Equation

Problem 13001

A store's inventory rose from 300 to 1200. What percent of the old inventory is the new inventory?

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Problem 13002

Frank owes \$50,400 on a 6%, 150-day note. After paying \$12,600 on day 30 and \$17,640 on day 100, calculate the balance.

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Problem 13003

Find the equation of a circle with center at the origin and radius $\frac{1}{2}$ . Options: A. $x^{2}+y^{2}=\frac{1}{4}$ B. $x^{2}+y^{2}=\frac{1}{2}$ C. $x^{2}+y^{2}=1$ D. $x^{2}+y^{2}=2$

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Problem 13004

Solve the equation: $0.25 r - 0.125 + 0.5 r = 0.5 + r$ . Show all steps.

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Problem 13005

Solve the equation: $12x - 11x - 18 = 11$ . What is the value of $x$ ?

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Problem 13006

Find the other endpoint of a segment with one endpoint at $(1,3)$ and midpoint at $(3,5)$ .

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Problem 13007

Isolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

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Problem 13008

A drug uses 3 mL of compound A for every 5 mL of compound B. How much A is needed for 544 mL of the drug?

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Problem 13009

A sculptor makes a $\frac{1}{10}$ scale model of a 56-ton landmark. Solve $10 x=56$ to find the model's weight.

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Problem 13010

Calculate the total calories in a serving with $2 \mathrm{~g}$ carbs, $16 \mathrm{~g}$ protein, $6 \mathrm{~g}$ fat. Options: 96, 116, 126, 136.

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Problem 13011

If a bag has 49 purple marbles, how many yellow marbles are there if the ratio is 5 yellow to 7 purple?

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Problem 13012

The city's yes to no vote ratio is 3:4. With 1743 yes votes, find the total number of votes.

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Problem 13013

Calculate the total kilocalories from 50 g fat, 40 g protein, and 235 g carbohydrates. Possible answers: 580, 930, 1550, 2020.

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Problem 13014

A sculptor is making a $\frac{1}{9}$ scale model of an 89-ton landmark. Find the model's weight by solving $9x=89$ .

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Problem 13015

Find $x$ given that $AC = 3x + 3$ , $AB = -1 + 2x$ , and $BC = 11$ with points $A$ , $B$ , and $C$ collinear.

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Problem 13016

Solve the equation: $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}$ . Provide exact answers, using radicals if necessary.

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Problem 13017

If Orly uses 2 cups of raisins for every 8 cups of trail mix, how much trail mix can she make with 10 cups of raisins?

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Problem 13018

Which option shows the commutative property of addition: A, B, C, or D?

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Problem 13019

Solve the equation: $5 x^{2}-6 x=8$ . Provide the exact solution set, using radicals if necessary.

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Problem 13020

Orly uses 2 cups of raisins for 8 cups of trail mix. How many cups of trail mix for 10 cups of raisins? Options: $1 \frac{3}{5}$ , $2 \frac{1}{2}$ , or 40 cups.

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Problem 13021

Given $y$ varies inversely with $x$ , and $y=3$ when $x=8$ , find the equation and $y$ when $x=15$ .

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Problem 13022

Solve the equation $2 x^{2}-3=-101$ using the square root property. Simplify and express complex numbers with $i$ .

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Problem 13023

Calculate the future value of \$10,000 at 3% interest compounded monthly for 7 years. Round to the nearest cent.

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Problem 13024

What is Travis's speed in mph if he traveled 290 miles in 5 hours? $\text{Speed} = \frac{290 \text{ miles}}{5 \text{ hours}}$

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Problem 13025

Solve the equation $4 x^{2}=192$ . Provide the simplified solution set using radicals and $i$ for complex answers.

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Problem 13026

Given $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

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Problem 13027

Given $y$ varies inversely with $x$ , and $y=8$ when $x=5$ : (a) Find the equation; (b) Determine $y$ when $x=10$ . $y=$

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Problem 13028

Solve the equation $2 x^{2}-3 x-1=0$ using the quadratic formula. Provide the exact solutions.

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Problem 13029

Find the future value of \$5,000 at 6\% annual interest compounded quarterly after 5 years. Round to the nearest cent.

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Problem 13030

Find the volume $V$ of a prism with length 6 m, width 2 m, and height 10 m using $V=\ell w h$ .

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Problem 13031

Prove that the solutions of $z^{2}-2 z+10=0$ are complex (not real).

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Problem 13032

Find the volume $V$ of a prism with length 6 ft, width 4 ft, and height 1 ft using $V=\ell w h$ . Choose: (A) 10, (B) 11, (C) 24.

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Problem 13033

Find the value of $a$ if the volume of a cylinder with radius 4 ft and height 30 ft is $a \pi$ cubic ft.

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Problem 13034

Which option shows the associative property of multiplication? A. $ab=ba$ B. $a(bc)=(ab)c$ C. $a \cdot 1=a$ D. $a(b+c)=ab+ac$

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Problem 13035

Mike initially stands $50 \mathrm{~m}$ from a tree, covering it with his $7 \mathrm{~cm}$ finger. After moving back, his $6 \mathrm{~cm}$ finger covers the tree. How far did he move back?

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Problem 13036

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

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Problem 13037

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

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Problem 13038

If \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

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Problem 13039

Solve for $x$ : $\frac{8}{17}=\frac{5}{7x}$ . Find $x$ in simplest form.

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Problem 13040

Solve for $x$ : $\frac{x+8}{13}=\frac{2}{9}$ . Find $x$ in simplest form.

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Problem 13041

Solve for $x$ in the equation $\frac{15}{10}=\frac{23}{x}$ . Reduce to simplest form.

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Problem 13042

Kevin drove 95 miles and Amanda drove 125 miles. How many more gallons did Kevin use than Amanda if his truck uses 1 gallon/15 miles and hers uses 1 gallon/40 miles?

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Problem 13043

Solve for $y$ in the equation $-\frac{1}{2} y=10$ .

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Problem 13044

If $60\%$ of a number is 18.0, find $25\%$ of that number. A. 2.7 B. 4.5 C. 7.5 D. 12.0 E. 13.5

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Problem 13045

Find the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

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Problem 13046

Given two figures, solve these:
1) For a light ray from A to B through I, express optical path AIB using $n_1$ , $n_2$ , and coordinates. Show $n_1 \sin i_1 = n_2 \sin i_2$ .
2) For a glass slab of thickness $a$ and $n=1.33$ , show the exiting ray is parallel to the incident ray.

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Problem 13047

Mitchell exchanges 150 US dollars for Canadian dollars, spends 20 CAD, then converts the rest back to USD. How much USD is left?

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Problem 13048

Find the $y$ -intercept of $y=\frac{1}{4} x-\frac{2}{3}$ . A. $-\frac{2}{3}$ B. $\frac{2}{3}$ C. $-\frac{1}{4}$ D. $\frac{1}{4}$

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Problem 13049

What percent of the 500 students at West Middle School play a musical instrument if 95 are boys and 75 are girls?

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Problem 13050

Find the $y$ -intercept of the line $2x + y = -3$ . A. -2 B. 2 C. 3 D. -3

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Problem 13051

Find the slope of the line given by the equation $y=-x+2$ .

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Problem 13052

What is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. $\frac{1}{300}$ G. $\frac{1}{60}$ H. $\frac{1}{59}$ J. $\frac{5}{59}$ K. $\frac{1}{5}$

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Problem 13053

Calculate the investment value using $A=5000(1+0.08)^{15}$ . What is $A$ after 15 years? Options: A. \$2,000 B. \$5,400 C. \$10,882 D. \$15,861 E. \$21,499

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Problem 13054

Find the smallest number of bingo chips that leaves a remainder of 2 when divided by 9, 10, or 12. Options: 80, 182, 360, 542, 1080.

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Problem 13055

Find the mode of the numbers $x, 2x, 2x+6, 3x-1, 4x-8$ if their average is 9.

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Problem 13056

Solve $(x+4)^{2}-4=0$ for real $x$ . Provide simplified solutions, separated by commas if multiple. $x=$

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Problem 13057

Hundreds equal 70 times tens. What is the value of hundreds in terms of tens? Express it as: $h = 70t$ .

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Problem 13058

If $\angle A$ is supplementary to $\angle B$ and $\angle B=115^{\circ}$ , find $\angle A$ .

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Problem 13059

Find the dimensions of a rectangle where length is $11 \mathrm{yd}$ more than twice the width and area is $63 \mathrm{yd}^{2}$ .

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Problem 13060

Solve the equation $x^{2}-12 x+61=0$ using the quadratic formula. Provide the exact solution with radicals and $i$ .

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Problem 13061

Grace read 10 minutes for 4 days. If she needs to read 60 minutes total, how many more minutes does she need?

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Problem 13062

In an evaporation experiment, initial mass is $10.5775 \pm 0.0002 \mathrm{~g}$ and final mass is $10.3005 \pm 0.0002 \mathrm{~g}$ . Find the propagated error on the evaporated mass. Options: a. $\pm 0.0006$ , b. $\pm 0.0004$ , c. $\pm 0.003$ , d. $\pm 0.0003$ .

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Problem 13063

In a water evaporation experiment, initial mass is $10.5775 \pm 0.0002 \mathrm{~g}$ and final mass is $10.3005 \pm 0.0002 \mathrm{~g}$ . What is the propagated error on the evaporated mass? Options: a. $\pm 0.0006$ , b. $\pm 0.0004$ , c. $\pm 0.003$ , d. $\pm 0.0003$ .

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Problem 13064

There are 700 paper clips. If 486 are used, how many are left? Calculate: $700 - 486$ .

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Problem 13065

Find the final propagated error in density when mass is $10.50 \pm 0.02 \mathrm{~g}$ and volume is $1.638 \pm 0.005 \mathrm{~mL}$ .

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Problem 13066

Find the dimensions of a rectangle with area $54 \mathrm{yd}^{2}$ , where length is $3 \mathrm{yd}$ more than double the width.

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Problem 13067

Find the slope of the line through points $(-1,3)$ and $(2,4)$ , and state if it rises, falls, is horizontal, or vertical.

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Problem 13068

Find the dimensions of a rectangle with area $50 \mathrm{yd}^{2}$ and length $5 \mathrm{yd}$ less than three times the width.

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Problem 13069

Graph the line with slope -4 and $y$ -intercept 5 given by the equation $y=-4x+5$ .

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Problem 13070

A ball is thrown from a building with height $S(t)=112+96t-16t^2$ .
(a) When does it hit the ground? (b) When does it pass the building's top again?

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Problem 13071

Find the probability that a person with a cat also has a dog, given 35 have dogs, 10 have both, 15 have cats, and 40 have neither.

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Problem 13072

Find the slope of the line through points $(22,40)$ and $(52,17)$ . Round your answer to one decimal place.

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Problem 13073

Find three fractions equal to $\frac{0}{7}$ and $\frac{a}{5}$ . Fill in the numerators for denominators 63, 42, 70, 10, and 90.

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Problem 13074

Find the numerator for the equation $\frac{a}{5}=\frac{\square}{30}$ (Simplify your answer.)

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Problem 13075

Find three fractions equal to $\frac{a}{5}$ :
1. $\frac{a}{5}=\frac{\square}{10}$
2. $\frac{a}{5}=\frac{\square}{90}$
3. $\frac{a}{5}=\frac{\square}{30}$ . Simplify each.

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Problem 13076

What percent of 60 is 72? Find $\square \%$ such that $72 = \frac{\square}{100} \times 60$ .

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Problem 13077

Find the side length $x$ of a square sheet to create a box with volume 100 cubic feet using $V(x)=(x-2)^{2}$ .

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Problem 13078

Find the zeros of the function $f(x)=x^{2}-7 x$ by factoring. What are the $x$ -intercepts?

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Problem 13079

Find the next equation in the sequence:
1 = $1^2$ , 1 + 2 + 1 = $2^2$ , 1 + 2 + 3 + 2 + 1 = $3^2$ , 1 + 2 + 3 + 4 + 3 + 2 + 1 = $4^2$ .
Verify your answer.

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Problem 13080

Todd used 3 gallons for 150 miles. Find the rate of change in gallons per mile: slope = $\frac{150 \text{ miles}}{3 \text{ gallons}}$ .

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Problem 13081

Find the cost in 2014 using the model $C=2.85n+30.52$ , where $n$ is the years since 1990.

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Problem 13082

Find the intercepts of the line given by $-4x + 7y = 3$ . Provide exact values.

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Problem 13083

Solve for real $x$ in the equation: $4 x^{3}-8 x^{2}=0$ . Provide answers as a comma-separated list.

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Problem 13084

Label the place value charts. Complete: $10 \times 4$ ones $=$ ones $=$ and show regrouping with disks and arrows.

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Problem 13085

Divide 18 by 153 using long division.

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Problem 13086

Diego paid a \$2.25 pickup fee and \$1.75 per mile. If his total fare was \$28.50, how far did he travel?

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Problem 13087

Find the intercepts of the line given by $y-3=5(x-2)$ . $y$ -intercept: $x$ -intercept:

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Problem 13088

Find Rosalyn's regular hourly wage given she worked 44 hours and earned \$1025, with overtime pay at 2.5 times her wage.

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Problem 13089

Find the missing side length in the second triangle given corresponding sides 66 and 154 from similar triangles.

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Problem 13090

Find the abundance of ${ }^{10} \mathrm{~B}$ and ${ }^{11} \mathrm{~B}$ given their masses and average atomic mass of boron, $10.81 \mathrm{~u}$ .

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Problem 13091

Gallium has two isotopes. One is ${ }^{71}$ Ga with mass $70.9247050 \mathrm{amu}$ and abundance $39.892 \%$ . Find the mass number of the other isotope.

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Problem 13092

Find the missing side length of two similar triangles with sides 36, 36, 18 and 24, 48.

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Problem 13093

Find the value of $d$ given that $d = a_2 - a_1$ , where $a_2 = 22$ and $a_1 = 12$ .

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Problem 13094

Find the length and width of a field with a perimeter of 100 m, where length is $14 \mathrm{~m}$ more than width.

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Problem 13095

Katrina has 60 GB. Her father has 10 times that. How much storage does he have? Explain your answer.

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Problem 13096

Find all real solutions for the equation $x^{3} = 81x$ . Enter answers as a comma-separated list.

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Problem 13097

Find all real solutions for the equation: $6x^5 - 24x = 0$ .

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Problem 13098

The first side of a triangle is $8 \mathrm{~m}$ shorter than the second side. The third side is 4 times the first side. The perimeter is $26 \mathrm{~m}$ . Find the length of each side.

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Problem 13099

Solve for all real values of $x$ in the equation $x = 5x^5 - 45x$ .

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Problem 13100

Find $t$ when the rocket's height $h=92$ feet, given $h=188t-16t^2$ . Round to the nearest hundredth.

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1 ...128 129 130 131 132 133 134 ...188

Equation

Problem 13001

A store's inventory rose from 300 to 1200. What percent of the old inventory is the new inventory?

Problem 13002

Frank owes \$50,400 on a 6%, 150-day note. After paying \$12,600 on day 30 and \$17,640 on day 100, calculate the balance.

Problem 13003

Find the equation of a circle with center at the origin and radius 12\frac{1}{2}21​. Options: A. x2+y2=14x^{2}+y^{2}=\frac{1}{4}x2+y2=41​ B. x2+y2=12x^{2}+y^{2}=\frac{1}{2}x2+y2=21​ C. x2+y2=1x^{2}+y^{2}=1x2+y2=1 D. x2+y2=2x^{2}+y^{2}=2x2+y2=2

Problem 13004

Solve the equation: 0.25r−0.125+0.5r=0.5+r0.25 r - 0.125 + 0.5 r = 0.5 + r0.25r−0.125+0.5r=0.5+r. Show all steps.

Problem 13005

Solve the equation: 12x−11x−18=1112x - 11x - 18 = 1112x−11x−18=11. What is the value of xxx?

Problem 13006

Find the other endpoint of a segment with one endpoint at (1,3)(1,3)(1,3) and midpoint at (3,5)(3,5)(3,5).

Problem 13007

Isolate yyy in the equation −56y−15y=43−15-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}−65​y−51​y=34​−51​. Express your answer as an integer.

Problem 13008

A drug uses 3 mL of compound A for every 5 mL of compound B. How much A is needed for 544 mL of the drug?

Problem 13009

A sculptor makes a 110\frac{1}{10}101​ scale model of a 56-ton landmark. Solve 10x=5610 x=5610x=56 to find the model's weight.

Problem 13010

Calculate the total calories in a serving with 2 g2 \mathrm{~g}2 g carbs, 16 g16 \mathrm{~g}16 g protein, 6 g6 \mathrm{~g}6 g fat. Options: 96, 116, 126, 136.

Problem 13011

If a bag has 49 purple marbles, how many yellow marbles are there if the ratio is 5 yellow to 7 purple?

Problem 13012

The city's yes to no vote ratio is 3:4. With 1743 yes votes, find the total number of votes.

Problem 13013

Calculate the total kilocalories from 50 g fat, 40 g protein, and 235 g carbohydrates. Possible answers: 580, 930, 1550, 2020.

Problem 13014

A sculptor is making a 19\frac{1}{9}91​ scale model of an 89-ton landmark. Find the model's weight by solving 9x=899x=899x=89.

Problem 13015

Find xxx given that AC=3x+3AC = 3x + 3AC=3x+3, AB=−1+2xAB = -1 + 2xAB=−1+2x, and BC=11BC = 11BC=11 with points AAA, BBB, and CCC collinear.

Problem 13016

Solve the equation: 1x+1x+2=17\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}x1​+x+21​=71​. Provide exact answers, using radicals if necessary.

Problem 13017

If Orly uses 2 cups of raisins for every 8 cups of trail mix, how much trail mix can she make with 10 cups of raisins?

Problem 13018

Which option shows the commutative property of addition: A, B, C, or D?

Problem 13019

Solve the equation: 5x2−6x=85 x^{2}-6 x=85x2−6x=8. Provide the exact solution set, using radicals if necessary.

Problem 13020

Orly uses 2 cups of raisins for 8 cups of trail mix. How many cups of trail mix for 10 cups of raisins? Options: 1351 \frac{3}{5}153​, 2122 \frac{1}{2}221​, or 40 cups.

Problem 13021

Given yyy varies inversely with xxx, and y=3y=3y=3 when x=8x=8x=8, find the equation and yyy when x=15x=15x=15.

Problem 13022

Solve the equation 2x2−3=−1012 x^{2}-3=-1012x2−3=−101 using the square root property. Simplify and express complex numbers with iii.

Problem 13023

Calculate the future value of \$10,000 at 3% interest compounded monthly for 7 years. Round to the nearest cent.

Problem 13024

What is Travis's speed in mph if he traveled 290 miles in 5 hours? Speed=290 miles5 hours\text{Speed} = \frac{290 \text{ miles}}{5 \text{ hours}}Speed=5 hours290 miles​

Problem 13025

Solve the equation 4x2=1924 x^{2}=1924x2=192. Provide the simplified solution set using radicals and iii for complex answers.

Problem 13026

Given yyy varies inversely with xxx and y=−32y=-\frac{3}{2}y=−23​ when x=−8x=-8x=−8, find the equation and yyy when x=6x=6x=6. y= y = y=

Problem 13027

Given yyy varies inversely with xxx, and y=8y=8y=8 when x=5x=5x=5: (a) Find the equation; (b) Determine yyy when x=10x=10x=10. y= y= y=

Problem 13028

Solve the equation 2x2−3x−1=02 x^{2}-3 x-1=02x2−3x−1=0 using the quadratic formula. Provide the exact solutions.

Problem 13029

Find the future value of \$5,000 at 6\% annual interest compounded quarterly after 5 years. Round to the nearest cent.

Problem 13030

Find the volume VVV of a prism with length 6 m, width 2 m, and height 10 m using V=ℓwhV=\ell w hV=ℓwh.

Problem 13031

Prove that the solutions of z2−2z+10=0z^{2}-2 z+10=0z2−2z+10=0 are complex (not real).

Problem 13032

Find the volume VVV of a prism with length 6 ft, width 4 ft, and height 1 ft using V=ℓwhV=\ell w hV=ℓwh. Choose: (A) 10, (B) 11, (C) 24.

Problem 13033

Find the value of aaa if the volume of a cylinder with radius 4 ft and height 30 ft is aπa \piaπ cubic ft.

Problem 13034

Which option shows the associative property of multiplication? A. ab=baab=baab=ba B. a(bc)=(ab)ca(bc)=(ab)ca(bc)=(ab)c C. a⋅1=aa \cdot 1=aa⋅1=a D. a(b+c)=ab+aca(b+c)=ab+aca(b+c)=ab+ac

Problem 13035

Mike initially stands 50 m50 \mathrm{~m}50 m from a tree, covering it with his 7 cm7 \mathrm{~cm}7 cm finger. After moving back, his 6 cm6 \mathrm{~cm}6 cm finger covers the tree. How far did he move back?

Problem 13036

Solve for yyy in the equation: 928y−127y+37=34\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}289​y−712​y+73​=43​.

Problem 13037

Solve for yyy in the equation: 928y−127y+37=34\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}289​y−712​y+73​=43​.

Problem 13038

If \$24 was invested at 3\% annual interest from 1626 to 2020, how much is in the account now? Round to the nearest dollar.

Problem 13039

Solve for xxx: 817=57x\frac{8}{17}=\frac{5}{7x}178​=7x5​. Find xxx in simplest form.

Problem 13040

Find the equation of a circle with center at the origin and radius $\frac{1}{2}$ . Options: A. $x^{2}+y^{2}=\frac{1}{4}$ B. $x^{2}+y^{2}=\frac{1}{2}$ C. $x^{2}+y^{2}=1$ D. $x^{2}+y^{2}=2$

Solve the equation: $0.25 r - 0.125 + 0.5 r = 0.5 + r$ . Show all steps.

Solve the equation: $12x - 11x - 18 = 11$ . What is the value of $x$ ?

Find the other endpoint of a segment with one endpoint at $(1,3)$ and midpoint at $(3,5)$ .

Isolate $y$ in the equation $-\frac{5}{6} y - \frac{1}{5} y = \frac{4}{3} - \frac{1}{5}$ . Express your answer as an integer.

A sculptor makes a $\frac{1}{10}$ scale model of a 56-ton landmark. Solve $10 x=56$ to find the model's weight.

Calculate the total calories in a serving with $2 \mathrm{~g}$ carbs, $16 \mathrm{~g}$ protein, $6 \mathrm{~g}$ fat. Options: 96, 116, 126, 136.

A sculptor is making a $\frac{1}{9}$ scale model of an 89-ton landmark. Find the model's weight by solving $9x=89$ .

Find $x$ given that $AC = 3x + 3$ , $AB = -1 + 2x$ , and $BC = 11$ with points $A$ , $B$ , and $C$ collinear.

Solve the equation: $\frac{1}{x}+\frac{1}{x+2}=\frac{1}{7}$ . Provide exact answers, using radicals if necessary.

Solve the equation: $5 x^{2}-6 x=8$ . Provide the exact solution set, using radicals if necessary.

Orly uses 2 cups of raisins for 8 cups of trail mix. How many cups of trail mix for 10 cups of raisins? Options: $1 \frac{3}{5}$ , $2 \frac{1}{2}$ , or 40 cups.

Given $y$ varies inversely with $x$ , and $y=3$ when $x=8$ , find the equation and $y$ when $x=15$ .

Solve the equation $2 x^{2}-3=-101$ using the square root property. Simplify and express complex numbers with $i$ .

What is Travis's speed in mph if he traveled 290 miles in 5 hours? $\text{Speed} = \frac{290 \text{ miles}}{5 \text{ hours}}$

Solve the equation $4 x^{2}=192$ . Provide the simplified solution set using radicals and $i$ for complex answers.

Given $y$ varies inversely with $x$ and $y=-\frac{3}{2}$ when $x=-8$ , find the equation and $y$ when $x=6$ . $y =$

Given $y$ varies inversely with $x$ , and $y=8$ when $x=5$ : (a) Find the equation; (b) Determine $y$ when $x=10$ . $y=$

Solve the equation $2 x^{2}-3 x-1=0$ using the quadratic formula. Provide the exact solutions.

Find the volume $V$ of a prism with length 6 m, width 2 m, and height 10 m using $V=\ell w h$ .

Prove that the solutions of $z^{2}-2 z+10=0$ are complex (not real).

Find the volume $V$ of a prism with length 6 ft, width 4 ft, and height 1 ft using $V=\ell w h$ . Choose: (A) 10, (B) 11, (C) 24.

Find the value of $a$ if the volume of a cylinder with radius 4 ft and height 30 ft is $a \pi$ cubic ft.

Which option shows the associative property of multiplication? A. $ab=ba$ B. $a(bc)=(ab)c$ C. $a \cdot 1=a$ D. $a(b+c)=ab+ac$

Mike initially stands $50 \mathrm{~m}$ from a tree, covering it with his $7 \mathrm{~cm}$ finger. After moving back, his $6 \mathrm{~cm}$ finger covers the tree. How far did he move back?

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

Solve for $y$ in the equation: $\frac{9}{28} y - \frac{12}{7} y + \frac{3}{7} = \frac{3}{4}$ .

Solve for $x$ : $\frac{8}{17}=\frac{5}{7x}$ . Find $x$ in simplest form.

Solve for $x$ : $\frac{x+8}{13}=\frac{2}{9}$ . Find $x$ in simplest form.

Solve for $x$ in the equation $\frac{15}{10}=\frac{23}{x}$ . Reduce to simplest form.

Solve for $y$ in the equation $-\frac{1}{2} y=10$ .

If $60\%$ of a number is 18.0, find $25\%$ of that number. A. 2.7 B. 4.5 C. 7.5 D. 12.0 E. 13.5

Find the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

Find the $y$ -intercept of $y=\frac{1}{4} x-\frac{2}{3}$ . A. $-\frac{2}{3}$ B. $\frac{2}{3}$ C. $-\frac{1}{4}$ D. $\frac{1}{4}$

Find the $y$ -intercept of the line $2x + y = -3$ . A. -2 B. 2 C. 3 D. -3

Find the slope of the line given by the equation $y=-x+2$ .

What is the probability the alarm sounds when a student enters the lab at 12:36, given it sounds for 5 seconds every 5 minutes? F. $\frac{1}{300}$ G. $\frac{1}{60}$ H. $\frac{1}{59}$ J. $\frac{5}{59}$ K. $\frac{1}{5}$

Calculate the investment value using $A=5000(1+0.08)^{15}$ . What is $A$ after 15 years? Options: A. \$2,000 B. \$5,400 C. \$10,882 D. \$15,861 E. \$21,499

Find the mode of the numbers $x, 2x, 2x+6, 3x-1, 4x-8$ if their average is 9.

Solve $(x+4)^{2}-4=0$ for real $x$ . Provide simplified solutions, separated by commas if multiple. $x=$

Hundreds equal 70 times tens. What is the value of hundreds in terms of tens? Express it as: $h = 70t$ .

If $\angle A$ is supplementary to $\angle B$ and $\angle B=115^{\circ}$ , find $\angle A$ .

Find the dimensions of a rectangle where length is $11 \mathrm{yd}$ more than twice the width and area is $63 \mathrm{yd}^{2}$ .

Solve the equation $x^{2}-12 x+61=0$ using the quadratic formula. Provide the exact solution with radicals and $i$ .

There are 700 paper clips. If 486 are used, how many are left? Calculate: $700 - 486$ .

Find the final propagated error in density when mass is $10.50 \pm 0.02 \mathrm{~g}$ and volume is $1.638 \pm 0.005 \mathrm{~mL}$ .

Find the dimensions of a rectangle with area $54 \mathrm{yd}^{2}$ , where length is $3 \mathrm{yd}$ more than double the width.

Find the slope of the line through points $(-1,3)$ and $(2,4)$ , and state if it rises, falls, is horizontal, or vertical.

Find the dimensions of a rectangle with area $50 \mathrm{yd}^{2}$ and length $5 \mathrm{yd}$ less than three times the width.

Graph the line with slope -4 and $y$ -intercept 5 given by the equation $y=-4x+5$ .

A ball is thrown from a building with height $S(t)=112+96t-16t^2$ .
(a) When does it hit the ground? (b) When does it pass the building's top again?

Find the slope of the line through points $(22,40)$ and $(52,17)$ . Round your answer to one decimal place.

Find three fractions equal to $\frac{0}{7}$ and $\frac{a}{5}$ . Fill in the numerators for denominators 63, 42, 70, 10, and 90.

Find the numerator for the equation $\frac{a}{5}=\frac{\square}{30}$ (Simplify your answer.)