Math

Problem 54001

Solve: 5 times the difference between 8 and 6. What is the expression?

See Solution

Problem 54002

Simplify the expression: $3 \sqrt{3} \cdot 6 \sqrt{6}$ . What is the result? A. $54 \sqrt{2}$ B. $18 \sqrt{2}$ C. 54 D. $18 \sqrt{3}$

See Solution

Problem 54003

Find the probability that a randomly chosen American has type B blood, given that $15\%$ of Americans have type B.

See Solution

Problem 54004

Simplify the expression: $\frac{3 x^{2}-18 x}{a x-6 a+2 c x-12 c}$

See Solution

Problem 54005

Calculate the range, variance, and standard deviation of these caffeine amounts (mg per 12 oz): 46, 41, 37, 44, 0, 42, 56, 57, 39, 49, 48, 42, 0, 0. Are the stats representative of all cans from these brands?

See Solution

Problem 54006

Solve for the values of $x$ in the equations: $\frac{2}{3}=x$ and $\frac{1}{2}=x$ .

See Solution

Problem 54007

Simplify $\sqrt{75}$ . Choose the correct option: A. $3 \sqrt{5}$ B. $15 \sqrt{5}$ C. $25 \sqrt{3}$ D. $5 \sqrt{3}$ .

See Solution

Problem 54008

Find the real zeros of the polynomial $f(x)=x^{3}+6x^{2}-9x-14$ using the rational zeros theorem.

See Solution

Problem 54009

Divide the polynomial $-8 x^{3}-12 x^{2}+16 x+20$ by $4 x+4$ and express the result as a quotient.

See Solution

Problem 54010

Is a score of $X=70$ extreme for a population with mean $\mu=50$ and $\sigma=20$ ? How about with $\sigma=5$ ?

See Solution

Problem 54011

Calculate: $6+\left(\frac{7}{3} \times 9\right)$

See Solution

Problem 54012

Rank the objects W, X, Y, Z by density: $W$ (16g, 84cm³), $X$ (12g, 5cm³), $Y$ (4g, 6cm³), $Z$ (408g, 216cm³).

See Solution

Problem 54013

A hotel photo has a perimeter of $368 \mathrm{in}$ . Width is $4 \mathrm{in}$ more than $4$ times the height. Find dimensions.

See Solution

Problem 54014

Find the real zeros of the polynomial $f(x)=x^{4}+10 x^{3}-20 x^{2}-90 x+99$ and factor it over the reals.

See Solution

Problem 54015

Calculate $\left(\frac{2}{5}+4\right)+\frac{3}{5} \times 20$ .

See Solution

Problem 54016

Find the mean and mode of the data: $x = [3, 4, 5, 6, 7, 8]$ , $y = [3, 6, 7, 3, 2, 1]$ .

See Solution

Problem 54017

How many miles long is a line of $5$ trillion bags, each $12$ inches long?

See Solution

Problem 54018

Find the mean absolute deviation of temperatures: 80°, 77°, 79°, 78°, 76° over 5 days in Austin, TX.

See Solution

Problem 54019

What was the regular price of running shoes if Amy paid \$ 79.13 after a 25% discount?

See Solution

Problem 54020

Find the value of $\sqrt{20}$ .

See Solution

Problem 54021

Find the probability that a random American has type B blood ( $15\%$ ) and the probability of having type A or B.

See Solution

Problem 54022

Simplify the expression: $\frac{-10 x^{3}+19 x^{2}+21 x-15}{2 x-5}$ .

See Solution

Problem 54023

Find the instantaneous rate of change of $R(t)=240+30 t^{3}$ at $t=1$ . Answer: $R^{\prime}(1)=90$ dollars/day.

See Solution

Problem 54024

Solve for $b$ in the equation $\frac{2}{8}=-\frac{b}{6}$ .

See Solution

Problem 54025

Evaluate the integral: $\int_{0}^{1} 6 \frac{\ln (x)}{\sqrt[3]{x}} d x$

See Solution

Problem 54026

Calculate the mean of 96, 85, 102, 90, 106, 88 and find how much each number differs from the mean.

See Solution

Problem 54027

Find the area of shapes $A$ ( $11 \, \text{cm} \times 8 \, \text{cm}$ ) and explain for shapes $B$ , $C$ , and $D$ .

See Solution

Problem 54028

Simplify the expression: $5 \sqrt{2} \cdot 9 \sqrt{6}$ . What is the result? A. $90 \sqrt{3}$ B. $45 \sqrt{3}$ C. $45 \sqrt{2}$ D. 90

See Solution

Problem 54029

Arthur wants to find the price of an item costing $p$ dollars after a $6\%$ tax. Show two equal expressions for the total cost.

See Solution

Problem 54030

What is the simplified form of $5 \sqrt{2} \cdot 9 \sqrt{6}$ ? A. $90 \sqrt{3}$ B. $45 \sqrt{3}$ C. $45 \sqrt{2}$ D. 90

See Solution

Problem 54031

Find the mean of the numbers $96, 85, 102, 90, 106, 88$ and calculate each number's difference from the mean.

See Solution

Problem 54032

Solve the equation $x^{4}-2 x^{3}+6 x^{2}-18 x-27=0$ . Find real solutions or state none exist.

See Solution

Problem 54033

Identify the justification for each step in the equation transformation from $5(x-1)=4x+13$ to $x=18$ .

See Solution

Problem 54034

Calculate $s$ using $u=12$ , $a=10$ , and $t=4$ : $s=u t+\frac{1}{2} a t^{2}$ .

See Solution

Problem 54035

Find the mean of $\{96, 85, 102, 90, 106, 88\}$ and calculate the difference from the mean for each number.

See Solution

Problem 54036

Brianna has \$ 60 and saves \$ 15 weekly. How many weeks until she has \$ 180 for sneakers? Show your work.

See Solution

Problem 54037

Choose the expressions that equal $\frac{2}{3}$ when multiplied.
1. $\frac{21}{25} \times \frac{50}{63}$
2. $\frac{7}{8} \times \frac{9}{25}$
3. $\frac{1}{30} \times \frac{2}{3}$
4. $\frac{20}{27} \times \frac{27}{30}$
5. $\frac{3}{25} \times \frac{7}{12}$

See Solution

Problem 54038

Find the real solutions of the equation $2 x^{3}+x^{2}-8 x+3=0$ . Choose A or B for the solution set.

See Solution

Problem 54039

Arthur wants to find the total cost of an item priced at $p$ with a $6\%$ sales tax. Show two equal expressions for total cost.

See Solution

Problem 54040

Calculate the product of $1 \frac{1}{4}$ and $5 \frac{3}{5}$ .

See Solution

Problem 54041

Find the inverse of the function $f(x)=8x+11$ .

See Solution

Problem 54042

Multiply $5 \frac{1}{2}$ by $3 \frac{3}{4}$ .

See Solution

Problem 54043

Calculate the expression: $\frac{30\left((0.1)^{3}+3 \times 1 \times 0.1 \times 1.1\right)}{1}$ .

See Solution

Problem 54044

Find the real solutions for the equation: $5 x^{3}+8 x^{2}-9 x+2=0$ . Choose A (list solutions) or B (no solutions).

See Solution

Problem 54045

Solve the equation $5x - 10 = -40$ and justify each step.

See Solution

Problem 54046

Arthur wants to find the total price of an item costing $p$ with a $6\%$ sales tax. Show two equal expressions for the total cost.

See Solution

Problem 54047

Multiply the mixed numbers: $3 \frac{1}{4} \times 2 \frac{5}{6}$ .

See Solution

Problem 54048

Calculate the product of $\frac{3}{8}$ and $\frac{4}{27}$ .

See Solution

Problem 54049

Find the inverse of $f(x)=x^{2}-6$ for $x \geq 0$ .

See Solution

Problem 54050

A teacher gives three test versions. Find these probabilities: a. $P($ pass $\mid$ Test A) $and b.$ P( $Test C$ \mid $fail)$ .

See Solution

Problem 54051

Calculate $h(-67)$ for $h(x)=-49x-125$ . Choose from A. $-3,408$ , B. -1.18, C. 3,283, D. 3,158.

See Solution

Problem 54052

Solve the inequality: $2-3(x+4)>17$ .

See Solution

Problem 54053

Find the total cost of an item with a \$p price and 6\% sales tax. Show that \$p + 0.06p = \$1.06p.

See Solution

Problem 54054

Find the real solutions of the equation $3x^{3} + x^{2} - 13x + 5 = 0$ . What is the solution set?

See Solution

Problem 54055

Find the range of the inverse function for $f(x)=(x+1)^{2}-1$ where $x \leq -1$ .

See Solution

Problem 54056

Find the range of the inverse function of $f(x)=(x+1)^{2}-1$ for $x \leq -1$ .

See Solution

Problem 54057

After 1 fold, the dough has 9 layers. If layers triple each fold, how many layers after 4 folds?

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Problem 54058

Find which point among (0,7), (-8,-5), (-1,0), (9,5) satisfies both $y<-\frac{3}{2} x+2$ and $y<2 x+6$ .

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Problem 54059

Solve for real solutions of $2x - 39x^3 + 193x^2 - 321x + 117 = 0$ . A. $x=$ (exact answer) B. No real solutions.

See Solution

Problem 54060

Find the profit function $p(g)$ for Betty's lemonade stand, where she sells $g$ glasses at \$1 each and setup cost \$50.

See Solution

Problem 54061

Two window washers start at 21 ft rising at 8 in/s and 50 ft descending at 11 in/s. Find when they meet in height.

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Problem 54062

Find the intersection of the lines $f(x)=2x+3$ and $g(x)=-4x-27$ . Choose the correct point: A. $(-5,-10)$ B. $(5,-7)$ C. $(-5,-7)$ D. $(5,13)$ .

See Solution

Problem 54063

Abby needs an equation to convert miles $(m)$ to kilometers $(k)$ . Which is correct? (A) $\frac{k}{1.61}=m$ (B) $1.61 m=k$ (C) $1.61=\frac{k}{m}$

See Solution

Problem 54064

Check if the points (1,0), (8,4), (0,9), and (-10,-1) meet these inequalities: $y > -\frac{2}{5} x + 6$ and $y > \frac{2}{3} x + 3$ .

See Solution

Problem 54065

Find the remaining zeros of the polynomial $f(x)$ of degree 5 with known zeros $-5, i, -7i$ .

See Solution

Problem 54066

Find when Plan A (0.09m) costs at least as much as Plan B (12.40 + 0.07m). Solve the inequality for $m$ .

See Solution

Problem 54067

Find the inverse of the function $f(x)=5x+3$ .

See Solution

Problem 54068

Find the other zeros of the function $f(x)=x^{3}-4 x^{2}+25 x-100$ given the zero $-5i$ .

See Solution

Problem 54069

Luis saves \ $45/week and has \$155 saved. Find his savings after 6 weeks:$ 45 \cdot 6 + 155 $. Compare savings in 1 year using$ w^{2}/64 + 45w + 155 $vs.$ 45w + 155$.

See Solution

Problem 54070

Find the length and width of a field with a perimeter of 96 m, where length is $14 \mathrm{~m}$ more than width.

See Solution

Problem 54071

j < 7

See Solution

Problem 54072

Find the inverse of the function $f(x)=\frac{2x-3}{7x-8}$ .

See Solution

Problem 54073

Find the complex zeros of the polynomial $f(x)=x^{3}-11 x^{2}+43 x-65$ and write it in factored form.

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Problem 54074

At a theater, child tickets are \$5.60 and adult tickets are \$9.30. If 165 tickets sold for \$1197.80, how many adult tickets were sold?

See Solution

Problem 54075

Check if the points (7,-3), (5,5), (-2,1), and (-7,8) meet these inequalities: 1. $y = -x + 3$ 2. $y > \frac{1}{4}x + 3$

See Solution

Problem 54076

How many pounds of type A coffee were used if type A costs \$5.70/lb, type B costs \$4.35/lb, and B is 3 times A with a total cost of \$581.25?

See Solution

Problem 54077

How many standard version downloads were there if the song was downloaded 1410 times, totaling $4662 \mathrm{MB}$ ?

See Solution

Problem 54078

A college charges a \ $48 fee plus \$5.70/hour. The film club wants to spend < \$76.50. Find possible hours$ t$.

See Solution

Problem 54079

Find the complex zeros of the polynomial $f(x)=x^{3}-13 x^{2}+59 x-87$ and write it in factored form.

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Problem 54080

When $5x=15$ , find the value of $12x$ .

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Problem 54081

Find the real solutions for the equation $5 x^{3}+7 x^{2}-11 x+3=0$ . Choose A or B for the solution set.

See Solution

Problem 54082

What is the probability that a randomly selected revenue source comes from excise or other taxes, given the percentages? $P($ excise or other taxes $)=$

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Problem 54083

Solve the inequality: $-3(4+2 x)<18$ .

See Solution

Problem 54084

Find $s$ using the formula $s=u t+\frac{1}{2} a t^{2}$ with $u=5.2$ , $t=7$ , and $a=1.6$ .

See Solution

Problem 54085

Solve the inequality: $10 < -2x - 5x - 4$ .

See Solution

Problem 54086

Juan has $t$ orders, Rob has 40, and together they have 75. Write an equation and find $t$ .

See Solution

Problem 54087

Find the domain of the function $R(x)=\frac{11 x}{x+2}$ . Is it A. $x \neq -2$ or B. all real numbers?

See Solution

Problem 54088

Calculate the sum: $\sum_{i=1}^{8} (2i + 1)$ .

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Problem 54089

Ariana's pet door has an area of 900 cm². Find the height $h$ in terms of width $b$ : $h = \frac{900}{b}$ . What is $h$ if $b = 25$ cm?

See Solution

Problem 54090

Solve the inequality: $2 - 3(x + 4) < 17$ .

See Solution

Problem 54091

Find the miles $x$ where costs for renting a truck from Company A ( $120 + 0.5x$ ) equals Company B ( $60 + 0.8x$ ).

See Solution

Problem 54092

What is Bryce's speed in miles per hour if one lap is $\frac{1}{3}$ mile and takes $\frac{1}{57}$ hour?

See Solution

Problem 54093

Find the probability of randomly selecting a school with 100 or fewer computers. Round to 3 decimal places.

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Problem 54094

How many days must a skier ski for a season pass at \$350 to be cheaper than daily passes at \$67 plus \$25 rental?

See Solution

Problem 54095

Ariadne's shadow is 15 ft, she's 5 ft tall. Dixon's shadow is 18 ft. How tall is Dixon? $15 \mathrm{ft}$ Dixon is feet tall.

See Solution

Problem 54096

Melissa and Rachel made 42 hats together. If Melissa made 20, write an equation for Rachel's $h$ striped hats: $20 + h = 42$ .

See Solution

Problem 54097

Barnes \& Noble had science and art books in a 2:5 ratio. After selling 20\% of each, 2,240 books remained. Find initial counts: $s=$ science, $a=$ art. Show your work.

See Solution

Problem 54098

Solve for $y$ : $6\left(y-\frac{1}{3}\right)=4(3y-5)$ . What is $y$ ?

See Solution

Problem 54099

Solve for $a$ : $3a + 1 > \frac{-7a - 14}{-4}$ . Determine the valid ranges for $a$ .

See Solution

Problem 54100

Subtract: $(6f^2 - 9f + 10) - (-2f^2 - f + 3)$ . What is the result?

See Solution

1 ...538 539 540 541 542 543 544 ...660

Math

Problem 54001

Solve: 5 times the difference between 8 and 6. What is the expression?

Problem 54002

Simplify the expression: 33⋅663 \sqrt{3} \cdot 6 \sqrt{6}33​⋅66​. What is the result? A. 54254 \sqrt{2}542​ B. 18218 \sqrt{2}182​ C. 54 D. 18318 \sqrt{3}183​

Problem 54003

Find the probability that a randomly chosen American has type B blood, given that 15%15\%15% of Americans have type B.

Problem 54004

Simplify the expression: 3x2−18xax−6a+2cx−12c\frac{3 x^{2}-18 x}{a x-6 a+2 c x-12 c}ax−6a+2cx−12c3x2−18x​

Problem 54005

Calculate the range, variance, and standard deviation of these caffeine amounts (mg per 12 oz): 46, 41, 37, 44, 0, 42, 56, 57, 39, 49, 48, 42, 0, 0. Are the stats representative of all cans from these brands?

Problem 54006

Solve for the values of xxx in the equations: 23=x\frac{2}{3}=x32​=x and 12=x\frac{1}{2}=x21​=x.

Problem 54007

Simplify 75\sqrt{75}75​. Choose the correct option: A. 353 \sqrt{5}35​ B. 15515 \sqrt{5}155​ C. 25325 \sqrt{3}253​ D. 535 \sqrt{3}53​.

Problem 54008

Find the real zeros of the polynomial f(x)=x3+6x2−9x−14f(x)=x^{3}+6x^{2}-9x-14f(x)=x3+6x2−9x−14 using the rational zeros theorem.

Problem 54009

Divide the polynomial −8x3−12x2+16x+20-8 x^{3}-12 x^{2}+16 x+20−8x3−12x2+16x+20 by 4x+44 x+44x+4 and express the result as a quotient.

Problem 54010

Is a score of X=70X=70X=70 extreme for a population with mean μ=50\mu=50μ=50 and σ=20\sigma=20σ=20? How about with σ=5\sigma=5σ=5?

Problem 54011

Calculate: 6+(73×9)6+\left(\frac{7}{3} \times 9\right)6+(37​×9)

Problem 54012

Rank the objects W, X, Y, Z by density: WWW (16g, 84cm³), XXX (12g, 5cm³), YYY (4g, 6cm³), ZZZ (408g, 216cm³).

Problem 54013

A hotel photo has a perimeter of 368in368 \mathrm{in}368in. Width is 4in4 \mathrm{in}4in more than 444 times the height. Find dimensions.

Problem 54014

Find the real zeros of the polynomial f(x)=x4+10x3−20x2−90x+99f(x)=x^{4}+10 x^{3}-20 x^{2}-90 x+99f(x)=x4+10x3−20x2−90x+99 and factor it over the reals.

Problem 54015

Calculate (25+4)+35×20\left(\frac{2}{5}+4\right)+\frac{3}{5} \times 20(52​+4)+53​×20.

Problem 54016

Find the mean and mode of the data: x=[3,4,5,6,7,8]x = [3, 4, 5, 6, 7, 8]x=[3,4,5,6,7,8], y=[3,6,7,3,2,1]y = [3, 6, 7, 3, 2, 1]y=[3,6,7,3,2,1].

Problem 54017

How many miles long is a line of 555 trillion bags, each 121212 inches long?

Problem 54018

Find the mean absolute deviation of temperatures: 80°, 77°, 79°, 78°, 76° over 5 days in Austin, TX.

Problem 54019

What was the regular price of running shoes if Amy paid \$ 79.13 after a 25% discount?

Problem 54020

Find the value of 20\sqrt{20}20​.

Problem 54021

Find the probability that a random American has type B blood (15%15\%15%) and the probability of having type A or B.

Problem 54022

Simplify the expression: −10x3+19x2+21x−152x−5\frac{-10 x^{3}+19 x^{2}+21 x-15}{2 x-5}2x−5−10x3+19x2+21x−15​.

Problem 54023

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. Answer: R′(1)=90R^{\prime}(1)=90R′(1)=90 dollars/day.

Problem 54024

Solve for bbb in the equation 28=−b6\frac{2}{8}=-\frac{b}{6}82​=−6b​.

Problem 54025

Evaluate the integral: ∫016ln⁡(x)x3dx\int_{0}^{1} 6 \frac{\ln (x)}{\sqrt[3]{x}} d x∫01​63x​ln(x)​dx

Problem 54026

Calculate the mean of 96, 85, 102, 90, 106, 88 and find how much each number differs from the mean.

Problem 54027

Find the area of shapes AAA (11 cm×8 cm11 \, \text{cm} \times 8 \, \text{cm}11cm×8cm) and explain for shapes BBB, CCC, and DDD.

Problem 54028

Simplify the expression: 52⋅965 \sqrt{2} \cdot 9 \sqrt{6}52​⋅96​. What is the result? A. 90390 \sqrt{3}903​ B. 45345 \sqrt{3}453​ C. 45245 \sqrt{2}452​ D. 90

Problem 54029

Arthur wants to find the price of an item costing ppp dollars after a 6%6\%6% tax. Show two equal expressions for the total cost.

Problem 54030

What is the simplified form of 52⋅965 \sqrt{2} \cdot 9 \sqrt{6}52​⋅96​? A. 90390 \sqrt{3}903​ B. 45345 \sqrt{3}453​ C. 45245 \sqrt{2}452​ D. 90

Problem 54031

Find the mean of the numbers 96,85,102,90,106,8896, 85, 102, 90, 106, 8896,85,102,90,106,88 and calculate each number's difference from the mean.

Problem 54032

Solve the equation x4−2x3+6x2−18x−27=0x^{4}-2 x^{3}+6 x^{2}-18 x-27=0x4−2x3+6x2−18x−27=0. Find real solutions or state none exist.

Problem 54033

Identify the justification for each step in the equation transformation from 5(x−1)=4x+135(x-1)=4x+135(x−1)=4x+13 to x=18x=18x=18.

Problem 54034

Calculate sss using u=12u=12u=12, a=10a=10a=10, and t=4t=4t=4: s=ut+12at2s=u t+\frac{1}{2} a t^{2}s=ut+21​at2.

Problem 54035

Find the mean of {96,85,102,90,106,88}\{96, 85, 102, 90, 106, 88\}{96,85,102,90,106,88} and calculate the difference from the mean for each number.

Problem 54036

Brianna has \$ 60 and saves \$ 15 weekly. How many weeks until she has \$ 180 for sneakers? Show your work.

Problem 54037

Problem 54038

Find the real solutions of the equation 2x3+x2−8x+3=02 x^{3}+x^{2}-8 x+3=02x3+x2−8x+3=0. Choose A or B for the solution set.

Problem 54039

Arthur wants to find the total cost of an item priced at ppp with a 6%6\%6% sales tax. Show two equal expressions for total cost.

Problem 54040

Calculate the product of 1141 \frac{1}{4}141​ and 5355 \frac{3}{5}553​.

Simplify the expression: $3 \sqrt{3} \cdot 6 \sqrt{6}$ . What is the result? A. $54 \sqrt{2}$ B. $18 \sqrt{2}$ C. 54 D. $18 \sqrt{3}$

Find the probability that a randomly chosen American has type B blood, given that $15\%$ of Americans have type B.

Simplify the expression: $\frac{3 x^{2}-18 x}{a x-6 a+2 c x-12 c}$

Solve for the values of $x$ in the equations: $\frac{2}{3}=x$ and $\frac{1}{2}=x$ .

Simplify $\sqrt{75}$ . Choose the correct option: A. $3 \sqrt{5}$ B. $15 \sqrt{5}$ C. $25 \sqrt{3}$ D. $5 \sqrt{3}$ .

Find the real zeros of the polynomial $f(x)=x^{3}+6x^{2}-9x-14$ using the rational zeros theorem.

Divide the polynomial $-8 x^{3}-12 x^{2}+16 x+20$ by $4 x+4$ and express the result as a quotient.

Is a score of $X=70$ extreme for a population with mean $\mu=50$ and $\sigma=20$ ? How about with $\sigma=5$ ?

Calculate: $6+\left(\frac{7}{3} \times 9\right)$

Rank the objects W, X, Y, Z by density: $W$ (16g, 84cm³), $X$ (12g, 5cm³), $Y$ (4g, 6cm³), $Z$ (408g, 216cm³).

A hotel photo has a perimeter of $368 \mathrm{in}$ . Width is $4 \mathrm{in}$ more than $4$ times the height. Find dimensions.

Find the real zeros of the polynomial $f(x)=x^{4}+10 x^{3}-20 x^{2}-90 x+99$ and factor it over the reals.

Calculate $\left(\frac{2}{5}+4\right)+\frac{3}{5} \times 20$ .

Find the mean and mode of the data: $x = [3, 4, 5, 6, 7, 8]$ , $y = [3, 6, 7, 3, 2, 1]$ .

How many miles long is a line of $5$ trillion bags, each $12$ inches long?

Find the value of $\sqrt{20}$ .

Find the probability that a random American has type B blood ( $15\%$ ) and the probability of having type A or B.

Simplify the expression: $\frac{-10 x^{3}+19 x^{2}+21 x-15}{2 x-5}$ .

Find the instantaneous rate of change of $R(t)=240+30 t^{3}$ at $t=1$ . Answer: $R^{\prime}(1)=90$ dollars/day.

Solve for $b$ in the equation $\frac{2}{8}=-\frac{b}{6}$ .

Evaluate the integral: $\int_{0}^{1} 6 \frac{\ln (x)}{\sqrt[3]{x}} d x$

Find the area of shapes $A$ ( $11 \, \text{cm} \times 8 \, \text{cm}$ ) and explain for shapes $B$ , $C$ , and $D$ .

Simplify the expression: $5 \sqrt{2} \cdot 9 \sqrt{6}$ . What is the result? A. $90 \sqrt{3}$ B. $45 \sqrt{3}$ C. $45 \sqrt{2}$ D. 90

Arthur wants to find the price of an item costing $p$ dollars after a $6\%$ tax. Show two equal expressions for the total cost.

What is the simplified form of $5 \sqrt{2} \cdot 9 \sqrt{6}$ ? A. $90 \sqrt{3}$ B. $45 \sqrt{3}$ C. $45 \sqrt{2}$ D. 90

Find the mean of the numbers $96, 85, 102, 90, 106, 88$ and calculate each number's difference from the mean.

Solve the equation $x^{4}-2 x^{3}+6 x^{2}-18 x-27=0$ . Find real solutions or state none exist.

Identify the justification for each step in the equation transformation from $5(x-1)=4x+13$ to $x=18$ .

Calculate $s$ using $u=12$ , $a=10$ , and $t=4$ : $s=u t+\frac{1}{2} a t^{2}$ .

Find the mean of $\{96, 85, 102, 90, 106, 88\}$ and calculate the difference from the mean for each number.

Find the real solutions of the equation $2 x^{3}+x^{2}-8 x+3=0$ . Choose A or B for the solution set.

Arthur wants to find the total cost of an item priced at $p$ with a $6\%$ sales tax. Show two equal expressions for total cost.

Calculate the product of $1 \frac{1}{4}$ and $5 \frac{3}{5}$ .

Find the inverse of the function $f(x)=8x+11$ .

Multiply $5 \frac{1}{2}$ by $3 \frac{3}{4}$ .

Calculate the expression: $\frac{30\left((0.1)^{3}+3 \times 1 \times 0.1 \times 1.1\right)}{1}$ .

Find the real solutions for the equation: $5 x^{3}+8 x^{2}-9 x+2=0$ . Choose A (list solutions) or B (no solutions).

Solve the equation $5x - 10 = -40$ and justify each step.

Arthur wants to find the total price of an item costing $p$ with a $6\%$ sales tax. Show two equal expressions for the total cost.

Multiply the mixed numbers: $3 \frac{1}{4} \times 2 \frac{5}{6}$ .

Calculate the product of $\frac{3}{8}$ and $\frac{4}{27}$ .

Find the inverse of $f(x)=x^{2}-6$ for $x \geq 0$ .

A teacher gives three test versions. Find these probabilities: a. $P($ pass $\mid$ Test A) $and b.$ P( $Test C$ \mid $fail)$ .

Calculate $h(-67)$ for $h(x)=-49x-125$ . Choose from A. $-3,408$ , B. -1.18, C. 3,283, D. 3,158.

Solve the inequality: $2-3(x+4)>17$ .

Find the real solutions of the equation $3x^{3} + x^{2} - 13x + 5 = 0$ . What is the solution set?

Find the range of the inverse function for $f(x)=(x+1)^{2}-1$ where $x \leq -1$ .

Find the range of the inverse function of $f(x)=(x+1)^{2}-1$ for $x \leq -1$ .

Find which point among (0,7), (-8,-5), (-1,0), (9,5) satisfies both $y<-\frac{3}{2} x+2$ and $y<2 x+6$ .

Solve for real solutions of $2x - 39x^3 + 193x^2 - 321x + 117 = 0$ . A. $x=$ (exact answer) B. No real solutions.

Find the profit function $p(g)$ for Betty's lemonade stand, where she sells $g$ glasses at \$1 each and setup cost \$50.

Find the intersection of the lines $f(x)=2x+3$ and $g(x)=-4x-27$ . Choose the correct point: A. $(-5,-10)$ B. $(5,-7)$ C. $(-5,-7)$ D. $(5,13)$ .

Abby needs an equation to convert miles $(m)$ to kilometers $(k)$ . Which is correct? (A) $\frac{k}{1.61}=m$ (B) $1.61 m=k$ (C) $1.61=\frac{k}{m}$

Check if the points (1,0), (8,4), (0,9), and (-10,-1) meet these inequalities: $y > -\frac{2}{5} x + 6$ and $y > \frac{2}{3} x + 3$ .

Find the remaining zeros of the polynomial $f(x)$ of degree 5 with known zeros $-5, i, -7i$ .

Find when Plan A (0.09m) costs at least as much as Plan B (12.40 + 0.07m). Solve the inequality for $m$ .

Find the inverse of the function $f(x)=5x+3$ .

Find the other zeros of the function $f(x)=x^{3}-4 x^{2}+25 x-100$ given the zero $-5i$ .

Find the length and width of a field with a perimeter of 96 m, where length is $14 \mathrm{~m}$ more than width.

Find the inverse of the function $f(x)=\frac{2x-3}{7x-8}$ .

Find the complex zeros of the polynomial $f(x)=x^{3}-11 x^{2}+43 x-65$ and write it in factored form.