Math

Problem 51001

Analyze the polynomial $f(x)=(x+8)(x-1)^{2}$ :
(a) End behavior: behaves like $y=x^{3}$ for large $|x|$ . (b) Intercepts: $x$ -intercepts are $-8, 1$ ; $y$ -intercept is 8. (c) Zeros: $-8, 1$ ; check if graph crosses/touches $x$ -axis. (d) Maximum turning points: (whole number).

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Problem 51002

Find all values of $x$ such that $y_{1} + y_{2} = y_{3}$ , where $y_{1}=\frac{4}{x+6}, y_{2}=\frac{5}{x+3}, y_{3}=\frac{12 x+30}{x^{2}+9 x+18}$ . Choices: A, B, C.

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Problem 51003

Find the mode, mean, and median of the following 30 adult heights (cm): 129.9, 118.2, 186, 217.7, 172.8, 178.4, 128.5, 192.6, 106.3, 183.8, 189.2, 170, 130.1, 159.3, 153.5, 160.8, 162.4, 174.9, 164, 160.9, 166.3, 157.9, 193.8, 128.7, 179.2, 173.2, 200.6, 169.1, 166.3, 179.7. Round answers to one decimal place.

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Problem 51004

A bookcase has 4 shelves. Width is 11 ft less than 3 times height. Total lumber is 26 ft. Find width and height.

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Problem 51005

Mr. Michaels has 40 m of wire. After wiring 16 lamps (0.45 m each), 12 wall lights (0.7 m each), and 1 floor lamp (2.6 m), how much is left? A) 7.2 m B) 18.2 m C) 21.8 m D) 15.6 m

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Problem 51006

Counseling Duration Data:
(1) How many clients completed 4-6 sessions? (2) What percentage completed 4-6 sessions? (3) What is the cumulative percentage for 4-6 sessions? (4) What percentage completed at least 1 but not more than 6 sessions? Data: $f$ : 21, $\%$ : 21.6, $\Sigma \%$ : 78.4.

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Problem 51007

Classify the shape: opposite sides are parallel, all sides congruent, vertices not necessarily right angles. Options: Square, Rectangle, Rhombus, Parallelogram.

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Problem 51008

Analyze the function $f(x)=(x+7)(x-5)^{2}$ : (a) Find end behavior; (b) Determine $x$ - and $y$ -intercepts.

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Problem 51009

Find the width of a 70" TV with a 16:9 aspect ratio. Options: $80.33^{\prime \prime}$ , $39.4^{\prime \prime}$ , $61^{\prime \prime}$ , $44.8^{\prime \prime}$ .

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Problem 51010

Identify a real-life situation that involves a quadrilateral: inflating a balloon, tiling a floor, building a pyramid, or baking a cake?

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Problem 51011

Analyze the function $f(x)=(x+7)(x-5)^{2}$ : find end behavior, intercepts, zeros, and their multiplicities.

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Problem 51012

Solve for $x$ in the equation: $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9 x+28}{x^{2}+10 x+24}$ , where $y_{1}+y_{2}=y_{3}$ .

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Problem 51013

Convert 10.7 m to cm using 1 m = 100 cm. What is $10.7 \times 100$ ?

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Problem 51014

Convert 10.7 meters to centimeters using the conversion factor: 1 meter = 100 centimeters.

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Problem 51015

Divide 3 by 5: what is the result of $3 \div 5$ ?

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Problem 51016

Calculate the following probabilities based on the data:
1. From the U.S.
2. At least 2 children.
3. From the U.S. and 1 child.
4. From the U.S. or 0 children.
5. From the U.S. with 3+ children.
6. 1 child and from the U.S.

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Problem 51017

(1) ¿Cuántos clientes completaron de 4 a 6 sesiones? $21$ (2) ¿Qué porcentaje de clientes completó de 4 a 6 sesiones? $21.6\%$ (3) ¿Cuál es el porcentaje acumulado para 4-6 sesiones? $78.4\%$ (4) ¿Qué porcentaje completó al menos una sesión pero no más de 6? $78.4\%$ (5) ¿Qué porcentaje completó al menos una sesión pero no más de 4? Entre $56.7\%$ y $100\%$

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Problem 51018

A bank loaned out \$7,500 at 6\% and 15\% interest, earning \$765 total. Find the amounts loaned at each rate.

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Problem 51019

Simplify the expression: $\frac{a^{2}-4}{a^{2}-5 a-14}$ .

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Problem 51020

Find $x$ such that $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9x+28}{x^2+10x+24}$ and $y_{1}+y_{2}=y_{3}$ .

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Problem 51021

Calculate: $165 \frac{1}{4} \div 41 \frac{1}{4} =$

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Problem 51022

Simplify the expression: $\frac{x^{2}-17 x+72}{x^{2}-100} \cdot \frac{x^{2}-18 x+80}{x^{2}+x-90}.$

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Problem 51023

Find $x$ when $y=0$ for the equation $y=2[x-(3-x)]-3(x+1)$ . Choose A, B, or C for the solution.

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Problem 51024

1) ¿Cuántos clientes completaron 4-6 sesiones? $21$ 2) ¿Qué porcentaje completó 4-6 sesiones? $21.6\%$ 3) ¿Cuál es el porcentaje acumulado para 4-6 sesiones? $78.4\%$ 4) ¿Qué porcentaje completó al menos una sesión pero no más de 6? $78.4\%$ 5) ¿Qué porcentaje completó al menos una sesión pero no más de 4? entre $56.7\%$ y...

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Problem 51025

Calculate the mean, median, and mode of dog weights: [44.4, 44.1, 43.9, 43.8, 43.2, 43.1, 42.8, 42.7, 42.3, 42, 41.7, 41.1, 40.9, 40.7, 40.6, 40.5, 40.4, 40.3, 40.2, 40.1, 40, 39.8, 38.5, 38.5, 38.3, 37.6, 37.5, 37.4, 37, 35]. Round to one decimal place.

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Problem 51026

Given a group of students' grades and gender, find the following probabilities:
A. Probability student is male: B. Probability student is male AND got a "C": C. Probability student is male OR got a "C": D. Probability student is male GIVEN they got a 'C':
Use totals: Males = 37, Females = 23, Total = 60.

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Problem 51027

Find $x$ values where $y=0$ for $y=\frac{x+6}{3x-12}-\frac{7}{x-4}-\frac{2}{3}$ . Choices: A, B, C.

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Problem 51028

Find $f(1+h)$ for $f(x)=\frac{x^{2}}{8}$ and $h=1, 0.1, 0.01, 0.001, 0.0001$ , rounding to seven decimal places.

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Problem 51029

Identify all numbers equivalent to $-\frac{3}{4}$ from the list below: $-\frac{3}{4}$ , $\frac{-3}{-4}$ , $-\left(\frac{3}{4}\right)$ , $\frac{4}{3}$ , $\frac{3}{4}$ , $\frac{3}{-4}$ , $-\frac{4}{3}$ , $-\left(\frac{-3}{-4}\right)$ .

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Problem 51030

Analyze the counseling session data. Answer true or false for these statements about client session completion percentages.

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Problem 51031

Complete the statements about place value: a. 10 times 1 hundred is _ (hundreds or thousand). b. 10 times hundreds is _ (60 hundreds or thousand).

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Problem 51032

Find the instantaneous rate of change of $R(t)=240+30 t^{3}$ at $t=1$ . Round to one decimal place.

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Problem 51033

Simplify the expression: $\frac{z^{2}-6 z-7}{z^{2}-7 z+10} \cdot \frac{z^{2}-10 z+25}{z^{2}-9 z+14}$ .

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Problem 51034

Find $x$ where $y=0$ for $y=\frac{x+3}{7x-35}-\frac{3}{x-5}-\frac{2}{7}$ .

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Problem 51035

A university has 22,028 students. Find these probabilities: a) Off-campus or junior. b) On-campus and senior. c) Freshman given on-campus. Use fractions or decimals rounded to three places.

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Problem 51036

Find the acute angle $x$ that the long diagonal of the parallelogram makes with Bridge Road, given $120^{\circ}$ and $25^{\circ}$ .

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Problem 51037

Calculate $\frac{3}{4} + \frac{5}{6} \div \frac{2}{3}$ .

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Problem 51038

Find the quotient of $5 \frac{3}{8} \div 7 \frac{1}{4}$ .

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Problem 51039

Identify the modes in this data set: 4, 2, 4, 1, $\frac{1}{2}$ , 7, 2, 4, 4, 3, 8, 4, 4, 2, 5, 2, $\frac{3}{5}$ , 5, 4, 4, 4, 4, 2, 6, 2, 2.

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Problem 51040

How long will it take George to mop a $95 \mathrm{ft}$ by $50 \mathrm{ft}$ gym floor if he mops $34 \mathrm{ft}^{2}$ per minute?

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Problem 51041

10 times 1 hundred equals how many hundreds or thousands?

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Problem 51042

A store has hats from 2 manufacturers in 3 colors. Find the probabilities for various selections based on the data provided.
a) P(Black or Manufacturer B) b) P(Red) c) P(Manufacturer B and Red) d) P(Manufacturer B or Red)
Use decimal or fraction rounded to three places.

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Problem 51043

Calculate $\frac{7}{8}-\frac{3}{8} \div 9$ .

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Problem 51044

Find $g(f(x))$ for $f(x)=x-3$ and $g(x)=x^{2}-4$ .

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Problem 51045

A home pregnancy test's results show: 52 positive, 7 negative for pregnant; 9 positive, 72 negative for not pregnant. Find:
a. P(Positive | Pregnant) = $b. P(Pregnant | Positive) =$ c. P(Negative | Pregnant) = $d. P(Not Pregnant | Negative) =$

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Problem 51046

Calculate the mode, mean, and median of the set $\{0, 1, 0, 0, 0, 0, 0, 3, 1, 0, 1, 1, 1, 0, 1, 1, 6, 1, 0, 0, 3, 1, 1, 0, 1, 1, 0, 0, 2, 2, 1\}$ , rounding to one decimal place.

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Problem 51047

You use $\frac{1}{8}$ of your battery every $\frac{2}{5}$ hour. If you used $\frac{3}{4}$ of your battery, how long did you chat?

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Problem 51048

You use $\frac{1}{8}$ of your battery every $\frac{2}{5}$ hour. If you used $\frac{3}{4}$ of your battery, how long did you chat?

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Problem 51049

Find the mode, mean, and median of these numbers, rounding to one decimal place: $129.9, 118.2, 186, 217.7, 172.8, 178.4, 128.5, 192.6, 106.3, 183.8, 189.2, 170, 130.1, 159.3, 153.5, 160.8, 162.4, 174.9, 164, 160.9, 166.3, 157.9, 193.8, 128.7, 179.2, 173.2, 200.6, 169.1, 166.3, 179.7$ .

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Problem 51050

Find the LCD of $\frac{3}{y^{2}-14y+49}$ and $\frac{4y}{y^{2}-9y+14}$ in factored form.

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Problem 51051

10 times the number of hundreds minus hundreds equals 60 hundreds. Find the number.

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Problem 51052

A pasta meal costs \$8.95 at a restaurant and \$4.75 to make at home.
1. The copycat meal costs \ $less than the restaurant meal.<br />2. The restaurant meal costs$ \frac{8.95}{4.75} $times as much as the copycat meal (round to two decimal places).<br />3. The cost of the copycat meal is$ \frac{4.75}{8.95} \times 100 $ % of the restaurant meal (round to the nearest whole percent).

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Problem 51053

Find the least common denominator of $\frac{1}{x+2}$ and $\frac{1}{x-9}$ in factored form.

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Problem 51054

Find the L C D of these expressions: $\frac{5}{x-7}$ , $\frac{x}{x-2}$ , $\frac{6x-17}{x^{2}-9x+14}$ .

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Problem 51055

Complete the equation: $(a^{m})^{n}=a^{\square}$ by finding the value of the box.

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Problem 51056

A pasta meal costs \$8.95 at a restaurant, and a copycat version costs \$4.75. Find the differences and percentages.
1. The copycat meal costs \ $less than the restaurant meal.<br />2. The restaurant meal costs$ \frac{8.95}{4.75} $times as much as the copycat meal. Round to two decimal places.<br />3. The cost of the copycat meal is$ \left( \frac{4.75}{8.95} \times 100 \right) \% $ of the restaurant meal. Round to the nearest whole percent.

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Problem 51057

Find the mode, mean, and median of these numbers: $0.237, 6.249, 0.244, 6.267, 8.262, 6.391, 0.304, 0.291, 0.232, 6.389, 0.269, 0.264, 0.261, 0.298, 0.300, 0.265, 0.311, 0.278, 0.274, 0.242, 0.219, 0.222, 0.234, 0.283, 0.272, 0.381, 0.276, 0.329, 0.263, 0.270$ .

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Problem 51058

Solve $5x - 8 = 3x + 8$ for $x$ and provide the answer as a reduced fraction. $x =$

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Problem 51059

Evaluate $x^{2}-x$ for $x$ from $5(x-4)+4=5x-4(4-x)$ . Find $x^{2}-x=$ (integer or fraction).

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Problem 51060

Solve $6(x+3)+5=1(x+7)$ for $x$ . Provide your answer as a reduced fraction. $x=$

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Problem 51061

Solve for $x$ in the equation $\frac{2 x}{3}+1=7$ . What is the value in the green box?

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Problem 51062

Simplify using the power rule: a. $(7^{4})^{9}$ b. $(k^{17})^{2}$ c. $(w^{100})^{20}$

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Problem 51063

Solve for $x$ in the equation $\frac{2 x}{3}+1=7$ . What number fits in the green box?

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Problem 51064

Estimate the 2018 cost of \ $100 in 1999 using models$ C=1.9x+120.5 $and$ C=0.03x^{2}+1.8x+120.6$.

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Problem 51065

Determine the cost of \ $100 in 1999 using models:$ C=1.9x+120.5 $and$ C=0.03x^2+1.8x+120.6$. Find cost in 2018.

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Problem 51066

A meal costs \$8.95 and a copycat meal costs \$4.75. Find the percentage increase from the copycat to the restaurant meal.

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Problem 51067

Identify and fix the error in solving $6x + 14 = 32$ and justify each step.

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Problem 51068

What is the term for patients feeling better after a sugar pill for headaches? A. randomization B. control C. experimental D. placebo.

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Problem 51069

Find the class width for data entries between 13 and 75, divided into 6 classes.

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Problem 51070

Solve for $y$ in the equation: $4(4y + 4) - 17 = 6(2y + 4) + 25$ .

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Problem 51071

What is the dependent variable in a sleep and memory test with 8 hours vs. 5 hours of sleep? A. Sleep amount B. Test results C. Second group D. First group

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Problem 51072

Mason pays \$51.50 monthly plus \$4 per whole GB. How many GB can he use to keep his bill under \$65?

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Problem 51073

Compare costs from $c=1.9x+120.5$ and $c=0.03x^2+1.8x+120.6$ for $x=136$ to see if they overestimate or underestimate.

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Problem 51074

Find the coordinate on $y=2 f(x-1)-3$ if $(2,-3)$ is on $y=f(x)$ .

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Problem 51075

Solve the equation: $6(x-9)-6=21x-240$ . Find $x=$ .

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Problem 51076

Raia buys a car for \$32,000 with a 6-year loan at 4.25\%. What are her monthly payments?

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Problem 51077

An experienced welder takes 22 min; an apprentice takes 37 min. Find the time differences and ratios.
1. Apprentice takes _ min MORE than experienced.
2. Experienced is _ times as long as apprentice (round to 2 decimal places).
3. Apprentice's time is ___% of experienced's time (round to nearest whole percent).

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Problem 51078

A group of friends can spend up to \$ 155 for parking (\$ 6.25) and tickets (\$ 20.50 each). What's the max number of people?

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Problem 51079

A shipping container can hold 25000 kg, but 7600 kg is already loaded. How many 110-kg crates can fit?

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Problem 51080

Calculate the mean, median, and mode of the commuting times: 20, 20, 41, 17, 12, 20, 15, 21, 24, 22, 23, 16, 18, 45, 24, 23, 17, 16, 8, 28, 28, 25, 19, 37, 14, 13, 29, 21, 29, 11. Round to one decimal point.

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Problem 51081

Simplify the expression: $\frac{1}{w^{10}} \cdot w^{25}$ .

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Problem 51082

Solve the inequality: $8 - (-4f - 3) \leq -f - 8 + 2f$ .

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Problem 51083

Calculate $\left(18-4^{2}\right)^{2}+8$ .

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Problem 51084

Solve for $x$ : $\frac{1}{4} x + \frac{1}{3} = 5$ . Enter as an improper fraction (e.g., 13/4).

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Problem 51085

Find the actual dimensions of a pool from a drawing where $1 \mathrm{~cm}$ equals $1 \mathrm{~m}$ . Also, compare a new scale of $1 \mathrm{~cm}$ to $2 \mathrm{~m}$ .

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Problem 51086

Solve for $x$ : $\frac{3}{4} x + 5 = -3$ . Enter your answer as a whole number or fraction.

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Problem 51087

Solve the inequality: $-7b + 3(-9b + 5) \geq 10b + 6 + 10$ .

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Problem 51088

Solve for $x$ : $3(-15 x-5)+18=-9(5 x-1)-12$ . Is it a conditional equation, identity, or contradiction?

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Problem 51089

Convert 1.212 m to cm. Remember, 1 m = 100 cm.

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Problem 51090

In a class of 30 boys studying Physics, Chemistry, and Biology, find how many study Physics using the given data.

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Problem 51091

Solve the equation for $x$ : $\frac{x-2}{2}-6=\frac{x-6}{3}$ . Provide the answer in reduced fraction form.

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Problem 51092

Calculate $10 + 8^{3} \div 16$ .

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Problem 51093

Simplify the expression: $x^{5} \cdot x^{3}$ .

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Problem 51094

Find the correct lower class limits for a dataset with minimum $=13$ , maximum $=75.6$ , and class width $=11$ . A. $23,34,46,56,67,78$ B. $13,23,35,45,56,68$ C. $24,34,46,57,68,78$ D. $13,24,35,46,57,68$

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Problem 51095

1.6 m equals how many cm?

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Problem 51096

Find the number of trials $x$ needed for the model $P=\frac{0.7 x-0.6}{0.7 x+0.2}$ to reach $P=0.92$ .

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Problem 51097

Analyze the function $f(x)=(x+4)(x-1)^{2}$ : (a) What is its end behavior? (b) Find the $x$ - and $y$ -intercepts.

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Problem 51098

Find the correct lower class limits for a minimum of 13, maximum of 75.6, and class width of 11. Options: A, B, C, D.

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Problem 51099

Find the depth $d$ in feet where pressure $P=408$ lbs/ft², given $P=16+\frac{8d}{13}$ .

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Problem 51100

Expand the expression $(x y)^5$ .

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Math

Problem 51001

Problem 51002

Find all values of xxx such that y1+y2=y3y_{1} + y_{2} = y_{3}y1​+y2​=y3​, where y1=4x+6,y2=5x+3,y3=12x+30x2+9x+18y_{1}=\frac{4}{x+6}, y_{2}=\frac{5}{x+3}, y_{3}=\frac{12 x+30}{x^{2}+9 x+18}y1​=x+64​,y2​=x+35​,y3​=x2+9x+1812x+30​. Choices: A, B, C.

Problem 51003

Problem 51004

A bookcase has 4 shelves. Width is 11 ft less than 3 times height. Total lumber is 26 ft. Find width and height.

Problem 51005

Mr. Michaels has 40 m of wire. After wiring 16 lamps (0.45 m each), 12 wall lights (0.7 m each), and 1 floor lamp (2.6 m), how much is left? A) 7.2 m B) 18.2 m C) 21.8 m D) 15.6 m

Problem 51006

Counseling Duration Data: (1) How many clients completed 4-6 sessions? (2) What percentage completed 4-6 sessions? (3) What is the cumulative percentage for 4-6 sessions? (4) What percentage completed at least 1 but not more than 6 sessions? Data: fff: 21, %\%%: 21.6, Σ%\Sigma \%Σ%: 78.4.

Problem 51007

Classify the shape: opposite sides are parallel, all sides congruent, vertices not necessarily right angles. Options: Square, Rectangle, Rhombus, Parallelogram.

Problem 51008

Analyze the function f(x)=(x+7)(x−5)2f(x)=(x+7)(x-5)^{2}f(x)=(x+7)(x−5)2: (a) Find end behavior; (b) Determine xxx- and yyy-intercepts.

Problem 51009

Find the width of a 70" TV with a 16:9 aspect ratio. Options: 80.33′′80.33^{\prime \prime}80.33′′, 39.4′′39.4^{\prime \prime}39.4′′, 61′′61^{\prime \prime}61′′, 44.8′′44.8^{\prime \prime}44.8′′.

Problem 51010

Identify a real-life situation that involves a quadrilateral: inflating a balloon, tiling a floor, building a pyramid, or baking a cake?

Problem 51011

Analyze the function f(x)=(x+7)(x−5)2f(x)=(x+7)(x-5)^{2}f(x)=(x+7)(x−5)2: find end behavior, intercepts, zeros, and their multiplicities.

Problem 51012

Solve for xxx in the equation: y1=3x+6,y2=4x+4,y3=9x+28x2+10x+24y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9 x+28}{x^{2}+10 x+24}y1​=x+63​,y2​=x+44​,y3​=x2+10x+249x+28​, where y1+y2=y3y_{1}+y_{2}=y_{3}y1​+y2​=y3​.

Problem 51013

Convert 10.7 m to cm using 1 m = 100 cm. What is 10.7×10010.7 \times 10010.7×100?

Problem 51014

Convert 10.7 meters to centimeters using the conversion factor: 1 meter = 100 centimeters.

Problem 51015

Divide 3 by 5: what is the result of 3÷53 \div 53÷5?

Problem 51016

Calculate the following probabilities based on the data: 1. From the U.S.2. At least 2 children.3. From the U.S. and 1 child.4. From the U.S. or 0 children.5. From the U.S. with 3+ children.6. 1 child and from the U.S.

Problem 51017

Problem 51018

A bank loaned out \$7,500 at 6\% and 15\% interest, earning \$765 total. Find the amounts loaned at each rate.

Problem 51019

Simplify the expression: a2−4a2−5a−14\frac{a^{2}-4}{a^{2}-5 a-14}a2−5a−14a2−4​.

Problem 51020

Find xxx such that y1=3x+6,y2=4x+4,y3=9x+28x2+10x+24y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9x+28}{x^2+10x+24}y1​=x+63​,y2​=x+44​,y3​=x2+10x+249x+28​ and y1+y2=y3y_{1}+y_{2}=y_{3}y1​+y2​=y3​.

Problem 51021

Calculate: 16514÷4114=165 \frac{1}{4} \div 41 \frac{1}{4} = 16541​÷4141​=

Problem 51022

Simplify the expression: x2−17x+72x2−100⋅x2−18x+80x2+x−90.\frac{x^{2}-17 x+72}{x^{2}-100} \cdot \frac{x^{2}-18 x+80}{x^{2}+x-90}.x2−100x2−17x+72​⋅x2+x−90x2−18x+80​.

Problem 51023

Find xxx when y=0y=0y=0 for the equation y=2[x−(3−x)]−3(x+1)y=2[x-(3-x)]-3(x+1)y=2[x−(3−x)]−3(x+1). Choose A, B, or C for the solution.

Problem 51024

Problem 51025

Calculate the mean, median, and mode of dog weights: [44.4, 44.1, 43.9, 43.8, 43.2, 43.1, 42.8, 42.7, 42.3, 42, 41.7, 41.1, 40.9, 40.7, 40.6, 40.5, 40.4, 40.3, 40.2, 40.1, 40, 39.8, 38.5, 38.5, 38.3, 37.6, 37.5, 37.4, 37, 35]. Round to one decimal place.

Problem 51026

Problem 51027

Find xxx values where y=0y=0y=0 for y=x+63x−12−7x−4−23y=\frac{x+6}{3x-12}-\frac{7}{x-4}-\frac{2}{3}y=3x−12x+6​−x−47​−32​. Choices: A, B, C.

Problem 51028

Find f(1+h)f(1+h)f(1+h) for f(x)=x28f(x)=\frac{x^{2}}{8}f(x)=8x2​ and h=1,0.1,0.01,0.001,0.0001h=1, 0.1, 0.01, 0.001, 0.0001h=1,0.1,0.01,0.001,0.0001, rounding to seven decimal places.

Problem 51029

Problem 51030

Analyze the counseling session data. Answer true or false for these statements about client session completion percentages.

Problem 51031

Complete the statements about place value: a. 10 times 1 hundred is ___ (hundreds or thousand). b. 10 times hundreds is ___ (60 hundreds or thousand).

Problem 51032

Find the instantaneous rate of change of R(t)=240+30t3R(t)=240+30 t^{3}R(t)=240+30t3 at t=1t=1t=1. Round to one decimal place.

Problem 51033

Simplify the expression: z2−6z−7z2−7z+10⋅z2−10z+25z2−9z+14\frac{z^{2}-6 z-7}{z^{2}-7 z+10} \cdot \frac{z^{2}-10 z+25}{z^{2}-9 z+14}z2−7z+10z2−6z−7​⋅z2−9z+14z2−10z+25​.

Problem 51034

Find xxx where y=0y=0y=0 for y=x+37x−35−3x−5−27y=\frac{x+3}{7x-35}-\frac{3}{x-5}-\frac{2}{7}y=7x−35x+3​−x−53​−72​.

Problem 51035

A university has 22,028 students. Find these probabilities: a) Off-campus or junior. b) On-campus and senior. c) Freshman given on-campus. Use fractions or decimals rounded to three places.

Problem 51036

Find the acute angle xxx that the long diagonal of the parallelogram makes with Bridge Road, given 120∘120^{\circ}120∘ and 25∘25^{\circ}25∘.

Problem 51037

Calculate 34+56÷23\frac{3}{4} + \frac{5}{6} \div \frac{2}{3}43​+65​÷32​.

Problem 51038

Find the quotient of 538÷7145 \frac{3}{8} \div 7 \frac{1}{4}583​÷741​.

Problem 51039

Identify the modes in this data set: 4, 2, 4, 1, 12\frac{1}{2}21​, 7, 2, 4, 4, 3, 8, 4, 4, 2, 5, 2, 35\frac{3}{5}53​, 5, 4, 4, 4, 4, 2, 6, 2, 2.

Problem 51040

How long will it take George to mop a 95ft95 \mathrm{ft}95ft by 50ft50 \mathrm{ft}50ft gym floor if he mops 34ft234 \mathrm{ft}^{2}34ft2 per minute?

Problem 51041

10 times 1 hundred equals how many hundreds or thousands?

Problem 51042

A store has hats from 2 manufacturers in 3 colors. Find the probabilities for various selections based on the data provided. a) P(Black or Manufacturer B) b) P(Red) c) P(Manufacturer B and Red) d) P(Manufacturer B or Red) Use decimal or fraction rounded to three places.

Problem 51043

Find all values of $x$ such that $y_{1} + y_{2} = y_{3}$ , where $y_{1}=\frac{4}{x+6}, y_{2}=\frac{5}{x+3}, y_{3}=\frac{12 x+30}{x^{2}+9 x+18}$ . Choices: A, B, C.

Counseling Duration Data:
(1) How many clients completed 4-6 sessions? (2) What percentage completed 4-6 sessions? (3) What is the cumulative percentage for 4-6 sessions? (4) What percentage completed at least 1 but not more than 6 sessions? Data: $f$ : 21, $\%$ : 21.6, $\Sigma \%$ : 78.4.

Analyze the function $f(x)=(x+7)(x-5)^{2}$ : (a) Find end behavior; (b) Determine $x$ - and $y$ -intercepts.

Find the width of a 70" TV with a 16:9 aspect ratio. Options: $80.33^{\prime \prime}$ , $39.4^{\prime \prime}$ , $61^{\prime \prime}$ , $44.8^{\prime \prime}$ .

Analyze the function $f(x)=(x+7)(x-5)^{2}$ : find end behavior, intercepts, zeros, and their multiplicities.

Solve for $x$ in the equation: $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9 x+28}{x^{2}+10 x+24}$ , where $y_{1}+y_{2}=y_{3}$ .

Convert 10.7 m to cm using 1 m = 100 cm. What is $10.7 \times 100$ ?

Divide 3 by 5: what is the result of $3 \div 5$ ?

Calculate the following probabilities based on the data:
1. From the U.S.
2. At least 2 children.
3. From the U.S. and 1 child.
4. From the U.S. or 0 children.
5. From the U.S. with 3+ children.
6. 1 child and from the U.S.

Simplify the expression: $\frac{a^{2}-4}{a^{2}-5 a-14}$ .

Find $x$ such that $y_{1}=\frac{3}{x+6}, y_{2}=\frac{4}{x+4}, y_{3}=\frac{9x+28}{x^2+10x+24}$ and $y_{1}+y_{2}=y_{3}$ .

Calculate: $165 \frac{1}{4} \div 41 \frac{1}{4} =$

Simplify the expression: $\frac{x^{2}-17 x+72}{x^{2}-100} \cdot \frac{x^{2}-18 x+80}{x^{2}+x-90}.$

Find $x$ when $y=0$ for the equation $y=2[x-(3-x)]-3(x+1)$ . Choose A, B, or C for the solution.

Find $x$ values where $y=0$ for $y=\frac{x+6}{3x-12}-\frac{7}{x-4}-\frac{2}{3}$ . Choices: A, B, C.

Find $f(1+h)$ for $f(x)=\frac{x^{2}}{8}$ and $h=1, 0.1, 0.01, 0.001, 0.0001$ , rounding to seven decimal places.

Complete the statements about place value: a. 10 times 1 hundred is _ (hundreds or thousand). b. 10 times hundreds is _ (60 hundreds or thousand).

Find the instantaneous rate of change of $R(t)=240+30 t^{3}$ at $t=1$ . Round to one decimal place.

Simplify the expression: $\frac{z^{2}-6 z-7}{z^{2}-7 z+10} \cdot \frac{z^{2}-10 z+25}{z^{2}-9 z+14}$ .

Find $x$ where $y=0$ for $y=\frac{x+3}{7x-35}-\frac{3}{x-5}-\frac{2}{7}$ .

Find the acute angle $x$ that the long diagonal of the parallelogram makes with Bridge Road, given $120^{\circ}$ and $25^{\circ}$ .

Calculate $\frac{3}{4} + \frac{5}{6} \div \frac{2}{3}$ .

Find the quotient of $5 \frac{3}{8} \div 7 \frac{1}{4}$ .

Identify the modes in this data set: 4, 2, 4, 1, $\frac{1}{2}$ , 7, 2, 4, 4, 3, 8, 4, 4, 2, 5, 2, $\frac{3}{5}$ , 5, 4, 4, 4, 4, 2, 6, 2, 2.

How long will it take George to mop a $95 \mathrm{ft}$ by $50 \mathrm{ft}$ gym floor if he mops $34 \mathrm{ft}^{2}$ per minute?

A store has hats from 2 manufacturers in 3 colors. Find the probabilities for various selections based on the data provided.
a) P(Black or Manufacturer B) b) P(Red) c) P(Manufacturer B and Red) d) P(Manufacturer B or Red)
Use decimal or fraction rounded to three places.

Calculate $\frac{7}{8}-\frac{3}{8} \div 9$ .

Find $g(f(x))$ for $f(x)=x-3$ and $g(x)=x^{2}-4$ .

You use $\frac{1}{8}$ of your battery every $\frac{2}{5}$ hour. If you used $\frac{3}{4}$ of your battery, how long did you chat?

You use $\frac{1}{8}$ of your battery every $\frac{2}{5}$ hour. If you used $\frac{3}{4}$ of your battery, how long did you chat?

Find the LCD of $\frac{3}{y^{2}-14y+49}$ and $\frac{4y}{y^{2}-9y+14}$ in factored form.

Find the least common denominator of $\frac{1}{x+2}$ and $\frac{1}{x-9}$ in factored form.

Find the L C D of these expressions: $\frac{5}{x-7}$ , $\frac{x}{x-2}$ , $\frac{6x-17}{x^{2}-9x+14}$ .

Complete the equation: $(a^{m})^{n}=a^{\square}$ by finding the value of the box.

Solve $5x - 8 = 3x + 8$ for $x$ and provide the answer as a reduced fraction. $x =$

Evaluate $x^{2}-x$ for $x$ from $5(x-4)+4=5x-4(4-x)$ . Find $x^{2}-x=$ (integer or fraction).

Solve $6(x+3)+5=1(x+7)$ for $x$ . Provide your answer as a reduced fraction. $x=$

Solve for $x$ in the equation $\frac{2 x}{3}+1=7$ . What is the value in the green box?

Simplify using the power rule: a. $(7^{4})^{9}$ b. $(k^{17})^{2}$ c. $(w^{100})^{20}$

Solve for $x$ in the equation $\frac{2 x}{3}+1=7$ . What number fits in the green box?

Estimate the 2018 cost of \ $100 in 1999 using models$ C=1.9x+120.5 $and$ C=0.03x^{2}+1.8x+120.6$.

Determine the cost of \ $100 in 1999 using models:$ C=1.9x+120.5 $and$ C=0.03x^2+1.8x+120.6$. Find cost in 2018.

Identify and fix the error in solving $6x + 14 = 32$ and justify each step.

Solve for $y$ in the equation: $4(4y + 4) - 17 = 6(2y + 4) + 25$ .

Compare costs from $c=1.9x+120.5$ and $c=0.03x^2+1.8x+120.6$ for $x=136$ to see if they overestimate or underestimate.

Find the coordinate on $y=2 f(x-1)-3$ if $(2,-3)$ is on $y=f(x)$ .