Math

Problem 40101

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

See Solution

Problem 40102

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.

See Solution

Problem 40103

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

See Solution

Problem 40104

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

See Solution

Problem 40105

Solve for $a$ in the equation $-5=\frac{a}{18}$ .

See Solution

Problem 40106

A group has 5 men and 7 women. 6 people are chosen.
a. How many ways to select 6 from 12? b. How many ways to select 6 women from 7? c. What is the probability all selected are women? a. Ways to select 6 from 12 is $\binom{12}{6}$ .

See Solution

Problem 40107

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

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Problem 40108

A group has 7 men and 6 women. Select 3 people. Find: a. Ways to choose 3 from 13. b. Ways to choose 3 women from 6. c. Probability all selected are women. a. The number of ways to select is $\binom{13}{3}$ .

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Problem 40109

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 40110

Calculate the length of the interval $[-6, 8]$ .

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Problem 40111

Solve for $m$ in the equation $\frac{m}{4}=-13$ .

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Problem 40112

Solve for $v$ in the equation $\frac{v}{7}=8$ .

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Problem 40113

Find the probabilities for the following scenarios with 6 comics (A, B, C, D, E, F): a. B first, b. F second & A fourth, c. order B, F, A, C, D, E, d. D or E fifth.

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Problem 40114

Solve for $x$ in the equation: $-17 = x - 15$ .

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Problem 40115

What is the probability of winning a lottery by matching 5 numbers from 1 to 43 and 1 from 1 to 34 with one ticket?

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Problem 40116

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 40117

On a number line, $A$ is at 5, $B$ at -10. If $C$ divides $AB$ in a $1:3$ ratio, find point $D$ on $BC$ that is $\frac{3}{8}$ of the way from $B$ to $C$ .

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Problem 40118

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 40119

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 40120

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 40121

A box has 12 transistors (5 defective). Find the probability for selecting 5: a. all defective, b. none defective.

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Problem 40122

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

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Problem 40123

A mechanic earns \$14/hr, with overtime at time-and-a-half. Find wages for 30, 40, 45, and 50 hours. New functions for 36 hrs and \$16/hr?

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Problem 40124

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

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Problem 40125

Find $x$ if $f(x) = x^{2} - 1$ and $f(x) = 99$ .

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Problem 40126

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 40127

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 40128

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

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Problem 40129

Macy earns \ $25 per lawn and \$10 per car. She wants at least \$120 in 7 hours. Find equations for lawns$ L $and cars$ C$.

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Problem 40130

In a lottery, players pick 4 numbers from 1 to 54 and 1 from 1 to 43. What is the probability of winning at least \$300?

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Problem 40131

Find the probability of selecting 2 Democrats and 2 Republicans from a committee of 4 chosen from 8 Democrats and 5 Republicans.

See Solution

Problem 40132

Find $x$ where $f(x) = 3$ .

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Problem 40133

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

See Solution

Problem 40134

Find the slope of the best fit line for clubhead speeds (mph) and distances (yards) from 20 games data.

See Solution

Problem 40135

Karen tests a bath fizzer weighing 5 ounces. It halves every minute. Find the equation $y=a(b)^{x}$ and weight after 3 minutes.

See Solution

Problem 40136

Find $x$ such that $f(x) = -3$ for the function $f(x) = |x|$ .

See Solution

Problem 40137

Find $f(2)$ and $f(5)$ for the function defined as $f(x)=2^{x}$ .

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Problem 40138

Antonio's county has a population of 66,500, decreasing by $4\%$ yearly. Model it with $y=a(b)^{x}$ and find $y$ in 10 years.

See Solution

Problem 40139

Dr. Powell gave Ruby 40 micrograms of medication. Model the remaining amount with $y=40(0.8)^{x}$ . How much is left after 4 hours?

See Solution

Problem 40140

Find the probability of drawing 3 clubs from a 52-card deck. Round to six decimal places.

See Solution

Problem 40141

Model Clover Hills' population with $y=a(b)^{x}$ , given it grew from 3,650 to 3,869 in 1 year. Predict after 4 years.

See Solution

Problem 40142

Find the probability that all 3 dealt cards are clubs from a 52-card deck.
$P(\text{all 3 cards are clubs}) = ?$

See Solution

Problem 40143

Find the probability of drawing 4 clubs from a 52-card deck. Round your answer to six decimal places.

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Problem 40144

Find $f(-4)$ using the function $f(x)=x^{2}-1$ given that $f(-2)=f(0)=f(1)=\;$ .

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Problem 40145

A hand has 5 cards from a 52-card deck. Find: a. Total 5-card hands, b. Heart flush hands, c. Probability of a heart flush.

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Problem 40146

Write an exponential equation $y=a(b)^{x}$ to model Lime County's declining population, starting with 711,500.

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Problem 40147

A steel rod of length $L_{0}=70 \mathrm{~cm}$ at $T_{0}=70^{\circ} \mathrm{C}$ expands. Find its length at $T=100^{\circ} \mathrm{C}$ . Also, find its length at $T=80^{\circ} \mathrm{C}$ if it was $85 \mathrm{in}$ at $T_{0}=170^{\circ} \mathrm{C}$ . Lastly, express $L$ as a function of $T$ and $\alpha$ for $L_{0}=50$ \mathrm{in} at $T_{0}=130^{\circ} \mathrm{C}$ .

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Problem 40148

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

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Problem 40149

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 40150

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

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Problem 40151

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

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Problem 40152

If lines $m$ and $n$ are parallel and $\angle 2 = 35^{\circ}$ , find $\angle 5$ . Choices: $145^{\circ}$ , $155^{\circ}$ , $180^{\circ}$ , $55^{\circ}$ .

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Problem 40153

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

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Problem 40154

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Problem 40155

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

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Problem 40156

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

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Problem 40157

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 40158

Solve for $x$ given that angle 4 is $4x - 6$ and angle 6 is $2x - 12$ .

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Problem 40159

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

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Problem 40160

Solve for $x$ if angle three is $6x + 16$ and angle seven is $2x + 2$ .

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Problem 40161

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

See Solution

Problem 40162

Solve the equation $2(x+3) + 3x = 16$ .

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Problem 40163

Solve the equation $3(x-4)+15=2(x+5)$ . What is the solution? A. Solution set is B. $\{x \mid x$ is a real number $\}$ C. $\varnothing$ .

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Problem 40164

Rationalize the denominator: (a) $\frac{24}{\sqrt{3}}$

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Problem 40165

Solve the equation $\frac{2 x}{x+4}-\frac{8}{x-4}=\frac{2 x^{2}+32}{x^{2}-16}$ . Is it an identity, conditional, or inconsistent?

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Problem 40166

Calculate $f(2)$ for the function $f(x)=x^{2}+3x-7$ .

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Problem 40167

Simplify the expression $\frac{4}{\sqrt{6}}$ .

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Problem 40168

Calculate $f(-1)$ for the function $f(x)=\frac{x^{2}-5}{x+3}$ .

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Problem 40169

Calculate $f(2)$ for the function $f(x)=\sqrt{x^{2}+3x}$ .

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Problem 40170

Simplify the expression $\frac{10 t^{2}-t}{5 t}$ .

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Problem 40171

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

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Problem 40172

Calculate $f(-9)$ for the function $f(x)=|x|-6$ .

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Problem 40173

Solve the equation $4 x^{2} = 7 x + 36$ by factoring. Provide the solution set.

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Problem 40174

Calculate $-f(x)$ for the function $f(x)=|x|-3$ .

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Problem 40175

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

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Problem 40176

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

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Problem 40177

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 40178

Find $h^{\prime}(-5)$ if $h(x)=f(x)-g(x)$ , given $f(-5)=8, f'(-5)=-2, g(-5)=3, g'(-5)=5$ .

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Problem 40179

Solve the system: $\frac{y}{4}=\frac{x-y}{2}$ and $3y-x=12$ .

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Problem 40180

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

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Problem 40181

Encik Amin simpan RM28,000 dengan faedah 3\% setahun, dikompaun setiap 3 bulan. Berapa jumlah simpanan pada akhir tahun $2022$ ?

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Problem 40182

Calculate the value of $X_{52.056+7.23}$ .

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Problem 40183

Find the product of matrices $Y=M X$ where $M=\begin{pmatrix}1 & -1 & 0 \\ -1 & 0 & 1 \\ 0 & 1 & -1\end{pmatrix}$ and $X=\begin{pmatrix}5 \\ -3 \\ 10\end{pmatrix}$ .

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Problem 40184

Lengkapkan urutan nombor Fibonacci: 5, 8, 13, 21, $\square$ , -

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Problem 40185

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

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Problem 40186

Find the matrix $C$ given $A=\begin{bmatrix}7 & -5 \\ 10 & 6\end{bmatrix}$ and $B=\begin{bmatrix}6 & 2 \\ -18 & 14\end{bmatrix}$ , where $C=-2A-B$ .

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Problem 40187

Find the integral of $\frac{1}{x^{2}-x+1}$ with respect to $x$ .

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Problem 40188

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

See Solution

Problem 40189

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

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Problem 40190

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 40191

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 40192

Find the value of the function $f(x)=4x-9$ at $x=3$ . What is $f(3)$ ?

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Problem 40193

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

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Problem 40194

Calculate $g(10)$ for the function $g(x) = 3(x-1)$ .

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Problem 40195

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

See Solution

Problem 40196

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

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Problem 40197

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

See Solution

Problem 40198

Simplify the expression: $\frac{18 w^{4} x^{9}}{14 w^{5} x^{5}}$ .

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Problem 40199

Calculate $\left(-4 a^{3} b^{2}\right)^{2} \cdot\left(3 a^{2} b\right)$ .

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Problem 40200

Simplify the expression: $(8 x^{3}-6 x^{4}+3)-(3 x^{3}-3+8 x^{4})$ .

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1 ...399 400 401 402 403 404 405 ...662

Math

Problem 40101

Find the missing particle in the decay: 84218Po→24He+?{ }_{84}^{218} \mathrm{Po} \rightarrow{ }_{2}^{4} \mathrm{He}+?84218​Po→24​He+?

Problem 40102

A survey of 825 California voters examines opinions on offshore drilling. Perform a chi-square test with H0H_{0}H0​: no difference, HAH_{A}HA​: difference. Test statistic is 12.32; confirm and find the ppp-value.

Problem 40103

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

Problem 40104

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

Problem 40105

Solve for aaa in the equation −5=a18-5=\frac{a}{18}−5=18a​.

Problem 40106

A group has 5 men and 7 women. 6 people are chosen. a. How many ways to select 6 from 12? b. How many ways to select 6 women from 7? c. What is the probability all selected are women? a. Ways to select 6 from 12 is (126)\binom{12}{6}(612​).

Problem 40107

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

Problem 40108

A group has 7 men and 6 women. Select 3 people. Find: a. Ways to choose 3 from 13. b. Ways to choose 3 women from 6. c. Probability all selected are women. a. The number of ways to select is (133)\binom{13}{3}(313​).

Problem 40109

Problem 40110

Calculate the length of the interval [−6,8][-6, 8][−6,8].

Problem 40111

Solve for mmm in the equation m4=−13\frac{m}{4}=-134m​=−13.

Problem 40112

Solve for vvv in the equation v7=8\frac{v}{7}=87v​=8.

Problem 40113

Find the probabilities for the following scenarios with 6 comics (A, B, C, D, E, F): a. B first, b. F second & A fourth, c. order B, F, A, C, D, E, d. D or E fifth.

Problem 40114

Solve for xxx in the equation: −17=x−15-17 = x - 15−17=x−15.

Problem 40115

What is the probability of winning a lottery by matching 5 numbers from 1 to 43 and 1 from 1 to 34 with one ticket?

Problem 40116

Problem 40117

On a number line, AAA is at 5, BBB at -10. If CCC divides ABABAB in a 1:31:31:3 ratio, find point DDD on BCBCBC that is 38\frac{3}{8}83​ of the way from BBB to CCC.

Problem 40118

Find the co-vertices of the ellipse given by (y−4)264+(x−2)24=1\frac{(y-4)^{2}}{64}+\frac{(x-2)^{2}}{4}=164(y−4)2​+4(x−2)2​=1.

Problem 40119

Find the value of mmm for the continuous piecewise function f(x)={mx−7 if x<−4x2+5x−3 if x≥−4f(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.f(x)={mx−7x2+5x−3​ if x<−4 if x≥−4​

Problem 40120

Find the ordered pair that satisfies the inequalities: 3x−5y≤153x - 5y \leq 153x−5y≤15 and 8x+5y>248x + 5y > 248x+5y>24. A) (0,3)(0,3)(0,3) B) (3,−3)(3,-3)(3,−3) C) (3,0)(3,0)(3,0) D) (3,3)(3,3)(3,3)

Problem 40121

A box has 12 transistors (5 defective). Find the probability for selecting 5: a. all defective, b. none defective.

Problem 40122

A mechanic earns \14/hour,$21forovertime.Find14/hour, \$21 for overtime. Find 14/hour,$21forovertime.FindW(30),, ,W(40),, ,W(45),and, and ,andW(50)$.

Problem 40123

A mechanic earns \$14/hr, with overtime at time-and-a-half. Find wages for 30, 40, 45, and 50 hours. New functions for 36 hrs and \$16/hr?

Problem 40124

A mechanic earns \14/hourregularand$21/hourovertime.Find14/hour regular and \$21/hour overtime. Find 14/hourregularand$21/hourovertime.FindW(30), W(40), W(45), W(50)$.

Problem 40125

Find xxx if f(x)=x2−1f(x) = x^{2} - 1f(x)=x2−1 and f(x)=99f(x) = 99f(x)=99.

Problem 40126

Problem 40127

A mechanic earns \14/hourregularand$21/hourovertime.Find14/hour regular and \$21/hour overtime. Find 14/hourregularand$21/hourovertime.FindW(30),, ,W(40),, ,W(45),, ,W(50)$ and new function for 36 hours.

Problem 40128

Find the value of the function f(x)=x3f(x) = x^{3}f(x)=x3 at x=5x = 5x=5.

Problem 40129

Macy earns \25perlawnand$10percar.Shewantsatleast$120in7hours.Findequationsforlawns25 per lawn and \$10 per car. She wants at least \$120 in 7 hours. Find equations for lawns 25perlawnand$10percar.Shewantsatleast$120in7hours.FindequationsforlawnsLandcars and cars andcarsC$.

Problem 40130

In a lottery, players pick 4 numbers from 1 to 54 and 1 from 1 to 43. What is the probability of winning at least \$300?

Problem 40131

Find the probability of selecting 2 Democrats and 2 Republicans from a committee of 4 chosen from 8 Democrats and 5 Republicans.

Problem 40132

Find xxx where f(x)=3f(x) = 3f(x)=3.

Problem 40133

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

Problem 40134

Find the slope of the best fit line for clubhead speeds (mph) and distances (yards) from 20 games data.

Problem 40135

Karen tests a bath fizzer weighing 5 ounces. It halves every minute. Find the equation y=a(b)xy=a(b)^{x}y=a(b)x and weight after 3 minutes.

Problem 40136

Find xxx such that f(x)=−3f(x) = -3f(x)=−3 for the function f(x)=∣x∣f(x) = |x|f(x)=∣x∣.

Problem 40137

Find f(2)f(2)f(2) and f(5)f(5)f(5) for the function defined as f(x)=2xf(x)=2^{x}f(x)=2x.

Problem 40138

Antonio's county has a population of 66,500, decreasing by 4%4\%4% yearly. Model it with y=a(b)xy=a(b)^{x}y=a(b)x and find yyy in 10 years.

Problem 40139

Dr. Powell gave Ruby 40 micrograms of medication. Model the remaining amount with y=40(0.8)xy=40(0.8)^{x}y=40(0.8)x. How much is left after 4 hours?

Problem 40140

Find the probability of drawing 3 clubs from a 52-card deck. Round to six decimal places.

Problem 40141

Model Clover Hills' population with y=a(b)xy=a(b)^{x}y=a(b)x, given it grew from 3,650 to 3,869 in 1 year. Predict after 4 years.

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?

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

Solve for $a$ in the equation $-5=\frac{a}{18}$ .

A group has 5 men and 7 women. 6 people are chosen.
a. How many ways to select 6 from 12? b. How many ways to select 6 women from 7? c. What is the probability all selected are women? a. Ways to select 6 from 12 is $\binom{12}{6}$ .

A group has 7 men and 6 women. Select 3 people. Find: a. Ways to choose 3 from 13. b. Ways to choose 3 women from 6. c. Probability all selected are women. a. The number of ways to select is $\binom{13}{3}$ .

Calculate the length of the interval $[-6, 8]$ .

Solve for $m$ in the equation $\frac{m}{4}=-13$ .

Solve for $v$ in the equation $\frac{v}{7}=8$ .

Solve for $x$ in the equation: $-17 = x - 15$ .

On a number line, $A$ is at 5, $B$ at -10. If $C$ divides $AB$ in a $1:3$ ratio, find point $D$ on $BC$ that is $\frac{3}{8}$ of the way from $B$ to $C$ .

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

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

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) $(3,3)$

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

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

Find $x$ if $f(x) = x^{2} - 1$ and $f(x) = 99$ .

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.

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

Macy earns \ $25 per lawn and \$10 per car. She wants at least \$120 in 7 hours. Find equations for lawns$ L $and cars$ C$.

Find $x$ where $f(x) = 3$ .

Karen tests a bath fizzer weighing 5 ounces. It halves every minute. Find the equation $y=a(b)^{x}$ and weight after 3 minutes.

Find $x$ such that $f(x) = -3$ for the function $f(x) = |x|$ .

Find $f(2)$ and $f(5)$ for the function defined as $f(x)=2^{x}$ .

Antonio's county has a population of 66,500, decreasing by $4\%$ yearly. Model it with $y=a(b)^{x}$ and find $y$ in 10 years.

Dr. Powell gave Ruby 40 micrograms of medication. Model the remaining amount with $y=40(0.8)^{x}$ . How much is left after 4 hours?

Model Clover Hills' population with $y=a(b)^{x}$ , given it grew from 3,650 to 3,869 in 1 year. Predict after 4 years.

Find the probability that all 3 dealt cards are clubs from a 52-card deck.
$P(\text{all 3 cards are clubs}) = ?$

Find $f(-4)$ using the function $f(x)=x^{2}-1$ given that $f(-2)=f(0)=f(1)=\;$ .

Write an exponential equation $y=a(b)^{x}$ to model Lime County's declining population, starting with 711,500.

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.

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

If lines $m$ and $n$ are parallel and $\angle 2 = 35^{\circ}$ , find $\angle 5$ . Choices: $145^{\circ}$ , $155^{\circ}$ , $180^{\circ}$ , $55^{\circ}$ .

Solve for $x$ given that angle 4 is $4x - 6$ and angle 6 is $2x - 12$ .

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

Solve for $x$ if angle three is $6x + 16$ and angle seven is $2x + 2$ .

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

Solve the equation $2(x+3) + 3x = 16$ .

Solve the equation $3(x-4)+15=2(x+5)$ . What is the solution? A. Solution set is B. $\{x \mid x$ is a real number $\}$ C. $\varnothing$ .

Rationalize the denominator: (a) $\frac{24}{\sqrt{3}}$

Solve the equation $\frac{2 x}{x+4}-\frac{8}{x-4}=\frac{2 x^{2}+32}{x^{2}-16}$ . Is it an identity, conditional, or inconsistent?

Calculate $f(2)$ for the function $f(x)=x^{2}+3x-7$ .

Simplify the expression $\frac{4}{\sqrt{6}}$ .

Calculate $f(-1)$ for the function $f(x)=\frac{x^{2}-5}{x+3}$ .

Calculate $f(2)$ for the function $f(x)=\sqrt{x^{2}+3x}$ .

Simplify the expression $\frac{10 t^{2}-t}{5 t}$ .

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

Calculate $f(-9)$ for the function $f(x)=|x|-6$ .

Solve the equation $4 x^{2} = 7 x + 36$ by factoring. Provide the solution set.

Calculate $-f(x)$ for the function $f(x)=|x|-3$ .