Word Problems

Problem 8501

Find the exact value of $\sin 405^{\circ}$ using a coterminal angle without a calculator. Options: $\frac{\sqrt{2}}{2}$ , $-\frac{\sqrt{2}}{2}$ , $\frac{1}{2}$ , $-\frac{1}{2}$ .

See Solution

Problem 8502

Solve for $\theta$ in the equation $2 \sin (\theta) = 0.651$ . What are the steps?

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Problem 8503

Gibson Company transactions for year 1:
1. Issued stock for \$12,000.
2. Materials cost \$4,700.
3. Paid workers \$2,400.
4. Equipment rental \$900.
5. Admin salaries \$350.
6. Office rental \$400.
7. Produced 400 units; sold 360 at \$25 each.
Create an income statement and balance sheet per GAAP.

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Problem 8504

Find the exact value of $\tan \theta$ for the point (7, -3). Options: $-\frac{3}{8}$ , $\frac{7}{8}$ , $-\frac{3}{7}$ , $-\frac{7}{3}$ .

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Problem 8505

Test if the average top speed of 87 cars (150 mph) differs from 145 mph using $H_0: \mu = 145$ at 1\% significance. Outcomes: 1-4.

See Solution

Problem 8506

Find the time $t$ for a block to slide down an incline with base $a=12$ and angle $\theta=45^{\circ}$ using $t=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}$ .

See Solution

Problem 8507

Find the length of a guy wire attached 10 ft from the top of a 230 ft tower at a $32^{\circ}$ angle. Round to the nearest tenth.

See Solution

Problem 8508

Find the radian measure of a $300^{\circ}$ angle: $\frac{3 \pi}{5}$ , $\frac{5 \pi}{3}$ , $2 \pi$ , $150 \pi$ .

See Solution

Problem 8509

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ .

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Problem 8510

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ . Round to $0.1 \mathrm{ft}$ .

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Problem 8511

Find the expression equivalent to $\frac{\tan x-1}{\tan x+1}$ using identities. Options include:
1. $\frac{\cot x}{1-\cot x}$
2. $\frac{\cot x}{1+\cot x}$
3. $\frac{1-\cot x}{1+\cot x}$
4. $\frac{1+\cot x}{1-\cot x}$

See Solution

Problem 8512

Find $\sin \theta$ for the point $(4,-3)$ . Options: $-3$ , $\frac{4}{5}$ , $-\frac{3}{5}$ , $\frac{5}{4}$ .

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Problem 8513

Calculate the distance between the points $(6,-6)$ and $(-1,1)$ . Options: $5 \sqrt{2}$ , $\sqrt{14}$ , 7, $7 \sqrt{2}$ .

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Problem 8514

A car on a $2.6^{\circ}$ incline faces $124 \mathrm{lb}$ resistance. Find the car's weight to the nearest hundred pounds.

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Problem 8515

Find the grade resistance in pounds for a 2000-pound car on a $2.4^{\circ}$ uphill grade using $F=W \sin \theta$ .

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Problem 8516

Pham can work 15 hours weekly. Maximize earnings: Bookstore at \$9/hr, Café at \$12/hr (6 hrs), Garage at \$10/hr (5 hrs), Daycare at \$8.50/hr. How many hours at the bookstore? (Whole number answer)

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Problem 8517

A. How many pounds of potatoes can Janice buy with \$ 5, considering their value? Use values \$ 1.50, \$ 1.14, \$ 1.05, \$ 0.30.

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Problem 8518

Find the constant of variation for the point $(12,9)$ in a direct variation. Options: $\frac{1}{2}$ , $\frac{3}{4}$ , 1, 2.

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Problem 8519

What is the opportunity cost of buying one stapler if staplers are \$10 and pens are \$2.50, with a \$100 budget?

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Problem 8520

A. How many pounds of potatoes will Janice buy with \$ 5? B. How many pounds if she had \$ 2? Values: 1st: \$ 1.50, 2nd: \$ 1.14, 3rd: \$ 1.05, others: \$ 0.30.

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Problem 8521

A. 3 B. 2

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Problem 8522

Nina has 5 hours for 12 crafting stations. How much time per station in hours? Provide as a fraction or mixed number.

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Problem 8523

You have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?
A: Budget increases to \$150, prices same. increase
B: Budget \$100, books \$25, tickets rise to \$20. decrease
C: Budget \$100, tickets \$10, books drop to \$15. increase

See Solution

Problem 8524

Find the range of the tangent function: all reals except odd multiples of $\frac{\pi}{2}$ , or other options?

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Problem 8525

If $\sin \theta=0.4$ , what is $\sin (\theta+\pi)$ ? Options: 0.4, -0.4, -0.6, 0.6.

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Problem 8526

Postage rates changed from 2006 to 2016.
(a) Let $f(x)$ be the cost of a first-class stamp in year $x$ . Find $f(2010)$ and $f(2015)$ given $f(2010)=\$0.36$ and $f(2015)=\$0.66$ .
(b) Why isn’t the graph of $f$ accurate? What changes are needed for accuracy?

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Problem 8527

Convert the mixed number $4 \frac{1}{4}$ into an improper fraction.

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Problem 8528

Find the cost to rent a trailer for 3.3, 4, and 8.6 hours, given the rate of \$20 for 2 hours and \$10 per additional hour.

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Problem 8529

Find $\tan \theta$ for the point $P(5,4)$ on the circle $x^{2}+y^{2}=r^{2}$ .

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Problem 8530

Find $\sin \theta$ for the point $P(-4,-3)$ on the circle $x^{2}+y^{2}=r^{2}$ . Choices: $-\frac{3}{5}$ , $\frac{3}{5}$ , $\frac{4}{5}$ , $-\frac{4}{5}$ .

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Problem 8531

Calculate the expected waiting time in hours for routine patients given 30 patients: 5 urgent, 1 critical, 4 doctors, 16 nurses.

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Problem 8532

Renting a trailer costs \$20 for 2 hours, then \$10 per extra hour. Find costs for 3.3, 4, and 8.6 hours.

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Problem 8533

Calculate the total copies of notes made for 34 routine, 9 urgent, and 1 critical patient.

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Problem 8534

Find $\sin t$ for the point $P\left(-\frac{\sqrt{77}}{9},-\frac{2}{9}\right)$ on the unit circle.

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Problem 8535

Find $\tan t$ for the point $\mathrm{P} = \left(\frac{3}{8}, \frac{\sqrt{55}}{8}\right)$ on the unit circle.

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Problem 8536

Estimate the population increase in year 1 for a country with a growth rate $r = 0.02$ and a population of 1,000,000.

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Problem 8537

Hornear un pavo a $3/4$ de hora por libra y cuarto. ¿Cuánto tiempo para un pavo de 7 y $1/2$ libras?

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Problem 8538

Estimate the growth rate of Whooping cranes in 2007 using $r$ and given values. Choose all correct answers. $d N / d t=r^{} N_{t} \\ r=\ln (\text { lambda }) \\ d N / d t=0.086^{} 258 \\ r=\ln (1.09)$

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Problem 8539

What is the range of the secant function? Options: 1) [-1, 1] 2) all reals except odd multiples of $\frac{\pi}{2}$ 3) $\geq 1$ or $\leq -1$ 4) all reals

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Problem 8540

What is the range of the sine function: $[-1, 1]$ ?

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Problem 8541

Determine the quadrant for angle $\theta$ if $\sec \theta<0$ and $\tan \theta<0$ .

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Problem 8542

What percent of students must be vaccinated for herd immunity against pertussis with an RO of 18? Options: $50 \%$ , $25 \%$ , $100 \%$ , $5 \%$ , $90 \%$ , $10 \%$ , $95 \%$ , $75 \%$ .

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Problem 8543

Evaluate $5+2(8^{0})$ using the order of operations.

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Problem 8544

Determine the quadrant for angle $\theta$ given that $\tan \theta>0$ and $\sin \theta<0$ .

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Problem 8545

Aluminum is an example of a(n) element, compound, solution, or mixture.

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Problem 8546

Find $\sec \theta$ if $\sin \theta = -\frac{4}{9}$ and $\tan \theta > 0$ .

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Problem 8547

Find $\cos \theta$ and $\tan \theta$ given $\sin \theta=\frac{1}{2}$ and $\sec \theta<0$ .

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Problem 8548

How much fishing line (in cm) is needed to wind around a spool with area $20.0 \mathrm{~cm}^{2}$ for 10 turns?

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Problem 8549

Find the reference angle for $-\frac{5 \pi}{6}$ . Options: $\frac{\pi}{12}$ , $\frac{\pi}{6}$ , $\frac{7 \pi}{6}$ , $\frac{5 \pi}{6}$ .

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Problem 8550

Find the distance you need to ride east before heading north to reach your friend's house, given a $10.0 \mathrm{~km}$ distance and $6.0 \mathrm{~km}$ north.

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Problem 8551

Find the unit rate of snowfall in Montreal if it snowed 20 inches in 10 days.

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Problem 8552

Find $\cos \theta$ if $\tan \theta = -\frac{10}{7}$ and $\theta$ is in quadrant II.

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Problem 8553

Find the quadrant for angle $\theta$ where $\tan \theta<0$ and $\sin \theta<0$ .

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Problem 8554

What is the reciprocal of $\frac{2}{5}$ ?

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Problem 8555

Find $\tan \theta$ given $\sec \theta = \frac{3}{2}$ and $\theta$ is in quadrant IV.

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Problem 8556

If two lines are perpendicular, what is the relationship between their slopes $m_1$ and $m_2$ ?

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Problem 8557

Calculate the cross-price elasticity of demand for hamburger buns when quantity demanded rises from 3,550 to 3,650 as price drops from \$1.65 to \$1.15. Round to the nearest hundredth.

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Problem 8558

Find the cross-price elasticity of demand for strawberries when quantity drops from 1,800 to 1,550 as price falls from \$2.35 to \$2.15. Round to the nearest hundredth.

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Problem 8559

In the formula $y=m x+b$ , what sign do you expect for $m$ regarding car prices over the years? Explain.

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Problem 8560

A family bought a jet ski for \$7,500 with a 10% down payment. What are the monthly installments at 696 simple interest for 12 months? Options: \$578.50, \$586.75, \$596.25, \$601.00, None of these choices.

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Problem 8561

Calculate $4 \frac{1}{2} \%$ of 280 and round to one decimal place. Choices: 1.6, 115.9, 1.2, 15.1, None.

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Problem 8562

Find $\cos \theta$ if $\tan \theta=-\frac{15}{8}$ and $90^{\circ}<\theta<180^{\circ}$ .

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Problem 8563

Find the sine of angle $t$ for the point $P\left(\frac{5}{8}, \frac{\sqrt{39}}{8}\right)$ on the unit circle.

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Problem 8564

Find the cosine of angle $t$ for the point $P\left(-\frac{\sqrt{55}}{8}, \frac{3}{8}\right)$ on the unit circle.

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Problem 8565

Find the domain of the sine function. What values can $x$ take for $\sin(x)$ ?

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Problem 8566

Is Mateo correct that $6^{8} \div 3^{4} = 6^{4}$ ? Explain using the Quotient of Powers Law.

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Problem 8567

Find the values of $x$ for which $x^{0}+\left(x^{6} \div x^{3}\right) > 9$ .

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Problem 8568

Ramon claims that $\left(\frac{1}{12}\right)^{4} = \frac{1}{12^{4}}$ . Jamal disagrees, saying both parts need the power. Who is right?

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Problem 8569

Calculate $127\%$ of 743 and round to one decimal place.

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Problem 8570

Identify expressions less than 2 for $x=5$ . Choose all that apply:
1. $\frac{x^{0}}{4}$
2. $\frac{x^{1}}{7^{0}}$
3. $\left(\frac{50}{x^{2}}\right)^{0}$
4. $2\left(\frac{10}{x}\right)^{0}$
5. $\frac{x^{0}}{x^{2}}$

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Problem 8571

Find $\csc \theta$ given $\cot \theta = -\frac{9}{4}$ and $\cos \theta < 0$ .

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Problem 8572

Identify which trigonometric values are negative: I. $\sin \left(-292^{\circ}\right)$ , II. $\tan \left(-193^{\circ}\right)$ , III. $\cos \left(-207^{\circ}\right)$ , IV. $\cot 222^{\circ}$ .

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Problem 8573

Identify which trigonometric values are negative: I. $\sin \left(-292^{\circ}\right)$ II. $\tan \left(-193^{\circ}\right)$ III. $\cos \left(-207^{\circ}\right)$ IV. $\cot 222^{\circ}$ . Options: I and III, II and III, III only, II, III, and IV.

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Problem 8574

Find the other three members of the fact family for $4+7=11$ . Choose from the options provided.

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Problem 8575

Given the fact $4+7=11$ , find the other three members of its fact family and draw number line models for each.

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Problem 8576

Find $\csc \theta$ for the point $P(-3,-1)$ on the circle $x^{2}+y^{2}=r^{2}$ .

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Problem 8577

Convert these numbers to scientific notation or standard form: 3,456,320; 4.563 × 10^{-4}; 0.0004322; 102.0; 7.8322 × 10^{0}; 20,100; 3.40 × 10^{1}; 2.41 × 10^{5}. Fix improper scientific notation: 53.21 × 10^{6}; 125.6800 × 10^{2}; 1003.879 × 10^{-8}; 002368.2 × 10^{-3}.

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Problem 8578

Fact family includes $4+7=11$ . Find the other three members and draw number line models for each.

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Problem 8579

Find $\cos \theta$ given $\sin \theta = -\frac{4}{5}$ and $\theta$ is in QIII. Use the first Pythagorean identity. $\cos \theta =$

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Problem 8580

Find $\sin \theta$ if $\cos \theta = \frac{1}{2}$ and $\theta$ is in quadrant I.

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Problem 8581

Find $\tan \theta$ given $\sin \theta = \frac{3}{4}$ and $\theta$ is in QI. What is $\tan \theta$ ?

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Problem 8582

Add parentheses to make these equations true: a. $4+3 \cdot 2=14$ b. $6 \div 2+1=4$ c. $5+4+9 \div 2=9$ d. $5+6 \div 2+2=10$ Choose the correct answer.

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Problem 8583

Find $\sec \theta$ given $\tan \theta = \frac{9}{40}$ and $\theta$ is in QIII. $\sec \theta =$

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Problem 8584

Find when the first three oil changes happen if the car's oil should be changed every 3500 miles, starting at 0 miles.

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Problem 8585

What is the relationship between correlation $r$ and slope $b$ of the least squares line for the same data set?

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Problem 8586

If the correlation $r=0.63$ for variables $(x, y)$ , what can we say about the slope $b$ of the least-squares line?

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Problem 8587

Find the trigonometric ratios for $\theta$ if $\sin \theta=-\frac{\sqrt{3}}{2}$ and $\theta$ is not in QIII. $\cos \theta=$ $\tan \theta=$ $\cot \theta=$ $\sec \theta=$ $\csc \theta=$

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Problem 8588

Convert the following using dimensional analysis: 175 lbs to kg, 2 days to seconds, and 38821 yen to dollars at \$1=102.70 yen.

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Problem 8589

If the oil should be changed every 3500 miles, when will the first three oil changes happen if you start at 0 miles?

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Problem 8590

Let $p$ : This is a turtle; $q$ : This is a reptile. Write "Not a turtle if not a reptile" in symbols.

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Problem 8591

Find the expected aptitude score for a 17-year-old using the formula: Aptitude = 111.5 - 1.14 * Age. Round to the nearest whole number.

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Problem 8592

Negate the statement: It is thundering and lightning.

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Problem 8593

Negate the statement: Thursday does not come after Wednesday.

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Problem 8594

Let s represent "One races fast." Express "One does not race fast" symbolically.

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Problem 8595

Express the statement "There are 31 days in September" using $p$ and $q$ .

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Problem 8596

a. Rephrase: Every dog is a rabbit. b. Negation: Some dogs are not rabbits.

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Problem 8597

Complete the statement: "If $p$ , then $q$ " is symbolized by _ and is called a _.

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Problem 8598

Find $b$ in the Pythagorean theorem $3^2 + b^2 = 5^2$ . Round your answer to two decimal places.

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Problem 8599

Write the symbolic form of "I study and I eat bananas" using $p$ and $q$ .

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Problem 8600

Symbolically express: The stove is hot and I do not get an A using $p$ and $q$ .

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1 ...83 84 85 86 87 88 89 ...101

Word Problems

Problem 8501

Find the exact value of sin⁡405∘\sin 405^{\circ}sin405∘ using a coterminal angle without a calculator. Options: 22\frac{\sqrt{2}}{2}22​​, −22-\frac{\sqrt{2}}{2}−22​​, 12\frac{1}{2}21​, −12-\frac{1}{2}−21​.

Problem 8502

Solve for θ\thetaθ in the equation 2sin⁡(θ)=0.6512 \sin (\theta) = 0.6512sin(θ)=0.651. What are the steps?

Problem 8503

Gibson Company transactions for year 1: 1. Issued stock for \$12,000.2. Materials cost \$4,700.3. Paid workers \$2,400.4. Equipment rental \$900.5. Admin salaries \$350.6. Office rental \$400.7. Produced 400 units; sold 360 at \$25 each.Create an income statement and balance sheet per GAAP.

Problem 8504

Find the exact value of tan⁡θ\tan \thetatanθ for the point (7, -3). Options: −38-\frac{3}{8}−83​, 78\frac{7}{8}87​, −37-\frac{3}{7}−73​, −73-\frac{7}{3}−37​.

Problem 8505

Test if the average top speed of 87 cars (150 mph) differs from 145 mph using H0:μ=145H_0: \mu = 145H0​:μ=145 at 1\% significance. Outcomes: 1-4.

Problem 8506

Find the time ttt for a block to slide down an incline with base a=12a=12a=12 and angle θ=45∘\theta=45^{\circ}θ=45∘ using t=2agsin⁡θcos⁡θt=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}t=gsinθcosθ2a​​.

Problem 8507

Find the length of a guy wire attached 10 ft from the top of a 230 ft tower at a 32∘32^{\circ}32∘ angle. Round to the nearest tenth.

Problem 8508

Find the radian measure of a 300∘300^{\circ}300∘ angle: 3π5\frac{3 \pi}{5}53π​, 5π3\frac{5 \pi}{3}35π​, 2π2 \pi2π, 150π150 \pi150π.

Problem 8509

Find the distance between two cars below a 1000-foot cliff with angles of depression 21∘21^{\circ}21∘ and 28∘28^{\circ}28∘.

Problem 8510

Find the distance between two cars below a 1000-foot cliff with angles of depression 21∘21^{\circ}21∘ and 28∘28^{\circ}28∘. Round to 0.1ft0.1 \mathrm{ft}0.1ft.

Problem 8511

Problem 8512

Find sin⁡θ\sin \thetasinθ for the point (4,−3)(4,-3)(4,−3). Options: −3-3−3, 45\frac{4}{5}54​, −35-\frac{3}{5}−53​, 54\frac{5}{4}45​.

Problem 8513

Calculate the distance between the points (6,−6)(6,-6)(6,−6) and (−1,1)(-1,1)(−1,1). Options: 525 \sqrt{2}52​, 14\sqrt{14}14​, 7, 727 \sqrt{2}72​.

Problem 8514

A car on a 2.6∘2.6^{\circ}2.6∘ incline faces 124lb124 \mathrm{lb}124lb resistance. Find the car's weight to the nearest hundred pounds.

Problem 8515

Find the grade resistance in pounds for a 2000-pound car on a 2.4∘2.4^{\circ}2.4∘ uphill grade using F=Wsin⁡θF=W \sin \thetaF=Wsinθ.

Problem 8516

Pham can work 15 hours weekly. Maximize earnings: Bookstore at \$9/hr, Café at \$12/hr (6 hrs), Garage at \$10/hr (5 hrs), Daycare at \$8.50/hr. How many hours at the bookstore? (Whole number answer)

Problem 8517

A. How many pounds of potatoes can Janice buy with \$ 5, considering their value? Use values \$ 1.50, \$ 1.14, \$ 1.05, \$ 0.30.

Problem 8518

Find the constant of variation for the point (12,9)(12,9)(12,9) in a direct variation. Options: 12\frac{1}{2}21​, 34\frac{3}{4}43​, 1, 2.

Problem 8519

What is the opportunity cost of buying one stapler if staplers are \$10 and pens are \$2.50, with a \$100 budget?

Problem 8520

A. How many pounds of potatoes will Janice buy with \$ 5? B. How many pounds if she had \$ 2? Values: 1st: \$ 1.50, 2nd: \$ 1.14, 3rd: \$ 1.05, others: \$ 0.30.

Problem 8521

A. 3 B. 2

Problem 8522

Nina has 5 hours for 12 crafting stations. How much time per station in hours? Provide as a fraction or mixed number.

Problem 8523

You have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?A: Budget increases to \$150, prices same. increase B: Budget \$100, books \$25, tickets rise to \$20. decrease C: Budget \$100, tickets \$10, books drop to \$15. increase

Problem 8524

Find the range of the tangent function: all reals except odd multiples of π2\frac{\pi}{2}2π​, or other options?

Problem 8525

If sin⁡θ=0.4\sin \theta=0.4sinθ=0.4, what is sin⁡(θ+π)\sin (\theta+\pi)sin(θ+π)? Options: 0.4, -0.4, -0.6, 0.6.

Problem 8526

Problem 8527

Convert the mixed number 4144 \frac{1}{4}441​ into an improper fraction.

Problem 8528

Find the cost to rent a trailer for 3.3, 4, and 8.6 hours, given the rate of \$20 for 2 hours and \$10 per additional hour.

Problem 8529

Find tan⁡θ\tan \thetatanθ for the point P(5,4)P(5,4)P(5,4) on the circle x2+y2=r2x^{2}+y^{2}=r^{2}x2+y2=r2.

Problem 8530

Find sin⁡θ\sin \thetasinθ for the point P(−4,−3)P(-4,-3)P(−4,−3) on the circle x2+y2=r2x^{2}+y^{2}=r^{2}x2+y2=r2. Choices: −35-\frac{3}{5}−53​, 35\frac{3}{5}53​, 45\frac{4}{5}54​, −45-\frac{4}{5}−54​.

Problem 8531

Calculate the expected waiting time in hours for routine patients given 30 patients: 5 urgent, 1 critical, 4 doctors, 16 nurses.

Problem 8532

Renting a trailer costs \$20 for 2 hours, then \$10 per extra hour. Find costs for 3.3, 4, and 8.6 hours.

Problem 8533

Calculate the total copies of notes made for 34 routine, 9 urgent, and 1 critical patient.

Problem 8534

Find sin⁡t\sin tsint for the point P(−779,−29)P\left(-\frac{\sqrt{77}}{9},-\frac{2}{9}\right)P(−977​​,−92​) on the unit circle.

Problem 8535

Find tan⁡t\tan ttant for the point P=(38,558)\mathrm{P} = \left(\frac{3}{8}, \frac{\sqrt{55}}{8}\right)P=(83​,855​​) on the unit circle.

Problem 8536

Estimate the population increase in year 1 for a country with a growth rate r=0.02r = 0.02r=0.02 and a population of 1,000,000.

Problem 8537

Hornear un pavo a 3/43/43/4 de hora por libra y cuarto. ¿Cuánto tiempo para un pavo de 7 y 1/21/21/2 libras?

Problem 8538

Problem 8539

What is the range of the secant function? Options: 1) [-1, 1] 2) all reals except odd multiples of π2\frac{\pi}{2}2π​ 3) ≥1\geq 1≥1 or ≤−1\leq -1≤−1 4) all reals

Problem 8540

What is the range of the sine function: [−1,1][-1, 1][−1,1]?

Problem 8541

Determine the quadrant for angle θ\thetaθ if sec⁡θ<0\sec \theta<0secθ<0 and tan⁡θ<0\tan \theta<0tanθ<0.

Find the exact value of $\sin 405^{\circ}$ using a coterminal angle without a calculator. Options: $\frac{\sqrt{2}}{2}$ , $-\frac{\sqrt{2}}{2}$ , $\frac{1}{2}$ , $-\frac{1}{2}$ .

Solve for $\theta$ in the equation $2 \sin (\theta) = 0.651$ . What are the steps?

Gibson Company transactions for year 1:
1. Issued stock for \$12,000.
2. Materials cost \$4,700.
3. Paid workers \$2,400.
4. Equipment rental \$900.
5. Admin salaries \$350.
6. Office rental \$400.
7. Produced 400 units; sold 360 at \$25 each.
Create an income statement and balance sheet per GAAP.

Find the exact value of $\tan \theta$ for the point (7, -3). Options: $-\frac{3}{8}$ , $\frac{7}{8}$ , $-\frac{3}{7}$ , $-\frac{7}{3}$ .

Test if the average top speed of 87 cars (150 mph) differs from 145 mph using $H_0: \mu = 145$ at 1\% significance. Outcomes: 1-4.

Find the time $t$ for a block to slide down an incline with base $a=12$ and angle $\theta=45^{\circ}$ using $t=\sqrt{\frac{2 a}{g \sin \theta \cos \theta}}$ .

Find the length of a guy wire attached 10 ft from the top of a 230 ft tower at a $32^{\circ}$ angle. Round to the nearest tenth.

Find the radian measure of a $300^{\circ}$ angle: $\frac{3 \pi}{5}$ , $\frac{5 \pi}{3}$ , $2 \pi$ , $150 \pi$ .

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ .

Find the distance between two cars below a 1000-foot cliff with angles of depression $21^{\circ}$ and $28^{\circ}$ . Round to $0.1 \mathrm{ft}$ .

Find $\sin \theta$ for the point $(4,-3)$ . Options: $-3$ , $\frac{4}{5}$ , $-\frac{3}{5}$ , $\frac{5}{4}$ .

Calculate the distance between the points $(6,-6)$ and $(-1,1)$ . Options: $5 \sqrt{2}$ , $\sqrt{14}$ , 7, $7 \sqrt{2}$ .

A car on a $2.6^{\circ}$ incline faces $124 \mathrm{lb}$ resistance. Find the car's weight to the nearest hundred pounds.

Find the grade resistance in pounds for a 2000-pound car on a $2.4^{\circ}$ uphill grade using $F=W \sin \theta$ .

Find the constant of variation for the point $(12,9)$ in a direct variation. Options: $\frac{1}{2}$ , $\frac{3}{4}$ , 1, 2.

You have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?
A: Budget increases to \$150, prices same. increase
B: Budget \$100, books \$25, tickets rise to \$20. decrease
C: Budget \$100, tickets \$10, books drop to \$15. increase

Find the range of the tangent function: all reals except odd multiples of $\frac{\pi}{2}$ , or other options?

If $\sin \theta=0.4$ , what is $\sin (\theta+\pi)$ ? Options: 0.4, -0.4, -0.6, 0.6.

Convert the mixed number $4 \frac{1}{4}$ into an improper fraction.

Find $\tan \theta$ for the point $P(5,4)$ on the circle $x^{2}+y^{2}=r^{2}$ .

Find $\sin \theta$ for the point $P(-4,-3)$ on the circle $x^{2}+y^{2}=r^{2}$ . Choices: $-\frac{3}{5}$ , $\frac{3}{5}$ , $\frac{4}{5}$ , $-\frac{4}{5}$ .

Find $\sin t$ for the point $P\left(-\frac{\sqrt{77}}{9},-\frac{2}{9}\right)$ on the unit circle.

Find $\tan t$ for the point $\mathrm{P} = \left(\frac{3}{8}, \frac{\sqrt{55}}{8}\right)$ on the unit circle.

Estimate the population increase in year 1 for a country with a growth rate $r = 0.02$ and a population of 1,000,000.

Hornear un pavo a $3/4$ de hora por libra y cuarto. ¿Cuánto tiempo para un pavo de 7 y $1/2$ libras?

What is the range of the secant function? Options: 1) [-1, 1] 2) all reals except odd multiples of $\frac{\pi}{2}$ 3) $\geq 1$ or $\leq -1$ 4) all reals

What is the range of the sine function: $[-1, 1]$ ?

Determine the quadrant for angle $\theta$ if $\sec \theta<0$ and $\tan \theta<0$ .

What percent of students must be vaccinated for herd immunity against pertussis with an RO of 18? Options: $50 \%$ , $25 \%$ , $100 \%$ , $5 \%$ , $90 \%$ , $10 \%$ , $95 \%$ , $75 \%$ .

Evaluate $5+2(8^{0})$ using the order of operations.

Determine the quadrant for angle $\theta$ given that $\tan \theta>0$ and $\sin \theta<0$ .

Find $\sec \theta$ if $\sin \theta = -\frac{4}{9}$ and $\tan \theta > 0$ .

Find $\cos \theta$ and $\tan \theta$ given $\sin \theta=\frac{1}{2}$ and $\sec \theta<0$ .

How much fishing line (in cm) is needed to wind around a spool with area $20.0 \mathrm{~cm}^{2}$ for 10 turns?

Find the reference angle for $-\frac{5 \pi}{6}$ . Options: $\frac{\pi}{12}$ , $\frac{\pi}{6}$ , $\frac{7 \pi}{6}$ , $\frac{5 \pi}{6}$ .

Find the distance you need to ride east before heading north to reach your friend's house, given a $10.0 \mathrm{~km}$ distance and $6.0 \mathrm{~km}$ north.

Find $\cos \theta$ if $\tan \theta = -\frac{10}{7}$ and $\theta$ is in quadrant II.

Find the quadrant for angle $\theta$ where $\tan \theta<0$ and $\sin \theta<0$ .

What is the reciprocal of $\frac{2}{5}$ ?

Find $\tan \theta$ given $\sec \theta = \frac{3}{2}$ and $\theta$ is in quadrant IV.

If two lines are perpendicular, what is the relationship between their slopes $m_1$ and $m_2$ ?

In the formula $y=m x+b$ , what sign do you expect for $m$ regarding car prices over the years? Explain.

Calculate $4 \frac{1}{2} \%$ of 280 and round to one decimal place. Choices: 1.6, 115.9, 1.2, 15.1, None.

Find $\cos \theta$ if $\tan \theta=-\frac{15}{8}$ and $90^{\circ}<\theta<180^{\circ}$ .

Find the sine of angle $t$ for the point $P\left(\frac{5}{8}, \frac{\sqrt{39}}{8}\right)$ on the unit circle.

Find the cosine of angle $t$ for the point $P\left(-\frac{\sqrt{55}}{8}, \frac{3}{8}\right)$ on the unit circle.

Find the domain of the sine function. What values can $x$ take for $\sin(x)$ ?

Is Mateo correct that $6^{8} \div 3^{4} = 6^{4}$ ? Explain using the Quotient of Powers Law.

Find the values of $x$ for which $x^{0}+\left(x^{6} \div x^{3}\right) > 9$ .

Ramon claims that $\left(\frac{1}{12}\right)^{4} = \frac{1}{12^{4}}$ . Jamal disagrees, saying both parts need the power. Who is right?

Calculate $127\%$ of 743 and round to one decimal place.

Identify expressions less than 2 for $x=5$ . Choose all that apply:
1. $\frac{x^{0}}{4}$
2. $\frac{x^{1}}{7^{0}}$
3. $\left(\frac{50}{x^{2}}\right)^{0}$
4. $2\left(\frac{10}{x}\right)^{0}$
5. $\frac{x^{0}}{x^{2}}$

Find $\csc \theta$ given $\cot \theta = -\frac{9}{4}$ and $\cos \theta < 0$ .

Identify which trigonometric values are negative: I. $\sin \left(-292^{\circ}\right)$ , II. $\tan \left(-193^{\circ}\right)$ , III. $\cos \left(-207^{\circ}\right)$ , IV. $\cot 222^{\circ}$ .

Find the other three members of the fact family for $4+7=11$ . Choose from the options provided.