Word Problems

Problem 4201

A steel rod of length L0=70 cmL_{0}=70 \mathrm{~cm} at T0=70CT_{0}=70^{\circ} \mathrm{C} expands. Find its length at T=100CT=100^{\circ} \mathrm{C}. Also, find its length at T=80CT=80^{\circ} \mathrm{C} if it was 85in85 \mathrm{in} at T0=170CT_{0}=170^{\circ} \mathrm{C}. Lastly, express LL as a function of TT and α\alpha for L0=50L_{0}=50 \mathrm{in} at T0=130CT_{0}=130^{\circ} \mathrm{C}.

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Problem 4202

A car goes 120 miles in 3 hours. How long for 200 miles at the same speed?

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Problem 4203

A machine produces 6 yards in 2 minutes. How much can it produce in 1 hour?

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Problem 4204

Find the measure of 5\angle 5 if line mm is parallel to line nn and 2=35\angle 2 = 35^{\circ}.

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Problem 4205

If lines mm and nn are parallel and 2=35\angle 2 = 35^{\circ}, find 5\angle 5. Choices: 145145^{\circ}, 155155^{\circ}, 180180^{\circ}, 5555^{\circ}.

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Problem 4206

Mike reads 4 pages in 18 minutes. How long for 30 pages? Calculate time using the ratio of pages to time.

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Problem 4208

If 13 candy bars weigh 26 ounces, find the weight of 35 candy bars using the formula: weight = (26/13) * 35.

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Problem 4209

Nathan packs 25 boxes in 2 hours. How many boxes can he pack in 8 hours?

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Problem 4210

Find values of aa for lines L1L_{1} and L2L_{2} with slopes m1=6a46m_{1}=\frac{-6 a-4}{-6} and m2=4a+85m_{2}=\frac{-4 a+8}{-5} such that: (i) L1L_{1} is parallel to L2L_{2}: a=a= (ii) L1L_{1} is perpendicular to L2L_{2}: a=a=

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Problem 4211

A steel rod of length L0L_{0} at T0T_{0} changes length with ΔL=αL0ΔT\Delta L=\alpha L_{0} \Delta T. Find lengths for given temps.

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Problem 4212

Solve for xx if angle three is 6x+166x + 16 and angle seven is 2x+22x + 2.

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Problem 4213

Solve 4=2m5n4=2 m-5 n for mm. Find mm when n=2,0,2n=-2,0,2. Options: A. m=5n+2m=5 n+2 B. m=25n4m=\frac{2}{5} n-4 C. m=5n+2m=5 n+2 D. m=25nm=2-5 n.

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Problem 4214

Moises's original volume is 37500 cm³. If shrunk by a scale factor of k=14k=\frac{1}{4}, what is his new volume?

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Problem 4215

Sarai is 200 ft from the platform with a 6262^{\circ} angle of elevation. Which side is 200 ft: opposite, adjacent, or hypotenuse?

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Problem 4216

Terdapat 15 kad hijau dan kebarangkalian memilih kad merah ialah 23\frac{2}{3}. Cari bilangan kad merah dalam kotak.

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Problem 4217

Encik Amin simpan RM28,000 dengan faedah 3\% setahun, dikompaun setiap 3 bulan. Berapa jumlah simpanan pada akhir tahun 20222022?

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Problem 4218

Find the number where 8x3x=1658x - 3x = 165. Options: (a) 32 (b) 33 (c) 34 (d) 38 (e) None.

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Problem 4219

Which coordinates for points AA^{\prime} and BB^{\prime} show that lines ABAB and ABA^{\prime}B^{\prime} are perpendicular?
1. A:(p,m)A^{\prime}:(p, m) and B:(z,w)B^{\prime}:(z, w)
2. A:(p,m)A^{\prime}:(p, m) and B:(z,w)B^{\prime}:(z,-w)
3. A:(p,m)A^{\prime}:(p,-m) and B:(z,w)B^{\prime}:(z, w)
4. A:(p,m)A^{\prime}:(p,-m) and B:(z,w)B^{\prime}:(z,-w)

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Problem 4220

Find the number where thrice it minus 11 equals 49: 3x11=493x - 11 = 49. Choices: (a) 19 (b) 23 (c) 20 (d) 24 (e) None.

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Problem 4221

If Ann's house is at 0, and Beth is 4 blocks away, what are the possible locations for Carol's house, given she is 2 blocks from Beth?

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Problem 4222

If Al's house is at 0, and Ben is 7 blocks away, what are Carol's possible locations if she's 5 blocks from Ben?

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Problem 4223

Find the greater number if it exceeds another by 7 and their sum is 33. Options: (a) 20 (b) 18 (c) 23 (d) 28

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Problem 4224

Find the greater number if the sum of two numbers is 6 and one is five times the other. Options: (a) 55, (b) 45, (c) 56, (d) 57, (e) None.

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Problem 4225

Find the smaller number if the difference is 3 and the sum is 99. Options: (a) 48 (b) 45 (c) 47 (d) 49 (e) None.

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Problem 4226

A volleyball player sets a ball up. Height h(t)=16t2+20t+6h(t) = -16t^2 + 20t + 6. What is the max height at t=0.625t = 0.625 seconds? A. 8.5 B. 11.625 C. 1225 D. 1.625

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Problem 4227

Find Letisha's total in checking, savings, and college accounts after 12 months if she deposits \$125, \$75, and \$50 monthly.

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Problem 4228

Calculate the total ticket cost for 23 students and 2 teachers at \$39 each. Find the expression and the total cost.

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Problem 4229

Find the zeros of the function f(x)=2x2+6x+1f(x)=2x^{2}+6x+1 using the quadratic formula. What are the x-intercepts?

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Problem 4230

Find the zeros of the function f(x)=4x2+6x+1f(x)=4x^{2}+6x+1 using the quadratic formula. What are the xx-intercepts?

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Problem 4231

West Elementary has 438 students and 22 teachers. East has 697 students and 27 teachers. Find students per teacher for both schools.

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Problem 4232

An adult needs 261mL261 \mathrm{mL} of oxygen/min. With 20% inhaled O2, find air volume per breath at 12 breaths/min.

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Problem 4233

Find the zeros of the function f(x)=3x2+10x+6f(x)=3x^{2}+10x+6 using the quadratic formula. What are the x-intercepts?

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Problem 4234

Un cohete "Pioneer" alcanzó 125.000 km125.000 \mathrm{~km}. ¿Cuál es su velocidad al regresar a la atmósfera a 130 km130 \mathrm{~km}?

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Problem 4235

How does the mass of an object on Neptune compare to its mass on Earth if Neptune's gravity is 1.1 times that of Earth? A, B, C, or D?

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Problem 4236

Find the zeros of the function g(x)=5x2+14x+8g(x)=5x^{2}+14x+8 using the quadratic formula. What are the x-intercepts?

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Problem 4237

Check Guy's calculation: Is 8,2657,1458,265 - 7,145 equal to 1,0101,010? Identify his mistake in the steps shown.

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Problem 4238

Demostrar que la serie n=1(sennx)/n2\sum_{n=1}^{\infty}(\operatorname{sen} n x) / n^{2} converge para todo xx, y que f(x)f(x) es continua en [0,π][0, \pi]. Luego, probar que 0πf(x)dx=2n=11(2n1)3\int_{0}^{\pi} f(x) d x=2 \sum_{n=1}^{\infty} \frac{1}{(2 n-1)^{3}}.

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Problem 4239

Find the zeros of the function g(x)=4x2+9x+5g(x)=4 x^{2}+9 x+5 using the quadratic formula. What are the x-intercepts?

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Problem 4240

Choose two properties of a leaf that affect its fall due to air resistance: mass, surface area, gravity, or initial distance?

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Problem 4241

Find rr for the point (2,r)(-2, r) on the line with slope m=4m=-4 passing through (12,10)(12,10).

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Problem 4242

Graph the system of equations for Melinda's coffee and pastry sales: x=y+2x = y + 2 and 6x+4y=726x + 4y = 72. Mark the solution.

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Problem 4243

Calculate students per teacher for West (438 students, 22 teachers) and East (697 students, 27 teachers). Discuss proportionality.

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Problem 4244

Identify and fix the mistake in this equation: 6(2y+6)=4(9+3y)6(2y+6)=4(9+3y) leading to 0=00=0. What is the correct conclusion?

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Problem 4245

Each kitten's weight after gaining 2.3 ounces: initial weights were 3.6, 4.2, and 3.3 ounces. Find final weights.

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Problem 4246

Find xx if BD=7x10BD=7x-10, BC=4x29BC=4x-29, and CD=5x9CD=5x-9.

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Problem 4247

Is Jaime's calculation of 4.40.33=1.14.4 - 0.33 = 1.1 reasonable? Explain your reasoning.

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Problem 4248

For a prime number w>2w > 2, when is w2zw^{2} z a negative even integer for zz in which set? A. Negative integers B. Positive odd integers C. Positive even integers D. Negative odd integers E. Negative even integers

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Problem 4249

Identify the false statement:
1. All integers are rational numbers
2. Some rational numbers are whole numbers
3. All whole numbers are natural numbers
4. All irrational numbers are real numbers

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Problem 4250

Find the area of a triangle with base 4ft4 \mathrm{ft} and height 3ft3 \mathrm{ft} using A=12bhA = \frac{1}{2} b h. What if height doubles?

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Problem 4251

Identify a rational number between 7 and 8 from these options: 7.837 . \overline{83}, 52\sqrt{52}, neither A and C, both A and C.

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Problem 4252

Which set has no irrational numbers? {5.15,π,30}\{-5.15, \pi, 30\}, {92,100,5.123}\left\{\frac{9}{2}, \sqrt{100}, 5.123\right\}, or {80,100,6.56}\{\sqrt{80}, 100, 6.56\}?

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Problem 4253

Write a scientific notation number greater than 500 and less than 5.000. Who did it right? Justice: 5.25×1035.25 \times 10^{3}, Blaire: 6.1×1036.1 \times 10^{3}, Denzet: 5.78×1025.78 \times 10^{2}, Piper: 3.5×103.5 \times 10.

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Problem 4254

Find the difference between -4 and 6. Options: 10-10, 2-2, 2, 10.

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Problem 4255

The combined cost of a washer and dryer is \$ 944, with the washer costing \$ 94 more than the dryer. Find the dryer cost.

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Problem 4256

A total of 267 tickets were sold, with student tickets being twice the adult tickets. Find the number of adult tickets sold.

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Problem 4257

Find the coordinates of point BB if the midpoint M(2,4)M(2,4) and point A(1,5)A(-1,5) are given.

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Problem 4258

How much flour is needed for 20 servings if 4 servings require 23\frac{2}{3} cup? Options: 6, 3133 \frac{1}{3}, 23\frac{2}{3}, 215\frac{2}{15}.

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Problem 4259

Gabrielle is 10 years older than Mikhail. Their ages sum to 72. Find Mikhail's age: M+(M+10)=72M + (M + 10) = 72.

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Problem 4260

A basketball player jumps to 1.1 m1.1 \mathrm{~m}. What is his hang time in the air before landing?

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Problem 4261

Which expression equals 22+(32)22 + (-32)? 22+(22)+(10)22 + (-22) + (-10), 22+22+(10)22 + 22 + (-10), 22+(22)+1022 + (-22) + 10, or 22+0+3222 + 0 + 32?

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Problem 4262

Find three consecutive integers whose sum is 51. Let the integers be nn, n+1n+1, and n+2n+2.

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Problem 4263

Find the percent of the sum of the two least box tops collected compared to the two most: Rooms 100, 159, 206, 215.

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Problem 4264

Jessica deposits \7000at67000 at 6% simple interest. How much interest will she earn in 3 years? Calculate x$.

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Problem 4265

Find two consecutive even integers whose sum is 38.

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Problem 4266

Translate into an equation: 7 plus 4 times bb equals 3.

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Problem 4267

Find the volume of a beach ball with a radius of 30 cm. Use π\pi or 3.14 for your answer in cm3\mathrm{cm}^{3}.

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Problem 4268

Round 518 to the nearest ten. Identify the two benchmark thousands for 1,742 and place them on a number line with 1,742.

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Problem 4269

Translate: 2 times (w - 7) = 2.

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Problem 4270

Hong deposits \200at5200 at 5% simple interest. How much interest will he earn in 5 years? 200 \times 0.05 \times 5$

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Problem 4271

Calculate the interest and total amount paid on a \10,550loanat12.25%for3yearsusing10,550 loan at 12.25\% for 3 years using I=Prt$. Round to the nearest dollar.

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Problem 4272

Deshaun deposits \4000at34000 at 3% simple interest. What interest will he earn in 2 years? I = P \times r \times t$

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Problem 4273

Identify the two thousand benchmarks around 1,742 and place them on a number line with 1,742.

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Problem 4274

Plot points D(-3,-3), E(4,-3), F(9,5), G(2,5) for parallelogram DEFG. Find the perimeter and round to the nearest tenth.

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Problem 4275

Find three numbers where their sum is 86, the second is 9 less than the first, and the third is 3 times the first.

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Problem 4276

Leila, Juan, and Chris have $94\$ 94 total. Chris has 4 times Leila's amount, and Juan has $8\$ 8 less than Leila. Find their amounts.

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Problem 4277

Find the slope of the line connecting the points (1,0) and (3,8). Choose the correct answer: (A) 14-\frac{1}{4}, (B) -4, (C) 4, (D) 14\frac{1}{4}.

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Problem 4278

Diane, Frank, and John served 102 orders total. If Diane served 10 more than Frank and John served 2 times Frank, find their orders.

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Problem 4279

Jenny works 15 hours a week, earns \$10/hour, and bakes 200 cupcakes daily. How much will she earn in 2 weeks?

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Problem 4280

Jude has half of Tobias's \$4,300. How much money does Jude have in his teddy bear?

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Problem 4281

Hector's insurance increases by 15% because he's male. Define the function M(x)M(x) for his new monthly premium.

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Problem 4282

Define a function S(x)S(x) for the 30% discount on monthly premiums for students with a 3.03.0 GPA or higher.

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Problem 4283

Define a function H(x)H(x) to calculate the cost after a 30% discount on Hector's original amount xx.

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Problem 4284

A study of 27,000 individuals tested if a herbal supplement reduces asthma attacks. What aspects relate to design and description?

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Problem 4285

Determine the transformations to show QRSTUV\triangle QRS \cong \triangle TUV. Choose all correct options: A) Reflect across xx, then yy, then xx. B) Reflect across yy. C) Rotate 9090^{\circ} clockwise, then reflect across yy. D) Rotate 180180^{\circ}, then reflect across xx. E) Translate 44 units left.

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Problem 4286

What type of statistics is it when 90%90 \% of taste testers prefer the new coffee brand? Options: Investigation, Description, Design, Inference, None.

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Problem 4287

Define a function H(x)H(x) for Hector's payment after a 30\% discount on the original amount xx.

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Problem 4288

How many times more Marvel graphic novels (10610^{6}) were sold than DC comic books (10310^{3})?

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Problem 4289

A survey asked 857 people about their pets. Identify (a) the sample, (b) the population, and (c) the statistic. What is the sample? A. The public in the country. B. People who didn't respond. C. The 857 respondents. D. The 9%9\% with 1 pet.

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Problem 4290

A survey asked 857 people about their pets. Identify the sample, population, and statistic: (a) sample? (b) population? (c) statistic?

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Problem 4291

A survey of 857 people asked about pet ownership. Identify (a) sample, (b) population, and (c) statistic (9%9\% with 1 pet).

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Problem 4292

Hector's premium increases by 35% after a speeding ticket. If he pays \$1260 yearly, find his new monthly premium.

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Problem 4293

Identify the subject, sample, and population for the government study on model A midsized cars. What is the subject? A. new model A cars B. midsized cars C. new midsized cars D. model A cars

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Problem 4294

Identify the subject, sample, and population for a study on model A midsized cars' emissions and mileage.
(a) Subject: A. new model A midsized cars (b) Sample: D. few new model A midsized cars chosen for study

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Problem 4295

Find the pre-image of vertex A(8,5)A^{\prime}(8,5) after reflection across the yy-axis. Options: (8,6)(-8,-6), (6,8)(-6,8), (8,6)(8,6), (6,8)(6,-8).

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Problem 4296

Figure BB is in Quadrant IV. After reflecting, rotating, and translating it, determine if these statements are true or false:
a. BB''' is in Quadrant II. b. BB is in Quadrant III. c. The xx-coordinates of BB''' are all negative. d. The yy-coordinates of BB'' are all positive.
Initial position and shape of BB are needed.

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Problem 4297

Compare 8.76×1068.76 \times 10^{6} and 8.76×1028.76 \times 10^{2}. Complete: 3.76×1063.76 \times 10^{6} is Choose... times Choose. than 8.76×1028.76 \times 10^{2}.

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Problem 4298

Find which reflection of the segment from (4,6)(-4,-6) to (6,4)(-6,4) gives endpoints (4,6)(4,-6) and (6,4)(6,4).

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Problem 4299

Identify (a) subject, (b) sample, and (c) population for model A midsized cars used in a pollution study.

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Problem 4300

How many grams of trash did the US throw away in 2013 if each person discarded 4.5×1024.5 \times 10^{2} grams daily? 5.3×10g 5.3 \times 10 \square \mathrm{g}

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