Analyze

Problem 10001

Solve for $x$ in the equation: $x - 10 + \frac{1}{2} x + 5 + 3 x - 85 = 180$ .

See Solution

Problem 10002

Find the constant of proportionality for the Cougar Basketball team's bread sales: 22 breads for \$99, 18 for \$81, 35 for \$157.50, and 15 for \$67.50.

See Solution

Problem 10003

How do integers differ from whole numbers? Choose the correct answer: A. Whole numbers include negatives; integers do not. B. Integers include negatives; whole numbers do not. C. Integers include negatives and zero; whole numbers do not. D. Whole numbers include negatives; integers do not.

See Solution

Problem 10004

Identify the angle pairs that are neither complementary nor supplementary: $72^{\circ}, 18^{\circ}$ ; $72^{\circ}, 28^{\circ}$ ; $72^{\circ}, 108^{\circ}$ .

See Solution

Problem 10005

Analyze LDL cholesterol levels and write inequalities for the "borderline high" category. Options: A. $128 \leq x \leq 159$ B. $127<x<159$ C. $x \leq 159$ D. $128 \leq x \leq 160$

See Solution

Problem 10006

Determine the inequalities for LDL cholesterol risk categories based on given ranges. What is the high category inequality?

See Solution

Problem 10007

Identify the error in solving $4x \geq -84$ . Correct the solution set and explain the mistake.
Solution set: $(-\infty, -21]$
Options: A. Reversed inequality when dividing by positive. B. Incorrect division; negative divided by positive is positive. C. Didn't reverse inequality when dividing negative by positive. D. Incorrect division; should divide by -84.

See Solution

Problem 10008

Find the angle between the nitrogen-oxygen bonds in the nitrate ion $\mathrm{NO}_{3}^{-}$ .

See Solution

Problem 10009

Calculate Spearman's rank correlation coefficient for the ranks: Geography: 6, 5, 4, 3, 2, 7, 1 and Economics: 7, 6, 2, 4, 1, 5, 3.

See Solution

Problem 10010

Find the domain of the piecewise function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ .

See Solution

Problem 10011

A student measures sugar solution densities: $1.07$ , $1.81$ , $1.93$ , and $1.75$ g/mL. How do her results compare to $1.75$ g/mL?

See Solution

Problem 10012

Define the function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ . Find its domain, intercepts, graph, and range.

See Solution

Problem 10013

Identify the pair of elements in the same period: Zinc & Nitrogen, Potassium & Sodium, Boron & Carbon, Lithium & Magnesium.

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Problem 10014

Identify the element with 18 protons and 8 valence electrons: atomic mass 18, highly reactive, metal, or stable?

See Solution

Problem 10015

What makes sodium ( $\mathrm{Na}$ ) highly reactive? Options: non-metal, 11 protons, atomic mass 22.990, or 1 valence electron?

See Solution

Problem 10016

Identify the atom with four valence electrons that is shiny and has both metallic and nonmetallic properties: B, Sb, Sn, or Ge.

See Solution

Problem 10017

Estimate the slope of the tangent line to $y=x^{1/2}$ at the point $(1,1)$ .

See Solution

Problem 10018

Shannon hits golf balls every 5 minutes. How many were in the full bucket? Data: 5 min: 54, 10 min: 47, 15 min: 40, 20 min: 33, 25 min: 26.

See Solution

Problem 10019

What inequality represents the number of people, $p$ , that can sit in a 320-seat auditorium? Options: $p < 321$ , $p > 320$ , $p < 319$ , $p > 319$ .

See Solution

Problem 10020

Determine which function best models the coyote population $N$ after $t$ years from the given data:
1. $N(t)=0.5 t^{2}+1$
2. $N(t)=1.95^{t}$
3. $N(t)=0.5 t^{3}-t^{2}+5 t+1$
4. $N(t)=2 t+1$

See Solution

Problem 10021

Find a function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ .

See Solution

Problem 10022

Find the function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ . Options: $x+4y=12$ , $\frac{2}{3}x+3y=-3$ , $6x-7y=21$ , $-\frac{2}{3}x+3y=6$ .

See Solution

Problem 10023

Determine if there was discrimination against females based on the admission data: males admitted = 17, females admitted = 33. Total applicants: males = 25, females = 45.

See Solution

Problem 10024

Who is more likely to be part-time: undergraduates (5,358) or graduates (1,769)? Choose the best answer.

See Solution

Problem 10025

Find the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

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Problem 10026

Analyze if hourly workers ( $31$ laid off) were more likely to be laid off than salaried ( $24$ laid off) using the data.

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Problem 10027

Find the week $x$ when a company produces 128 turtle necklaces, given the equation $2^{x}=128$ .

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Problem 10028

Tony wants the best smartphone deal. Compare prices: (a) Store website offers $60\%$ off \ $749. What’s the price? (b) Store has$ 40\% $off plus$ 20\%$ off the sale price. What’s the price? (c) Who pays more: website, store, or the same?

See Solution

Problem 10029

Select $<$ or $>$ to make this true: -20 ? -13.

See Solution

Problem 10030

Joe compares refrigerator prices: (a) Dept store: 50% markup, 20% discount. (b) Superstore: 30% markup. Which is cheaper?

See Solution

Problem 10031

Select either $<$ or $>$ to make the statement true: -20 ? -13. Choose the correct answer.

See Solution

Problem 10032

What function results from horizontally stretching $y=\sqrt{x}$ and reflecting it in the $x$ -axis? Options are:
1. $y=-\sqrt{2 x}$
2. $y=\sqrt{\frac{1}{2}(-x)}$
3. $y=\sqrt{2(-x)}$
4. $y=-\sqrt{\frac{1}{2} x}$

See Solution

Problem 10033

Check if each value of $w$ is a solution to the inequality $13 > -4w - 3$ . Values: 0, -6, -4, 3.

See Solution

Problem 10034

Which function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

See Solution

Problem 10035

Calculate: $7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})$ equals what?

See Solution

Problem 10036

Identify the pattern in the numbers $6, 18, 54, 162, 486$ and find the next number.

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Problem 10037

Estimate the sum of $6.86 + 2.11 + 19.33$ by rounding to the nearest integer. Compare the estimate with the actual sum.

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Problem 10038

Estimate the product of $20.17 \times 2.5$ by rounding for easy calculation, then compare it to the actual answer.

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Problem 10039

Estimate the product of $20.23 \times 8.5$ by rounding. Compare your estimate to the actual answer. What is your estimate?

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Problem 10040

You rent 6 DVDs for a month. Calculate if Option C's \$15.99 streaming is cheaper than renting at \$1.45/night.

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Problem 10041

Count the significant figures in these values: 0.052000, 0.05, 10590, 3000, 2300, 0.0090, 7.000.

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Problem 10042

Check if 8248 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12 using divisibility rules.

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Problem 10043

Identify the measurements with three significant figures: 395, 500, 0.00100, 0.001, $1.00 \times 10^{-3}$ , $5.0 \times 10^{2}$ .

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Problem 10044

Complete the table with energy content in calories, kilocalories, and kilojoules, ensuring correct significant digits.
a small apple: $1.25 \times 10^{5}$ cal, $\square$ kcal, $\square$ kJ a cup of cooked white rice: $\square$ cal, 225. kcal, $\square$ kJ an ear of cooked corn: $\square$ cal, $\square$ kcal, 356. kJ

See Solution

Problem 10045

Omar needs to find $\cos \left(-\frac{2 \pi}{3}\right)$ . Use the reference angle and quadrant info to solve.

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Problem 10046

Which expression equals $4^{5} \times 4^{-7} \div 4^{-2}$ ? Choices: $4^{-4}$ , $4^{5} \div 4^{-9}$ , $4^{0}$ .

See Solution

Problem 10047

Find $(g \circ f \circ h)(x)$ for $f(x)=4x-8$ , $g(x)=x^4$ , and $h(x)=\sqrt[5]{x}$ .

See Solution

Problem 10048

Evaluate $(f \circ g)(x)$ and find its domain. Given $f(x)=\frac{5}{x^{2}+36}$ and $g(x)=\sqrt{4+x}$ .

See Solution

Problem 10049

Find the discriminant of the equations: 83. $x^{2}-4x-5=0$ and 84. $4x^{2}-2x+3=0$ . What does it reveal about solutions?

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Problem 10050

Find $(s \cdot t)(x)$ for $s(x) = \frac{x-3}{x^{2}-36}$ and $t(x) = \frac{x-6}{3-x}$ . State the domain in interval notation.

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Problem 10051

The town's population decreases by $8\%$ yearly. If $P(x)=0.92x$ , find $(P \circ P)(x)$ in exact form.

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Problem 10052

Find $(f \circ g)(x)$ and its domain in interval notation for $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

See Solution

Problem 10053

Evaluate $(f \circ g)(x)$ and find its domain in interval notation, where $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

See Solution

Problem 10054

The town's population decreases by $8\%$ yearly. Find $(P \circ P)(x)$ and explain its meaning. Answer in exact form.

See Solution

Problem 10055

Find $(f \circ g)(x)$ for $f(x)=\frac{x}{x+9}$ and $g(x)=\frac{8}{x^{2}-1}$ ; state the domain in interval notation.

See Solution

Problem 10056

Find the domain of $(s \cdot t)(x)=\frac{-1}{x+6}$ , where $s(x)=\frac{x-3}{x^{2}-36}$ and $t(x)=\frac{x-6}{3-x}$ .

See Solution

Problem 10057

Find the domain, range, inverse domain, and inverse range of the function $f(x)=\frac{5}{4 x+1}$ .

See Solution

Problem 10058

Find the domain, range, inverse domain, and inverse range of the function $f(x)=2x-6$ .

See Solution

Problem 10059

A company makes products A and B with constraints: $x \leq 2y + 500$ and $\sqrt{35x + 50y} > 22,500$ . What are the inequalities?

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Problem 10060

Find the domain and range of $f(x)=\sqrt{3+2x}$ and the domain and range of its inverse.

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Problem 10061

Find how many times greater the max speed of a giraffe ( $L=6$ ft) is than a hippo ( $L=3$ ft) using $S=\sqrt{g L}$ with $g=32$ .

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Problem 10062

Find the domain and range of $f(x)=\sqrt{3+2x}$ and its inverse $f^{-1}(x)$ .

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Problem 10063

Determine the new chair of the Natural Science Division using the Borda count method for Professors D, E, F, and H.

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Problem 10064

Find the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

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Problem 10065

The theater society votes for a play: comedy (C), drama (D). Find the selected play using plurality-with-elimination method.

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Problem 10066

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, \frac{8}{7}), (0, 1), (1, \frac{7}{8}), (2, \frac{49}{64}), (3, \frac{343}{512})$ .

See Solution

Problem 10067

Four professors are running for chair: D, E, F, H. Who wins using plurality-with-elimination? Votes: 29 D, 21 E, 20 H, 10 F, 2 F. Options: A. E B. F C. D D. H.

See Solution

Problem 10068

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, 7)$ , $(0, 9)$ , $(1, 11)$ , $(2, 13)$ , $(3, 15)$ .

See Solution

Problem 10069

65 voters ranked cereals A, B, C, D. Use the plurality method to find the winner based on the votes: 36 for C, 20 for A, 6 for D, 3 for B. The winner is

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Problem 10070

66 voters ranked cereals $A, B, C$ , and $D$ . Use the Borda count method to find the winner.

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Problem 10071

83 voters ranked cereals A, B, C, D. Use plurality-with-elimination to find the winner. Who is it?

See Solution

Problem 10072

Determine the selected musical using the plurality method from 88 votes for Musicals R, J, M, H, and T.

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Problem 10073

Determine the next semester's play type (C, D, M) using votes: 14, 12, 11, 9, 4, 3. Choose A, B, C, or D.

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Problem 10074

Is it possible for a candidate with a majority of votes to lose an election using plurality-with-elimination? Explain.

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Problem 10075

Determine the winner among candidates A, B, and C using the plurality method and Borda count if there's a tie. Votes: A: 15,920, B: 9,950, C: 5,970.

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Problem 10076

Does it make sense that a candidate with a plurality of votes lost using the Borda count method? Explain.

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Problem 10077

Can a candidate with a majority lose using the plurality method? Explain your reasoning. Choose A, B, C, or D.

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Problem 10078

Create a preference table for candidates A, B, C where B wins all voting methods. Select the correct option.

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Problem 10079

Determine which voting method (plurality, Borda, plurality-with-elimination, pairwise) shows B winning from the options.

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Problem 10080

Find the new chair of the Natural Science Division using the Borda count method based on the given votes. Who is it? A. E B. D C. H D. F

See Solution

Problem 10081

Determine the new chair of the Natural Science Division using Borda count from the votes for Professors D, E, F, and H. Choices: A. E, B. D, C. H, D. F.

See Solution

Problem 10082

Candidates $A$ , $B$ , and $C$ are running for mayor. Based on the votes, who wins using pairwise comparison?

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Problem 10083

Voters choose between designs $A, B, C$ , and $D$ . A. Which design has most first-place votes? B. Which wins by Borda count? Majority?

See Solution

Problem 10084

A reality show is voting on three cities: Paris (P), Orlando (O), Dublin (D). Determine the winning city using plurality.
A. Which city wins in head-to-head comparisons? B. Which city wins by plurality? C. Does head-to-head criterion hold? Why or why not?

See Solution

Problem 10085

Find the winner using plurality-with-elimination for candidates A, B, C. How does a vote change affect the outcome? Is monotonicity met?

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Problem 10086

A town votes on smoking regulations: options A (unrestricted), B (designated areas), C (ban). Use Borda count to analyze. What wins?

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Problem 10087

Three directors (Fred, Steve, Eddie) are voted for. Using pairwise comparison, determine who is the selected speaker.

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Problem 10088

Determine the election winner using the Borda count method and check if the majority criterion is met.

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Problem 10089

Three directors (Fred, Steve, Eddie) were voted for. Who wins using pairwise comparison? Does the irrelevant alternatives criterion hold?

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Problem 10090

Three directors (Fred, Steve, Eddie) received votes: 10 for E, 7 for F, 5 for S. Use pairwise comparison to select a speaker.

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Problem 10091

Given the election preference table, determine the Borda count winner, check majority and head-to-head criteria, and analyze A's dropout.

See Solution

Problem 10092

Determine the election winner using plurality-with-elimination and check if the head-to-head criterion is met.

See Solution

Problem 10093

Determine the election winner using Borda count, and analyze majority and head-to-head criteria based on the votes.

See Solution

Problem 10094

Given the election preferences, find the Borda count winner, check majority and head-to-head criteria, and analyze if A's dropout changes the result.

See Solution

Problem 10095

Given the vote preferences, determine the winner using Borda count, check majority and head-to-head criteria, and analyze A's dropout.

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Problem 10096

Election problem:
a. Find the winner using plurality-with-elimination from the votes: 14(B), 12(A), 10(C), 6(D).
b. If B is moved to first choice for all, create a new table and find the winner again.
c. Does improving B's position affect the outcome? Explain if monotonicity is satisfied.

See Solution

Problem 10097

Determine the election winner using Borda count. Check if majority and head-to-head criteria are met.

See Solution

Problem 10098

$\text { Let } A=\left[\begin{array}{ccc} 0 & 0 & 4 \\ 0 & -4 & 0 \\ -2 & 0 & -6 \end{array}\right]$ (a) Determine the eigenvalues $\lambda_{1}$ and $\lambda_{2}$ of $A$ where $\lambda_{1}<\lambda_{2}$ . $\lambda_{1}=$ $\square$ $\lambda_{2}=$ $\square$ (b) Determine the algebraic multiplicity $m$ of each of the eigenvalues in part (a). $m\left(\lambda_{1}\right)=$ $\square$ $m\left(\lambda_{2}\right)=$ $\square$

See Solution

Problem 10099

State whether each of the following changes would make a confidence interval wider or narrower. (Assume that nothing else changes.) a. Changing from a $95 \%$ confidence level to a $90 \%$ confidence level. b. Changing from a sample size of 400 to a sample size of 30 . c. Changing from a standard deviation of 30 pounds to a standard deviation of 15 pounds.
Click the icon to view the $t$ -table. a. How will changing from a $95 \%$ confidence level to a $90 \%$ confidence level affect the width of the confidence interval? A. The interval will become wider. B. The interval will become narrower. C. This change will not affect the width of the interval.

See Solution

Problem 10100

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

See Solution

1 ...98 99 100 101 102 103 104 ...160

Analyze

Problem 10001

Solve for xxx in the equation: x−10+12x+5+3x−85=180x - 10 + \frac{1}{2} x + 5 + 3 x - 85 = 180x−10+21​x+5+3x−85=180.

Problem 10002

Find the constant of proportionality for the Cougar Basketball team's bread sales: 22 breads for \$99, 18 for \$81, 35 for \$157.50, and 15 for \$67.50.

Problem 10003

How do integers differ from whole numbers? Choose the correct answer: A. Whole numbers include negatives; integers do not. B. Integers include negatives; whole numbers do not. C. Integers include negatives and zero; whole numbers do not. D. Whole numbers include negatives; integers do not.

Problem 10004

Identify the angle pairs that are neither complementary nor supplementary: 72∘,18∘72^{\circ}, 18^{\circ}72∘,18∘; 72∘,28∘72^{\circ}, 28^{\circ}72∘,28∘; 72∘,108∘72^{\circ}, 108^{\circ}72∘,108∘.

Problem 10005

Analyze LDL cholesterol levels and write inequalities for the "borderline high" category. Options: A. 128≤x≤159128 \leq x \leq 159128≤x≤159 B. 127<x<159127<x<159127<x<159 C. x≤159x \leq 159x≤159 D. 128≤x≤160128 \leq x \leq 160128≤x≤160

Problem 10006

Determine the inequalities for LDL cholesterol risk categories based on given ranges. What is the high category inequality?

Problem 10007

Problem 10008

Find the angle between the nitrogen-oxygen bonds in the nitrate ion NO3−\mathrm{NO}_{3}^{-}NO3−​.

Problem 10009

Calculate Spearman's rank correlation coefficient for the ranks: Geography: 6, 5, 4, 3, 2, 7, 1 and Economics: 7, 6, 2, 4, 1, 5, 3.

Problem 10010

Find the domain of the piecewise function f(x)={2+xif x<0x2if x≥0f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}f(x)={2+xx2​if x<0if x≥0​.

Problem 10011

A student measures sugar solution densities: 1.071.071.07, 1.811.811.81, 1.931.931.93, and 1.751.751.75 g/mL. How do her results compare to 1.751.751.75 g/mL?

Problem 10012

Define the function f(x)={2+xif x<0x2if x≥0f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}f(x)={2+xx2​if x<0if x≥0​. Find its domain, intercepts, graph, and range.

Problem 10013

Identify the pair of elements in the same period: Zinc & Nitrogen, Potassium & Sodium, Boron & Carbon, Lithium & Magnesium.

Problem 10014

Identify the element with 18 protons and 8 valence electrons: atomic mass 18, highly reactive, metal, or stable?

Problem 10015

What makes sodium (Na\mathrm{Na}Na) highly reactive? Options: non-metal, 11 protons, atomic mass 22.990, or 1 valence electron?

Problem 10016

Identify the atom with four valence electrons that is shiny and has both metallic and nonmetallic properties: B, Sb, Sn, or Ge.

Problem 10017

Estimate the slope of the tangent line to y=x1/2y=x^{1/2}y=x1/2 at the point (1,1)(1,1)(1,1).

Problem 10018

Shannon hits golf balls every 5 minutes. How many were in the full bucket? Data: 5 min: 54, 10 min: 47, 15 min: 40, 20 min: 33, 25 min: 26.

Problem 10019

What inequality represents the number of people, ppp, that can sit in a 320-seat auditorium? Options: p<321p < 321p<321, p>320p > 320p>320, p<319p < 319p<319, p>319p > 319p>319.

Problem 10020

Determine which function best models the coyote population NNN after ttt years from the given data: 1. N(t)=0.5t2+1N(t)=0.5 t^{2}+1N(t)=0.5t2+1 2. N(t)=1.95tN(t)=1.95^{t}N(t)=1.95t 3. N(t)=0.5t3−t2+5t+1N(t)=0.5 t^{3}-t^{2}+5 t+1N(t)=0.5t3−t2+5t+1 4. N(t)=2t+1N(t)=2 t+1N(t)=2t+1

Problem 10021

Find a function with the same yyy-intercept as y=23x−3y=\frac{2}{3} x-3y=32​x−3.

Problem 10022

Find the function with the same yyy-intercept as y=23x−3y=\frac{2}{3} x-3y=32​x−3. Options: x+4y=12x+4y=12x+4y=12, 23x+3y=−3\frac{2}{3}x+3y=-332​x+3y=−3, 6x−7y=216x-7y=216x−7y=21, −23x+3y=6-\frac{2}{3}x+3y=6−32​x+3y=6.

Problem 10023

Determine if there was discrimination against females based on the admission data: males admitted = 17, females admitted = 33. Total applicants: males = 25, females = 45.

Problem 10024

Who is more likely to be part-time: undergraduates (5,358) or graduates (1,769)? Choose the best answer.

Problem 10025

Find the yyy-intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Problem 10026

Analyze if hourly workers (313131 laid off) were more likely to be laid off than salaried (242424 laid off) using the data.

Problem 10027

Find the week xxx when a company produces 128 turtle necklaces, given the equation 2x=1282^{x}=1282x=128.

Problem 10028

Problem 10029

Select <<< or >>> to make this true: -20 ? -13.

Problem 10030

Joe compares refrigerator prices: (a) Dept store: 50% markup, 20% discount. (b) Superstore: 30% markup. Which is cheaper?

Problem 10031

Select either <<< or >>> to make the statement true: -20 ? -13. Choose the correct answer.

Problem 10032

What function results from horizontally stretching y=xy=\sqrt{x}y=x​ and reflecting it in the xxx-axis? Options are: 1. y=−2xy=-\sqrt{2 x}y=−2x​2. y=12(−x)y=\sqrt{\frac{1}{2}(-x)}y=21​(−x)​3. y=2(−x)y=\sqrt{2(-x)}y=2(−x)​4. y=−12xy=-\sqrt{\frac{1}{2} x}y=−21​x​

Problem 10033

Check if each value of www is a solution to the inequality 13>−4w−313 > -4w - 313>−4w−3. Values: 0, -6, -4, 3.

Problem 10034

Which function's graph is y=1xy=\frac{1}{x}y=x1​ shifted right 5 units and up 2 units? y=1x+5+2y=\frac{1}{x+5}+2y=x+51​+2

Problem 10035

Calculate: 712÷(412−518)7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})721​÷(421​−581​) equals what?

Problem 10036

Identify the pattern in the numbers 6,18,54,162,4866, 18, 54, 162, 4866,18,54,162,486 and find the next number.

Problem 10037

Estimate the sum of 6.86+2.11+19.336.86 + 2.11 + 19.336.86+2.11+19.33 by rounding to the nearest integer. Compare the estimate with the actual sum.

Problem 10038

Estimate the product of 20.17×2.520.17 \times 2.520.17×2.5 by rounding for easy calculation, then compare it to the actual answer.

Problem 10039

Estimate the product of 20.23×8.520.23 \times 8.520.23×8.5 by rounding. Compare your estimate to the actual answer. What is your estimate?

Problem 10040

You rent 6 DVDs for a month. Calculate if Option C's \$15.99 streaming is cheaper than renting at \$1.45/night.

Problem 10041

Solve for $x$ in the equation: $x - 10 + \frac{1}{2} x + 5 + 3 x - 85 = 180$ .

Identify the angle pairs that are neither complementary nor supplementary: $72^{\circ}, 18^{\circ}$ ; $72^{\circ}, 28^{\circ}$ ; $72^{\circ}, 108^{\circ}$ .

Analyze LDL cholesterol levels and write inequalities for the "borderline high" category. Options: A. $128 \leq x \leq 159$ B. $127<x<159$ C. $x \leq 159$ D. $128 \leq x \leq 160$

Find the angle between the nitrogen-oxygen bonds in the nitrate ion $\mathrm{NO}_{3}^{-}$ .

Find the domain of the piecewise function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ .

A student measures sugar solution densities: $1.07$ , $1.81$ , $1.93$ , and $1.75$ g/mL. How do her results compare to $1.75$ g/mL?

Define the function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ . Find its domain, intercepts, graph, and range.

What makes sodium ( $\mathrm{Na}$ ) highly reactive? Options: non-metal, 11 protons, atomic mass 22.990, or 1 valence electron?

Estimate the slope of the tangent line to $y=x^{1/2}$ at the point $(1,1)$ .

What inequality represents the number of people, $p$ , that can sit in a 320-seat auditorium? Options: $p < 321$ , $p > 320$ , $p < 319$ , $p > 319$ .

Determine which function best models the coyote population $N$ after $t$ years from the given data:
1. $N(t)=0.5 t^{2}+1$
2. $N(t)=1.95^{t}$
3. $N(t)=0.5 t^{3}-t^{2}+5 t+1$
4. $N(t)=2 t+1$

Find a function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ .

Find the function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ . Options: $x+4y=12$ , $\frac{2}{3}x+3y=-3$ , $6x-7y=21$ , $-\frac{2}{3}x+3y=6$ .

Find the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

Analyze if hourly workers ( $31$ laid off) were more likely to be laid off than salaried ( $24$ laid off) using the data.

Find the week $x$ when a company produces 128 turtle necklaces, given the equation $2^{x}=128$ .

Select $<$ or $>$ to make this true: -20 ? -13.

Select either $<$ or $>$ to make the statement true: -20 ? -13. Choose the correct answer.

What function results from horizontally stretching $y=\sqrt{x}$ and reflecting it in the $x$ -axis? Options are:
1. $y=-\sqrt{2 x}$
2. $y=\sqrt{\frac{1}{2}(-x)}$
3. $y=\sqrt{2(-x)}$
4. $y=-\sqrt{\frac{1}{2} x}$

Check if each value of $w$ is a solution to the inequality $13 > -4w - 3$ . Values: 0, -6, -4, 3.

Which function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

Calculate: $7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8})$ equals what?

Identify the pattern in the numbers $6, 18, 54, 162, 486$ and find the next number.

Estimate the sum of $6.86 + 2.11 + 19.33$ by rounding to the nearest integer. Compare the estimate with the actual sum.

Estimate the product of $20.17 \times 2.5$ by rounding for easy calculation, then compare it to the actual answer.

Estimate the product of $20.23 \times 8.5$ by rounding. Compare your estimate to the actual answer. What is your estimate?

Identify the measurements with three significant figures: 395, 500, 0.00100, 0.001, $1.00 \times 10^{-3}$ , $5.0 \times 10^{2}$ .

Omar needs to find $\cos \left(-\frac{2 \pi}{3}\right)$ . Use the reference angle and quadrant info to solve.

Which expression equals $4^{5} \times 4^{-7} \div 4^{-2}$ ? Choices: $4^{-4}$ , $4^{5} \div 4^{-9}$ , $4^{0}$ .

Find $(g \circ f \circ h)(x)$ for $f(x)=4x-8$ , $g(x)=x^4$ , and $h(x)=\sqrt[5]{x}$ .

Evaluate $(f \circ g)(x)$ and find its domain. Given $f(x)=\frac{5}{x^{2}+36}$ and $g(x)=\sqrt{4+x}$ .

Find the discriminant of the equations: 83. $x^{2}-4x-5=0$ and 84. $4x^{2}-2x+3=0$ . What does it reveal about solutions?

Find $(s \cdot t)(x)$ for $s(x) = \frac{x-3}{x^{2}-36}$ and $t(x) = \frac{x-6}{3-x}$ . State the domain in interval notation.

The town's population decreases by $8\%$ yearly. If $P(x)=0.92x$ , find $(P \circ P)(x)$ in exact form.

Find $(f \circ g)(x)$ and its domain in interval notation for $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

Evaluate $(f \circ g)(x)$ and find its domain in interval notation, where $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{13}{x^{2}-36}$ .

The town's population decreases by $8\%$ yearly. Find $(P \circ P)(x)$ and explain its meaning. Answer in exact form.

Find $(f \circ g)(x)$ for $f(x)=\frac{x}{x+9}$ and $g(x)=\frac{8}{x^{2}-1}$ ; state the domain in interval notation.

Find the domain of $(s \cdot t)(x)=\frac{-1}{x+6}$ , where $s(x)=\frac{x-3}{x^{2}-36}$ and $t(x)=\frac{x-6}{3-x}$ .

Find the domain, range, inverse domain, and inverse range of the function $f(x)=\frac{5}{4 x+1}$ .

Find the domain, range, inverse domain, and inverse range of the function $f(x)=2x-6$ .

A company makes products A and B with constraints: $x \leq 2y + 500$ and $\sqrt{35x + 50y} > 22,500$ . What are the inequalities?

Find the domain and range of $f(x)=\sqrt{3+2x}$ and the domain and range of its inverse.

Find how many times greater the max speed of a giraffe ( $L=6$ ft) is than a hippo ( $L=3$ ft) using $S=\sqrt{g L}$ with $g=32$ .

Find the domain and range of $f(x)=\sqrt{3+2x}$ and its inverse $f^{-1}(x)$ .

Find the inverse of the function $f(x)=\frac{9}{5}x+32$ that converts Celsius to Fahrenheit.

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, \frac{8}{7}), (0, 1), (1, \frac{7}{8}), (2, \frac{49}{64}), (3, \frac{343}{512})$ .

Is the function $H(x)$ exponential? If yes, find the base $a$ . Given points: $(-1, 7)$ , $(0, 9)$ , $(1, 11)$ , $(2, 13)$ , $(3, 15)$ .

66 voters ranked cereals $A, B, C$ , and $D$ . Use the Borda count method to find the winner.