Word Problems

Problem 2601

Find three numbers where their sum is 61, the first is 7 less than the second, and the third is 2 times the second.

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Problem 2602

Find the volume (in mL) of a 5 g solution with a density of 7.48 g/mL. Round your answer to 2 decimal places.

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Problem 2603

Calculate the dollar amount decrease in your \$6,875 salary after a \$6.5\% pay cut. Round to the nearest cent.

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Problem 2604

Calculate the moles of rubidium chloride ( $\mathrm{RbCl}$ ) produced from $303 \, \mathrm{g}$ , using significant digits.

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Problem 2605

Find the hypotenuse $x$ of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

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Problem 2606

Find the system of equations for tickets sold: $x + y = 120$ and $90x + 250y = 27,600$ . Options: A, B, C, D.

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Problem 2607

Find the midpoint of points $A(-7,-7)$ and $B(-5,5)$ on line segment $\overline{AB}$ .

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Problem 2608

Find the coordinates of point $B$ if point $A$ is at $(-1,8)$ and midpoint $M$ is at $(3,5.5)$ .

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Problem 2609

Find the unit price for a 12.3-ounce package costing \$2.74 and a 30.6-ounce package costing \$7.48. Which is cheaper?

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Problem 2610

Calculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

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Problem 2611

Find the midpoint of the line segment connecting points A(-7,-7) and B(-5,5).

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Problem 2612

Calculate the total interest for two loans of \$2,500: Loan A (3 years, 15\%, \$86.66/month) and Loan B (5 years, 10\%, \$53.12/month). Find the absolute difference, rounding to the nearest ten dollars.

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Problem 2613

Find the distance between the points $(-5,-5)$ and $(-9,-2)$ . Choose: (A) 5, (B) 7, (C) $\sqrt{12}$ , (D) $\sqrt{29}$ .

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Problem 2614

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly for 5 years. What is the total amount paid?

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Problem 2615

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly, to be paid in 5 years. What is the total amount paid?

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Problem 2616

Elise has two loans: a \$20,000 fixed-rate at 4.5\% and a \$20,000 variable-rate at 4.15\%. Which is more predictable in total cost?

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Problem 2617

You have \$400,000 saved at 4\% interest. How much can you withdraw monthly for 20 years?

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Problem 2618

Complete the financial statements with the following:
1. Revenues $= 27,000$ ; Expenses $= 18,000$ ; Net income $=$
2. Increase in equity $= 17,000$ ; Issuance $= 11,000$ ; Net income $= 12,000$ ; Dividends $=$
3. Assets $= 24,000$ ; Equity $= 15,000$ ; Liabilities $=$
4. Change in cash $= 26,000$ ; Operating cash flows $= 34,000$ ; Investing flows $= (17,000)$ ; Financing flows $=$

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Problem 2619

Bea can spend $\$ 200$ monthly on a $\$ 22,500$ loan at $6\%$ . Check if 12-year or 20-year loans fit her budget.

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Problem 2620

You want \$600,000 in 25 years with 8% interest. a) Monthly deposit needed? b) Total interest earned?

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Problem 2621

To have \$500,000 in 20 years at 9% interest, how much to deposit monthly and total interest earned?

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Problem 2622

You deposit \$500 monthly at 2% interest compounded monthly. Find the account balance in 20 years, total deposits, and interest earned.

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Problem 2623

Find the value of $\frac{2+a}{10-3 a}$ when $a=2$ .

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Problem 2624

Form a true equation using the numbers 2, 3, 4, 5 and the symbols = and +, using each only once. How?

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Problem 2625

Form an equation using 2, 3, 4, 5, =, and + once each to create a true statement. How can you do this?

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Problem 2626

Elk County Telephone's next dividend is \$3.02. Calculate share price for 13% and 10% returns, then compare results.

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Problem 2627

Estimate the cost to install an 18 ft by 23 ft brick patio, given that a 15 ft by 20 ft patio costs \$2,275. Round to the nearest dollar.

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Problem 2628

Stacey earns \ $15 weekly plus \$0.50 per customer. What equation finds$ x$, customers needed for \$25?

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Problem 2629

Calculate the total payback for a \ $249,000 mortgage: 15 years at 4\% ($ 1841.82/month) and 20 years at 5\% ($1643.29/month).

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Problem 2630

What percent of the original price do you pay after a $25\%$ and then an additional $30\%$ off clearance items?

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Problem 2631

List the numbers $\frac{1}{6}, -3, \sqrt{7}, -\frac{6}{5}, 4.5$ from least to greatest. Which is first? Explain.

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Problem 2632

Encrypt the word SCORE using a Caesar shift of 23 (A becomes X). What is the encrypted result?

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Problem 2633

Given the universal set $S=\{1,2,\ldots,20\}$ and subsets $A=\{1,3,4,7,10,13,17,18,19,20\}$ and $B=\{1,2,5,9,10,12,17,20\}$ , find $(A \cup B)$ and $(A \cap B)$ .

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Problem 2634

Decrypt the message TDGM CORF NISM NHAH WDRT NNAI ITRT ASOL E using the keyword OAK in a tabular transposition cipher.

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Problem 2635

Deposit $\$ 5000$ at $7\%$ interest compounded monthly. What is the total in 10 years?

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Problem 2636

How much energy is absorbed by $10.0 \mathrm{~g}$ of nickel when heated from $2.0^{\circ} \mathrm{C}$ to $63.4^{\circ} \mathrm{C}$ ? Use $\mathrm{C}_{\mathrm{Ni}}=0.120 \frac{\mathrm{J}}{\mathrm{g} \cdot{ }^{\circ} \mathrm{C}}$ .

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Problem 2637

Find the temperature change of a $25.0 \mathrm{~g}$ brass piece from $325^{\circ} \mathrm{C}$ to $42.0^{\circ} \mathrm{C}$ . $\Delta \mathrm{T}_{\text {brass }}=[?]^{\circ} \mathrm{C}$

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Problem 2638

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

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Problem 2639

A metal was heated and placed in 100.0 mL of water at 21.2°C, reaching 32.0°C. How much energy did the water absorb? $\mathrm{C}_{\mathrm{H}_{2} \mathrm{O}}=4.18 \frac{\mathrm{J}}{\mathrm{g} \cdot{ }^{\circ} \mathrm{C}} \\ \mathrm{q}_{\mathrm{H}_{2} \mathrm{O}}=[?] \mathrm{J}$

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Problem 2640

Find the formula for the $n^{\text{th}}$ term of the sequence $5, 9, 13, 17, 21, \ldots$ . What is $a_{n}=$ ?

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Problem 2641

Aspin Corp can issue 2M shares; 1.4M are out, 100K are treasury. They need \$48M at \$60/share. Find max new shares, if they can raise funds, and steps for more authorization.

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Problem 2642

Slater Lamp Manufacturing has preferred stock with a \$80 par value and an 11% annual dividend.
a. Find the annual and quarterly dividend amounts. b. For noncumulative stock, how much is owed after 3 missed quarters? c. For cumulative stock, how much is owed after 3 missed quarters?

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Problem 2643

Find (a) the complement and (b) the supplement of the angle measuring $20^{\circ} 18^{\prime}$ .

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Problem 2644

Scotto Manufacturing's stock pays a \$2.40 dividend. Find its value at 12% and 20% required returns. Discuss risk's impact.

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Problem 2645

Sally bought 100 shares of Kelsey Drums stock at a 16% return. Now, with a 12% return, find her capital gain or loss.

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Problem 2646

Find the value of $b$ in the line equation $y = mx + b$ for points $C(1,3)$ and $D(4,-3)$ .

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Problem 2647

Solve the inequality $9|2 x-1|+4<49$ .

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Problem 2648

Who has a steeper slope: Marty's function $v+3=\frac{1}{3}(x+9)$ or Ethan's from the table of values?

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Problem 2649

Convert 0.595 to a fraction in simplest form and as a percent.

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Problem 2650

Find the graph of the inequality $|\frac{1}{2} x + 2| \geq 1$ .

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Problem 2651

Tom walks dogs for \ $6/hr and washes cars for \$7.50/hr. He can work max 15 hrs and needs at least \$75. Find inequalities for$ d $and$ c$.

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Problem 2652

Find $\csc \theta$ if $\cot \theta = -\frac{1}{5}$ and $\theta$ is in quadrant IV.

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Problem 2653

Which option shows the associative property of addition? a. $(1+\sqrt{3})^{2}+\sqrt{7}=1+(\sqrt{3}+\sqrt{7})^{2}$ b. $(-2+7 i)+4 i=-2+(7 i+4 i)$ c. $\sqrt{18}+5 \sqrt{3}(\sqrt{6}+5)$ d. $(5 i \cdot 2 i)+11 i=11 i+(5 i \cdot 2 i)$

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Problem 2654

Dan bought an item priced at \$63 with a 95% discount. How much did he pay?

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Problem 2655

Find the six trigonometric functions for $\theta$ with point $P(-7,4)$ on its terminal side.

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Problem 2656

Find the sale price of an item that costs $60\%$ of the original price of \$93. Use the ALEKS calculator.

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Problem 2657

An item costs 80% of its original price of \$50. What is the sale price?

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Problem 2658

Find a number $x$ such that $6x + 2 = 2 \times 19$ .

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Problem 2659

Find the new price after a 25% reduction from the original price of \$85. Use the ALEKS calculator.

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Problem 2660

How many ways can you choose a president and vice-president from 9 people? Use the formula for permutations: $P(n, r) = \frac{n!}{(n-r)!}$ .

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Problem 2661

Find the height of a mountain peak given a distance of 27.2193 miles and an angle of elevation of $5.75^{\circ}$ .

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Problem 2662

Amy uses 48-cent and 7-cent stamps for a \$2.07 gift card. How many of each stamp did she use?

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Problem 2663

Caitlyn uses 40-cent and 7-cent stamps to pay \$1.76. How many of each stamp did she use?

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Problem 2664

Identify the equation pair that cannot be solved as a system: 1) $2x + 3y = 4$ and $y = 4 - x$ 2) $z = 3y + 4$ and $z = -y$ 3) $z = 3x - 2$ and $y = 2z - 3$ .

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Problem 2665

Find the max price per share for Grips Tool if growth is 25% for 3 years, then 10%, and required return is 15%.

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Problem 2666

Find the value of $y$ from the equations $y = 2x - 3$ and $x = 2$ .

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Problem 2667

Calculate the sum of all whole numbers from 1 to 550, which is given by the formula $\frac{n(n+1)}{2}$ .

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Problem 2668

Find two whole numbers whose product is 378 and sum is 41.

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Problem 2669

Calculate the ratio of the value of 7 in $Z,892$ to 7 in 34,206, and 7 in 5,073 to 7 in 18,749.

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Problem 2670

In a field with 31 heads and 86 feet, how many horses and geese are there? Let horses = x and geese = y. Solve: $x + y = 31$ and $4x + 2y = 86$ .

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Problem 2671

Calculate the number of ways to choose a president and vice-president from 7 people.

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Problem 2672

Find the slope of the line through points $(7,9)$ and $(5,7)$ using the slope formula. What is the slope?

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Problem 2673

How many ounces of coffee can you buy for \$1 if 1 pound costs \$10? Round to the nearest hundredth.

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Problem 2674

How many ounces of rice flour can you buy for \$2.10 if it costs \$8 per pound?

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Problem 2675

Find how many times larger the 7 in $5,0\underline{7}3$ is than the 7 in $18,749$ .

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Problem 2676

Calculate the sum of whole numbers from 1 to 880: $\sum_{n=1}^{880} n$ .

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Problem 2677

A garden's length is twice its width. If the perimeter is 48 m, find the garden's dimensions (length and width).

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Problem 2678

Identify the equation of the vertically stretched and shifted absolute value function: 3 left, 8 down. Options: a. $f(x)=2|x+3|-8$ b. $f(x)=\frac{1}{2}|x+3|-8$ c. $f(x)=2|x=3|-8$ d. $f(x)=\frac{1}{2}|x-3|-8$

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Problem 2679

Find the slope of the line through points (1,-1) and (-3,-1) using the slope formula. What is the slope?

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Problem 2680

Amy uses 47-cent and 8-cent stamps for \$2.13 postage. How many of each stamp did she use?

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Problem 2681

Identify the function with two distinct real zeros: a. $f(x)=2 x+2$ , b. $f(x)=(x-2)^{2}$ , c. $f(x)=x^{3}+2$ , d. $f(x)=|x|-2$ .

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Problem 2682

Find a number $x$ such that $8x + 4 = 2 \times 22$ .

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Problem 2683

How many ways can you elect a president and vice-president from 8 people? Use the formula for permutations: $P(n, r) = \frac{n!}{(n-r)!}$ .

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Problem 2684

In a biology course with a 4:3 boy-to-girl ratio and 371 students, how many boys are there?

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Problem 2685

Which function has a restricted domain? a. $f(x)=\sqrt{x}-1$ b. $f(x)=-x^{3}+4 x$ c. $f(x)=-|x-5|+1$ d. $f(x)=\frac{1}{2} \sqrt[3]{x+6}$

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Problem 2686

Find the coordinate of $P$ as the weighted average of points $B$ and $D$ , where $B$ at -6 weighs 3 times $D$ at 2.

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Problem 2687

Find the mean, median, and mode of the data set: 45.4, 75.2, 38.8, 56.6, 40.4, 75.2, 62.9, 75.2, 53.1, 59.8. Round to two decimal places.

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Problem 2688

Which polygon is also a rectangle: kite, rhombus, trapezoid, or square?

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Problem 2689

Which polygon is also a rectangle: kite, rhombus, trapezoid, or square?

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Problem 2690

How many ways can you choose a president and vice-president from 7 people? Calculate using permutations: $P(7, 2)$ .

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Problem 2691

Find the market value of Lawrence's shares given a \$1.80 dividend and an 11% return with varying growth rates.

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Problem 2692

Find point $P$ as the weighted average of points $W$ , $X$ , and $Y$ where $W=-7$ , $X=-4$ , $Y=0$ with weights 2, 1, and 3.

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Problem 2693

Write $<_{,}>$ or $=$ to make these statements true: 42,333 _ 42,303; 53,191 _ 53,091; 1,785 ___ 1,758.

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Problem 2694

Find the volume of the solid formed by rotating the area between $y=x^{3}+1$ and $y=1$ around the $y$ -axis.

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Problem 2695

Identify the place values of the digits 9, 6, and 5 in 456,975,321.

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Problem 2696

What is the end behavior of the reflected cubic function as $x$ approaches negative infinity? Choose: a. $f(x) \to -\infty$ , b. $f(x) \to \infty$ , c. $f(x) \to 0$ , d. $f(x) \to 3.

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Problem 2697

Which function can have multiple increasing intervals? a. Square root b. Cube root c. Quadratic d. Cubic

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Problem 2698

Find the unit rate for 44 points in 4 quarters. What is it? $= \frac{44}{4}$

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Problem 2699

Kate sold 42 books for \$441. Coupon books are \$12 each, recipe books are \$7.50. How many coupon books did she sell?

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Problem 2700

Calculate your final course average using the weights: Tests (13\%), Labs (10\%), Homework (32\%), Final Exam (45\%). Grades: Tests (75\%), Labs (54\%), Homework (63\%), Final Exam (84\%). What is your weighted average?

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Word Problems

Problem 2601

Find three numbers where their sum is 61, the first is 7 less than the second, and the third is 2 times the second.

Problem 2602

Find the volume (in mL) of a 5 g solution with a density of 7.48 g/mL. Round your answer to 2 decimal places.

Problem 2603

Calculate the dollar amount decrease in your \$6,875 salary after a \$6.5\% pay cut. Round to the nearest cent.

Problem 2604

Calculate the moles of rubidium chloride (RbCl\mathrm{RbCl}RbCl) produced from 303 g303 \, \mathrm{g}303g, using significant digits.

Problem 2605

Find the hypotenuse xxx of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Problem 2606

Find the system of equations for tickets sold: x+y=120x + y = 120x+y=120 and 90x+250y=27,60090x + 250y = 27,60090x+250y=27,600. Options: A, B, C, D.

Problem 2607

Find the midpoint of points A(−7,−7)A(-7,-7)A(−7,−7) and B(−5,5)B(-5,5)B(−5,5) on line segment AB‾\overline{AB}AB.

Problem 2608

Find the coordinates of point BBB if point AAA is at (−1,8)(-1,8)(−1,8) and midpoint MMM is at (3,5.5)(3,5.5)(3,5.5).

Problem 2609

Find the unit price for a 12.3-ounce package costing \$2.74 and a 30.6-ounce package costing \$7.48. Which is cheaper?

Problem 2610

Calculate the circumference and area of a circle with diameter 6yd6 \mathrm{yd}6yd using π≈3.14\pi \approx 3.14π≈3.14. Include units.

Problem 2611

Find the midpoint of the line segment connecting points A(-7,-7) and B(-5,5).

Problem 2612

Calculate the total interest for two loans of \$2,500: Loan A (3 years, 15\%, \$86.66/month) and Loan B (5 years, 10\%, \$53.12/month). Find the absolute difference, rounding to the nearest ten dollars.

Problem 2613

Find the distance between the points (−5,−5)(-5,-5)(−5,−5) and (−9,−2)(-9,-2)(−9,−2). Choose: (A) 5, (B) 7, (C) 12\sqrt{12}12​, (D) 29\sqrt{29}29​.

Problem 2614

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly for 5 years. What is the total amount paid?

Problem 2615

Caden takes a \$15,000 loan at 3.5\% interest, compounded monthly, to be paid in 5 years. What is the total amount paid?

Problem 2616

Elise has two loans: a \$20,000 fixed-rate at 4.5\% and a \$20,000 variable-rate at 4.15\%. Which is more predictable in total cost?

Problem 2617

You have \$400,000 saved at 4\% interest. How much can you withdraw monthly for 20 years?

Problem 2618

Problem 2619

Bea can spend $200\$ 200$200 monthly on a $22,500\$ 22,500$22,500 loan at 6%6\%6%. Check if 12-year or 20-year loans fit her budget.

Problem 2620

You want \$600,000 in 25 years with 8% interest. a) Monthly deposit needed? b) Total interest earned?

Problem 2621

To have \$500,000 in 20 years at 9% interest, how much to deposit monthly and total interest earned?

Problem 2622

You deposit \$500 monthly at 2% interest compounded monthly. Find the account balance in 20 years, total deposits, and interest earned.

Problem 2623

Find the value of 2+a10−3a\frac{2+a}{10-3 a}10−3a2+a​ when a=2a=2a=2.

Problem 2624

Form a true equation using the numbers 2, 3, 4, 5 and the symbols = and +, using each only once. How?

Problem 2625

Form an equation using 2, 3, 4, 5, =, and + once each to create a true statement. How can you do this?

Problem 2626

Elk County Telephone's next dividend is \$3.02. Calculate share price for 13% and 10% returns, then compare results.

Problem 2627

Estimate the cost to install an 18 ft by 23 ft brick patio, given that a 15 ft by 20 ft patio costs \$2,275. Round to the nearest dollar.

Problem 2628

Stacey earns \15weeklyplus$0.50percustomer.Whatequationfinds15 weekly plus \$0.50 per customer. What equation finds 15weeklyplus$0.50percustomer.Whatequationfindsx$, customers needed for \$25?

Problem 2629

Calculate the total payback for a \249,000mortgage:15yearsat4%(249,000 mortgage: 15 years at 4\% (249,000mortgage:15yearsat4%(1841.82/month) and 20 years at 5\% ($1643.29/month).

Problem 2630

What percent of the original price do you pay after a 25%25\%25% and then an additional 30%30\%30% off clearance items?

Problem 2631

List the numbers 16,−3,7,−65,4.5\frac{1}{6}, -3, \sqrt{7}, -\frac{6}{5}, 4.561​,−3,7​,−56​,4.5 from least to greatest. Which is first? Explain.

Problem 2632

Encrypt the word SCORE using a Caesar shift of 23 (A becomes X). What is the encrypted result?

Problem 2633

Problem 2634

Decrypt the message TDGM CORF NISM NHAH WDRT NNAI ITRT ASOL E using the keyword OAK in a tabular transposition cipher.

Problem 2635

Deposit $5000\$ 5000$5000 at 7%7\%7% interest compounded monthly. What is the total in 10 years?

Problem 2636

Problem 2637

Find the temperature change of a 25.0 g25.0 \mathrm{~g}25.0 g brass piece from 325∘C325^{\circ} \mathrm{C}325∘C to 42.0∘C42.0^{\circ} \mathrm{C}42.0∘C. ΔTbrass =[?]∘C \Delta \mathrm{T}_{\text {brass }}=[?]^{\circ} \mathrm{C} ΔTbrass ​=[?]∘C

Problem 2638

Find two positive and two negative angles coterminal with the angle A=90∘A=90^{\circ}A=90∘.

Problem 2639

Problem 2640

Find the formula for the nthn^{\text{th}}nth term of the sequence 5,9,13,17,21,…5, 9, 13, 17, 21, \ldots5,9,13,17,21,…. What is an=a_{n}=an​=?

Problem 2641

Aspin Corp can issue 2M shares; 1.4M are out, 100K are treasury. They need \$48M at \$60/share. Find max new shares, if they can raise funds, and steps for more authorization.

Problem 2642

Calculate the moles of rubidium chloride ( $\mathrm{RbCl}$ ) produced from $303 \, \mathrm{g}$ , using significant digits.

Find the hypotenuse $x$ of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Find the system of equations for tickets sold: $x + y = 120$ and $90x + 250y = 27,600$ . Options: A, B, C, D.

Find the midpoint of points $A(-7,-7)$ and $B(-5,5)$ on line segment $\overline{AB}$ .

Find the coordinates of point $B$ if point $A$ is at $(-1,8)$ and midpoint $M$ is at $(3,5.5)$ .

Calculate the circumference and area of a circle with diameter $6 \mathrm{yd}$ using $\pi \approx 3.14$ . Include units.

Find the distance between the points $(-5,-5)$ and $(-9,-2)$ . Choose: (A) 5, (B) 7, (C) $\sqrt{12}$ , (D) $\sqrt{29}$ .

Bea can spend $\$ 200$ monthly on a $\$ 22,500$ loan at $6\%$ . Check if 12-year or 20-year loans fit her budget.

Find the value of $\frac{2+a}{10-3 a}$ when $a=2$ .

Stacey earns \ $15 weekly plus \$0.50 per customer. What equation finds$ x$, customers needed for \$25?

Calculate the total payback for a \ $249,000 mortgage: 15 years at 4\% ($ 1841.82/month) and 20 years at 5\% ($1643.29/month).

What percent of the original price do you pay after a $25\%$ and then an additional $30\%$ off clearance items?

List the numbers $\frac{1}{6}, -3, \sqrt{7}, -\frac{6}{5}, 4.5$ from least to greatest. Which is first? Explain.

Deposit $\$ 5000$ at $7\%$ interest compounded monthly. What is the total in 10 years?

Find the temperature change of a $25.0 \mathrm{~g}$ brass piece from $325^{\circ} \mathrm{C}$ to $42.0^{\circ} \mathrm{C}$ . $\Delta \mathrm{T}_{\text {brass }}=[?]^{\circ} \mathrm{C}$

Find two positive and two negative angles coterminal with the angle $A=90^{\circ}$ .

Find the formula for the $n^{\text{th}}$ term of the sequence $5, 9, 13, 17, 21, \ldots$ . What is $a_{n}=$ ?

Slater Lamp Manufacturing has preferred stock with a \$80 par value and an 11% annual dividend.
a. Find the annual and quarterly dividend amounts. b. For noncumulative stock, how much is owed after 3 missed quarters? c. For cumulative stock, how much is owed after 3 missed quarters?

Find (a) the complement and (b) the supplement of the angle measuring $20^{\circ} 18^{\prime}$ .

Find the value of $b$ in the line equation $y = mx + b$ for points $C(1,3)$ and $D(4,-3)$ .

Solve the inequality $9|2 x-1|+4<49$ .

Who has a steeper slope: Marty's function $v+3=\frac{1}{3}(x+9)$ or Ethan's from the table of values?

Find the graph of the inequality $|\frac{1}{2} x + 2| \geq 1$ .

Find $\csc \theta$ if $\cot \theta = -\frac{1}{5}$ and $\theta$ is in quadrant IV.

Find the six trigonometric functions for $\theta$ with point $P(-7,4)$ on its terminal side.

Find the sale price of an item that costs $60\%$ of the original price of \$93. Use the ALEKS calculator.

Find a number $x$ such that $6x + 2 = 2 \times 19$ .

How many ways can you choose a president and vice-president from 9 people? Use the formula for permutations: $P(n, r) = \frac{n!}{(n-r)!}$ .

Find the height of a mountain peak given a distance of 27.2193 miles and an angle of elevation of $5.75^{\circ}$ .

Identify the equation pair that cannot be solved as a system: 1) $2x + 3y = 4$ and $y = 4 - x$ 2) $z = 3y + 4$ and $z = -y$ 3) $z = 3x - 2$ and $y = 2z - 3$ .

Find the value of $y$ from the equations $y = 2x - 3$ and $x = 2$ .

Calculate the sum of all whole numbers from 1 to 550, which is given by the formula $\frac{n(n+1)}{2}$ .

Calculate the ratio of the value of 7 in $Z,892$ to 7 in 34,206, and 7 in 5,073 to 7 in 18,749.

In a field with 31 heads and 86 feet, how many horses and geese are there? Let horses = x and geese = y. Solve: $x + y = 31$ and $4x + 2y = 86$ .

Find the slope of the line through points $(7,9)$ and $(5,7)$ using the slope formula. What is the slope?