Natural Numbers

Problem 401

Find the volume of a sphere with radius $r=1$ . Round the volume to the nearest hundredth.

See Solution

Problem 402

Evaluate the expression $\left(3^{2}\right)^{4}$ and select the correct answer. A) $(3 \times 3)(3 \times 3 \times 3 \times 3)$ B) $(3 \times 3 \times 3 \times 3 \times 3 \times 3)$ C) $(3 \times 3)(3 \times 3)(3 \times 3)(3 \times 3)$ D) $(3 \times 3 \times 3 \times 3)(3 \times 3 \times 3 \times 3)$

See Solution

Problem 403

Find the unknown value in the proportions: (a) $a: 6=7: 2$ and (b) $5: 4=b: 20$ .

See Solution

Problem 404

Find the areas and volumes of a round 11-inch and 8-inch by 10-inch rectangular pan. Determine which has the larger volume.
a) Area of round pan: $\pi (11/2)^2$ Area of rectangular pan: $8 \times 10$ b) Volume of round pan: $\pi (11/2)^2 \times 2$ Volume of rectangular pan: $8 \times 10 \times 2$ c) Compare the volumes to determine the larger pan.

See Solution

Problem 405

Find the value of $(\sqrt{a})^{2}$ for any nonnegative real number $a$ .

See Solution

Problem 406

Divide the expression $\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}$ .

See Solution

Problem 407

Simplify the expression $2^{2} + \sqrt{9} \cdot 3$ using the order of operations.

See Solution

Problem 408

Solve the quadratic equation $3x^2 + 8x - 1 = 0$ and select the correct solution set.

See Solution

Problem 409

Solve for the variable $v$ given the equation $25.6=\frac{v}{2}$ .

See Solution

Problem 410

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.
Let $p$ be the total number of people.
Equation: $p = \frac{93}{\frac{3}{5}}$

See Solution

Problem 411

Solve for $w$ in the equation $-5+w=7$ .

See Solution

Problem 412

Expand and simplify polynomial expressions, including binomial squares, products, and factorials. Determine equivalence of expanded polynomial expressions.
$2 x(3 x-5 x^{2}+4 y)$ $(x+4)^{2}$ $(3 x-4)(2 x+5)$ $(x+1)(x^{2}+2 x-3)$ $4 x(x+5)(x-5)$ $-2 a(a+4)^{2}$ $(x+2)(x-5)(x-2)$ $(2 x+1)(3 x-5)(4-x)$ $(9 a-5)^{3}$ $(a-b+c-d)(a+b-c-d)$

See Solution

Problem 413

Find the positive value of $p$ that satisfies the equation $\sqrt{4p^2 + 28} - 8 = 0$ .

See Solution

Problem 414

Rewrite interval with given values: $\hat{p} = 0.61, z^* = 0.82, SE_{\text{est}} = 0.00157$ . The interval is $[0.607, 0.613]$ .

See Solution

Problem 415

Find the decimal representation of $\sqrt{65}$ rounded to two decimal places.

See Solution

Problem 416

Solve for $y$ in the equation $5 y^{\frac{2}{3}} + 7 = 27$ .

See Solution

Problem 417

Find the area of a town with an area of $4.36$ square miles, given that $1$ mile $=1,760$ yards. The correct answer is $13,505,536$ square yards.

See Solution

Problem 418

Find the product of 9.2 and 9 1/2.

See Solution

Problem 419

Solve the linear equation $3x + 5 = 9x + 8$ for the unknown variable $x$ .

See Solution

Problem 420

Determine if all numbers are solutions to the inequality $\frac{60}{9} > 3 \times 5$ .

See Solution

Problem 421

Find the sum of two linear functions $h(n) = 2n - 4$ and $g(n) = n - 2$ .

See Solution

Problem 422

Solve the quadratic equation $-7x^2 - 2x + 6 = 0$ and find its roots.

See Solution

Problem 423

Find the unit that is to litre as gallon is to meter.
$A \text{ yard } = k \text{ meter}$ $A \text{ gallon } = x \text{ litre}$

See Solution

Problem 424

Find 4% of 250.

See Solution

Problem 425

Find inverse function $f^{-1}(x)$ of $f(x)=3x+4$ , then verify $f(f^{-1}(x))=x$ and $f^{-1}(f(x))=x$ .

See Solution

Problem 426

Show that if $a$ and $b$ are relatively prime, then $\operatorname{gcd}(da, db) = d$ for any positive integer $d$ .

See Solution

Problem 427

Divide $256$ by $24$ and write the result.

See Solution

Problem 428

Solve for $x$ given the equation $4x = 4.56$ .

See Solution

Problem 429

Simplify the expression: $\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}$ .

See Solution

Problem 430

Solve for $w$ in the formula $v = \frac{1}{3} w b$ .

See Solution

Problem 431

Simplify the expression $(b^{12})^{3}$ and write the answer as a power.

See Solution

Problem 432

Express $16 \sin (50 r) \sin (23 r)$ as a sum or difference of trigonometric functions.

See Solution

Problem 433

Solve for $n$ if $P(n, 2)=1482$ . Alicia's formula is $n^{2}-n-1482=0$ . Explain how she created the formula and use it to solve for $n$ .

See Solution

Problem 434

Express quadratic functions in standard form, find y-intercept. a) $f(x)=3x(x-4)$ , c) $f(x)=2(x-4)(3x+2)$ , b) $f(x)=(x-5)(x+7)$ , d) $f(x)=(3x-4)(2x+5)$ .

See Solution

Problem 435

Find the value of $p$ that satisfies the equation $\frac{6p+4}{6}=\frac{4p-8}{3}$ .

See Solution

Problem 436

Identify the critical points of $y=x^{2}e^{x}$ . State the $x$ - and $y$ -coordinates. Determine if they are local max, min, or neither.

See Solution

Problem 437

Convert $\frac{3}{4}$ pound to ounces.

See Solution

Problem 438

Verify $\cos^2 x \sec^2 x + \tan^2 x = \sec^2 x$ by transforming the left side.

See Solution

Problem 439

Analyze exponential growth/decay functions: $y=(\frac{3}{2})^{x}$ , $y=-4(0.5)^{x}$ , $y=4(0.25)^{x}$ , $y=-2(2)^{x}$ . Determine growth/decay, y-intercept, asymptote.

See Solution

Problem 440

Find the inverse of the one-to-one functions $g$ and $h$ , where $g=\{(1,3),(3,-1),(4,-7),(6,8),(7,6)\}$ and $h(x)=\frac{x-13}{5}$ . Determine $g^{-1}(6)$ , $h^{-1}(x)$ , and $\left(h \circ h^{-1}\right)(-4)$ .

See Solution

Problem 441

Engineers must design helmets to fit the normal distribution of male head breadths with $\mu = 6.1$ -in and $\sigma = 1.2$ -in.
Find the middle $99\%$ of head breadths: Between $3.71$ -in and $8.49$ -in.
Find the middle $99\%$ of sample averages for head breadths of size $60$ : Between $5.86$ -in and $6.34$ -in.

See Solution

Problem 442

Convert 6 tons to pounds. Solve for the unknown value that, when multiplied by 6, equals 12,000 pounds.

See Solution

Problem 443

Translate the phrase "42 decreased by twice Vanessa's age" into an algebraic expression using the variable $v$ to represent Vanessa's age.

See Solution

Problem 444

Solve for $y$ in the equation $-63=-2 y^{2}+9$ , expressing the answer as an integer or in simplest radical form.

See Solution

Problem 445

Solve the linear equation $4b + 6 = 2 - b + 4$ and select the correct solution.

See Solution

Problem 446

Find the quotient of -16 divided by -2, or state if undefined. $\frac{-16}{-2}=\square$

See Solution

Problem 447

Find the minimum $y$ -value of $f(x)=x^{2}+\frac{2}{x}$ on $\frac{1}{2} \leq x \leq 2$ .

See Solution

Problem 448

Find the number of oranges between 3 oz and 5 oz in a batch of 2300, given a normal distribution with $\mu = 6$ oz and $\sigma = 1.5$ oz.

See Solution

Problem 449

Find the solution, rounded to one decimal place, to the equation $e^{x} = \sqrt{x+8}$ using a graphing calculator.

See Solution

Problem 450

Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

See Solution

Problem 451

Find the equation that represents "three minus the difference of a number and one equals one-half of the difference of three times the same number and four".
$3 - (n - 1) = \frac{1}{2}(3n - 4)$

See Solution

Problem 452

Solve the equation $5^{\frac{x}{3}}=4$ . The exact solution is $x=\log_5(4)$ . The approximate solution, rounded to 4 decimal places, is $x=3.0910$ .

See Solution

Problem 453

Find the error in Jane's solution of the quadratic equation $x^2 - 5x - 24 = 0$ using the quadratic formula.

See Solution

Problem 454

Find the range of $x$ values where the function $f(x) = x^3 + 3x^2 - 9x + 7$ is increasing.

See Solution

Problem 455

Convert the total surface area of Africa, approximately 11,700,000 square miles, to scientific notation.

See Solution

Problem 456

Solve the linear equation $6x + 6 = 0$ for the unknown variable $x$ .

See Solution

Problem 457

1. Find the antiderivative of $f(x)$ : a) $f(x)=4x^3+3x^4$ b) $f(x)=\frac{1}{10}x^4-\frac{10}{x^4}$ e) $f(x)=2e^x+1$ f) $f(x)=\frac{1}{3}e^x-\frac{x^2}{2}$
2. Find the antiderivative of $f(x)$ : a) $f(x)=(3x-1)^2$ b) $f(x)=\frac{3}{(-5x+1)^4}$ e) $f(x)=e^{4x-1}$ f) $f(x)=\frac{2}{5}e^{2-5x}$ i) $f(x)=\sqrt{6x}$ j) $f(x)=\sqrt{9-\frac{1}{3}x}$

See Solution

Problem 458

Find a recursive formula for the number of seats in each row of a movie theater, where the explicit formula is $a_{n}=6+6 n$ and $n$ represents the row number.

See Solution

Problem 459

Find the value of $x$ in the system of linear equations $15x + 7y = 4$ , $-5x - 7y = 2$ , and $10x = 2$ . Enter the answer as a simplified fraction.

See Solution

Problem 460

Plot the quadratic equation $y = x^{2} + 10x + 21$ and find its roots using the graph.

See Solution

Problem 461

Evaluate the factorial ratio $\frac{16 !}{13 !}$ . The solution is $\square$ .

See Solution

Problem 462

Find the value of $n$ that satisfies the equation $n \times \frac{3}{4} = \frac{3}{16}$ .

See Solution

Problem 463

Graph the set of all $(x, y)$ satisfying $x + 2y > 2$ .

See Solution

Problem 464

Find the degree of the polynomial equation $2 x^{5} - 6 x^{4} = 0$ .

See Solution

Problem 465

Solve for h in the equation $7x + 4 = 7x + h$ to find the value of h that results in zero solutions.

See Solution

Problem 466

Solve for $f$ by completing the square: $2f^2 - 56f + 34 = 0$ . Express your answers as integers, simplified fractions, or rounded decimals.

See Solution

Problem 467

Divide $4x^3 - 16x^2 + 18x - 28$ by $-x + 3$ using long division. Find the quotient and remainder.

See Solution

Problem 468

Find $\alpha$ and $\beta$ values in $\cos(\alpha-\beta)$ expression. Write as $\cos(\square^\circ)$ and find exact value.

See Solution

Problem 469

Find all real numbers $x$ that satisfy the equation $\cos x = 15$ .

See Solution

Problem 470

Solve for the missing value in the proportion $44: 20 = \square: 5$ .

See Solution

Problem 471

Solve for $x$ in the inequality $3x - 7 > 7x + 9$ and graph the solution.

See Solution

Problem 472

Greg used $31/4$ feet of cloth for shorts and $22/3$ feet for a shirt. Which expression gives the total cloth used?

See Solution

Problem 473

Find the value of $b$ that satisfies the equation $14_b + 23_b = 40_b$ , where $b \in \{4, 5, 7\}$ .

See Solution

Problem 474

Find the number $x$ such that $x + 5/x = 6$ .

See Solution

Problem 475

Solve for y: $\sqrt{y+4}-4=0$

See Solution

Problem 476

Determine if half of all teens aged 13-17 have made new friends online using a 0.05 significance level and the normal distribution.
$H_0: p = 0.5$ $H_1: p \neq 0.5$

See Solution

Problem 477

Find the gradient of the line segment connecting the points $C(-5,6)$ and $D(2,-1)$ .

See Solution

Problem 478

Evaluate the expression $x^{2} + 4y \div 2w + 3z$ when $w=1, x=4, y=7, z=0$ .

See Solution

Problem 479

Find the value of the 4 digit in the number $2.34_{\text{five}}$ expressed as a fraction or in words.

See Solution

Problem 480

Demarco substitutes a value for $x$ in $\frac{1}{2} x=4$ . How can Demarco determine if the value is a solution?

See Solution

Problem 481

Multiply and simplify the expression $6 x y^{3} z \cdot 3 x^{2} y x^{2}$ .

See Solution

Problem 482

Solve the rational equation $\frac{4}{x+4}-\frac{2}{x-1}=\frac{4}{x^{2}+3x-4}$ .

See Solution

Problem 483

Polygraph experiment has 99 results: 22 wrong, 77 correct. Test if correct results are <80% using 0.05 significance. Find null/alt hypotheses, test statistic, P-value, conclusion.
$H_0: p = 0.80, H_1: p < 0.80$ Test statistic $z = -0.55$ P-value = 0.2912 (rounded to four decimal places)

See Solution

Problem 484

Estimate the absolute uncertainty for the result of the calculation: $\frac{157.2 \pm 6.0 - 59.3 \pm 1.9}{122.0 \pm 1.1} = 0.802459$ .

See Solution

Problem 485

Solve for the integer value(s) of $n$ in the equation $-62=-8 n^{2}+10$ .

See Solution

Problem 486

Simplify $3u + 3u = 42$ to find the value of $u$ .

See Solution

Problem 487

Radioactive substance decreases by 1/3 each year. Find recursive formula for amount left after $n$ years, where initial amount is $1,452 \mathrm{~g}$ . Is the sequence arithmetic or geometric?

See Solution

Problem 488

Jim is computing $3^{5}$ on a calculator, but gets an incorrect answer of 2,187. What is the correct operation to fix the error?

See Solution

Problem 489

Find the doubling time of an economic indicator increasing at 3% per year. Discuss the validity of the doubling time formula. Calculate the indicator's increase over 5 years.
$\text{Doubling time} = \frac{\ln 2}{r}$ , where $r$ is the growth rate. Determine if this formula is appropriate for the given case.

See Solution

Problem 490

Solve $x^{2}+28x=5$ by completing the square. Select the correct answer: A) $x=14 \pm \sqrt{191}$ B) $x=-14 \pm \sqrt{191}$ C) $x=-14 \pm \sqrt{201}$ D) $x=14 \pm \sqrt{201}$

See Solution

Problem 491

Simplify the equation $2(3v+4)=26$ to find the value of $v$ .

See Solution

Problem 492

Find the least common denominator (LCD) of the rational expressions $\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}$ . The LCD is $\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}$ .

See Solution

Problem 493

Solve for y, where 6 is greater than or equal to (y/8) - 4.

See Solution

Problem 494

Solve the system of linear equations $4x - y = 11$ and $x + y = 4$ using the elimination method. The system has no solution.

See Solution

Problem 495

Find the solutions to the equation $4x+21=-\left(\frac{1}{3}\right)^{x+4}+6$ .

See Solution

Problem 496

Find the cost of 4 potted plants and 5 bags of compost given the costs of 7 plants + 2 compost and 3 plants + 4 compost.
Cost of 7 potted plants and 2 bags of compost: $£ 41$ Cost of 3 potted plants and 4 bags of compost: $£ 27$

See Solution

Problem 497

Compare the doubling times using approximate and exact formulas. Find the population after 30 years if a nation of 100 million grows at $9\%$ per year.
The approximate doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years and the exact doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years.

See Solution

Problem 498

Solve for the value of $f$ that satisfies the inequality $-21 > 13 - 17f$ .

See Solution

Problem 499

Simplify the expression $25 a^{2} - 4 b^{2}$ to find the preferred form.

See Solution

Problem 500

Verify identity $\frac{1-\cos \theta}{\sin \theta}+\frac{\sin \theta}{1-\cos \theta}=2 \csc \theta$ . Simplify numerator $1+\sin^2 \theta$ .

See Solution

1 2 3 4 5 6 7 8 ...28

Natural Numbers

Problem 401

Find the volume of a sphere with radius r=1r=1r=1. Round the volume to the nearest hundredth.

Problem 402

Problem 403

Find the unknown value in the proportions: (a) a:6=7:2a: 6=7: 2a:6=7:2 and (b) 5:4=b:205: 4=b: 205:4=b:20.

Problem 404

Problem 405

Find the value of (a)2(\sqrt{a})^{2}(a​)2 for any nonnegative real number aaa.

Problem 406

Divide the expression v2−93v+v2+6v+96v\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}3vv2−9​+6vv2+6v+9​.

Problem 407

Simplify the expression 22+9⋅32^{2} + \sqrt{9} \cdot 322+9​⋅3 using the order of operations.

Problem 408

Solve the quadratic equation 3x2+8x−1=03x^2 + 8x - 1 = 03x2+8x−1=0 and select the correct solution set.

Problem 409

Solve for the variable vvv given the equation 25.6=v225.6=\frac{v}{2}25.6=2v​.

Problem 410

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.Let ppp be the total number of people.Equation: p=9335p = \frac{93}{\frac{3}{5}}p=53​93​

Problem 411

Solve for www in the equation −5+w=7-5+w=7−5+w=7.

Problem 412

Problem 413

Find the positive value of ppp that satisfies the equation 4p2+28−8=0\sqrt{4p^2 + 28} - 8 = 04p2+28​−8=0.

Problem 414

Rewrite interval with given values: p^=0.61,z∗=0.82,SEest=0.00157\hat{p} = 0.61, z^* = 0.82, SE_{\text{est}} = 0.00157p^​=0.61,z∗=0.82,SEest​=0.00157. The interval is [0.607,0.613][0.607, 0.613][0.607,0.613].

Problem 415

Find the decimal representation of 65\sqrt{65}65​ rounded to two decimal places.

Problem 416

Solve for yyy in the equation 5y23+7=275 y^{\frac{2}{3}} + 7 = 275y32​+7=27.

Problem 417

Find the area of a town with an area of 4.364.364.36 square miles, given that 111 mile =1,760=1,760=1,760 yards. The correct answer is 13,505,53613,505,53613,505,536 square yards.

Problem 418

Find the product of 9.2 and 9 1/2.

Problem 419

Solve the linear equation 3x+5=9x+83x + 5 = 9x + 83x+5=9x+8 for the unknown variable xxx.

Problem 420

Determine if all numbers are solutions to the inequality 609>3×5\frac{60}{9} > 3 \times 5960​>3×5.

Problem 421

Find the sum of two linear functions h(n)=2n−4h(n) = 2n - 4h(n)=2n−4 and g(n)=n−2g(n) = n - 2g(n)=n−2.

Problem 422

Solve the quadratic equation −7x2−2x+6=0-7x^2 - 2x + 6 = 0−7x2−2x+6=0 and find its roots.

Problem 423

Find the unit that is to litre as gallon is to meter.A yard =k meterA \text{ yard } = k \text{ meter}A yard =k meter A gallon =x litreA \text{ gallon } = x \text{ litre}A gallon =x litre

Problem 424

Find 4% of 250.

Problem 425

Find inverse function f−1(x)f^{-1}(x)f−1(x) of f(x)=3x+4f(x)=3x+4f(x)=3x+4, then verify f(f−1(x))=xf(f^{-1}(x))=xf(f−1(x))=x and f−1(f(x))=xf^{-1}(f(x))=xf−1(f(x))=x.

Problem 426

Show that if aaa and bbb are relatively prime, then gcd⁡(da,db)=d\operatorname{gcd}(da, db) = dgcd(da,db)=d for any positive integer ddd.

Problem 427

Divide 256256256 by 242424 and write the result.

Problem 428

Solve for xxx given the equation 4x=4.564x = 4.564x=4.56.

Problem 429

Simplify the expression: 1−2x1+x∗−7−7x2x−1\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}1+x1−2x​∗2x−1−7−7x​.

Problem 430

Solve for www in the formula v=13wbv = \frac{1}{3} w bv=31​wb.

Problem 431

Simplify the expression (b12)3(b^{12})^{3}(b12)3 and write the answer as a power.

Problem 432

Express 16sin⁡(50r)sin⁡(23r)16 \sin (50 r) \sin (23 r)16sin(50r)sin(23r) as a sum or difference of trigonometric functions.

Problem 433

Solve for nnn if P(n,2)=1482P(n, 2)=1482P(n,2)=1482. Alicia's formula is n2−n−1482=0n^{2}-n-1482=0n2−n−1482=0. Explain how she created the formula and use it to solve for nnn.

Problem 434

Express quadratic functions in standard form, find y-intercept. a) f(x)=3x(x−4)f(x)=3x(x-4)f(x)=3x(x−4), c) f(x)=2(x−4)(3x+2)f(x)=2(x-4)(3x+2)f(x)=2(x−4)(3x+2), b) f(x)=(x−5)(x+7)f(x)=(x-5)(x+7)f(x)=(x−5)(x+7), d) f(x)=(3x−4)(2x+5)f(x)=(3x-4)(2x+5)f(x)=(3x−4)(2x+5).

Problem 435

Find the value of ppp that satisfies the equation 6p+46=4p−83\frac{6p+4}{6}=\frac{4p-8}{3}66p+4​=34p−8​.

Problem 436

Identify the critical points of y=x2exy=x^{2}e^{x}y=x2ex. State the xxx- and yyy-coordinates. Determine if they are local max, min, or neither.

Problem 437

Convert 34\frac{3}{4}43​ pound to ounces.

Problem 438

Verify cos⁡2xsec⁡2x+tan⁡2x=sec⁡2x\cos^2 x \sec^2 x + \tan^2 x = \sec^2 xcos2xsec2x+tan2x=sec2x by transforming the left side.

Problem 439

Analyze exponential growth/decay functions: y=(32)xy=(\frac{3}{2})^{x}y=(23​)x, y=−4(0.5)xy=-4(0.5)^{x}y=−4(0.5)x, y=4(0.25)xy=4(0.25)^{x}y=4(0.25)x, y=−2(2)xy=-2(2)^{x}y=−2(2)x. Determine growth/decay, y-intercept, asymptote.

Problem 440

Problem 441

Problem 442

Convert 6 tons to pounds. Solve for the unknown value that, when multiplied by 6, equals 12,000 pounds.

Find the volume of a sphere with radius $r=1$ . Round the volume to the nearest hundredth.

Find the unknown value in the proportions: (a) $a: 6=7: 2$ and (b) $5: 4=b: 20$ .

Find the value of $(\sqrt{a})^{2}$ for any nonnegative real number $a$ .

Divide the expression $\frac{v^{2}-9}{3 v}+\frac{v^{2}+6 v+9}{6 v}$ .

Simplify the expression $2^{2} + \sqrt{9} \cdot 3$ using the order of operations.

Solve the quadratic equation $3x^2 + 8x - 1 = 0$ and select the correct solution set.

Solve for the variable $v$ given the equation $25.6=\frac{v}{2}$ .

Find the total number of people in the senior center dining room if 3/5 of them are men and there are 93 men.
Let $p$ be the total number of people.
Equation: $p = \frac{93}{\frac{3}{5}}$

Solve for $w$ in the equation $-5+w=7$ .

Find the positive value of $p$ that satisfies the equation $\sqrt{4p^2 + 28} - 8 = 0$ .

Rewrite interval with given values: $\hat{p} = 0.61, z^* = 0.82, SE_{\text{est}} = 0.00157$ . The interval is $[0.607, 0.613]$ .

Find the decimal representation of $\sqrt{65}$ rounded to two decimal places.

Solve for $y$ in the equation $5 y^{\frac{2}{3}} + 7 = 27$ .

Find the area of a town with an area of $4.36$ square miles, given that $1$ mile $=1,760$ yards. The correct answer is $13,505,536$ square yards.

Solve the linear equation $3x + 5 = 9x + 8$ for the unknown variable $x$ .

Determine if all numbers are solutions to the inequality $\frac{60}{9} > 3 \times 5$ .

Find the sum of two linear functions $h(n) = 2n - 4$ and $g(n) = n - 2$ .

Solve the quadratic equation $-7x^2 - 2x + 6 = 0$ and find its roots.

Find the unit that is to litre as gallon is to meter.
$A \text{ yard } = k \text{ meter}$ $A \text{ gallon } = x \text{ litre}$

Find inverse function $f^{-1}(x)$ of $f(x)=3x+4$ , then verify $f(f^{-1}(x))=x$ and $f^{-1}(f(x))=x$ .

Show that if $a$ and $b$ are relatively prime, then $\operatorname{gcd}(da, db) = d$ for any positive integer $d$ .

Divide $256$ by $24$ and write the result.

Solve for $x$ given the equation $4x = 4.56$ .

Simplify the expression: $\frac{1-2 x}{1+x} * \frac{-7-7 x}{2 x-1}$ .

Solve for $w$ in the formula $v = \frac{1}{3} w b$ .

Simplify the expression $(b^{12})^{3}$ and write the answer as a power.

Express $16 \sin (50 r) \sin (23 r)$ as a sum or difference of trigonometric functions.

Solve for $n$ if $P(n, 2)=1482$ . Alicia's formula is $n^{2}-n-1482=0$ . Explain how she created the formula and use it to solve for $n$ .

Express quadratic functions in standard form, find y-intercept. a) $f(x)=3x(x-4)$ , c) $f(x)=2(x-4)(3x+2)$ , b) $f(x)=(x-5)(x+7)$ , d) $f(x)=(3x-4)(2x+5)$ .

Find the value of $p$ that satisfies the equation $\frac{6p+4}{6}=\frac{4p-8}{3}$ .

Identify the critical points of $y=x^{2}e^{x}$ . State the $x$ - and $y$ -coordinates. Determine if they are local max, min, or neither.

Convert $\frac{3}{4}$ pound to ounces.

Verify $\cos^2 x \sec^2 x + \tan^2 x = \sec^2 x$ by transforming the left side.

Analyze exponential growth/decay functions: $y=(\frac{3}{2})^{x}$ , $y=-4(0.5)^{x}$ , $y=4(0.25)^{x}$ , $y=-2(2)^{x}$ . Determine growth/decay, y-intercept, asymptote.

Translate the phrase "42 decreased by twice Vanessa's age" into an algebraic expression using the variable $v$ to represent Vanessa's age.

Solve for $y$ in the equation $-63=-2 y^{2}+9$ , expressing the answer as an integer or in simplest radical form.

Solve the linear equation $4b + 6 = 2 - b + 4$ and select the correct solution.

Find the quotient of -16 divided by -2, or state if undefined. $\frac{-16}{-2}=\square$

Find the minimum $y$ -value of $f(x)=x^{2}+\frac{2}{x}$ on $\frac{1}{2} \leq x \leq 2$ .

Find the number of oranges between 3 oz and 5 oz in a batch of 2300, given a normal distribution with $\mu = 6$ oz and $\sigma = 1.5$ oz.

Find the solution, rounded to one decimal place, to the equation $e^{x} = \sqrt{x+8}$ using a graphing calculator.

Solve the linear inequality $18 < 4m - 15$ for the variable $m$ .

Find the equation that represents "three minus the difference of a number and one equals one-half of the difference of three times the same number and four".
$3 - (n - 1) = \frac{1}{2}(3n - 4)$

Solve the equation $5^{\frac{x}{3}}=4$ . The exact solution is $x=\log_5(4)$ . The approximate solution, rounded to 4 decimal places, is $x=3.0910$ .

Find the error in Jane's solution of the quadratic equation $x^2 - 5x - 24 = 0$ using the quadratic formula.

Find the range of $x$ values where the function $f(x) = x^3 + 3x^2 - 9x + 7$ is increasing.

Solve the linear equation $6x + 6 = 0$ for the unknown variable $x$ .

Find a recursive formula for the number of seats in each row of a movie theater, where the explicit formula is $a_{n}=6+6 n$ and $n$ represents the row number.

Find the value of $x$ in the system of linear equations $15x + 7y = 4$ , $-5x - 7y = 2$ , and $10x = 2$ . Enter the answer as a simplified fraction.

Plot the quadratic equation $y = x^{2} + 10x + 21$ and find its roots using the graph.

Evaluate the factorial ratio $\frac{16 !}{13 !}$ . The solution is $\square$ .

Find the value of $n$ that satisfies the equation $n \times \frac{3}{4} = \frac{3}{16}$ .

Graph the set of all $(x, y)$ satisfying $x + 2y > 2$ .

Find the degree of the polynomial equation $2 x^{5} - 6 x^{4} = 0$ .

Solve for h in the equation $7x + 4 = 7x + h$ to find the value of h that results in zero solutions.

Solve for $f$ by completing the square: $2f^2 - 56f + 34 = 0$ . Express your answers as integers, simplified fractions, or rounded decimals.

Divide $4x^3 - 16x^2 + 18x - 28$ by $-x + 3$ using long division. Find the quotient and remainder.

Find $\alpha$ and $\beta$ values in $\cos(\alpha-\beta)$ expression. Write as $\cos(\square^\circ)$ and find exact value.

Find all real numbers $x$ that satisfy the equation $\cos x = 15$ .

Solve for the missing value in the proportion $44: 20 = \square: 5$ .

Solve for $x$ in the inequality $3x - 7 > 7x + 9$ and graph the solution.

Greg used $31/4$ feet of cloth for shorts and $22/3$ feet for a shirt. Which expression gives the total cloth used?

Find the value of $b$ that satisfies the equation $14_b + 23_b = 40_b$ , where $b \in \{4, 5, 7\}$ .

Find the number $x$ such that $x + 5/x = 6$ .