Word Problems

Problem 8601

Find cc in a right triangle where a=13a=13 and b=12b=12 using the Pythagorean theorem.

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Problem 8602

Write the symbolic form of "You're here, but I'm not there" using pp and qq.

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Problem 8603

Find the third angle zz in a triangle if x=41x=41 and y=68y=68.

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Problem 8604

Write the symbolic form of "I eat bananas or it is time to sleep" using pp and qq.

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Problem 8605

In a right triangle, if the side opposite the 3030^\circ angle is 66, find the length of the side opposite the 6060^\circ angle.

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Problem 8606

Write the compound statement "If this is a gorilla, then this is a mammal" in symbolic form using pp and qq.

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Problem 8607

Write the symbolic form of "I get a promotion if and only if I work hard" using pp and qq.

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Problem 8608

Write the symbolic form of: "It is not Sunday if and only if the campus is not closed." using pp and qq.

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Problem 8609

Symbolically express: If the chair is broken or not an octopus, then I get an A. Use pp, qq, and rr.

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Problem 8610

Symbolically represent: If the chair is broken or not an octopus, then I get an A.

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Problem 8611

Write the symbolic form of: "I get an A if and only if the job pays well and I do not work hard." Use pp, qq, and rr.

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Problem 8612

Symbolically express: "The chair is broken and it is time to sleep, or I get an A" using pp, qq, and rr.

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Problem 8613

Write the symbolic form of: Not having a job or not following a budget implies being in debt.

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Problem 8614

Find the position of the word RUSE among the permutations of SURE, numbered 1 to 24 in alphabetical order.

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Problem 8615

Sasha's 9-digit passcode starts and ends with 6. Each set of 3 consecutive digits sums to 14. Find the 5th digit.

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Problem 8616

Find the yy-intercept bb of the line through points (6,10)(6,10) and (15,22)(15,22).

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Problem 8617

Find the fraction of the area shaded in a circle of radius 7, where smaller circles have radius 75\frac{7}{5}.

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Problem 8618

Find the value of kk in the equation: 24856=10k2 \cdot 4 \cdot 8 \cdot 5^6 = 10^{k}.

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Problem 8619

Find the area of a rectangle with a perimeter of 24 cm and length 3 times its breadth.

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Problem 8620

What fraction of customers ordered a hamburger over the last two days if 7/8 ordered yesterday and 2/4 today?

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Problem 8621

The perimeter of a square clock is 166916 \frac{6}{9} in, and a rectangle's is 16161816 \frac{16}{18} in. Compare the perimeters.

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Problem 8622

Tushar's age is 7 times his daughter's. In 5 years, he'll be 4 times her age. Find their current ages.

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Problem 8623

Lalit studies 7 hours daily: 2452 \frac{4}{5} hours for Math, 1141 \frac{1}{4} for English. Find time for other subjects.

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Problem 8624

Garima's father is 43, 19 years older than twice her age. Set up and solve the equation: 43=2x+1943 = 2x + 19.

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Problem 8625

Determine the number of significant figures in the sum 8.520+2.78.520 + 2.7.

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Problem 8626

The average distance from Earth to the sun is 9.3×1079.3 \times 10^{7} miles. Convert this to kilometers.

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Problem 8627

Convert 0.000053 to scientific notation.

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Problem 8628

True or False: The number 0.07010 has four significant figures.

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Problem 8629

How many cm³ of ore with 0.22%0.22\% gold is needed for \100worth?Densityis100 worth? Density is 8.0 \mathrm{~g/cm}^3$, gold is \$818/oz.

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Problem 8630

Convert the U.S. dime diameter of 18 mm18 \mathrm{~mm} to nanometers.

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Problem 8631

The average distance from Earth to the sun is 9.3×1079.3 \times 10^{7} miles. Convert this to kilometers.

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Problem 8632

Convert 26.7 to scientific notation.

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Problem 8633

A metal piece of mass 611 g611 \mathrm{~g} displaces water from 25.1 mL25.1 \mathrm{~mL} to 56.7 mL56.7 \mathrm{~mL}. Find its density.

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Problem 8634

A flask weighs 17.4916 g17.4916 \mathrm{~g} empty. With water, it weighs 43.9616 g43.9616 \mathrm{~g}. What is its mass with heavy water (1.1053 g/mL1.1053 \mathrm{~g/mL})?

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Problem 8635

Calculate the mass in pounds of 1.0 gallons of mercury given its density is 13.6 g/cm313.6 \mathrm{~g} / \mathrm{cm}^{3}.

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Problem 8636

Convert the U.S. dime diameter of 18 mm18 \mathrm{~mm} to nanometers.

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Problem 8637

Find the mass of a graphite block with the same volume as a 483 g483 \mathrm{~g} iron block, given their densities.

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Problem 8638

Calculate the simple interest on ₹ 4000 at 10\% per annum for 3 months. Use the formula I=PrtI = P \cdot r \cdot t.

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Problem 8639

Identify hydrocarbon Q\mathrm{Q} if burning 1.00 g1.00 \mathrm{~g} produces 3.22 g3.22 \mathrm{~g} of CO₂. Options: A) cyclohexene B) cyclopentane C) ethene D) pentane.

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Problem 8640

Factor the number 96 and list its prime factors in order.

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Problem 8641

Find the hyperbola equation with vertices at (3,3)(-3,-3) and (7,3)(7,-3), and foci at (5,3)(-5,-3) and (9,3)(9,-3).

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Problem 8642

Find the average car production rate if a factory makes 200 cars in 8 hours and 45 cars in 2 overtime hours.

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Problem 8643

Find the growth rate of corn if it is 1 m tall after 4 weeks and 1.8 m tall after 9 weeks. Options: A) 0.16 B) 0.31 C) 0.089 D) 6.25 E) 11.25.

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Problem 8644

A bushwalker walks 10 km10 \mathrm{~km} in 2 hours, rests for 30 min, then walks 8 km8 \mathrm{~km} in 2 hours. Find avg speed.

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Problem 8645

Find the number of sides nn in a polygon with exterior angles 6565^{\circ}, 8585^{\circ}, and remaining interior angles 150150^{\circ}.

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Problem 8646

The bakery uses 1.75 cups of flour per batch. If 5.25 cups were used, how many batches were made and how many cookies are there?

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Problem 8647

Jason eats 10 ounces of candy in 5 days. Find his daily consumption in pounds and time to eat 1 pound.

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Problem 8648

Find the area of a rectangular bulletin board that is 115 m1 \frac{1}{5} \mathrm{~m} wide and 2 m2 \mathrm{~m} long.

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Problem 8649

Write the inequality: 6n+3146 \leq n + 3 \frac{1}{4}. Then solve for nn.

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Problem 8650

What is the probability of rolling a sum of 3 with two 12-sided dice in 5 out of 10 trials?

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Problem 8651

Convert the mixed number 6386 \frac{3}{8} into an improper fraction.

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Problem 8652

Compare earnings per item sold: Lincoln School: $5\$ 5 for 4 boxes; Williams School: $7\$ 7 for 6 rolls.

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Problem 8653

Determine if the product of 10.4×78.2-10.4 \times -78.2 is positive (+) or negative (-).

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Problem 8654

Reyna needs to make 4 batches of punch using 12 ounces of orange juice each. How many quarts is that?

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Problem 8655

Multiply 116-1 \frac{1}{6} by 7 and express the result as a mixed number.

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Problem 8656

Convert 4.20 grams of SnO2\mathrm{SnO}_{2} to moles using its molar mass.

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Problem 8657

What fraction of cars in a lot are both gray and electric if 25\frac{2}{5} are gray and 13\frac{1}{3} of gray are electric?

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Problem 8658

Divide -72 by -4, then take that result and divide by -9. What is the final result?

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Problem 8659

Lake Segundo's depth is 56\frac{5}{6} of Lake Profondo's 84 feet. What is Lake Segundo's elevation below sea level?

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Problem 8660

Calculate the number of moles of CS2 with a weight of 4.20 g and molar mass 76.13 g/mol using the formula:
Number of moles = 4.20g76.13g/mol\frac{4.20 \, \text{g}}{76.13 \, \text{g/mol}}.

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Problem 8661

Convert 4.20 grams of Ca3 N2\mathrm{Ca}_{3} \mathrm{~N}_{2} to moles.

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Problem 8662

Convert 4.20 g of vitamin C (C6H8O6\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}) to moles.

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Problem 8663

Find the result of 842.4÷0.6842.4 \div -0.6.

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Problem 8664

Find the result of 100÷(10)÷5100 \div (-10) \div 5.

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Problem 8665

A band around Earth is lengthened by 1 m. How far above the equator is it now? Use Earth's radius of 6400 km.

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Problem 8666

Find the result of the division 842.4÷0.6842.4 \div -0.6.

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Problem 8667

Convert 4.65 to a fraction in simplest form.

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Problem 8668

Convert the mixed number 27162 \frac{7}{16} to a decimal using long division.

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Problem 8669

Convert 67156 \frac{7}{15} to a decimal using long division.

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Problem 8670

A pilot descends 4,000 feet in 3.5 minutes. Find the rate of change in altitude to the nearest hundredth.

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Problem 8671

A fire engine's tank has 750 gallons. If 250 gallons are removed in 5 minutes, find the change in gallons per minute.

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Problem 8672

Find kk for which the line y=2x+3y=-2x+3 is tangent to the curve f(x)=kx2f(x)=k x^{2}.

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Problem 8673

A fish starts at -10.8 m and descends 1.5 m every 2 min. How long to reach -37.8 m? Show your work and explain.

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Problem 8674

A plane flies from city A to city B, 2140 miles apart at 400 mph. Find the function f(t)f(t) for distance from B at time tt.

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Problem 8675

Find a point that is 2\sqrt{2} units from (1,5)(-1,5).

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Problem 8676

A pretzel factory has daily costs of \2100and10centsperbag.Eachbagsellsfor$1.70.Findthecostfunction2100 and 10 cents per bag. Each bag sells for \$1.70. Find the cost function c(x).. c(x)=2100+0.10x c(x) = 2100 + 0.10x $

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Problem 8677

Find the average rate of change of f(x)f(x) from x1=3x_{1}=-3 to x2=8.5x_{2}=8.5 for f(x)=7x8f(x)=7x-8. Round to the nearest hundredth.

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Problem 8678

Find a point (x,y)(x, y) that is between 50 and 60 units from (7,2)(7, -2) using the distance formula: (x7)2+(y+2)2\sqrt{(x-7)^2 + (y+2)^2}.

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Problem 8679

Classify the following matter types: hot coffee, salt water, aluminum, gold, orange juice with pulp, magnesium, carbon dioxide, air, sugar, toluene, soil.

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Problem 8680

Find kk so that the line y=2x+ky=2x+k goes through the minimum point of the curve y=3x2+12x+13y=3x^2+12x+13.

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Problem 8681

Find the average rate of change of f(x)f(x) from x1=2x_{1}=2 to x2=4x_{2}=4 for f(x)=3x+1f(x)=\sqrt{3x+1}, rounded to the nearest hundredth.

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Problem 8682

Find values of xx for which the volume of a prism is 500\geq 500 cubic units, given width =x5= x - 5 and height =2x= 2x.

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Problem 8683

Mary bought a \$30,000 boat with a \$2,000 down payment. What happened to her assets and liabilities? A) Both decreased B) Both increased C) Assets decreased, liabilities increased D) Assets increased, liabilities decreased. Choose the best answer.

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Problem 8684

Find possible lengths for a garden with 80 ft of fencing, area > 400 sq ft and < 600 sq ft. Options are: (0,10)(30,40)(0,10) \cup(30,40), (20102,20+102)(20-10 \sqrt{2}, 20+10 \sqrt{2}), (0,20102)(20+102,40)(0,20-10 \sqrt{2}) \cup(20+10 \sqrt{2}, 40), (20102,10)(30,20+102)(20-10 \sqrt{2}, 10) \cup(30,20+10 \sqrt{2}).

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Problem 8685

What type of asset is money in a retirement fund? a. investment asset b. liquid asset c. long term asset d. use asset. Select the best answer.

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Problem 8686

Find the length of segment FG\overline{F G} given FH=5x+2F H=5 x+2, GH=5x9G H=5 x-9, and FG=x+5F G=x+5.

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Problem 8687

Classify these as pure substances or mixtures: 1. baking soda (NaHCO₃), 2. blueberry muffin, 3. ice (H₂O), 4. zinc (Zn), 5. Trimix (O₂, N₂, He).

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Problem 8688

Find the length of RS\overline{R S} given QS=5x2Q S=5 x-2, QR=3x6Q R=3 x-6, and RS=4x2R S=4 x-2.

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Problem 8689

Find the length of segment AC\overline{A C} given AB=2x+10A B=2 x+10, BC=xB C=x, and AC=5xA C=5 x.

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Problem 8690

Mikah buys a TV for \$1,600 valued at \$1,800 with a \$300 down payment. How much did his assets increase? A, B, C, or D?

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Problem 8691

Find the average rate of change of f(x)=6x+9f(x)=6x+9 from x1=3.5x_1=3.5 to x2=9x_2=9, rounded to the nearest whole number.

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Problem 8692

Find KLK L if points K,L,M,NK, L, M, N are in the ratio 3:1:13:1:1 and KN=20K N=20.

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Problem 8693

Classify these substances as elements or compounds: 1. silicon (Si), 2. oxygen (O2\mathrm{O}_{2}), 3. hydrogen peroxide (H2O2\mathrm{H}_{2} \mathrm{O}_{2}), 4. rust (Fe2O3\mathrm{Fe}_{2} \mathrm{O}_{3}), 5. methane (CH4\mathrm{CH}_{4}).

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Problem 8694

Find QRQR if points P,Q,R,SP, Q, R, S are on a line with PQ:QR:RS=3:1:2PQ:QR:RS = 3:1:2 and PS=18PS = 18.

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Problem 8695

Maximize area with 480 ft of fencing for a lot bordered by a highway. What are the optimal dimensions?

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Problem 8696

Find the average rate of change of f(x)f(x) from x1=9x_{1}=-9 to x2=1x_{2}=-1, rounded to the nearest hundred. f(x)=8x+6 f(x)=\sqrt{-8 x+6}

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Problem 8697

Find the density of an object with mass 15 g15 \mathrm{~g} and volume 5 cm35 \mathrm{~cm}^{3}. Include the unit.

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Problem 8698

Classify these mixtures as homogeneous or heterogeneous: 1. vegetable soup 2. tea 3. tea with ice and lemon 4. seawater 5. fruit salad.

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Problem 8699

Classify lemon-flavored water as a homogeneous or heterogeneous mixture.

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Problem 8700

Convert 1.55×1051.55 \times 10^{-5} grams to milligrams.

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