Word Problems

Problem 1301

Compare the values of the underlined digits:
1. In 6,3006,300, the value of 3 is ____ times the value of 3 in 530530.
2. In 34,25834,258, the value of 4 is ____ times the value of 4 in 47,16347,163.

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Problem 1302

Find the equation of a line through (4,4)(-4,4) that is perpendicular to y=12x+2y=\frac{1}{2}x+2.

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Problem 1303

Find the slope of the line through points (3,8)(-3,8) and (4,7)(4,7). Show your calculations.

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Problem 1304

Find the slope of the line through points (3,8)(-3,8) and (4,7)(4,7). Show your work.

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Problem 1305

How many times is the value of 2 in 2783 vs. 7283? Also, compare the value of 5 in 503,491 to 7 in 26,475.

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Problem 1306

Multiply the fractions: 910(2811)\frac{9}{10}\left(2 \frac{8}{11}\right) and simplify to lowest terms.

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Problem 1307

Identify the student who erred in writing equivalent fractions/decimals: KEITH, SOREN 0.04=250.04=\frac{2}{5} 56=0.83\frac{5}{6}=0.8 \overline{3} Correct their statement.

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Problem 1308

Identify the student who made an error in their fractions/decimals: Keith (0.04=250.04=\frac{2}{5}) or Soren (56=0.83\frac{5}{6}=0.8 \overline{3})? Correct their statement.

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Problem 1309

Compare the place values of '2' in 2,783 and 7,283, and '7' in 503,497 and 26,475. Find the value ratios.

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Problem 1310

Convert the repeating decimal 0.20.\overline{2} into a fraction.

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Problem 1311

Rewrite the decimal 6.1256.125 by expanding it using powers of 10 and as a fraction.

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Problem 1312

A panda eats 30 kg30 \mathrm{~kg} of bamboo daily. How many pounds does it eat in 6 weeks? Use 1 kg2.2lb1 \mathrm{~kg} \approx 2.2 \mathrm{lb}.

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Problem 1313

Convert the repeating decimal 0.60.\overline{6} to a fraction.

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Problem 1314

Determine which postcard size matches the shape of a painting with dimensions 30.25 inches by 25.25 inches. Options:
1. 5 inches by 5 inches
2. 8 inches by 4 inches
3. 6.05 inches by 5.05 inches

Show your work.

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Problem 1315

Do 1.583 and 1 one + 58 hundredths + 3 thousandths represent the same number? Justify your answer.

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Problem 1316

Which postcard matches the shape of a painting where the long side is 1.2 times the short side? Options: A (5x5), B (8x4), C (6.05x5.05).

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Problem 1317

How can you use a scale drawing with scale ss to find an actual length LL?

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Problem 1318

What factors convert 12 m/s12 \mathrm{~m/s} to kilometers per minute? Choose correct options from:
- 1 km1000 m\frac{1 \mathrm{~km}}{1000 \mathrm{~m}} - 60 s1 min\frac{60 \mathrm{~s}}{1 \mathrm{~min}} - 1000 m1 km\frac{1000 \mathrm{~m}}{1 \mathrm{~km}} - 1 min60 s\frac{1 \mathrm{~min}}{60 \mathrm{~s}}

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Problem 1319

What is 5 tens + 1 one + 4 tenths + 39 hundredths in standard form? Options: (A) 51.439 (B) 51.1439 (C) 51.79 (D) 52.79

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Problem 1320

Select all correct representations of 73.218. Options: 1) 73 ones + 218 thousandths 2) 7 tens + 3 ones + 218 thousandths 3) 73 tens + 218 thousandths 4) 7 tens + 3 ones + 2 tenths + 18 hundredths 5) 7 tens + 3 ones + 2 tenths + 18 thousandths

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Problem 1321

Write 2.075 in words and identify the place and value of the digit 5.

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Problem 1322

A \250,000houseisassessedat250,000 house is assessed at 1/5$ of its value. With a tax rate of \$3.20 per hundred, what is the yearly tax?

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Problem 1323

Find the height change per second as the elevator descends 420 meters in 60 seconds. What is the integer value?

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Problem 1324

A submarine goes 660 feet down in 11 minutes. What is the change in feet per minute?

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Problem 1325

Two numbers, xx and yy, are reciprocals. Which expression is always true? A. xy=1xy=1 B. xy=0x-y=0 C. xy=1\frac{x}{y}=1 D. x+y=1x+y=-1 E. xy=1x^{y}=1

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Problem 1326

Arrange these fractions in decreasing order: 56,13,73,52,54\frac{5}{6}, \frac{1}{3}, \frac{7}{3}, \frac{5}{2}, \frac{5}{4}.

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Problem 1327

Aaron made 3 equal withdrawals totaling \$375. What is the amount withdrawn each time?

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Problem 1328

Find the altitude change per minute for a balloon that descended 2,700 feet in 135 minutes. What is the value?

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Problem 1329

If aa and bb are reciprocals with 0<a<10<a<1, what is the range of bb? Options: F. < -1, G. (-1, 0), H. 0, J. (0, 1), K. > 1.

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Problem 1330

A scientist enlarges a photo of an elm leaf beetle. If 2in2 \mathrm{in} in the photo equals 8mm8 \mathrm{mm} on the beetle, find the actual length (1121 \frac{1}{2} in) and width (34\frac{3}{4} in) of the beetle. Show your work.

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Problem 1331

What is the distance between two towns on a map if 2 cm2 \mathrm{~cm} equals 30mi30 \mathrm{mi} and the actual distance is 75mi75 \mathrm{mi}?

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Problem 1332

Find xx if the length of DF\overline{D F} is (4x+2)(4x + 2) inches and DE\overline{D E} is 17 inches.

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Problem 1333

Explain how the Distributive Property aids in solving problems.

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Problem 1334

A marine biologist studies a dolphin's speed. It swims 55 meters in 5 seconds. Graph the distance over time. How far in 1 second?

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Problem 1335

Reflect point C(1,6)C(-1,-6) across the line y=4y=4. What are the coordinates of CC^{\prime}?

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Problem 1336

Two trees: one is 3m tall with an 18m shadow. Find the height of the other tree with a 39m shadow. Options: 12.5 m12.5 \mathrm{~m}, 6.5 m6.5 \mathrm{~m}, 3.25 m3.25 \mathrm{~m}, 2.17 m2.17 \mathrm{~m}.

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Problem 1337

Find the new vertices K,L,M,NK^{\prime}, L^{\prime}, M^{\prime}, N^{\prime} after rotating polygon KLMN by 9090^{\circ} clockwise.

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Problem 1338

Convert the unit fraction 14\frac{1}{4} to a percentage. What is it?

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Problem 1339

Convert 80%80\% to its simplest fraction form. Options: 18\frac{1}{8}, 45\frac{4}{5}, 810\frac{8}{10}, 4050\frac{40}{50}.

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Problem 1340

Convert 49%49\% to a decimal. How many places does the decimal point move? What is the decimal form?

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Problem 1341

А) 20. Ако x:y=2:3x: y=2: 3, x:z=4:3x: z=4: 3 и 2xy+z=152x-y+z=15, намерете стойността на yy.

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Problem 1342

A spiral is made of semicircles with the first diameter 10 cm10 \mathrm{~cm}, each next being 45\frac{4}{5} of the last.
1) Find the total length of the spiral.
2) How far is point EE (midpoint of the 6th semicircle) from point AA?

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Problem 1343

Find the actual distance from town A to town B at a scale of 1 cm: 100 km. Choose A-D. 400 cm, 400 km, 25 km, 0.04 cm.

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Problem 1344

Find the probability of the letter OO in "BOOK". What is the distance from town AA to town BB at a scale of 1 cm:100 km1 \mathrm{~cm}: 100 \mathrm{~km}? Round 55.89934 to three decimals.

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Problem 1345

Which word is spelled correctly? A. Perfectible B. Unpredictible C. Believible D. Incomparible

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Problem 1346

Überprüfe die Konvergenz der geometrischen Reihen und gib die Summen an: a) 1+2+22+1+2+2^{2}+\ldots, b) 1+12+(12)2+1+\frac{1}{2}+\left(\frac{1}{2}\right)^{2}+\ldots, c) 1+(12)+(12)2+1+\left(-\frac{1}{2}\right)+\left(-\frac{1}{2}\right)^{2}+\ldots, d) 1+(1)+(1)2+1+(-1)+(-1)^{2}+\ldots, e) 3+314+3(14)2+3+3 \cdot \frac{1}{4}+3 \cdot\left(\frac{1}{4}\right)^{2}+\ldots, f) 550,1+50,1250,13+5-5 \cdot 0,1+5 \cdot 0,1^{2}-5 \cdot 0,1^{3}+\ldots.

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Problem 1347

Find the principal amount deposited at 10%10\% p.a. if it grows to \$31,460 after 2 years.

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Problem 1348

Find the compound interest on \$70000 at 6\% p.a. compounded monthly after 8 months.

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Problem 1349

Find the compound interest on \$ 38000 borrowed at 4\% p.a. compounded quarterly after 2.5 years.

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Problem 1350

Find the principal amount deposited at 10% p.a. if it grows to \$31460 in 2 years.

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Problem 1351

A merchant mixes xx kg of tea at \72/kgwith72/kg with ykgat$97/kgforamixturecostof$82/kg.Find kg at \$97/kg for a mixture cost of \$82/kg. Find x:y$ and profit from 15 kg of tea P sold at \$120/kg.

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Problem 1352

Berechne den Flächeninhalt AA des Dreiecks und die gesuchten Längen: a) hah_a, b) hbh_b, c) hch_c, d) hbh_b.

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Problem 1353

Find the rectangle dimensions and max area with a perimeter of 36 mm36 \mathrm{~mm}. Dimensions: mm\mathbf{mm}, Area: mm2\mathrm{mm}^{2}.

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Problem 1354

Berechne die gesuchten Längen für die gegebenen Flächeninhalte und Höhen der Dreiecke:
a) A=17,55 cm2,a=7,8 cm,ha=A=17,55 \mathrm{~cm}^{2}, a=7,8 \mathrm{~cm}, h_{a}= ?
b) A=2340 mm2,hb=36 mm,b=A=2340 \mathrm{~mm}^{2}, h_{b}=36 \mathrm{~mm}, b= ?
c) A=18,25 cm2,c=73 mm,hc=A=18,25 \mathrm{~cm}^{2}, c=73 \mathrm{~mm}, h_{c}= ?
d) A=34,1 cm2,ha=62 mm,a=A=34,1 \mathrm{~cm}^{2}, h_{a}=62 \mathrm{~mm}, a= ?

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Problem 1355

En un colegio hay 648 estudiantes. 5/9 son varones. Calcula: I. Parte de varones que practica deporte. II. Número de varones. III. Parte de mujeres que practica deporte. IV. Número de mujeres.

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Problem 1356

Berechne das Guthaben nach 10 Jahren, wenn jährlich 5 mal 10001000 € und 3 mal 800800 € bei 0,7\% Zinsen eingezahlt werden.

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Problem 1357

Identify the true properties of parallelograms from these options: A. Adjacent sides congruent, B. Opposite angles congruent, C. Opposite angles parallel, D. Opposite sides parallel, E. Consecutive angles supplementary, F. Diagonals bisect each other.

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Problem 1358

Graig has 200 yards of fencing for a garden next to his house. Find dimensions for max area. Possible: 50x100, 50x50, 50x200.

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Problem 1359

Divide 14 kids in Camp A and 21 kids in Camp B into equal-sized groups. How many kids are in each group?

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Problem 1360

Divide 14 kids in Camp A and 21 kids in Camp B into equal-sized groups. How many kids are in each group?

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Problem 1361

Which quadrilaterals have opposite angles that are always congruent? Check all that apply: A. Parallelogram B. Square C. Quadrilateral D. Rhombus

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Problem 1362

Разделите отрезок ABA B на 4 равные части.

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Problem 1363

Jane buys 1 carton of eggs every 10 days for \$3.50. With \$20, how many days of eggs can she buy and how many cartons?

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Problem 1364

A Tik Tokker gains 20 more subscribers daily, starting with 100 on day 1. How many total subscribers after 5 days?

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Problem 1365

En un congreso, la relación inicial es 8 varones por 5 mujeres. Tras retirar 25 mujeres, hay 5 mujeres por 12 varones. ¿Cuántas personas había inicialmente?

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Problem 1366

Find an index ii in array A\mathrm{A} where the sum before ii equals the sum after ii. Return 1-1 if none exist.

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Problem 1367

Find the other trigonometric functions of θ\theta if sinθ=36\sin \theta=-\frac{\sqrt{3}}{6} and cosθ>0\cos \theta>0.

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Problem 1368

Find the remaining trigonometric functions of θ\theta if sinθ=36\sin \theta=\frac{\sqrt{3}}{6} and cosθ>0\cos \theta>0. What is cosθ\cos \theta?

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Problem 1369

Find sinθ\sin \theta given cscθ=204\csc \theta = \frac{\sqrt{20}}{4}. Simplify your answer, including any radicals.

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Problem 1370

Find the quadrants for angle θ\theta where cosθ<0\cos \theta < 0 and tanθ>0\tan \theta > 0. Choose from: A. IV, B. II, C. I, D. III.

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Problem 1371

Find the quadrant(s) where sinα<0\sin \alpha<0 and secα<0\sec \alpha<0. Answer as 1,2,31,2,3, or 4, separated by commas.

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Problem 1372

Find tanθ\tan \theta if sinθ=12\sin \theta = -\frac{1}{2} and θ\theta is in quadrant IV.

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Problem 1373

Show 13×34\frac{1}{3} \times \frac{3}{4} on a number line and compare it to 34\frac{3}{4}. Is it less, greater, or equal?

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Problem 1374

Find the remaining trigonometric functions of θ\theta if tanθ=34\tan \theta=-\frac{3}{4} in quadrant II.

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Problem 1375

Find the exact values of sinθ\sin \theta and cosθ\cos \theta if tanθ=34\tan \theta = -\frac{3}{4} in quadrant II.

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Problem 1376

Find the other trigonometric functions of θ\theta if tanθ=34\tan \theta=-\frac{3}{4} in quadrant II.

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Problem 1377

Find all trigonometric functions for θ\theta if tanθ=34\tan \theta=-\frac{3}{4} in quadrant II.

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Problem 1378

Can different functions share the same xx-intercepts (5,0)(-5,0), (2,0)(2,0), (6,0)(6,0), domain 5x7-5 \leq x \leq 7, and range 4y10-4 \leq y \leq 10? Provide examples.

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Problem 1379

What is the probability of guessing a 5-digit code from 5 unique numbers? A. 112\frac{1}{12} B. 1120\frac{1}{120} C. 140\frac{1}{40} D. 160\frac{1}{60}

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Problem 1380

Aaron filled a bird bath with 64 ounces. After blue jays drank 5.17 ounces and a vulture drank 114511 \frac{4}{5} ounces, how much is left?

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Problem 1381

Find (a) the complement and (b) the supplement of an angle measuring 171517^{\circ} 15^{\prime}.

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Problem 1382

Find cscθ\csc \theta if cotθ=16\cot \theta = -\frac{1}{6} and θ\theta is in quadrant IV.

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Problem 1383

Jodie spent 401440 \frac{1}{4} seconds and 12.84 seconds. How much time does she need to match 68.2 seconds?

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Problem 1384

Raya buys a van for £8500 plus 20% VAT. She pays a deposit and then 12 monthly payments of £531.25. Find the deposit to total payments ratio in simplest form.

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Problem 1385

Find (a) the complement and (b) the supplement of an angle measuring 171517^{\circ} 15^{\prime}.

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Problem 1386

Freddie needs \$120,000 for a prototype and pays \$9,000 interest yearly. What is the annual interest rate in percent?

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Problem 1387

Find the complement and supplement of an angle measuring 221322^{\circ} 13^{\prime}.

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Problem 1388

How many elements are in the union of sets A and B if A has 8 elements, B has 20, and 5 are common?

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Problem 1389

If the final price is \$3 after halving the new price, what was the original price before the \$2 increase?

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Problem 1390

Calculate the sum of the points on a number line from -2 to 2. Possible answers: (A) -4, (B) 0, (C) 2, (D) 4.

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Problem 1391

In a pet supply store survey, 27 owned dogs, 30 owned mice, and 17 owned both. Find how many owned either a dog or a mouse.

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Problem 1392

Two cities are 3.75 inches apart on a map where 2 inches = 50 miles. How far apart are they in miles?

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Problem 1393

Round 6.241596.24159 to two decimal places.

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Problem 1394

Colleen uses blue yarn bb and red yarn rr. What equation shows their proportional relationship? Options: (A) b=25rb=\frac{2}{5} r, (B) r=25br=\frac{2}{5} b, (C) b=27rb=\frac{2}{7} r, (D) r=27br=\frac{2}{7} b.

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Problem 1395

A restaurant gives 10%10\% of customers a discount coupon. Which model simulates this? A) Spinner, B) Dice, C) Cards, D) Random numbers?

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Problem 1396

Concert tickets cost \$35 and \$55. If 95 tickets sold for \$4325, find how many of each type were sold.

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Problem 1397

Mr. Barton's garden has sides 16ft16 \mathrm{ft}, xftx \mathrm{ft}, xftx \mathrm{ft}, and 20ft20 \mathrm{ft}. If the perimeter is 60ft60 \mathrm{ft}, find xx. Options: (A) 12ft12 \mathrm{ft} (B) 15ft15 \mathrm{ft} (C) 18ft18 \mathrm{ft} (D) 24ft24 \mathrm{ft}.

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Problem 1398

Mr. Barton's rectangular garden has a top side of 16 ft, bottom side of 20 ft, and perimeter of 60 ft. Find xx.

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Problem 1399

A square's perimeter is 8g+168 g+16. Which expression matches this perimeter based on the side length? (A) 2(4g+8)2(4 g+8) (B) 4(2g+4)4(2 g+4) (C) 4(2g)+164(2 g)+16 (D) 4(g+2)+4(g+2)4(g+2)+4(g+2)

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Problem 1400

A diver descends to 18 feet, ascends 7 feet, then descends 18 feet again. What's the final depth? (A) -29 (B) -43 (C) 29 (D) 43

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