Analyze

Problem 10201

Create a dot plot in Excel for these household children counts: 0, 2, 2, 0, 1, 4, 1, 2, 0, 1, 2, 1, 1, 6, 1, 0, 3, 2, 1. Find the median and mode.

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Problem 10202

Create a dot plot in Excel for the data: $0.25, 0.5, 0.25, 0.025, 1, 0.25, 0.5, 0.25, 0.25, 1, 1.25, 0.25, 0.75, 1, 0.25, 0.25, 1.25, 0.25, 1, 0.5, 0.5, 1.75, 2, 1, 1$ . Find the median and mode.

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Problem 10203

Create a dot plot in Excel for the data: 12, 3, 4, 8, 4, 4, 5, 5, 11, 8, 3, 3, 12, 5, 5, 10, 8, 10, 6, 6, 6, 6, 2, 2, 16, 8, 8. Interpret the plot.

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Problem 10204

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

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Problem 10205

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

See Solution

Problem 10206

Create a dot plot in Excel for the data: 0, 2, 2, 0, 1, 4, 1, 2, 0, 1, 2, 1, 1, 1, 6, 1, 0, 3, 2, 1. Find the median and mode.

See Solution

Problem 10207

Analyze the function $f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}$ . Is it constant, increasing, or decreasing returns to scale?

See Solution

Problem 10208

Does Lagrange's mean value theorem apply to $f(x)=x^{1/3}$ on $[-1, 1]$ ? What can we conclude?

See Solution

Problem 10209

Express $1058_{10}$ in expanded form and identify the place value of the digit '1' in 105810.

See Solution

Problem 10210

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+7$ . Find max height and distance.

See Solution

Problem 10211

Arrange $2^{16}, 4^{7}, 8^{5}$ , and $64^{3}$ in ascending order with " $<$ ".

See Solution

Problem 10212

Find the atom counts in the formula for aluminum sulfate $=\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}$ .

See Solution

Problem 10213

Graph the solution to the inequality $0.3(x-4)>-0.3$ on a number line.

See Solution

Problem 10214

Amy types 38 words/min. She typed 1,450 words. Which inequality finds $x$ , minutes to reach over 4,000 words?

See Solution

Problem 10215

Danny drives 36 miles, then must drive at 60 mph. Solve $60t + 36 \geq 300$ to find how long he needs. Which is true?

See Solution

Problem 10216

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=x^{2}-7x+2$ , where $h \neq 0$ .

See Solution

Problem 10217

Are $x$ and $y$ proportional? Answer Yes or No for the pairs: (2, 4), (4, 2), (6, 1), (8, $\frac{1}{2}$ ), (10, $\frac{1}{4}$ ).

See Solution

Problem 10218

Find the probability of spinning an even number and flipping heads with a spinner and a coin.

See Solution

Problem 10219

Is the sample of every 10th person entering the park biased or unbiased for estimating opinions on park remodeling?

See Solution

Problem 10220

Name a pair of angles that add up to 180 degrees.

See Solution

Problem 10221

Determine if the quadratic function $f(x)=3 x^{2}+12 x-7$ has a max or min value, then find that value.

See Solution

Problem 10222

Find the vertex coordinates of the parabola defined by $f(x)=-4(x+2)^{2}+3$ . Provide as an ordered pair.

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Problem 10223

Determine if the quadratic function $f(x)=3x^{2}+18x-9$ has a maximum or minimum value and find that value.

See Solution

Problem 10224

Identify if the function $f(x)=-3 x^{2}+6 x$ has a max or min value, then find that value.

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Problem 10225

In triangle $ABC$ , with points $D$ on $AB$ and $E$ on $BC$ , find angles given $\angle ABC=28^{\circ}$ , $\angle BED=38^{\circ}$ . (a) Find $\angle ACD$ . (b) Express $\angle DFE$ in terms of $\theta$ where $\angle CAE=\theta$ .

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Problem 10226

Sketch the graph of the quadratic function $f(x)=(x+2)^{2}-9$ . Find the axis of symmetry, domain, and range.

See Solution

Problem 10227

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

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Problem 10228

Sketch the graph of the quadratic $f(x)=(x-2)^{2}-9$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

See Solution

Problem 10229

Find the probability that a randomly chosen student is in chorus given they are not in photography, from 60 students.

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Problem 10230

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range.

See Solution

Problem 10231

Sketch the graph of $f(x)=(x-2)^{2}+4$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

See Solution

Problem 10232

Find the probability that a randomly chosen employee has at least one child given they are married: $\mathrm{P}(\text{child} | \text{married})$ .

See Solution

Problem 10233

What is the probability a student has a part-time job given they have a cell phone, if $P(A) = 0.8$ , $P(B) = 0.45$ , and $P(A \cap B) = 0.3$ ?

See Solution

Problem 10234

Sketch the graph of $f(x)=3(x+1)^{2}-1$ , find the axis of symmetry, domain, and range. Use vertex and intercepts.

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Problem 10235

What operation isolates $x$ in $8 x=72$ ? Options: A. +8 B. $\times \frac{1}{8}$ C. ÷8 D. ÷72 E. ÷ $8x$ F. $\times$ 8 G. - $8x$ . Also, solve $8x=72$ : $x=$ help (numbers).

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Problem 10236

Solve $\frac{x+7}{5}=15$ by stating the order of two operations. Then, find $x$ . What is $x=\square$ ?

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Problem 10237

For the function $f(x)=x^{2}-4 x$ , find the x-intercepts, y-intercept, and graph it.

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Problem 10238

Which table shows values of $g$ with $\lim_{x \to 7} g(x) = 6$ ? Options: (A), (B), (C), (D).

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Problem 10239

What does $\lim _{x \rightarrow 3} f(x)=5$ mean? Choose the correct interpretation: (A), (B), (C), or (D).

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Problem 10240

A car's distance is $s(t)$ in feet after $t$ seconds. Estimate its velocity at $t=6$ using options (A) to (D).

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Problem 10241

Find $\lim _{x \rightarrow 2^{+}} f(x)$ for the piecewise function: $f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}$ .

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Problem 10242

Given the table of values for $f(x)$ at $x$ near 4, what limit conclusion is supported? (A) $\lim _{x \rightarrow 4} f(x)=6$ , (B) $\lim _{x \rightarrow 4} f(x)=7$ , (C) $\lim _{x \rightarrow 4^{-}} f(x)=6$ and $\lim _{x \rightarrow 4^{+}} f(x)=7$ , (D) $\lim _{x \rightarrow 4^{-}} f(x)=7$ and $\lim _{x \rightarrow 4^{+}} f(x)=6$ .

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Problem 10243

Given the table of $x$ and $f(x)$ values, which limit conclusion about $f(x)$ as $x$ approaches 6 is correct? (A) $\lim _{x \rightarrow 6} f(x)=0$ (B) $\lim _{x \rightarrow 6} f(x)=6$ (C) $\lim _{x \rightarrow 6} f(x)=10$ (D) $\lim _{x \rightarrow 6} f(x)$ does not exist.

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Problem 10244

Given the table values of $f(x)$ for $x$ near 4, which limit conclusion is correct? (A) $\lim _{x \rightarrow 4} f(x)=6$ (B) $\lim _{x \rightarrow 4} f(x)=7$ (C) $\lim _{x \rightarrow 4^{-}} f(x)=6$ and $\lim _{x \rightarrow 4^{+}} f(x)=7$ (D) $\lim _{x \rightarrow 4^{-}} f(x)=7$ and $\lim _{x \rightarrow 4^{+}} f(x)=6$

See Solution

Problem 10245

Find $\lim _{x \rightarrow 2}(h(x)(5 f(x)+g(x)))$ given $f(2)=3$ , $g(2)=-6$ , $h(2)=-3$ , limits at $x=2$ .

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Problem 10246

Find the probability $\mathrm{P}$ (checked bags | final destination) using the given passenger data.

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Problem 10247

Find $\lim _{x \rightarrow 2} f(x)$ for the function $f(x)=\frac{x^{2}-4}{x^{2}+x-6}$ . Choices: (A) 0, (B) $\frac{2}{3}$ , (C) $\frac{4}{5}$ , (D) nonexistent.

See Solution

Problem 10248

Find the value of $k$ such that $\lim _{x \rightarrow 2} f(x)=3$ for $f(x)=\frac{(x-2)(x^{2}-k^{2})}{(x^{2}-4)(x-k)}$ .

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Problem 10249

Find $\lim _{x \rightarrow \frac{\pi}{4}} g(x)$ for $g(x)=\frac{\cos x-\sin x}{1-2 \sin ^{2} x}$ . Options: (A) 0 (B) $\frac{1}{\sqrt{2}}$ (C) $\sqrt{2}$ (D) Limit does not exist.

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Problem 10250

Find $\lim _{x \rightarrow 1} f(x)$ for $f(x)=\frac{x^{2}-1}{\sqrt{x}-1}$ . Choices: (A) 4, (B) 2, (C) 0, (D) nonexistent.

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Problem 10251

Identify the graph of $f(x)=\frac{1}{3} x$ and its parent function. Describe the transformation.

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Problem 10252

Find the probability that a randomly chosen gym member does not attend classes, given they track their fitness. Use $P(\text{No Classes} | \text{Track Fitness})$ .

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Problem 10253

A plumber has 19 handles for 9 sinks. Each sink needs 2 handles (hot and cold). Does he have enough?

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Problem 10254

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

See Solution

Problem 10255

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

See Solution

Problem 10256

For what number of checks per month does the Simple Checking plan ( $4 + 0.15x$ ) cost less than the No Frills plan ( $0.35x$ )?

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Problem 10257

Laurie's candy dispenser dispenses candy tripling for each pound per square inch of pressure. Is this a relation, function, both, or neither?

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Problem 10258

Which set does the number $\sqrt{23}$ belong to: irrational, integers, rational, or whole numbers?

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Problem 10259

Compare $\sqrt{11}$ and 3.7 using $<, >$ , or $=$ .

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Problem 10260

Calculate $18 - 0$ . What is the result?

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Problem 10261

Find the production level $x$ where revenue $R=26x$ is less than cost $C=91,000+19x$ . What is $x$ ?

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Problem 10262

Find the production level $x$ where revenue $R=29x$ is less than cost $C=90,000+19x$ . When does R < C?

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Problem 10263

Nicole and Chris each deposit \$90,000 at 3\% interest. Calculate their interest for the first three years and compare.

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Problem 10264

Nicole and Chris each deposit \$20,000 at 2\% interest. Find their earnings for 3 years and compare.

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Problem 10265

Ian's diet has $30\%$ Fat and $50\%$ Carbs in a total of $3,000 \mathrm{kcal}$ . How many kcal is he getting from Protein? a) $400 \mathrm{kcal}$ b) $500 \mathrm{kcal}$ c) $600 \mathrm{kcal}$ d) $700 \mathrm{kcal}$

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Problem 10266

Laura and Eric each deposit \$70,000 at 6\% interest. Calculate their yearly interest for 3 years and compare.

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Problem 10267

Debra deposits \$30,000 at 4\% compounded annually, while Dan uses simple interest. Calculate their interest for 3 years and compare.

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Problem 10268

Debra and Dan each deposit \$30,000 at 4\% interest. Calculate their yearly interest for 3 years and compare.

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Problem 10269

Create the cumulative frequency distribution for the ages of Best Actresses when they won awards:
Ages: $20-29$ (29), $30-39$ (33), $40-49$ (15), $50-59$ (2), $60-69$ (4), $70-79$ (1), $80-89$ (2).

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Problem 10270

Amy deposits \$60,000 at 3\% annual compound interest, Bill at 3\% simple interest. Calculate their interest for 3 years.

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Problem 10271

Create a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

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Problem 10272

Sketch the graph for the constraints: $x \geq 50$ , $y \geq 60$ , $x+y \leq 200$ , $4x+5y \leq 900$ . Find the feasible region and minimize $P=0.3x+0.5y$ .

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Problem 10273

Is Frank's 1,200 calorie diet (20\% carbs) providing at least 130 grams of carbs? Calculate carbs in calories.

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Problem 10274

Calculate the relative frequency of plane crash causes: pilot error, other human error, weather, mechanical problems, and sabotage. Round to one decimal place.

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Problem 10275

What type of graph should a researcher use to compare logo recognition levels: scatter, line, pie, or bar graph?

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Problem 10276

Find the limit of $\frac{f(x+h)-f(x)}{h}$ for $f(x)=x^{2}+1$ as $h \neq 0$ .

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Problem 10277

Identify which numbers in the set $A=\{-6, \frac{1}{7}, -8.333\ldots, 3\pi, 2, 8\}$ are natural, integer, rational, irrational, and real numbers.

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Problem 10278

Name a point that is not in the same plane as points A, B, and C.

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Problem 10279

How many runners are aged 40 or older based on the relative frequency of ages: $40-49$ (40\%), $50-59$ (12\%), $60-69$ (8\%)?

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Problem 10280

What percent of math/science majors are seniors given 330 seniors out of 260+310+200+330?

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Problem 10281

Identify the types of numbers in the set $C=\{0,1, \frac{1}{9}, \frac{1}{12}, \frac{1}{15}\}$ .

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Problem 10282

Identify the quantitative variable among: monthly electric bill, square footage, monthly gas bill, or all of the above.

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Problem 10283

Identify which numbers in the set $E=\{\sqrt{14}, \pi, \sqrt{14}+1, \pi+\frac{1}{14}\}$ are (a) Natural, (b) Integers, (c) Rational, (d) Irrational, (e) Real.

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Problem 10284

What is the experimental probability of rolling a 4 based on Greg's tosses: 1(7), 2(5), 3(6), 4(4), 5(8), 6(6)?

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Problem 10285

Bestimmen Sie die Hochpunkt-Koordinaten der Funktion $f(x)=x^{4}-\frac{4}{3} x^{3}-4 x^{2}$ .

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Problem 10286

Find $f[g(x)]$ and $g[f(x)]$ for $f(x)=\frac{4}{x+3}$ and $g(x)=x^{2}-3$ .

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Problem 10287

Create a relative frequency distribution for births: $54, 65, 70, 59, 55, 45, 52$ . Do they occur equally weekly?

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Problem 10288

Determine the type of triangle formed by sides 60 cm, 100 cm, and 40 cm: unique, similar, or none?

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Problem 10289

What is the probability of a patient needing treatment for a broken bone during ski season if there are 160 broken bones out of 260 total injuries?

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Problem 10290

A dice is rolled 100 times. Find the range, mode, and median from the frequencies: 16, 25, 17, 19, 8, 15. Also, estimate the mean time from: 2, 8, 12, 16, 12 in intervals (10-20, 20-25, 25-30, 30-50, 50-80).

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Problem 10291

Juego de dados: Tira 3 dados de 4 caras. Gana un punto si suma 7 o 10, pierde si suma 3, 4, 5 o 12. Responde las preguntas sobre probabilidades.

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Problem 10292

What percent of the 200 freshmen voted for the change or had no opinion? Freshmen: For 20, Against 100, No Opinion 80.

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Problem 10293

50 students answered a math question. Given the time intervals and frequencies, estimate the mean time taken. Use intervals: $10<t \leqslant 20$ , $20<t \leqslant 25$ , $25<t \leqslant 30$ , $30<t \leqslant 50$ , $50<t \leqslant 80$ . Frequencies: 2, 8, 12, 16, 12.

See Solution

Problem 10294

Determine if $-7$ is less than, greater than, or equal to $-8$ : $-7 ? -8$

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Problem 10295

Replace the question mark with $<,>$ , or $=$ : $\sqrt{37} ? 6.08$

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Problem 10296

Replace the question mark with $<,>$ , or $=$ for the equation: $\frac{11}{4} ? 2.75$ .

See Solution

Problem 10297

Replace the question mark with $<$ , $>$ , or $=$ in the equation: $\frac{11}{4} ? 2.75$

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Problem 10298

What is the probability of moving forward an even number of spaces when spinning a pointer and rolling a number cube?

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Problem 10299

Is $\frac{4}{7}$ less than, greater than, or equal to 0.57?

See Solution

Problem 10300

Create a frequency distribution for 100 earthquake magnitudes (rounded to 3 decimal places) using a 0.5 class width, starting at 0.1. Check for normality.

See Solution

1 ...100 101 102 103 104 105 106 ...160

Analyze

Problem 10201

Create a dot plot in Excel for these household children counts: 0, 2, 2, 0, 1, 4, 1, 2, 0, 1, 2, 1, 1, 6, 1, 0, 3, 2, 1. Find the median and mode.

Problem 10202

Problem 10203

Create a dot plot in Excel for the data: 12, 3, 4, 8, 4, 4, 5, 5, 11, 8, 3, 3, 12, 5, 5, 10, 8, 10, 6, 6, 6, 6, 2, 2, 16, 8, 8. Interpret the plot.

Problem 10204

Graph the hyperbola y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1 and determine its asymptotes.

Problem 10205

Determine the transverse and conjugate axes of the hyperbola y216−x2=1\frac{y^{2}}{16}-x^{2}=116y2​−x2=1 and sketch its graph.

Problem 10206

Create a dot plot in Excel for the data: 0, 2, 2, 0, 1, 4, 1, 2, 0, 1, 2, 1, 1, 1, 6, 1, 0, 3, 2, 1. Find the median and mode.

Problem 10207

Analyze the function f(x1,x2)=x12x22f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}f(x1​,x2​)=x12​x22​. Is it constant, increasing, or decreasing returns to scale?

Problem 10208

Does Lagrange's mean value theorem apply to f(x)=x1/3f(x)=x^{1/3}f(x)=x1/3 on [−1,1][-1, 1][−1,1]? What can we conclude?

Problem 10209

Express 1058101058_{10}105810​ in expanded form and identify the place value of the digit '1' in 105810.

Problem 10210

A ball is thrown from 7 feet high. Its height is modeled by f(x)=−0.2x2+2.1x+7f(x)=-0.2 x^{2}+2.1 x+7f(x)=−0.2x2+2.1x+7. Find max height and distance.

Problem 10211

Arrange 216,47,852^{16}, 4^{7}, 8^{5}216,47,85, and 64364^{3}643 in ascending order with "<<<".

Problem 10212

Find the atom counts in the formula for aluminum sulfate =Al2(SO4)3=\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}=Al2​(SO4​)3​.

Problem 10213

Graph the solution to the inequality 0.3(x−4)>−0.30.3(x-4)>-0.30.3(x−4)>−0.3 on a number line.

Problem 10214

Amy types 38 words/min. She typed 1,450 words. Which inequality finds xxx, minutes to reach over 4,000 words?

Problem 10215

Danny drives 36 miles, then must drive at 60 mph. Solve 60t+36≥30060t + 36 \geq 30060t+36≥300 to find how long he needs. Which is true?

Problem 10216

Find the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ for the function f(x)=x2−7x+2f(x)=x^{2}-7x+2f(x)=x2−7x+2, where h≠0h \neq 0h=0.

Problem 10217

Are xxx and yyy proportional? Answer Yes or No for the pairs: (2, 4), (4, 2), (6, 1), (8, 12\frac{1}{2}21​), (10, 14\frac{1}{4}41​).

Problem 10218

Find the probability of spinning an even number and flipping heads with a spinner and a coin.

Problem 10219

Is the sample of every 10th person entering the park biased or unbiased for estimating opinions on park remodeling?

Problem 10220

Name a pair of angles that add up to 180 degrees.

Problem 10221

Determine if the quadratic function f(x)=3x2+12x−7f(x)=3 x^{2}+12 x-7f(x)=3x2+12x−7 has a max or min value, then find that value.

Problem 10222

Find the vertex coordinates of the parabola defined by f(x)=−4(x+2)2+3f(x)=-4(x+2)^{2}+3f(x)=−4(x+2)2+3. Provide as an ordered pair.

Problem 10223

Determine if the quadratic function f(x)=3x2+18x−9f(x)=3x^{2}+18x-9f(x)=3x2+18x−9 has a maximum or minimum value and find that value.

Problem 10224

Identify if the function f(x)=−3x2+6xf(x)=-3 x^{2}+6 xf(x)=−3x2+6x has a max or min value, then find that value.

Problem 10225

Problem 10226

Sketch the graph of the quadratic function f(x)=(x+2)2−9f(x)=(x+2)^{2}-9f(x)=(x+2)2−9. Find the axis of symmetry, domain, and range.

Problem 10227

Sketch the graph of the quadratic function f(x)=(x+1)2−9f(x)=(x+1)^{2}-9f(x)=(x+1)2−9. Find the axis of symmetry, domain, and range.

Problem 10228

Sketch the graph of the quadratic f(x)=(x−2)2−9f(x)=(x-2)^{2}-9f(x)=(x−2)2−9 using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Problem 10229

Find the probability that a randomly chosen student is in chorus given they are not in photography, from 60 students.

Problem 10230

Sketch the graph of f(x)=(x−4)2−9f(x)=(x-4)^{2}-9f(x)=(x−4)2−9. Find the axis of symmetry, domain, and range.

Problem 10231

Sketch the graph of f(x)=(x−2)2+4f(x)=(x-2)^{2}+4f(x)=(x−2)2+4 using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Problem 10232

Find the probability that a randomly chosen employee has at least one child given they are married: P(child∣married)\mathrm{P}(\text{child} | \text{married})P(child∣married).

Problem 10233

What is the probability a student has a part-time job given they have a cell phone, if P(A)=0.8P(A) = 0.8P(A)=0.8, P(B)=0.45P(B) = 0.45P(B)=0.45, and P(A∩B)=0.3P(A \cap B) = 0.3P(A∩B)=0.3?

Problem 10234

Sketch the graph of f(x)=3(x+1)2−1f(x)=3(x+1)^{2}-1f(x)=3(x+1)2−1, find the axis of symmetry, domain, and range. Use vertex and intercepts.

Problem 10235

What operation isolates xxx in 8x=728 x=728x=72? Options: A. +8 B. ×18\times \frac{1}{8}×81​ C. ÷8 D. ÷72 E. ÷8x8x8x F. ×\times×8 G. -8x8x8x. Also, solve 8x=728x=728x=72: x=x=x= help (numbers).

Problem 10236

Solve x+75=15\frac{x+7}{5}=155x+7​=15 by stating the order of two operations. Then, find xxx. What is x=□x=\squarex=□?

Problem 10237

For the function f(x)=x2−4xf(x)=x^{2}-4 xf(x)=x2−4x, find the x-intercepts, y-intercept, and graph it.

Problem 10238

Which table shows values of ggg with lim⁡x→7g(x)=6\lim_{x \to 7} g(x) = 6limx→7​g(x)=6? Options: (A), (B), (C), (D).

Problem 10239

What does lim⁡x→3f(x)=5\lim _{x \rightarrow 3} f(x)=5limx→3​f(x)=5 mean? Choose the correct interpretation: (A), (B), (C), or (D).

Problem 10240

A car's distance is s(t)s(t)s(t) in feet after ttt seconds. Estimate its velocity at t=6t=6t=6 using options (A) to (D).

Problem 10241

Graph the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and determine its asymptotes.

Determine the transverse and conjugate axes of the hyperbola $\frac{y^{2}}{16}-x^{2}=1$ and sketch its graph.

Analyze the function $f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}$ . Is it constant, increasing, or decreasing returns to scale?

Does Lagrange's mean value theorem apply to $f(x)=x^{1/3}$ on $[-1, 1]$ ? What can we conclude?

Express $1058_{10}$ in expanded form and identify the place value of the digit '1' in 105810.

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+7$ . Find max height and distance.

Arrange $2^{16}, 4^{7}, 8^{5}$ , and $64^{3}$ in ascending order with " $<$ ".

Find the atom counts in the formula for aluminum sulfate $=\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}$ .

Graph the solution to the inequality $0.3(x-4)>-0.3$ on a number line.

Amy types 38 words/min. She typed 1,450 words. Which inequality finds $x$ , minutes to reach over 4,000 words?

Danny drives 36 miles, then must drive at 60 mph. Solve $60t + 36 \geq 300$ to find how long he needs. Which is true?

Find the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the function $f(x)=x^{2}-7x+2$ , where $h \neq 0$ .

Are $x$ and $y$ proportional? Answer Yes or No for the pairs: (2, 4), (4, 2), (6, 1), (8, $\frac{1}{2}$ ), (10, $\frac{1}{4}$ ).

Determine if the quadratic function $f(x)=3 x^{2}+12 x-7$ has a max or min value, then find that value.

Find the vertex coordinates of the parabola defined by $f(x)=-4(x+2)^{2}+3$ . Provide as an ordered pair.

Determine if the quadratic function $f(x)=3x^{2}+18x-9$ has a maximum or minimum value and find that value.

Identify if the function $f(x)=-3 x^{2}+6 x$ has a max or min value, then find that value.

Sketch the graph of the quadratic function $f(x)=(x+2)^{2}-9$ . Find the axis of symmetry, domain, and range.

Sketch the graph of the quadratic function $f(x)=(x+1)^{2}-9$ . Find the axis of symmetry, domain, and range.

Sketch the graph of the quadratic $f(x)=(x-2)^{2}-9$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Sketch the graph of $f(x)=(x-4)^{2}-9$ . Find the axis of symmetry, domain, and range.

Sketch the graph of $f(x)=(x-2)^{2}+4$ using its vertex and intercepts. Find the axis of symmetry, domain, and range.

Find the probability that a randomly chosen employee has at least one child given they are married: $\mathrm{P}(\text{child} | \text{married})$ .

What is the probability a student has a part-time job given they have a cell phone, if $P(A) = 0.8$ , $P(B) = 0.45$ , and $P(A \cap B) = 0.3$ ?

Sketch the graph of $f(x)=3(x+1)^{2}-1$ , find the axis of symmetry, domain, and range. Use vertex and intercepts.

What operation isolates $x$ in $8 x=72$ ? Options: A. +8 B. $\times \frac{1}{8}$ C. ÷8 D. ÷72 E. ÷ $8x$ F. $\times$ 8 G. - $8x$ . Also, solve $8x=72$ : $x=$ help (numbers).

Solve $\frac{x+7}{5}=15$ by stating the order of two operations. Then, find $x$ . What is $x=\square$ ?

For the function $f(x)=x^{2}-4 x$ , find the x-intercepts, y-intercept, and graph it.

Which table shows values of $g$ with $\lim_{x \to 7} g(x) = 6$ ? Options: (A), (B), (C), (D).

What does $\lim _{x \rightarrow 3} f(x)=5$ mean? Choose the correct interpretation: (A), (B), (C), or (D).

A car's distance is $s(t)$ in feet after $t$ seconds. Estimate its velocity at $t=6$ using options (A) to (D).

Find $\lim _{x \rightarrow 2^{+}} f(x)$ for the piecewise function: $f(x)=\{5x-3 \text{ if } x<2, 9 \text{ if } x=2, 4x+3 \text{ if } x>2\}$ .

Find $\lim _{x \rightarrow 2}(h(x)(5 f(x)+g(x)))$ given $f(2)=3$ , $g(2)=-6$ , $h(2)=-3$ , limits at $x=2$ .

Find the probability $\mathrm{P}$ (checked bags | final destination) using the given passenger data.

Find $\lim _{x \rightarrow 2} f(x)$ for the function $f(x)=\frac{x^{2}-4}{x^{2}+x-6}$ . Choices: (A) 0, (B) $\frac{2}{3}$ , (C) $\frac{4}{5}$ , (D) nonexistent.

Find the value of $k$ such that $\lim _{x \rightarrow 2} f(x)=3$ for $f(x)=\frac{(x-2)(x^{2}-k^{2})}{(x^{2}-4)(x-k)}$ .

Find $\lim _{x \rightarrow \frac{\pi}{4}} g(x)$ for $g(x)=\frac{\cos x-\sin x}{1-2 \sin ^{2} x}$ . Options: (A) 0 (B) $\frac{1}{\sqrt{2}}$ (C) $\sqrt{2}$ (D) Limit does not exist.

Find $\lim _{x \rightarrow 1} f(x)$ for $f(x)=\frac{x^{2}-1}{\sqrt{x}-1}$ . Choices: (A) 4, (B) 2, (C) 0, (D) nonexistent.

Identify the graph of $f(x)=\frac{1}{3} x$ and its parent function. Describe the transformation.

Find the probability that a randomly chosen gym member does not attend classes, given they track their fitness. Use $P(\text{No Classes} | \text{Track Fitness})$ .

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

Which function has a horizontal asymptote at 4? A. $f(x)=2(3)^{x}+4$ B. $f(x)=2 x-4$ C. $f(x)=3(2)^{x}-4$ D. $f(x)=-3 x+4$

For what number of checks per month does the Simple Checking plan ( $4 + 0.15x$ ) cost less than the No Frills plan ( $0.35x$ )?

Which set does the number $\sqrt{23}$ belong to: irrational, integers, rational, or whole numbers?

Compare $\sqrt{11}$ and 3.7 using $<, >$ , or $=$ .

Calculate $18 - 0$ . What is the result?

Find the production level $x$ where revenue $R=26x$ is less than cost $C=91,000+19x$ . What is $x$ ?

Find the production level $x$ where revenue $R=29x$ is less than cost $C=90,000+19x$ . When does R < C?

Ian's diet has $30\%$ Fat and $50\%$ Carbs in a total of $3,000 \mathrm{kcal}$ . How many kcal is he getting from Protein? a) $400 \mathrm{kcal}$ b) $500 \mathrm{kcal}$ c) $600 \mathrm{kcal}$ d) $700 \mathrm{kcal}$

Create the cumulative frequency distribution for the ages of Best Actresses when they won awards:
Ages: $20-29$ (29), $30-39$ (33), $40-49$ (15), $50-59$ (2), $60-69$ (4), $70-79$ (1), $80-89$ (2).

Create a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

Sketch the graph for the constraints: $x \geq 50$ , $y \geq 60$ , $x+y \leq 200$ , $4x+5y \leq 900$ . Find the feasible region and minimize $P=0.3x+0.5y$ .