Math

Problem 2201

Convert 168 km to miles using unit ratios.

See Solution

Problem 2202

Find the reciprocal of -8.

See Solution

Problem 2203

Write the equation of a cosine function with range $[2,10]$ , period $\frac{2\pi}{3}$ , and midline $-2$ .

See Solution

Problem 2204

Find the value of $\frac{-b-\sqrt{b^{2}-4ac}}{2a}$ when $a=11, b=7$ , and $c=-4$ .

See Solution

Problem 2205

Find the equation of the line passing through (3,10) and (7,28) in the form $y=mx+c$ , where $m$ and $c$ are integers or simplified fractions.

See Solution

Problem 2206

Divide the decimal 0.16 by 4,692.08 and express the exact answer as a decimal.

See Solution

Problem 2207

Find the solutions to the equation $4 w^{2}-3 w-3=0$ . Round each solution to two decimal places and enter them as a comma-separated list.

See Solution

Problem 2208

Find the interval for the inequality $3 > -x > -4$ .

See Solution

Problem 2209

Simplify the expression $(-8)^{-2}$ without using an exponent.

See Solution

Problem 2210

Determine the quadrant where $\theta$ satisfies $\sec \theta > 0$ and $\sin \theta < 0$ .

See Solution

Problem 2211

Find the standard form, roots, degree, and leading coefficient of the function $g(x) = -x(x-1)(x-3)$ .

See Solution

Problem 2212

Evaluate the expression $\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1}$ without a calculator, then simplify the result.

See Solution

Problem 2213

Evaluate $13+\frac{6}{y}$ when $y=6$

See Solution

Problem 2214

Solve the equation $\frac{1}{16^{2x+1}} = 16$ for $x$ .

See Solution

Problem 2215

Evaluate the expression $9-\frac{8}{S}$ when $S=4$ .

See Solution

Problem 2216

Find Sharon's mistake in solving the equation $9=-3(e-2)$ step-by-step.

See Solution

Problem 2217

Determine market equilibrium, shortage, and quantity supplied/demanded for a product with $p_a(x) = 0.5x^2 + 2x + 4$ and $p_n(x) = -x^2 + 100$ .

See Solution

Problem 2218

Find the equation with a unique solution from the given options: (1) $9x+1=9x+11$ , (2) $4x+8=4(x+2)$ , (3) $5x+2=3x+14$ , (4) $6(x-1)=2(3x+5)$ .

See Solution

Problem 2219

Find the area of the sector with central angle $76^{\circ}$ in a circle with radius $11$ . Round to the nearest hundredth.

See Solution

Problem 2220

Rewrite $f(x)=4(x-1)^{2}-2$ in the form $f(x)=a x^{2}+b x+c$ .

See Solution

Problem 2221

Use sum/diff identities to find the value of $\sin 125^{\circ} \cos 55^{\circ} + \cos 125^{\circ} \sin 55^{\circ}$ . If undefined, write DNE.

See Solution

Problem 2222

Solve the exponential equation $25^{x-2}=\frac{1}{5}$ for the unknown variable $x$ .

See Solution

Problem 2223

Rewrite the equation $y-8=-\frac{1}{2}(x-3)$ to standard form.

See Solution

Problem 2224

Find the value of $p$ where the derivative $H'(p)$ of the function $H(p) = 2p(1-p)$ is zero.

See Solution

Problem 2225

An elevator has a capacity of 2385 lb for 15 passengers. Find the probability that 15 adult males with $\mu = 165$ lb, $\sigma = 32$ lb have a mean weight > 159 lb, indicating an overload. Does the elevator appear safe?

See Solution

Problem 2226

Solve for $v$ in the equation $-8=2v-6$ . Simplify the solution.

See Solution

Problem 2227

Solve for $x$ and identify the solution type. $5x=10$ . (5) $x=2$ , Single Solution. (8) All Real Numbers.

See Solution

Problem 2228

Find the rat population in 2000 given the formula $n(t)=86 e^{0.04 t}$ where $t$ is years since 2000 and $n(t)$ is in millions.

See Solution

Problem 2229

Convert units of length: $26\,\mathrm{m}$ to cm, $97\,\mathrm{m}$ to cm, $69\,\mathrm{m}$ to mm, $97\,\mathrm{cm}$ to m, $35\,\mathrm{m}$ to cm, $86\,\mathrm{m}$ to m.

See Solution

Problem 2230

Find the value of $(-2-2i)^7$ using De Moivre's Theorem. Express the result in standard form.

See Solution

Problem 2231

Solve for the missing variable $a$ in the equation $6=\frac{a}{4}+2$ .

See Solution

Problem 2232

Solve for $x$ in the equation $-14x - 26 = \frac{-7}{8}(16x - 6)$ .

See Solution

Problem 2233

Simplify the expressions: (a) $e^{\ln (\sqrt{7})}$ , (b) $e^{\ln (1 / \pi)}$ , (c) $10^{\log (15)}$ .

See Solution

Problem 2234

Subtract $6 z^{2} - 8 z + 2$ and $-(4 z^{2} + 7 z - 4)$ .

See Solution

Problem 2235

Select the two true equations: $5=\frac{5}{1}$ and $\frac{4}{1}=4$

See Solution

Problem 2236

Solve the absolute value equation $\left|\frac{x}{8}\right|+4=5$ for the value of $x$ .

See Solution

Problem 2237

Simplify the expression $(16x)^{1/2}$ to radical form.

See Solution

Problem 2238

Find the change in temperature from Monday ( $-2$ degrees) to Tuesday ( $-10$ degrees).

See Solution

Problem 2239

Find the value of $x$ that satisfies the equation $10(x+2) = 5(x+8)$ . Choose from options A-E.

See Solution

Problem 2240

Find the percentage increase in the price of a technology stock from yesterday's price of $\$ 9.62$ to today's price of $\$ 9.73$ . Round the answer to the nearest tenth of a percent.

See Solution

Problem 2241

Find the range of the quadratic function $f(x) = 2(x - 5)(x + 5)$ .

See Solution

Problem 2242

Evaluate $8.591-0.6 \times 1.4^{2}$ .

See Solution

Problem 2243

Find solutions to $|5x-2| = 12$ . Options: a. $\frac{14}{5}$ , b. -2, c. 2, d. $-\frac{14}{5}$ .

See Solution

Problem 2244

Solve for $y$ in the equation $7^{2y} = 12$ . Round the solution to the nearest hundredth.

See Solution

Problem 2245

Find $x$ -intercepts of the quadratic function $y = x^2 + 8x + 15$ by graphing.

See Solution

Problem 2246

Solve the linear equation $8x - 2.5 = 5.5$ for $x$ .

See Solution

Problem 2247

Simplify the square root expression $-\frac{1}{7} \sqrt{98}$ .

See Solution

Problem 2248

Determine if the student's ratio of $3:4$ for purple to green buttons in a bag with 2 red, 3 green, and 4 purple buttons is correct. Explain.

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Problem 2249

Find the product of -8 and 6.

See Solution

Problem 2250

Is $g=11$ a solution to the equation $8g=88$ ?

See Solution

Problem 2251

Solve the linear equation $8.6x + 4.4x - 11 = 54$ for the value of $x$ .

See Solution

Problem 2252

Find the equation of the function passing through $(3,-2)$ with derivative $\frac{dy}{dx}=3x-4$ .

See Solution

Problem 2253

Find the quotient of $\frac{-16.8}{-2}$ .

See Solution

Problem 2254

Find common denominator for $\frac{5}{6}$ and $\frac{7}{10}$ .

See Solution

Problem 2255

Find $f(g(h(11/2)))$ given $f(x)=\sqrt{x-4}$ , $g(x)=\frac{1}{2}x+1$ , and $h(x)=2x-3$ .

See Solution

Problem 2256

Solve the equation $4x + 9 = 33$ and check the solutions $x = 7$ and $x = 6$ using substitution.

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Problem 2257

Find the square root of 50, 8, and 14, rounded to the nearest hundredth.

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Problem 2258

Solve the quadratic equation $2y(y+5)-5=0$ using the quadratic formula. Provide the solution(s) in the form $y=\square$ .

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Problem 2259

Find your age if $x^2 - 28x = 60$ , where $x$ represents your age.

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Problem 2260

Solve the equation $4(0.2x - 5) = 12$ . Find all real solutions.

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Problem 2261

Solve the equation $x^{\frac{2}{5}} = 300$ for the value of $x$ .

See Solution

Problem 2262

Solve the inequality $2x + 1 < 5$ .

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Problem 2263

a. In how many ways can 8 people arrive randomly at a dinner party? $\square$ (Type an integer)
b. In how many ways can Kim arrive first and Sarah last? $\square$ (Type an integer.)
c. What is the probability that Kim will arrive first and Sarah last? $\square$ (Type a fraction. Simplify your answer.)

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Problem 2264

Solve for the absolute value of $k$ equals 72 minus 9.

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Problem 2265

Find the real numbers $x$ that satisfy the equation $|x| = x$ . Express the solution set in set-builder notation.

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Problem 2266

Find the equation representing "0.9 increased by a number is 5.2".
$0.9 + n = 5.2$

See Solution

Problem 2267

Find the age $x$ where the percentage of Americans with coronary heart disease is $67\%$ using the logistic growth function $P(x)=\frac{90}{1+271 e^{-0.122 x}}$ .

See Solution

Problem 2268

Find the approximation for $f(24.85)$ using the tangent line of $f(x) = -4x^{1/2}$ at $x = 25$ .

See Solution

Problem 2269

If triangle ABC and triangle DEF are similar, then the proportion $\frac{6}{4} = \frac{x}{7}$ must be true.

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Problem 2270

Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

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Problem 2271

Determine the values of $\hat{p}, \hat{q}, n, E$ , and $p$ in a poll of 500 adults about favorite pie, where 11% chose chocolate pie with a margin of error of ±4 percentage points and a 95% confidence level.

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Problem 2272

Solve the absolute value equation $|x+12|=15$ for the value of $x$ .

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Problem 2273

In a group of two people, the probability of not having the same birthday is $\frac{365}{365} \cdot \frac{364}{365}$ . Explain why this is so, ignoring leap years and assuming 365 days in a year. The first person can have any of the $\square$ days, and the second person must have one of the remaining $\square$ days to not have the same birthday.

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Problem 2274

Find the number of students $x$ in a classroom where 9 students left and there are now 36 students.

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Problem 2275

Find the y-intercept of the additive relationship between $x$ and $y$ given in the table: $x = \{2, 3, 4, 5, 6\}$ , $y = \{7, 8, 9, 10, 11\}$ .

See Solution

Problem 2276

Rewrite $h(x)=2x^2+11x+15$ as $(x+a)^2+b$ , where $a$ and $b$ are constants.

See Solution

Problem 2277

Solve $\ln (6x + 2) = 3$ for $x$ . The exact solution is $x = (e^3 - 2)/6$ . Rounded to 4 decimal places, $x = 1.1709$ .

See Solution

Problem 2278

Use implicit differentiation to find the derivative dy/dx. Find the slope of the curve at the point (9,1) for the equation $2xy + 5x^(3/2)y^(-1/2) = 153$ .

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Problem 2279

Solve for $x$ in the equation $6x = 42$ .

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Problem 2280

Solve for $x$ in the linear equation $3x + 4 = 9x + 3$ .

See Solution

Problem 2281

Calculate $8 \times \frac{4}{5}$ and express the result as a decimal.

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Problem 2282

Explain the difference between a median and an altitude in a triangle $ABC$ .

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Problem 2283

Solve the equation with rational exponents: $(x-5)^{2/3} = 64$ . Select the correct choice: A. The solution set is $x = 10$ B. The solution set is the empty set

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Problem 2284

Solve the linear equation $x+13=-19$ for the value of $x$ .

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Problem 2285

Divide the multivariate polynomial $-27 u^{2} z^{3}+12 u^{3} z^{6}-8 u z^{2}$ by the monomial $-4 u^{2} z^{3}$ and simplify the result.

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Problem 2286

Simplify the expression: $3.2 - 9x + 7.1 - 3x$ .

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Problem 2287

Find $C-A+B$ and simplify, if possible. Give exact answers in fraction form, if necessary. Select "Undefined" if applicable.

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Problem 2288

Find the value of $x$ that makes $4 \mid 8473x$ true, where $\mid$ represents divisibility.

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Problem 2289

Find equation for total cost $y$ of tile backsplash with installation fee $\$ 150$ and tile price $\$ 2.75$ per square foot $x$ .

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Problem 2290

Determine the type of translation that maps point $M(7,10)$ to $M'(5,5)$ .

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Problem 2291

Solve the equation $7z - 23 = z + 7$ using addition and multiplication properties of equality, then check the solution.

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Problem 2292

Choose the correct expression equivalent to $2^{2} \cdot 2^{3}$ , $\frac{2^{5}}{2^{1}}$ , and $\left(2^{2}\right)^{3}$ .

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Problem 2293

Find the expression equivalent to $9 a^{1 / 2} b^{14} c^{3 / 2}$ . Options: A) $\sqrt{3 a b^{28} c^{3}}$ , B) $\sqrt{3 a b^{7} c^{3}}$ , C) $\sqrt{81 a b^{28} c^{3}}$ , D) $\sqrt{81 a b^{7} c^{3}}$ .

See Solution

Problem 2294

Solve the equation $6d=342$ and find the value of $d$ .

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Problem 2295

Solve the linear equation $10+5x=-10$ for $x$ .

See Solution

Problem 2296

Insect population of $\mathrm{P}(t) = 600e^{0.02t}$ at time $t$ days. Find: (a) population at $t=0$ , (b) growth rate, (c) graph, (d) population after 10 days, (e) when population reaches 900, (f) when population doubles.

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Problem 2297

Use De Morgan's laws to write an equivalent statement to " $\neg (4:00 \vee \text{time to go})$ ". Choose the correct answer: B. $\neg 4:00 \wedge \neg \text{time to go}$

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Problem 2298

Simplify $18/21 \times 7/16$ and find the values of $3/8$ , $7/24$ , $9/16$ , and $9/22$ .

See Solution

Problem 2299

Solve for the absolute value of $u$ that satisfies the equation $5|2u| = 20$ .

See Solution

Problem 2300

Find the equation of a parabola with vertex at $(-1,-3)$ passing through $(3,-1)$ and $(0,-4)$ .

See Solution

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Math

Problem 2201

Convert 168 km to miles using unit ratios.

Problem 2202

Find the reciprocal of -8.

Problem 2203

Write the equation of a cosine function with range [2,10][2,10][2,10], period 2π3\frac{2\pi}{3}32π​, and midline −2-2−2.

Problem 2204

Find the value of −b−b2−4ac2a\frac{-b-\sqrt{b^{2}-4ac}}{2a}2a−b−b2−4ac​​ when a=11,b=7a=11, b=7a=11,b=7, and c=−4c=-4c=−4.

Problem 2205

Find the equation of the line passing through (3,10) and (7,28) in the form y=mx+cy=mx+cy=mx+c, where mmm and ccc are integers or simplified fractions.

Problem 2206

Divide the decimal 0.16 by 4,692.08 and express the exact answer as a decimal.

Problem 2207

Find the solutions to the equation 4w2−3w−3=04 w^{2}-3 w-3=04w2−3w−3=0. Round each solution to two decimal places and enter them as a comma-separated list.

Problem 2208

Find the interval for the inequality 3>−x>−43 > -x > -43>−x>−4.

Problem 2209

Simplify the expression (−8)−2(-8)^{-2}(−8)−2 without using an exponent.

Problem 2210

Determine the quadrant where θ\thetaθ satisfies sec⁡θ>0\sec \theta > 0secθ>0 and sin⁡θ<0\sin \theta < 0sinθ<0.

Problem 2211

Find the standard form, roots, degree, and leading coefficient of the function g(x)=−x(x−1)(x−3)g(x) = -x(x-1)(x-3)g(x)=−x(x−1)(x−3).

Problem 2212

Evaluate the expression (−11)⋅(−12)⋅(−13)3⋅2⋅1\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1}3⋅2⋅1(−11)⋅(−12)⋅(−13)​ without a calculator, then simplify the result.

Problem 2213

Evaluate 13+6y13+\frac{6}{y}13+y6​ when y=6y=6y=6

Problem 2214

Solve the equation 1162x+1=16\frac{1}{16^{2x+1}} = 16162x+11​=16 for xxx.

Problem 2215

Evaluate the expression 9−8S9-\frac{8}{S}9−S8​ when S=4S=4S=4.

Problem 2216

Find Sharon's mistake in solving the equation 9=−3(e−2)9=-3(e-2)9=−3(e−2) step-by-step.

Problem 2217

Determine market equilibrium, shortage, and quantity supplied/demanded for a product with pa(x)=0.5x2+2x+4p_a(x) = 0.5x^2 + 2x + 4pa​(x)=0.5x2+2x+4 and pn(x)=−x2+100p_n(x) = -x^2 + 100pn​(x)=−x2+100.

Problem 2218

Find the equation with a unique solution from the given options: (1) 9x+1=9x+119x+1=9x+119x+1=9x+11, (2) 4x+8=4(x+2)4x+8=4(x+2)4x+8=4(x+2), (3) 5x+2=3x+145x+2=3x+145x+2=3x+14, (4) 6(x−1)=2(3x+5)6(x-1)=2(3x+5)6(x−1)=2(3x+5).

Problem 2219

Find the area of the sector with central angle 76∘76^{\circ}76∘ in a circle with radius 111111. Round to the nearest hundredth.

Problem 2220

Rewrite f(x)=4(x−1)2−2f(x)=4(x-1)^{2}-2f(x)=4(x−1)2−2 in the form f(x)=ax2+bx+cf(x)=a x^{2}+b x+cf(x)=ax2+bx+c.

Problem 2221

Use sum/diff identities to find the value of sin⁡125∘cos⁡55∘+cos⁡125∘sin⁡55∘\sin 125^{\circ} \cos 55^{\circ} + \cos 125^{\circ} \sin 55^{\circ}sin125∘cos55∘+cos125∘sin55∘. If undefined, write DNE.

Problem 2222

Solve the exponential equation 25x−2=1525^{x-2}=\frac{1}{5}25x−2=51​ for the unknown variable xxx.

Problem 2223

Rewrite the equation y−8=−12(x−3)y-8=-\frac{1}{2}(x-3)y−8=−21​(x−3) to standard form.

Problem 2224

Find the value of ppp where the derivative H′(p)H'(p)H′(p) of the function H(p)=2p(1−p)H(p) = 2p(1-p)H(p)=2p(1−p) is zero.

Problem 2225

An elevator has a capacity of 2385 lb for 15 passengers. Find the probability that 15 adult males with μ=165\mu = 165μ=165 lb, σ=32\sigma = 32σ=32 lb have a mean weight > 159 lb, indicating an overload. Does the elevator appear safe?

Problem 2226

Solve for vvv in the equation −8=2v−6-8=2v-6−8=2v−6. Simplify the solution.

Problem 2227

Solve for xxx and identify the solution type. 5x=105x=105x=10. (5) x=2x=2x=2, Single Solution. (8) All Real Numbers.

Problem 2228

Find the rat population in 2000 given the formula n(t)=86e0.04tn(t)=86 e^{0.04 t}n(t)=86e0.04t where ttt is years since 2000 and n(t)n(t)n(t) is in millions.

Problem 2229

Convert units of length: 26 m26\,\mathrm{m}26m to cm, 97 m97\,\mathrm{m}97m to cm, 69 m69\,\mathrm{m}69m to mm, 97 cm97\,\mathrm{cm}97cm to m, 35 m35\,\mathrm{m}35m to cm, 86 m86\,\mathrm{m}86m to m.

Problem 2230

Find the value of (−2−2i)7(-2-2i)^7(−2−2i)7 using De Moivre's Theorem. Express the result in standard form.

Problem 2231

Solve for the missing variable aaa in the equation 6=a4+26=\frac{a}{4}+26=4a​+2.

Problem 2232

Solve for xxx in the equation −14x−26=−78(16x−6)-14x - 26 = \frac{-7}{8}(16x - 6)−14x−26=8−7​(16x−6).

Problem 2233

Simplify the expressions: (a) eln⁡(7)e^{\ln (\sqrt{7})}eln(7​), (b) eln⁡(1/π)e^{\ln (1 / \pi)}eln(1/π), (c) 10log⁡(15)10^{\log (15)}10log(15).

Problem 2234

Subtract 6z2−8z+26 z^{2} - 8 z + 26z2−8z+2 and −(4z2+7z−4)-(4 z^{2} + 7 z - 4)−(4z2+7z−4).

Problem 2235

Select the two true equations: 5=515=\frac{5}{1}5=15​ and 41=4\frac{4}{1}=414​=4

Problem 2236

Solve the absolute value equation ∣x8∣+4=5\left|\frac{x}{8}\right|+4=5∣∣​8x​∣∣​+4=5 for the value of xxx.

Problem 2237

Simplify the expression (16x)1/2(16x)^{1/2}(16x)1/2 to radical form.

Problem 2238

Find the change in temperature from Monday (−2-2−2 degrees) to Tuesday (−10-10−10 degrees).

Problem 2239

Find the value of xxx that satisfies the equation 10(x+2)=5(x+8)10(x+2) = 5(x+8)10(x+2)=5(x+8). Choose from options A-E.

Problem 2240

Write the equation of a cosine function with range $[2,10]$ , period $\frac{2\pi}{3}$ , and midline $-2$ .

Find the value of $\frac{-b-\sqrt{b^{2}-4ac}}{2a}$ when $a=11, b=7$ , and $c=-4$ .

Find the equation of the line passing through (3,10) and (7,28) in the form $y=mx+c$ , where $m$ and $c$ are integers or simplified fractions.

Find the solutions to the equation $4 w^{2}-3 w-3=0$ . Round each solution to two decimal places and enter them as a comma-separated list.

Find the interval for the inequality $3 > -x > -4$ .

Simplify the expression $(-8)^{-2}$ without using an exponent.

Determine the quadrant where $\theta$ satisfies $\sec \theta > 0$ and $\sin \theta < 0$ .

Find the standard form, roots, degree, and leading coefficient of the function $g(x) = -x(x-1)(x-3)$ .

Evaluate the expression $\frac{(-11) \cdot(-12) \cdot(-13)}{3 \cdot 2 \cdot 1}$ without a calculator, then simplify the result.

Evaluate $13+\frac{6}{y}$ when $y=6$

Solve the equation $\frac{1}{16^{2x+1}} = 16$ for $x$ .

Evaluate the expression $9-\frac{8}{S}$ when $S=4$ .

Find Sharon's mistake in solving the equation $9=-3(e-2)$ step-by-step.

Determine market equilibrium, shortage, and quantity supplied/demanded for a product with $p_a(x) = 0.5x^2 + 2x + 4$ and $p_n(x) = -x^2 + 100$ .

Find the equation with a unique solution from the given options: (1) $9x+1=9x+11$ , (2) $4x+8=4(x+2)$ , (3) $5x+2=3x+14$ , (4) $6(x-1)=2(3x+5)$ .

Find the area of the sector with central angle $76^{\circ}$ in a circle with radius $11$ . Round to the nearest hundredth.

Rewrite $f(x)=4(x-1)^{2}-2$ in the form $f(x)=a x^{2}+b x+c$ .

Use sum/diff identities to find the value of $\sin 125^{\circ} \cos 55^{\circ} + \cos 125^{\circ} \sin 55^{\circ}$ . If undefined, write DNE.

Solve the exponential equation $25^{x-2}=\frac{1}{5}$ for the unknown variable $x$ .

Rewrite the equation $y-8=-\frac{1}{2}(x-3)$ to standard form.

Find the value of $p$ where the derivative $H'(p)$ of the function $H(p) = 2p(1-p)$ is zero.

An elevator has a capacity of 2385 lb for 15 passengers. Find the probability that 15 adult males with $\mu = 165$ lb, $\sigma = 32$ lb have a mean weight > 159 lb, indicating an overload. Does the elevator appear safe?

Solve for $v$ in the equation $-8=2v-6$ . Simplify the solution.

Solve for $x$ and identify the solution type. $5x=10$ . (5) $x=2$ , Single Solution. (8) All Real Numbers.

Find the rat population in 2000 given the formula $n(t)=86 e^{0.04 t}$ where $t$ is years since 2000 and $n(t)$ is in millions.

Convert units of length: $26\,\mathrm{m}$ to cm, $97\,\mathrm{m}$ to cm, $69\,\mathrm{m}$ to mm, $97\,\mathrm{cm}$ to m, $35\,\mathrm{m}$ to cm, $86\,\mathrm{m}$ to m.

Find the value of $(-2-2i)^7$ using De Moivre's Theorem. Express the result in standard form.

Solve for the missing variable $a$ in the equation $6=\frac{a}{4}+2$ .

Solve for $x$ in the equation $-14x - 26 = \frac{-7}{8}(16x - 6)$ .

Simplify the expressions: (a) $e^{\ln (\sqrt{7})}$ , (b) $e^{\ln (1 / \pi)}$ , (c) $10^{\log (15)}$ .

Subtract $6 z^{2} - 8 z + 2$ and $-(4 z^{2} + 7 z - 4)$ .

Select the two true equations: $5=\frac{5}{1}$ and $\frac{4}{1}=4$

Solve the absolute value equation $\left|\frac{x}{8}\right|+4=5$ for the value of $x$ .

Simplify the expression $(16x)^{1/2}$ to radical form.

Find the change in temperature from Monday ( $-2$ degrees) to Tuesday ( $-10$ degrees).

Find the value of $x$ that satisfies the equation $10(x+2) = 5(x+8)$ . Choose from options A-E.

Find the percentage increase in the price of a technology stock from yesterday's price of $\$ 9.62$ to today's price of $\$ 9.73$ . Round the answer to the nearest tenth of a percent.

Find the range of the quadratic function $f(x) = 2(x - 5)(x + 5)$ .

Evaluate $8.591-0.6 \times 1.4^{2}$ .

Find solutions to $|5x-2| = 12$ . Options: a. $\frac{14}{5}$ , b. -2, c. 2, d. $-\frac{14}{5}$ .

Solve for $y$ in the equation $7^{2y} = 12$ . Round the solution to the nearest hundredth.

Find $x$ -intercepts of the quadratic function $y = x^2 + 8x + 15$ by graphing.

Solve the linear equation $8x - 2.5 = 5.5$ for $x$ .

Simplify the square root expression $-\frac{1}{7} \sqrt{98}$ .

Determine if the student's ratio of $3:4$ for purple to green buttons in a bag with 2 red, 3 green, and 4 purple buttons is correct. Explain.

Is $g=11$ a solution to the equation $8g=88$ ?

Solve the linear equation $8.6x + 4.4x - 11 = 54$ for the value of $x$ .

Find the equation of the function passing through $(3,-2)$ with derivative $\frac{dy}{dx}=3x-4$ .

Find the quotient of $\frac{-16.8}{-2}$ .

Find common denominator for $\frac{5}{6}$ and $\frac{7}{10}$ .

Find $f(g(h(11/2)))$ given $f(x)=\sqrt{x-4}$ , $g(x)=\frac{1}{2}x+1$ , and $h(x)=2x-3$ .

Solve the equation $4x + 9 = 33$ and check the solutions $x = 7$ and $x = 6$ using substitution.

Solve the quadratic equation $2y(y+5)-5=0$ using the quadratic formula. Provide the solution(s) in the form $y=\square$ .

Find your age if $x^2 - 28x = 60$ , where $x$ represents your age.

Solve the equation $4(0.2x - 5) = 12$ . Find all real solutions.

Solve the equation $x^{\frac{2}{5}} = 300$ for the value of $x$ .

Solve the inequality $2x + 1 < 5$ .

Solve for the absolute value of $k$ equals 72 minus 9.

Find the real numbers $x$ that satisfy the equation $|x| = x$ . Express the solution set in set-builder notation.

Find the equation representing "0.9 increased by a number is 5.2".
$0.9 + n = 5.2$

Find the age $x$ where the percentage of Americans with coronary heart disease is $67\%$ using the logistic growth function $P(x)=\frac{90}{1+271 e^{-0.122 x}}$ .

Find the approximation for $f(24.85)$ using the tangent line of $f(x) = -4x^{1/2}$ at $x = 25$ .

If triangle ABC and triangle DEF are similar, then the proportion $\frac{6}{4} = \frac{x}{7}$ must be true.

Predict Janelle's final exam score using the linear regression equation $\hat{y}=11+0.5\mathrm{x}$ where $\mathrm{x}=90$ . Calculate the residual between the predicted and actual final exam scores.

Determine the values of $\hat{p}, \hat{q}, n, E$ , and $p$ in a poll of 500 adults about favorite pie, where 11% chose chocolate pie with a margin of error of ±4 percentage points and a 95% confidence level.

Solve the absolute value equation $|x+12|=15$ for the value of $x$ .

Find the number of students $x$ in a classroom where 9 students left and there are now 36 students.