Analyze

Problem 9501

Find $(k \circ m)(x)$ and $(m \circ k)(x)$ for $k(x)=9x-5$ and $m(x)=x^2$ . Are they equal?

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Problem 9502

Find $(m \circ n)(x)$ for $m(x)=\sqrt{x+9}$ and $n(x)=x+6$ , then determine its domain in interval notation.

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Problem 9503

Evaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9x$ and $q(x)=\frac{1}{x-10}$ . What is the domain?

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Problem 9504

Evaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9 x$ and $q(x)=\frac{1}{x-10}$ . Find its domain in interval notation.

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Problem 9505

Evaluate $(q \circ r)(x)$ for $q(x)=\frac{1}{x-10}$ and $r(x)=|4x-5|$ . What is the domain?

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Problem 9506

Inches per 25 miles equals inches per 12.5 miles: $\frac{\text { inches }}{25 \text{ miles}}=\frac{\text { inches }}{12.5 \text{ miles }}$ .

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Problem 9507

Inches to mils ratio: $\frac{\text{Inches}}{25 \text{ mils}} = \frac{\text{Inches}}{12.5 \text{ miles}}$

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Problem 9508

Find $(q \circ r)(x)$ for $q(x)=\frac{1}{x-10}$ and $r(x)=|4x-5|$ . What is the domain in interval notation?

See Solution

Problem 9509

Find the value of inches in the equation: $\frac{1 \text { inch }}{25 \text { miles }}=\frac{x \text { inches }}{12.5 \text { miles }}$ .

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Problem 9510

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

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Problem 9511

Find $f(x)$ for $x=-1$ and $x=4$ if $f(x)=x^{3}$ . Also, determine the domain of $f$ .

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Problem 9512

Find the domain of the composite function $(f \circ g)(x) = \frac{5}{40+x}$ in interval notation, given $f(x)=\frac{5}{x^{2}+36}$ and $g(x)=\sqrt{4+x}$ .

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Problem 9513

Explain how to find $f(g(x))$ from $f(x)$ and $g(x)$ , and determine its domain in interval notation.

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Problem 9514

Given the function $g(x)=1-x^2$ , find the domain, range, and evaluate $g(-1)$ and $g(2)$ . Describe the graph.

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Problem 9515

The histogram shows test scores of 30 students. Answer these questions:
1. Count students in $91-100$ .
2. Count students in $61-70$ .
3. What percent scored $91-100$ ?

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Problem 9516

Given $g(x)=1-x^2$ :
(a) Determine the domain and range.
(b) Calculate $g(-1)$ and $g(2)$ .
(c) Use the graph to find $g(-1)$ and $g(2)$ .

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Problem 9517

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

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Problem 9518

9.002 - 3 = 1.001

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Problem 9519

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

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Problem 9520

Estimate the mean survival time (in months) for 21 multiple myeloma patients treated with Thalidomide using the given frequency data.

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Problem 9521

A tree company's delivery fee varies with the number of trees. Why is the cost function nonlinear? Consider the rates of change.

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Problem 9522

Evaluate the expression $6^{2}+10 \div(-5)(3)-5$ using order of operations. What to do first?

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Problem 9523

Alejandro studied for 5 more minutes each day for 6 days. What is the change in study time from day 1 to day 6? -30 minutes -11 minutes 11 minutes 30 minutes

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Problem 9524

Analyze the customer wait data for 40 Saturdays at Bobak's. Are they discrete or continuous? Choose A, B, C, or D.

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Problem 9525

At a debate tournament with 175 students, if the ratio of Illinois to Michigan students is $6:5$ , find Michigan and Indiana students.

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Problem 9526

(a) What is the most common year of birth reported by the football team? Mean, Median, or Mode? (b) For the data set 28,29,31,32,33,34,35,36,39, which measure summarizes it best? Mean, Median, or Mode? (c) For the ratings 40,41,44,46,48,50,51,52,87, which measure summarizes it best? Mean, Median, or Mode?

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Problem 9527

How many times heavier is an anaconda weighing $8,643.2$ ounces than a common rat that weighs $11.8$ ounces?

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Problem 9528

Analyze the disposable income data for 25 cities.
(a) What analysis do you need to perform?
(b) Calculate the mean, median, mode, or range.

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Problem 9529

What number can multiply the equation to remove decimals? $-m + 0.02 + 2.1m = -1.45 - 4.81m$ Options: 0.01, 0.1, 10, 100

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Problem 9530

Compare the cost graphs of a prepaid plan at \ $0.20/min and a contracted plan at \$50/month + \$0.02/min for$ x$ minutes.

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Problem 9531

A boys' basketball team has a seniors to juniors ratio of $7:4$ . What is the seniors to total ratio? Girls' team has $3:2$ ratio with 12 juniors; which team has more seniors?

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Problem 9532

Fill in the Venn diagram using: $n(A)=30$ , $n(B)=38$ , $n(C)=23$ , $n(A \cap B)=12$ , $n(B \cap C)=14$ , $n(A \cap C)=5$ , $n(A \cap B \cap C)=2$ , $n(U)=71$ .

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Problem 9533

Find the zeros of $f(x)=2x^2+10x+9$ and determine their relationship to the $x$ -intercepts.

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Problem 9534

Use the Law of Syllogism to create a new conditional statement from these true statements: If $x<-2$ , then $|x|>2$ ; If $x>2$ , then $|x|>2$ .

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Problem 9535

If $a=3$ , then $5a=15$ . Use the Law of Syllogism to create a new conditional statement.

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Problem 9536

Compare monthly costs of two ISPs: Company A's costs for $x$ months and Company B's $y = 45x + 50$ . Which is cheaper?

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Problem 9537

Graph $f(x) = x^2 - 4x$ . Determine if it opens up or down, and find the vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts.

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Problem 9538

If a figure is a square, what can we conclude about its angles and sides using the Law of Syllogism?

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Problem 9539

Use the Law of Syllogism to create a new conditional statement from these: If a figure is a square, then it has four congruent sides and four right angles.

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Problem 9540

Identify the logical law shown: If you miss practice, you won't start. You missed practice, so you won't start.

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Problem 9541

Compare the initial fees of Carrier A (total costs: \ $500 for 3 months, \$650 for 6 months) and Carrier B ($ y=55x+300$).

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Problem 9542

For the function $f(x)=x^{2}+6x$ , find if it opens up or down, and determine the vertex and intercepts.

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Problem 9543

Find the percent of 3,408 students at Van Buren High with incomes between \$1,000 and \$2,000, and those under \$800.

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Problem 9544

Which number is closest to $\sqrt{66}$ ? (A) 9.1 (B) 8.8 (C) 8.2 (D) 8.1

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Problem 9545

Find the percentage of riders at Splash City Water Park who go on more than 10 rides, given a normal distribution with mean 8.4 and SD 2. Round to the nearest percent.

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Problem 9546

Calculate the mean of Ashley's friends' expenses: \$ 2,800, \$ 1,990, \$ 2,005, \$ 2,400, \$ 1,860, \$ 2,200, \$ 2,000. Is it higher or lower than \$ 2,110? What must Ashley spend for the average to be \$ 2,110?

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Problem 9547

You're comparing phone costs from two carriers. Carrier A's costs for months $x$ are: 3 months: \ $500, 6 months: \$650, 9 months: \$800, 12 months: \$950, 15 months: \$1100. Carrier B's cost is given by$ y=55x+300$.
1. Which carrier has a lower initial fee?
2. When do total costs equal for both carriers?

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Problem 9548

Key Club students at Peconic High made trips to Echo Beach.
a. Total students? b. Find mean, median, mode, range, variance, and standard deviation (round to 1 decimal). c. For a normal distribution with mean 6.2 and SD 2, what % went >8 times? (round to nearest %) d. What % went 5-7 times? (round to nearest %)

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Problem 9549

Shannon's train fares from NYC to D.C. are: 49, 88, 119, 133, 161, 173, 272. Find the percentile ranks for \$119 and \$272, then identify the fare with a rank of about 82\%.

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Problem 9550

At Van Buren High, students' summer incomes are normally distributed: mean \$1,751, SD \$421. Find: a. Percent with incomes between \$1,000 and \$2,000? b. Students with incomes less than \$800?

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Problem 9551

Find the probability of getting at least one question wrong when guessing on 5 multiple choice questions ( $P(\text{at least 1 wrong})$ ).

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Problem 9552

Determine which scenario requires permutations to count the arrangements: A, B, C, or D.

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Problem 9553

Calculate the expected winnings when rolling a die: win \$25 for even, \$5 for second even, lose for odd.

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Problem 9554

Predict heart weight (g) from body weight (kg) using regression.
(i) (a) Model: $\hat{y}=-0.339+4.028 x$ (b) Intercept: Expected heart weight at 0 kg is $-0.339$ g. (c) Slope: Each kg increases heart weight by 4.028 g. (d) $R^{2}$ : Body weight explains $64.65\%$ of heart weight variability. (e) Correlation coefficient: $0.8049$

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Problem 9555

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans.
(a) Expectation for Republicans not supporting: $48$ (b) Expectation for Democrats supporting: $?$ (c) Expectation for Independents unsure: $22$

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Problem 9556

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at $\alpha = 0.05$ . State hypotheses, calculate test statistic (2 decimal places), and find $p$ -value (3 decimal places). Note data discrepancies.

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Problem 9557

Write the nuclear equation for beta decay of ${ }_{82}^{210} \mathrm{~Pb}$ . Options include:
1. ${ }_{82}^{210} \mathrm{~Pb} \rightarrow{ }^{2}{ }_{-1}^{0} \beta+{ }_{84}^{210} \mathrm{Po}$
2. None of these
3. ${ }_{82}^{210} \mathrm{~Pb}+{ }_{-1}^{0} \beta \longrightarrow{ }_{81}^{210} \mathrm{Tl}$
4. ${ }_{82}^{210} \mathrm{~Pb} \rightarrow{ }_{-1}^{0} \beta+{ }_{84}^{210} \mathrm{At}$
5. ${ }_{82}^{210} \mathrm{~Pb} \rightarrow{ }_{2}^{4} \beta+{ }^{2010} \mathrm{Hg}$
6. ${ }_{82}^{210} \mathrm{pb} \longrightarrow{ }^{0} \beta+{ }^{210} \mathrm{p} i$
7. ${ }^{210} \mathrm{~Pb}, \frac{110+210}{811}$

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Problem 9558

Find the sum of the weighted average and the mode of these home costs: 6 homes at \$65000, 8 homes at \$85000, 6 homes at \$105000.

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Problem 9559

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at $\alpha=0.05$ . Find test statistic and $p$ -value.

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Problem 9560

A bacterial colony of 1000 doubles in 12 hours. Find growth rate $k$ and time to reach 200,000 bacteria.

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Problem 9561

An outdoor concert arena's attendance drops with snow. Analyze data and answer:
(a) Is a linear model appropriate? Yes/No (b) Find slope and $y$ -intercept: Attendance $=$ (Inches of Snow) + (c) Predict attendance for 9.1 inches of snow.

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Problem 9562

Complete the trigonometric table for $30^{\circ}$ and verify if " $45^{\circ}$ " in $\sin(\theta)$ is an error.

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Problem 9563

Order 549 apples, 498 oranges, and 794 pears from greatest to least, then round each to the nearest hundred.

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Problem 9564

Identify the missing particle in the nuclear equation: $_{10}^{43} \mathrm{~K} \rightarrow{ }_{20}^{43} \mathrm{Ca}+?$

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Problem 9565

Identify the hyphen notation for the element with 15 electrons and 15 neutrons: 1. phosphorus-30 2. silicon-30 3. $\sin 0-60$ 4. vinospliomestal 5. flicrine-15 6. sulfur-3 7. oxyentistis

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Problem 9566

Explain your solution for $10 \times 4$ thousands using a place value chart.

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Problem 9567

What melide is formed when $^{50} \mathrm{Sr}$ undergoes $\beta$ decay?

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Problem 9568

Explain the pattern of zeros in the products of $6 \times 10^n$ for $n = 0, 1, 2, 3$ .

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Problem 9569

If $-3 \leq x \leq 10$ , find the interval for $-x$ . Explain the changes in inequality when multiplying by -1.

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Problem 9570

Calculate the sum: $\frac{(155-151.49)^{2}}{151.49} + \frac{(131-134.51)^{2}}{134.51} + \frac{(179-161.03)^{2}}{161.03} + \frac{(125-142.97)^{2}}{142.97} + \frac{(103-124.48)^{2}}{124.48} + \frac{(132-110.52)^{2}}{110.52}$ .

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Problem 9571

Match the graph to the inequality $x \geq -3$ .

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Problem 9572

Find the missing particle in the decay: ${ }_{84}^{218} \mathrm{Po} \rightarrow{ }_{2}^{4} \mathrm{He}+?$

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Problem 9573

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with $H_{0}$ : no difference, $H_{A}$ : difference. Test statistic is 12.32; confirm and find the $p$ -value.

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Problem 9574

A classmate claims the system $x=0, y=0, z=0$ has no solution. What is the mistake in their reasoning?

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Problem 9575

Test if skier level and preferred ski area are independent at $\alpha = 0.05$ . Calculate test statistic, p-value, and conclusions.

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Problem 9576

Solve the system of equations: 2y - 3z = 0, x + 3y = -4, 3x + 4y = 3.

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Problem 9577

Identify the center and radius of these circles: 1. $x^{2}+y^{2}=49$ 2. $5(x^{2}+y^{2})=125$ 3. $(x+4)^{2}+(y-2)^{2}=9$ . Find standard forms for: 4. center at origin, radius $5\sqrt{3}$ 5. center $(17,5)$ , radius 12 6. center $(-8,4)$ , contains $(-4,2)$ 7. center $(15,7)$ , tangent to $x$ -axis.

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Problem 9578

Given the function $f(x)=\left\{\begin{array}{lll}2 x+18 & \text { if } & x<-6 \\ \sqrt{x+42} & \text { if } & x>-6 \\ 2 & \text { if } & x=-6\end{array}\right.$ , determine the truth of the following statements about $f(-6)$ and its limits.

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Problem 9579

Find the co-vertices of the ellipse given by $\frac{(y-4)^{2}}{64}+\frac{(x-2)^{2}}{4}=1$ .

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Problem 9580

Find the value of $m$ for the continuous piecewise function $f(x)=\left\{\begin{array}{ll}m x-7 & \text { if } \quad x<-4 \\ x^{2}+5 x-3 & \text { if } \quad x \geq-4\end{array}\right.$

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Problem 9581

Find the ordered pair that satisfies the inequalities: $3x - 5y \leq 15$ and $8x + 5y > 24$ . A) $(0,3)$ B) $(3,-3)$ C) $(3,0)$ D) $(3,3)$

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Problem 9582

A mechanic earns \ $14/hour regular and \$21/hour overtime. Find$ W(30) $,$ W(40) $,$ W(45) $, and$ W(50)$.
(b) What is the new wage function if the work week is 36 hours?
(c) If pay is \$16/hour for 40 hours, what is the new wage function?

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Problem 9583

A mechanic earns \ $14/hour regular and \$21/hour overtime. Find$ W(30) $,$ W(40) $,$ W(45) $,$ W(50)$ and new function for 36 hours.

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Problem 9584

Find the value of the function $f(x) = x^{3}$ at $x = 5$ .

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Problem 9585

Calculate the number of diamond flushes in a 3-card poker hand and its probability. Also, find total 3-card hands.

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Problem 9586

A concert venue seats 7,500. Analyze snow vs. attendance data, then: (a) Is a linear model suitable? Yes/No (b) Find slope and $y$ -intercept: Attendance $=$ (Inches of Snow) + (c) Predict attendance with 9.1 inches of snow: $\times$ people.

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Problem 9587

Find values of $a$ for lines $L_{1}$ and $L_{2}$ with slopes $m_{1}=\frac{-6 a-4}{-6}$ and $m_{2}=\frac{-4 a+8}{-5}$ such that: (i) $L_{1}$ is parallel to $L_{2}$ : $a=$ (ii) $L_{1}$ is perpendicular to $L_{2}$ : $a=$

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Problem 9588

Calculate $-f(x)$ for the function $f(x)=-2 x^{2}-3 x-1$ .

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Problem 9589

Sarai is 200 ft from the platform with a $62^{\circ}$ angle of elevation. Which side is 200 ft: opposite, adjacent, or hypotenuse?

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Problem 9590

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 9591

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 9592

Find the end behavior of the function $h(x) = -4x^2 + 11$ as $x$ approaches $\pm \infty$ .

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Problem 9593

Identify functions with a range of $\{y \in \mathbb{R} \mid-\infty<y<\infty\}$ :
1. $f(x)=\frac{2}{3} x-8$
2. $f(x)=x^{2}+7 x-9$
3. $f(x)=-4 x+11$
4. $f(x)=-(x+1)^{2}-4$
5. $f(x)=2^{x+3}$

See Solution

Problem 9594

Factor the polynomial $4 m^{3}-9 m^{2}-m+25$ .

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Problem 9595

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 9596

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

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Problem 9597

Determina el dominio de la función $f(x)=\frac{x^{2}-20}{\sqrt{x+6}}-\frac{x-4}{x^{2}-49}$ .

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Problem 9598

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 9599

Encuentra las nuevas coordenadas del punto $P(4, -3)$ tras aplicar la transformación $g(x)=3-f(x+4)$ .

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Problem 9600

Determine the zeros of the function $f(x)=2x^{2}+10x+11$ and identify the $x$ -intercepts. Choose A, B, or C.

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1 ...93 94 95 96 97 98 99 ...160

Analyze

Problem 9501

Find (k∘m)(x)(k \circ m)(x)(k∘m)(x) and (m∘k)(x)(m \circ k)(x)(m∘k)(x) for k(x)=9x−5k(x)=9x-5k(x)=9x−5 and m(x)=x2m(x)=x^2m(x)=x2. Are they equal?

Problem 9502

Find (m∘n)(x)(m \circ n)(x)(m∘n)(x) for m(x)=x+9m(x)=\sqrt{x+9}m(x)=x+9​ and n(x)=x+6n(x)=x+6n(x)=x+6, then determine its domain in interval notation.

Problem 9503

Evaluate (q∘p)(x)(q \circ p)(x)(q∘p)(x) for p(x)=x2−9xp(x)=x^{2}-9xp(x)=x2−9x and q(x)=1x−10q(x)=\frac{1}{x-10}q(x)=x−101​. What is the domain?

Problem 9504

Evaluate (q∘p)(x)(q \circ p)(x)(q∘p)(x) for p(x)=x2−9xp(x)=x^{2}-9 xp(x)=x2−9x and q(x)=1x−10q(x)=\frac{1}{x-10}q(x)=x−101​. Find its domain in interval notation.

Problem 9505

Evaluate (q∘r)(x)(q \circ r)(x)(q∘r)(x) for q(x)=1x−10q(x)=\frac{1}{x-10}q(x)=x−101​ and r(x)=∣4x−5∣r(x)=|4x-5|r(x)=∣4x−5∣. What is the domain?

Problem 9506

Inches per 25 miles equals inches per 12.5 miles: inches 25 miles= inches 12.5 miles \frac{\text { inches }}{25 \text{ miles}}=\frac{\text { inches }}{12.5 \text{ miles }}25 miles inches ​=12.5 miles inches ​.

Problem 9507

Inches to mils ratio: Inches25 mils=Inches12.5 miles\frac{\text{Inches}}{25 \text{ mils}} = \frac{\text{Inches}}{12.5 \text{ miles}}25 milsInches​=12.5 milesInches​

Problem 9508

Find (q∘r)(x)(q \circ r)(x)(q∘r)(x) for q(x)=1x−10q(x)=\frac{1}{x-10}q(x)=x−101​ and r(x)=∣4x−5∣r(x)=|4x-5|r(x)=∣4x−5∣. What is the domain in interval notation?

Problem 9509

Find the value of inches in the equation: 1 inch 25 miles =x inches 12.5 miles \frac{1 \text { inch }}{25 \text { miles }}=\frac{x \text { inches }}{12.5 \text { miles }}25 miles 1 inch ​=12.5 miles x inches ​.

Problem 9510

Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) and its domain for f(x)=5x2+36f(x)=\frac{5}{x^{2}+36}f(x)=x2+365​ and g(x)=4+xg(x)=\sqrt{4+x}g(x)=4+x​.

Problem 9511

Find f(x)f(x)f(x) for x=−1x=-1x=−1 and x=4x=4x=4 if f(x)=x3f(x)=x^{3}f(x)=x3. Also, determine the domain of fff.

Problem 9512

Find the domain of the composite function (f∘g)(x)=540+x(f \circ g)(x) = \frac{5}{40+x}(f∘g)(x)=40+x5​ in interval notation, given f(x)=5x2+36f(x)=\frac{5}{x^{2}+36}f(x)=x2+365​ and g(x)=4+xg(x)=\sqrt{4+x}g(x)=4+x​.

Problem 9513

Explain how to find f(g(x))f(g(x))f(g(x)) from f(x)f(x)f(x) and g(x)g(x)g(x), and determine its domain in interval notation.

Problem 9514

Given the function g(x)=1−x2g(x)=1-x^2g(x)=1−x2, find the domain, range, and evaluate g(−1)g(-1)g(−1) and g(2)g(2)g(2). Describe the graph.

Problem 9515

The histogram shows test scores of 30 students. Answer these questions: 1. Count students in 91−10091-10091−100.2. Count students in 61−7061-7061−70.3. What percent scored 91−10091-10091−100?

Problem 9516

Given g(x)=1−x2g(x)=1-x^2g(x)=1−x2: (a) Determine the domain and range. (b) Calculate g(−1)g(-1)g(−1) and g(2)g(2)g(2). (c) Use the graph to find g(−1)g(-1)g(−1) and g(2)g(2)g(2).

Problem 9517

Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) and its domain. Given f(x)=xx−1f(x)=\frac{x}{x-1}f(x)=x−1x​ and g(x)=13x2−36g(x)=\frac{13}{x^{2}-36}g(x)=x2−3613​.

Problem 9518

9.002 - 3 = 1.001

Problem 9519

Find (f∘g)(x)(f \circ g)(x)(f∘g)(x) and its domain in interval notation, where f(x)=xx−1f(x)=\frac{x}{x-1}f(x)=x−1x​ and g(x)=13x2−36g(x)=\frac{13}{x^{2}-36}g(x)=x2−3613​.

Problem 9520

Estimate the mean survival time (in months) for 21 multiple myeloma patients treated with Thalidomide using the given frequency data.

Problem 9521

A tree company's delivery fee varies with the number of trees. Why is the cost function nonlinear? Consider the rates of change.

Problem 9522

Evaluate the expression 62+10÷(−5)(3)−56^{2}+10 \div(-5)(3)-562+10÷(−5)(3)−5 using order of operations. What to do first?

Problem 9523

Alejandro studied for 5 more minutes each day for 6 days. What is the change in study time from day 1 to day 6? -30 minutes -11 minutes 11 minutes 30 minutes

Problem 9524

Analyze the customer wait data for 40 Saturdays at Bobak's. Are they discrete or continuous? Choose A, B, C, or D.

Problem 9525

At a debate tournament with 175 students, if the ratio of Illinois to Michigan students is 6:56:56:5, find Michigan and Indiana students.

Problem 9526

Problem 9527

How many times heavier is an anaconda weighing 8,643.28,643.28,643.2 ounces than a common rat that weighs 11.811.811.8 ounces?

Problem 9528

Analyze the disposable income data for 25 cities. (a) What analysis do you need to perform? (b) Calculate the mean, median, mode, or range.

Problem 9529

What number can multiply the equation to remove decimals? −m+0.02+2.1m=−1.45−4.81m -m + 0.02 + 2.1m = -1.45 - 4.81m −m+0.02+2.1m=−1.45−4.81m Options: 0.01, 0.1, 10, 100

Problem 9530

Compare the cost graphs of a prepaid plan at \0.20/minandacontractedplanat$50/month+$0.02/minfor0.20/min and a contracted plan at \$50/month + \$0.02/min for 0.20/minandacontractedplanat$50/month+$0.02/minforx$ minutes.

Problem 9531

A boys' basketball team has a seniors to juniors ratio of 7:47:47:4. What is the seniors to total ratio? Girls' team has 3:23:23:2 ratio with 12 juniors; which team has more seniors?

Problem 9532

Fill in the Venn diagram using: n(A)=30n(A)=30n(A)=30, n(B)=38n(B)=38n(B)=38, n(C)=23n(C)=23n(C)=23, n(A∩B)=12n(A \cap B)=12n(A∩B)=12, n(B∩C)=14n(B \cap C)=14n(B∩C)=14, n(A∩C)=5n(A \cap C)=5n(A∩C)=5, n(A∩B∩C)=2n(A \cap B \cap C)=2n(A∩B∩C)=2, n(U)=71n(U)=71n(U)=71.

Problem 9533

Find the zeros of f(x)=2x2+10x+9f(x)=2x^2+10x+9f(x)=2x2+10x+9 and determine their relationship to the xxx-intercepts.

Problem 9534

Use the Law of Syllogism to create a new conditional statement from these true statements: If x<−2x<-2x<−2, then ∣x∣>2|x|>2∣x∣>2; If x>2x>2x>2, then ∣x∣>2|x|>2∣x∣>2.

Problem 9535

If a=3a=3a=3, then 5a=155a=155a=15. Use the Law of Syllogism to create a new conditional statement.

Problem 9536

Compare monthly costs of two ISPs: Company A's costs for xxx months and Company B's y=45x+50y = 45x + 50y=45x+50. Which is cheaper?

Problem 9537

Graph f(x)=x2−4xf(x) = x^2 - 4xf(x)=x2−4x. Determine if it opens up or down, and find the vertex, axis of symmetry, yyy-intercept, and xxx-intercepts.

Problem 9538

If a figure is a square, what can we conclude about its angles and sides using the Law of Syllogism?

Problem 9539

Use the Law of Syllogism to create a new conditional statement from these: If a figure is a square, then it has four congruent sides and four right angles.

Problem 9540

Identify the logical law shown: If you miss practice, you won't start. You missed practice, so you won't start.

Find $(k \circ m)(x)$ and $(m \circ k)(x)$ for $k(x)=9x-5$ and $m(x)=x^2$ . Are they equal?

Find $(m \circ n)(x)$ for $m(x)=\sqrt{x+9}$ and $n(x)=x+6$ , then determine its domain in interval notation.

Evaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9x$ and $q(x)=\frac{1}{x-10}$ . What is the domain?

Evaluate $(q \circ p)(x)$ for $p(x)=x^{2}-9 x$ and $q(x)=\frac{1}{x-10}$ . Find its domain in interval notation.

Evaluate $(q \circ r)(x)$ for $q(x)=\frac{1}{x-10}$ and $r(x)=|4x-5|$ . What is the domain?

Inches per 25 miles equals inches per 12.5 miles: $\frac{\text { inches }}{25 \text{ miles}}=\frac{\text { inches }}{12.5 \text{ miles }}$ .

Inches to mils ratio: $\frac{\text{Inches}}{25 \text{ mils}} = \frac{\text{Inches}}{12.5 \text{ miles}}$

Find $(q \circ r)(x)$ for $q(x)=\frac{1}{x-10}$ and $r(x)=|4x-5|$ . What is the domain in interval notation?

Find the value of inches in the equation: $\frac{1 \text { inch }}{25 \text { miles }}=\frac{x \text { inches }}{12.5 \text { miles }}$ .

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

Find $f(x)$ for $x=-1$ and $x=4$ if $f(x)=x^{3}$ . Also, determine the domain of $f$ .

Find the domain of the composite function $(f \circ g)(x) = \frac{5}{40+x}$ in interval notation, given $f(x)=\frac{5}{x^{2}+36}$ and $g(x)=\sqrt{4+x}$ .

Explain how to find $f(g(x))$ from $f(x)$ and $g(x)$ , and determine its domain in interval notation.

Given the function $g(x)=1-x^2$ , find the domain, range, and evaluate $g(-1)$ and $g(2)$ . Describe the graph.

The histogram shows test scores of 30 students. Answer these questions:
1. Count students in $91-100$ .
2. Count students in $61-70$ .
3. What percent scored $91-100$ ?

Given $g(x)=1-x^2$ :
(a) Determine the domain and range.
(b) Calculate $g(-1)$ and $g(2)$ .
(c) Use the graph to find $g(-1)$ and $g(2)$ .

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

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

Evaluate the expression $6^{2}+10 \div(-5)(3)-5$ using order of operations. What to do first?

At a debate tournament with 175 students, if the ratio of Illinois to Michigan students is $6:5$ , find Michigan and Indiana students.

How many times heavier is an anaconda weighing $8,643.2$ ounces than a common rat that weighs $11.8$ ounces?

Analyze the disposable income data for 25 cities.
(a) What analysis do you need to perform?
(b) Calculate the mean, median, mode, or range.

What number can multiply the equation to remove decimals? $-m + 0.02 + 2.1m = -1.45 - 4.81m$ Options: 0.01, 0.1, 10, 100

Compare the cost graphs of a prepaid plan at \ $0.20/min and a contracted plan at \$50/month + \$0.02/min for$ x$ minutes.

A boys' basketball team has a seniors to juniors ratio of $7:4$ . What is the seniors to total ratio? Girls' team has $3:2$ ratio with 12 juniors; which team has more seniors?

Fill in the Venn diagram using: $n(A)=30$ , $n(B)=38$ , $n(C)=23$ , $n(A \cap B)=12$ , $n(B \cap C)=14$ , $n(A \cap C)=5$ , $n(A \cap B \cap C)=2$ , $n(U)=71$ .

Find the zeros of $f(x)=2x^2+10x+9$ and determine their relationship to the $x$ -intercepts.

Use the Law of Syllogism to create a new conditional statement from these true statements: If $x<-2$ , then $|x|>2$ ; If $x>2$ , then $|x|>2$ .

If $a=3$ , then $5a=15$ . Use the Law of Syllogism to create a new conditional statement.

Compare monthly costs of two ISPs: Company A's costs for $x$ months and Company B's $y = 45x + 50$ . Which is cheaper?

Graph $f(x) = x^2 - 4x$ . Determine if it opens up or down, and find the vertex, axis of symmetry, $y$ -intercept, and $x$ -intercepts.

Compare the initial fees of Carrier A (total costs: \ $500 for 3 months, \$650 for 6 months) and Carrier B ($ y=55x+300$).

For the function $f(x)=x^{2}+6x$ , find if it opens up or down, and determine the vertex and intercepts.

Which number is closest to $\sqrt{66}$ ? (A) 9.1 (B) 8.8 (C) 8.2 (D) 8.1

Find the probability of getting at least one question wrong when guessing on 5 multiple choice questions ( $P(\text{at least 1 wrong})$ ).

Calculate expected values under the null hypothesis for party affiliation and support of full-body scans.
(a) Expectation for Republicans not supporting: $48$ (b) Expectation for Democrats supporting: $?$ (c) Expectation for Independents unsure: $22$

Analyze responses from 825 voters on oil drilling in CA. Perform a chi-square test for college grads vs non-grads at $\alpha = 0.05$ . State hypotheses, calculate test statistic (2 decimal places), and find $p$ -value (3 decimal places). Note data discrepancies.

Survey skiers' preferences for ski areas. Test if preference is independent of skill level at $\alpha=0.05$ . Find test statistic and $p$ -value.

A bacterial colony of 1000 doubles in 12 hours. Find growth rate $k$ and time to reach 200,000 bacteria.

An outdoor concert arena's attendance drops with snow. Analyze data and answer:
(a) Is a linear model appropriate? Yes/No (b) Find slope and $y$ -intercept: Attendance $=$ (Inches of Snow) + (c) Predict attendance for 9.1 inches of snow.

Complete the trigonometric table for $30^{\circ}$ and verify if " $45^{\circ}$ " in $\sin(\theta)$ is an error.

Identify the missing particle in the nuclear equation: $_{10}^{43} \mathrm{~K} \rightarrow{ }_{20}^{43} \mathrm{Ca}+?$

Identify the hyphen notation for the element with 15 electrons and 15 neutrons: 1. phosphorus-30 2. silicon-30 3. $\sin 0-60$ 4. vinospliomestal 5. flicrine-15 6. sulfur-3 7. oxyentistis

Explain your solution for $10 \times 4$ thousands using a place value chart.

What melide is formed when $^{50} \mathrm{Sr}$ undergoes $\beta$ decay?

Explain the pattern of zeros in the products of $6 \times 10^n$ for $n = 0, 1, 2, 3$ .

If $-3 \leq x \leq 10$ , find the interval for $-x$ . Explain the changes in inequality when multiplying by -1.

Match the graph to the inequality $x \geq -3$ .

Find the missing particle in the decay: ${ }_{84}^{218} \mathrm{Po} \rightarrow{ }_{2}^{4} \mathrm{He}+?$

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with $H_{0}$ : no difference, $H_{A}$ : difference. Test statistic is 12.32; confirm and find the $p$ -value.

A classmate claims the system $x=0, y=0, z=0$ has no solution. What is the mistake in their reasoning?