-6)=2(x+3)$ for $x$ .

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Problem 5690

Compute the tax owed by a married couple with $\$ 226,000$ taxable income and a $\$ 6,000$ tax credit, using the 2021 marginal tax rates.

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Problem 5691

Add $2.3 \cdot 10^{8}$ and $4.7 \cdot 10^{7}$ and express the result in scientific notation.

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Problem 5692

Find the amounts of 16% and 35% alcohol solutions to mix for a 38 oz, 27% alcohol solution.

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Problem 5693

Find the expression for 9 more than the quotient of 2 and $x$ .

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Problem 5694

Solve for $x$ where $6^{x}=11$ .

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Problem 5695

Write the sum using sigma notation: $\sum_{k=1}^{8} k^2$ .

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Problem 5696

Solve $|5 x-8|=2$ algebraically and verify the solution(s) meet the restrictions.

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Problem 5697

Generate at least 8 binary characters to distinguish species. List each character, its possible states, and abbreviations.
Example: $C_1$ - Presence of Tail (Absent $C_{1a}$ , Present $C_{1p}$ )

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Problem 5698

Solve the quadratic equation $2-3y+5(3y-2)^2=0$ for the value of $y$ .

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Problem 5699

Find the number of pet owners who own a dog but not a cat, given that 136 pet owners were surveyed, 94 own a dog, 12 own a cat, and 2 own both. $\text{Answer} = \square \text{ owners}$

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Problem 5700

Find the product of $(9x+2)(9x-2)$ and verify the result using a graphing calculator.

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Math

Problem 5601

Find two standard form equations with the same solutions as 4x−5y=104x - 5y = 104x−5y=10.

Problem 5602

Determine which of the given expressions are real numbers: (−1024)1/5(-1024)^{1 / 5}(−1024)1/5, (−256)1/8(-256)^{1 / 8}(−256)1/8, (−531441)1/12(-531441)^{1 / 12}(−531441)1/12, (−131072)1/17(-131072)^{1 / 17}(−131072)1/17.

Problem 5603

Who is right about the GCF of 161616 and 121212? Explain the correct GCF.

Problem 5604

Convert 4.744.744.74 imperial gallons to cubic feet, rounded to the nearest whole number.

Problem 5605

Problem 5606

Approximate eee by substituting large nnn into (1+1n)n\left(1+\frac{1}{n}\right)^{n}(1+n1​)n.

Problem 5607

Find the value of yyy given the equation y−4=37y-4=\frac{3}{7}y−4=73​. Write the answer as a fraction or rounded to two decimal places.

Problem 5608

Find the product of two linear functions g(x)=2x−1g(x) = 2x - 1g(x)=2x−1 and h(x)=3x+4h(x) = 3x + 4h(x)=3x+4.

Problem 5609

Convert 9 feet 10 inches to inches. Given: 1 foot = 12 inches, find the length of the board in inches.

Problem 5610

Expand (1−2x)1/2(1-2x)^{1/2}(1−2x)1/2 as a power series in xxx up to and including x3x^3x3, simplifying coefficients, where −1/2<x<1/2-1/2<x<1/2−1/2<x<1/2.

Problem 5611

Write a proportion for the statement: 777 is to 353535 as 444 is to 202020.

Problem 5612

Contractor needs nails for house. Small boxes have 200 nails, large 400. Bought 3 times more large boxes. Solve 3y+x=283y + x = 283y+x=28 and 2x+3y=142x + 3y = 142x+3y=14 to find small boxes xxx and large boxes yyy.

Problem 5613

Find the number of chickens (xxx) and cows (yyy) if the total number of legs is 18, where 2x+4y=182x + 4y = 182x+4y=18.

Problem 5614

Find the value of zzz given x=59x=59x=59, μ=43\mu=43μ=43, and σ=6.2\sigma=6.2σ=6.2. (Round your answer to two decimal places.)

Problem 5615

Problem 5616

Find the first two approximations of the root of f(x)=x2−2x−8f(x) = x^2 - 2x - 8f(x)=x2−2x−8 using Newton's method, given x0=3x_0 = 3x0​=3.

Problem 5617

Find the final coordinates after moving left 2 units and down 1 unit from the starting point (4,2)(4,2)(4,2).

Problem 5618

Complete the table for y=−6x+19y=-6x+19y=−6x+19 and graph the function.

Problem 5619

Rafael took a taxi, paid $46\$ 46$46 and gave a 15%15\%15% tip. (a) Create a proportion to find the tip amount xxx. (b) Use the proportion to find the tip amount without rounding. Amount of tip: $x\$ x$x

Problem 5620

Problem 5621

Find the product of two 2×22 \times 22×2 matrices: [−200−403−20]\left[\begin{array}{cc}-2 & 0\\0 & -4\\0 & 3\\-2 & 0\end{array}\right]⎣⎡​−200−2​0−430​⎦⎤​ and [−1−13−1]\left[\begin{array}{cc}-1 & -1\\3 & -1\end{array}\right][−13​−1−1​].

Problem 5622

Complete the equation and identify the property used. Determine the value of the underlined expression. 8×(14+7)=84+(8×7)8 \times(14+7)=84+(8 \times 7)8×(14+7)=84+(8×7) 7+(8+12)=47‾+127+(8+12)=\underline{47}+127+(8+12)=47​+12

Problem 5623

Find the probability that event A occurs given that event B occurs, given that the probabilities of A, B, and A and B occurring are 58\frac{5}{8}85​, 45\frac{4}{5}54​, and 59\frac{5}{9}95​ respectively.

Problem 5624

Find the sum of the first 12 terms of an arithmetic progression with first term 151515 and common difference 131313.

Problem 5625

Solve the equation −2.9x−3.1=5.6-2.9 x - 3.1 = 5.6−2.9x−3.1=5.6 and check the result.

Problem 5626

Find the probability of selecting 3 women as officers from a club with 8 men and 7 women.

Problem 5627

Solve the equation y−5=3y - 5 = 3y−5=3.

Problem 5628

Simplify the expression 42+2÷2+364^{2} + 2 \div 2 + \sqrt{36}42+2÷2+36​ and select the correct answer from the given options.

Problem 5629

Solve for xxx in the equation y=9x−77x+5y = \frac{9x-7}{7x+5}y=7x+59x−7​.

Problem 5630

Solve for bbb in the equation 2Ab=h\frac{2 A}{b} = hb2A​=h.

Problem 5631

Solve the equation 9x+2⋅3x+1=19^x + 2 \cdot 3^{x+1} = 19x+2⋅3x+1=1 for the value of xxx.

Problem 5632

Dr. Potter gave 606060 vaccinations with a total of 184184184 doses. Each polio vaccination has 444 doses, and each measles vaccination has 222 doses. Find the number of polio and measles vaccinations given.

Problem 5633

Find the TFT_FTF​- and TCT_CTC​-intercepts of the linear equation TF=95TC+32T_F = \frac{9}{5}T_C + 32TF​=59​TC​+32 (rounded to the nearest integer).

Problem 5634

If a line on a graph is horizontal, it has a zero slope\textbf{zero slope}zero slope.

Problem 5635

Problem 5636

Find the solution to the system of linear inequalities x≥−4,x+2y<10,3x+6y≥9x \geq -4, x + 2y < 10, 3x + 6y \geq 9x≥−4,x+2y<10,3x+6y≥9. Determine if the point (3,0)(3,0)(3,0) satisfies the system.

Problem 5637

Match each (x,y)(x,y)(x,y) pair with the corresponding linear function y=mx+by = mx + by=mx+b.

Problem 5638

Problem 5639

Simplify the expression: 5+510(32−5)\sqrt{5}+\frac{\sqrt{5}}{10}(\sqrt{32}-5)5​+105​​(32​−5).

Problem 5640

Find the real numbers xxx that satisfy the equation 38−x=27x3^{8-x}=27^{x}38−x=27x.

Problem 5641

Find the coordinates of the vertex A′A'A′ after rotating triangle ABCABCABC with vertices A(1,5),B(5,2)A(1,5), B(5,2)A(1,5),B(5,2), and C(−1,2)C(-1,2)C(−1,2) by 90∘90^{\circ}90∘.

Problem 5642

Find the exact value of xxx given the equation 5⋅84x=3765 \cdot 8^{4 x}=3765⋅84x=376.

Find two standard form equations with the same solutions as $4x - 5y = 10$ .

Determine which of the given expressions are real numbers: $(-1024)^{1 / 5}$ , $(-256)^{1 / 8}$ , $(-531441)^{1 / 12}$ , $(-131072)^{1 / 17}$ .

Who is right about the GCF of $16$ and $12$ ? Explain the correct GCF.

Convert $4.74$ imperial gallons to cubic feet, rounded to the nearest whole number.

Approximate $e$ by substituting large $n$ into $\left(1+\frac{1}{n}\right)^{n}$ .

Find the value of $y$ given the equation $y-4=\frac{3}{7}$ . Write the answer as a fraction or rounded to two decimal places.

Find the product of two linear functions $g(x) = 2x - 1$ and $h(x) = 3x + 4$ .

Expand $(1-2x)^{1/2}$ as a power series in $x$ up to and including $x^3$ , simplifying coefficients, where $-1/2<x<1/2$ .

Write a proportion for the statement: $7$ is to $35$ as $4$ is to $20$ .

Contractor needs nails for house. Small boxes have 200 nails, large 400. Bought 3 times more large boxes. Solve $3y + x = 28$ and $2x + 3y = 14$ to find small boxes $x$ and large boxes $y$ .

Find the number of chickens ( $x$ ) and cows ( $y$ ) if the total number of legs is 18, where $2x + 4y = 18$ .

Find the value of $z$ given $x=59$ , $\mu=43$ , and $\sigma=6.2$ . (Round your answer to two decimal places.)

Find the first two approximations of the root of $f(x) = x^2 - 2x - 8$ using Newton's method, given $x_0 = 3$ .

Find the final coordinates after moving left 2 units and down 1 unit from the starting point $(4,2)$ .

Complete the table for $y=-6x+19$ and graph the function.

Rafael took a taxi, paid $\$ 46$ and gave a $15\%$ tip. (a) Create a proportion to find the tip amount $x$ . (b) Use the proportion to find the tip amount without rounding. Amount of tip: $\$ x$

Find the product of two $2 \times 2$ matrices: $\left[\begin{array}{cc}-2 & 0\\0 & -4\\0 & 3\\-2 & 0\end{array}\right]$ and $\left[\begin{array}{cc}-1 & -1\\3 & -1\end{array}\right]$ .

Complete the equation and identify the property used. Determine the value of the underlined expression. $8 \times(14+7)=84+(8 \times 7)$ $7+(8+12)=\underline{47}+12$

Find the probability that event A occurs given that event B occurs, given that the probabilities of A, B, and A and B occurring are $\frac{5}{8}$ , $\frac{4}{5}$ , and $\frac{5}{9}$ respectively.

Find the sum of the first 12 terms of an arithmetic progression with first term $15$ and common difference $13$ .

Solve the equation $-2.9 x - 3.1 = 5.6$ and check the result.

Solve the equation $y - 5 = 3$ .

Simplify the expression $4^{2} + 2 \div 2 + \sqrt{36}$ and select the correct answer from the given options.

Solve for $x$ in the equation $y = \frac{9x-7}{7x+5}$ .

Solve for $b$ in the equation $\frac{2 A}{b} = h$ .

Solve the equation $9^x + 2 \cdot 3^{x+1} = 1$ for the value of $x$ .

Dr. Potter gave $60$ vaccinations with a total of $184$ doses. Each polio vaccination has $4$ doses, and each measles vaccination has $2$ doses. Find the number of polio and measles vaccinations given.

Find the $T_F$ - and $T_C$ -intercepts of the linear equation $T_F = \frac{9}{5}T_C + 32$ (rounded to the nearest integer).

If a line on a graph is horizontal, it has a $\textbf{zero slope}$ .

Find the solution to the system of linear inequalities $x \geq -4, x + 2y < 10, 3x + 6y \geq 9$ . Determine if the point $(3,0)$ satisfies the system.

Match each $(x,y)$ pair with the corresponding linear function $y = mx + b$ .

Simplify the expression: $\sqrt{5}+\frac{\sqrt{5}}{10}(\sqrt{32}-5)$ .

Find the real numbers $x$ that satisfy the equation $3^{8-x}=27^{x}$ .

Find the coordinates of the vertex $A'$ after rotating triangle $ABC$ with vertices $A(1,5), B(5,2)$ , and $C(-1,2)$ by $90^{\circ}$ .

Find the exact value of $x$ given the equation $5 \cdot 8^{4 x}=376$ .

Solve the quadratic equation $4a^2 = 1 - 16a$ for the variable $a$ .

Determine if $0$ is a perfect square and justify your answer.

Find the probability of rolling a 2 or 7 on a number cube. Express the answer as a decimal or simplified fraction.
$P(2 \text{ or } 7) = \frac{2}{6}$

Find the solution set for the absolute value equation $12-|m-4|=8$ .

Solve for $x$ in the linear equation $\frac{-3x+y}{6}=1$ , then evaluate the function at $x=2$ .

Which paper towel product offers the better value? Product A: $\$ 5.16$ for 6 rolls, or Product B: $\$ 7.04$ for 8 rolls?

Solve $3x^2=15$ and find the $x$ -intercepts of $f(x)=3x^2-15$ . The solution(s) is/are $x=\pm\sqrt{5}$ .

Find the rate of boxes of spaghetti to ounces. Jacob uses $14$ boxes of spaghetti weighing $168$ ounces total.

Solve the equation $11r + 9 + 2r = 9$ , simplifying and finding the value of $r$ .

Find the rental cost for each movie and video game given that Lisa rented 3 movies, 2 games for $18, and 8 movies, 4 games for$ 41.

Find the least common denominator for $4/5 + 18/100$ .

Solve the equation $2(y-1.1)+0.5=-0.5$ and verify the solution.

Graph the rational function $f(x)=\frac{-3}{-x-2}$ .

Solve for $f$ in the equation $-10+f=10-5j+4$ .

Find the probability of not being dealt a queen from a standard 52-card deck. The probability is $\frac{48}{52}$ .

Find the value of $\cot 80^{\circ}$ rounded to the nearest thousandth.

Find the sum of squared differences between $x_k$ and $y_k$ values from the given table, rounded to 4 decimal places.
$\sum_{k=1}^{4}\left(x_{k}-y_{k}\right)^{2}$

Simplify $(5 x)^{2}$ and verify using a graphing calculator.

Sketch the graph of $y=x^{4}-8x^{3}+16x^{2}-2$ and summarize key points in a table.

Solve for $x$ and round to nearest whole number in the equation $-12(2 x+12)=-6$ .

Simplify the expression $\frac{1}{4}+\frac{9}{10} y-\frac{3}{5} y+\frac{7}{8}$ and select the correct answer.

A car worth $\$ 42,000$ depreciates by $\$ 6000$ per year. The model is $y=-6000 x+42,000$ . Find the missing coordinate $(4, ?)$ and interpret the $y$ -intercept. What does the $x$ -intercept represent?

Find the value of a number if $150\%$ of it is 50.

Rewrite the quadratic equation $y = -(x - 1)^2$ in standard form.

Is $8,397$ divisible by $9$ ? If so, express it as $9 \times$ another factor. If not, explain.

Find the number that is 40% of 13. Translate to an equation: $x = 0.4 \times 13$ . Solve for $x$ .

Convert $0.\overline{72}$ to a rational number in simplest form.

Solve the linear equation $2(x-4)=16$ for the value of $x$ .

Solve for $x$ in the equation $-14x = \frac{-9}{2}$ . Express the final answer as a decimal rounded to 2 decimal places.