Natural Numbers

Problem 301

Interpret $3-(-5)$ : A) 5 left of 3 B) 5 right of 3 C) 3 left of -5 D) 3 right of -5

See Solution

Problem 302

Find the value of the expression $|-6|-|6|-(-6)$ .

See Solution

Problem 303

Find $r$ given $4r-2=r$ , then calculate $27r$ .

See Solution

Problem 304

Find the roots of the equation $\sqrt{5x-1} = \sqrt{2x+5}$ using algebraic methods.

See Solution

Problem 305

Find the value of $x$ that satisfies the equation $1=\frac{x}{2}$ .

See Solution

Problem 306

Find the height of a radio antenna given the horizontal distance, angles of elevation to the roof and antenna top, and eye height. Use $\tan(\theta) = \text{opposite}/\text{adjacent}$ to solve for the antenna height.

See Solution

Problem 307

Solve the absolute value equation $|4-2x| = 7$ and find the value of $x$ . If no roots exist, enter NA. (Round to 3 decimal places)

See Solution

Problem 308

Find the exact value of $\tan (\arctan (55))$ using inverse function properties. Enter the answer in radians or UNDEFINED if it is undefined.

See Solution

Problem 309

Solve the linear equation $-15x-14=-104$ by applying the Addition and Division Properties of Equality.

See Solution

Problem 310

Select equations that reasonably estimate $2.83-1.19$ , such as (B) $3-1.25=1.75$ and (E) $2.75-1.25=1.5$ .

See Solution

Problem 311

Find the values of $a$ , $b$ , y-intercept, and domain for the function $f(x)=2\left(\frac{3}{4}\right)^{x}$ .

See Solution

Problem 312

Complete the proportion: $10$ apartments on $2$ floors = $\square$ apartments on $1$ floor.

See Solution

Problem 313

Solve for $R$ in the equation $5 R - 1 = R$ , then find the value of $32 R$ .

See Solution

Problem 314

Solve the equation $3.9x-10.6=1.1$ using equality properties. Select all applicable: A. Addition, B. Multiplication, C. Division, D. Subtraction.

See Solution

Problem 315

Evaluate the indefinite integral $\int x \sqrt{29 x-7} d x$ .

See Solution

Problem 316

Solve the system of linear equations to find the values of $x$ and $y$ . Substitute $y$ from the second equation into the first equation to get the resulting equation. Determine the values of $x$ and $y$ .

See Solution

Problem 317

Find the number of cupcakes in 8 boxes if there are 10 cupcakes in 1 box.

See Solution

Problem 318

What is the y-intercept of the exponential function $F(x) = a \cdot b^{x}$ ?

See Solution

Problem 319

Find the positive solution of the equation $7 x^{6/5} - 12 = 5091$ .

See Solution

Problem 320

Ahmad bought $b$ books online for $\$ 5$ each, paid $\$ 4$ for shipping, and the total cost was $\$ 89$ . Find the number of books $b$ he bought.

See Solution

Problem 321

Evaluate the expression $-8^{4}$ .

See Solution

Problem 322

Find the value of $p$ that satisfies the equation $-0.65 p - 3 = 0.35 p$ .

See Solution

Problem 323

Solve the expression $4[9+3(6 \cdot 3-4)]$ to find the missing value.

See Solution

Problem 324

Which of the following statements about a normal distribution are true? $\mu = \text{mode} = \text{median}$

See Solution

Problem 325

Find the least common multiple of $16 u^{8} x^{7} y^{2}$ and $6 u^{5} x^{6}$ .

See Solution

Problem 326

Solve for y in the equation $3(4y-1) = 2(5y+1/2)$ . The solution is $y=$

See Solution

Problem 327

Find and correct the error in the step-by-step solution to the linear equation $x-5(x+1)=3x+2$ .

See Solution

Problem 328

Evaluate the integral of $\tan^2 x \sec x$ with respect to $x$ .

See Solution

Problem 329

Soit la fonction $g(x) = e^{x}(1-x)-1$ définie sur $\mathbb{R}$ . Étudier le sens de variation et le signe de $g$ . Soit la fonction $f(x) = \frac{x}{e^{x}-1}+2$ pour $x \neq 0$ , et $f(0)=3$ . Déterminer les limites de $f$ , étudier son sens de variation, et trouver l'équation de la tangente à $(\mathscr{E})$ à l'origine. Soit $h(x) = f(x)-x$ , montrer que $h'(x)<0$ et en déduire qu'il existe une solution unique $\alpha$ à l'équation $f(x)=x$ dans l'intervalle $] 2 ; \frac{5}{2}[$ .

See Solution

Problem 330

Convert the angle $\alpha = 81^{\circ} 19^{\prime} 30^{\prime \prime}$ to decimal degrees.

See Solution

Problem 331

Solve exponential equations, analyze errors, and explain logarithm laws. Equations: $7=(3)^{x}-2$ , $(16)^{x}=(2)^{x-2}$ . Error analysis: $5^{3x+2}=25^{x-8}$ , $\left(\frac{1}{6}\right)^{5x}=32^{x+8}$ . Logarithm laws: relation to exponential numbers, 7 laws.

See Solution

Problem 332

Find the common denominator for $\frac{5}{6} + \frac{1}{8}$ and simplify the expression.

See Solution

Problem 333

Simplify the expression $5x + x$ .

See Solution

Problem 334

Simplify the expression $\frac{3}{5} \times 5$ .

See Solution

Problem 335

Use remainder theorem to determine if $x=2$ is a zero of $p(x)=x^{3}+21 x^{2}+74 x-240$ . Find quotient and remainder.

See Solution

Problem 336

Simplify the expression $\sqrt{5} \cdot \sqrt{12}$ using positive exponents.

See Solution

Problem 337

Solve the linear equation $1.5 z + 4 = 2.2 z + 7.5$ by first subtracting a constant from both sides, then subtracting a variable term, and finally dividing to find $z$ .

See Solution

Problem 338

Find the exact value of $y$ or state that $y$ is undefined. $y=\tan^{-1}\frac{\sqrt{3}}{3}$ . Select the correct choice: A. $y=\frac{\pi}{6}$ B. The answer is undefined.

See Solution

Problem 339

Find the value of $(h/g)(3)$ where $g(x)=2x$ and $h(x)=x-9$ .

See Solution

Problem 340

Simplify the expression $-3 \times (8 - 5)$ .

See Solution

Problem 341

Find $x$ and $y$ where $2x + 3y = 5$ and $x - y = 5$ . Graph the solutions: $y = 4, -2, 2, -1$ .

See Solution

Problem 342

Find all values of $t$ where the parametric curve $x=4t^3-2t^2+4t, y=2t^3+4t^2-2$ has a horizontal tangent.

See Solution

Problem 343

Find the energy efficiency of a system with energy output of 25 units and energy input of 100 units.
$Energy\,Efficiency = \frac{Energy\,Output}{Energy\,Input} \times 100$

See Solution

Problem 344

Order the numbers $7.19, \frac{157}{20}, 7 \frac{8}{9}, 7.886$ from least to greatest.

See Solution

Problem 345

Simplify the expression $y^{\frac{50}{56}}$ where $y$ is a positive real number.

See Solution

Problem 346

Find the value of $m$ that makes the system of linear equations $y=mx-6$ and $8x-4y=12$ have no solution.

See Solution

Problem 347

Find the equation of the tangent line to $f(x) = \sqrt{5x-1}$ at the point $(1,2)$ in slope-intercept form.

See Solution

Problem 348

Evaluate the compound interest formula $A=P\left(1+\frac{r}{n}\right)^{n t}$ with $P=2000, r=0.05, n=12, t=5$ . Round the result to the nearest cent and show the exact calculation.

See Solution

Problem 349

Find the value of $n$ that satisfies $\sqrt[4]{3n-11}=3$ .

See Solution

Problem 350

Find the value of $v$ that satisfies the quadratic equation $v^2 + 18v + 9 = -8$ .

See Solution

Problem 351

Peaches cost $2 per pound. The customer's model represents total cost$ y $based on pounds$ x $bought. The values of$ x $and$ y $are:$ x \geq 0 $,$ y \geq 0 $, and$ y = 2x$.

See Solution

Problem 352

Interpret the slope of the regression equation $\text{Salary} = \$95,000 + \$1,280 \cdot (\text{Years})$ in the context of professor salaries.

See Solution

Problem 353

Find the value of $Z$ in the equation $8Z=64$ .

See Solution

Problem 354

Find the value of $2k$ when $k$ more than 7 subtracted from 18 results in 2.

See Solution

Problem 355

Calculate the standard error of the sample proportion $\hat{p}$ for $n=100$ and various values of $p$ . Observe how the standard error changes as $p$ approaches 0 or 1.

See Solution

Problem 356

Solve the polynomial $9x^3 - 12x^2 - 8x - 1 = 0$ using Rational Zero Theorem and Descartes's Rule of Signs. The solution set is { $-1, \frac{1}{3}, 1$ }.

See Solution

Problem 357

Verify that the given function $f(x) = 6e^{-6x}$ over $[0, \infty)$ satisfies the property that the area under the curve is 1. Compute the antiderivative $F(x) = -\frac{1}{e^{6x}}$ and evaluate the limit $\lim_{b \to \infty} [F(b) - F(0)]$ to show the area is 1.

See Solution

Problem 358

Audrey predicts she will make 15 free throws before missing one, but makes 20. What is the percent error in her prediction?
$\text{Percent Error} = \frac{|\text{Actual} - \text{Predicted}|}{\text{Predicted}} \times 100$

See Solution

Problem 359

Find $dy/dt$ when $x^2 + y^2 = 36$ and $dx/dt = 3$ , for $y > 0$ and (a) $x = 0$ , (b) $x = 2$ , (c) $x = 3$ .

See Solution

Problem 360

Find the value of $x$ given a parallelogram DECK with $DE=x+y, EC=12, CK=2x-y$ , and $KD=3x-2y$ .

See Solution

Problem 361

Simplify the expression $7(-6+8)+8(-4+5)$ using the order of operations rule.

See Solution

Problem 362

Find the product of coefficients a, b, and c when the expression $x^{-\frac{5}{4}} y^{-\frac{8}{3}} \sqrt{25 x^{4} y^{2}}$ is written in the form $a x^{b} y^{c}$ .

See Solution

Problem 363

Solve and round to the nearest hundredth: a) $\frac{26}{b+5}=1+\frac{3}{b-2}$ , b) $\frac{c}{c+2}-3=\frac{-6}{c^{2}-4}$

See Solution

Problem 364

If $4p=16$ , find the value of $8p+5$ .

See Solution

Problem 365

Find the equations where $x=-26$ . Options: A. $-1.5(x+12)=21$ , B. $\square-1.2(x-9)=42$ , C. $\square-1.5(x+6)=-21$ , D. $1.25(x+7)=30$ .

See Solution

Problem 366

Find the real number $x$ such that $x^{1/3} = -5$ . The solution is $x = -125$ .

See Solution

Problem 367

Solve for $x$ in the equation $-15 = -\frac{5}{3}x$ . Simplify the solution.

See Solution

Problem 368

Find the degrees of freedom, critical values $\chi_{L}^{2}$ and $\chi_{R}^{2}$ , and $\sigma$ confidence interval for a normal distribution sample with $n=149, s=1.95$ (1000 cells/ $\mu \mathrm{L}$ ) at 99% confidence.

See Solution

Problem 369

Solve for the variable $m$ in the equation $4-\frac{m}{2}=10$ .

See Solution

Problem 370

Find the value of $n$ in the equation $\frac{6^{8}}{6^{n}}=6^{2}$ .

See Solution

Problem 371

Find the basic function $r(x) = (x+7)^3$ is derived from, and how it has been transformed.

See Solution

Problem 372

Find the middle value $m$ and distance $E$ of the interval $6<\mu<24$ , then write the interval as $m \pm E$ .

See Solution

Problem 373

Find the inverse function of $y=6^{x}$ . Options: $y=\log_{6} x$ , $y=\log_{x} 6$ , $y=\log \frac{1}{6} x$ , $y=\log_{6} 6x$ .

See Solution

Problem 374

Solve for $x$ given the equation $10=8x$ .

See Solution

Problem 375

Find the exponential function passing through $(2,80)$ : $f(x)=4(5)^{x}$ or $f(x)=5(4)^{x}$ ?

See Solution

Problem 376

Find the value of $y$ when $x=4$ .

See Solution

Problem 377

Find the value of the coefficient $C$ in the partial fraction expansion of the rational expression $(4x^2 + 6)/(x+1)$ .

See Solution

Problem 378

Solve for s where s-14 is greater than or equal to -15. $s \geq -1$ .

See Solution

Problem 379

An individual sets up an IRA at age 21 with a 6% APR, depositing $45 monthly. How much will the IRA contain at age 65? Compare to total deposits.
The IRA will contain $\$ 318,443.15$ after retirement.

See Solution

Problem 380

Solve the system of linear equations $x-y=4$ and $x+2y=4$ for $x$ and $y$ .

See Solution

Problem 381

Find the product of $-10x$ and 1.

See Solution

Problem 382

Express 0.26, $0 . \overline{72}$ , and $0.4 \overline{13}$ as simplified fractions.

See Solution

Problem 383

The standard deviation is the square root of the variance.

See Solution

Problem 384

Solve the quadratic equation $(x-7)^{2} = -81$ for real values of $x$ .

See Solution

Problem 385

Find the Left and Right Riemann sums, then use them to find the Trapezoidal sum on the interval $[-3,7]$ given the table of $x$ and $f(x)$ values.

See Solution

Problem 386

Maximize $3x_1 + 4x_2$ subject to $2x_1 + x_2 \leq 18$ , $2x_1 + 3x_2 \leq 42$ , $3x_1 + x_2 \leq 24$ , and $x_1, x_2 \geq 0$ using the Simplex method.

See Solution

Problem 387

Solve $25=5e^{2t}$ for $t$ . Exact solution required.

See Solution

Problem 388

Simplify $e^{\ln (1.61)}$ using the definitions of common and natural logarithms.

See Solution

Problem 389

Determine the horizontal asymptote of the function $f(x) = \frac{16 x^{3}-7 x+8}{20 x^{3}+8 x-3}$ . If none exists, state that fact.

See Solution

Problem 390

Find the missing value in the first equation and solve the second equation. $-3 \cdot \square = 21$ $21 \div (-3) = ?$

See Solution

Problem 391

Find the value of the permutation ${ }_{9} P_{5}$ .

See Solution

Problem 392

Find the price per padlock given a pack of 8 costs $\$19.20$ . Round the answer to the nearest cent.

See Solution

Problem 393

Find the equation of a line passing through (2,4) and perpendicular to $y = \frac{1}{6}x + 3$ in slope-intercept form.

See Solution

Problem 394

Find the roots and their multiplicities of the function $f(t) = (t-3)(-6t+7)^7(t-6)^3$ .

See Solution

Problem 395

Find the values of the integers $A$ and $B$ in the simplified expression $\frac{A x^{2}}{x y-B y}$ for $\frac{4 x y}{x-2} \cdot \frac{x^{2}}{y^{2} x}$ .

See Solution

Problem 396

Simplify the expression $\frac{7}{2-6 \sqrt{2}}$ .

See Solution

Problem 397

Solve the trigonometric equation $(\sec \theta-1)(\sec \theta+1)=\tan^2 \theta$ for $\theta$ .

See Solution

Problem 398

Find the value of the expression $(1/2)^4$ . Solve on paper if needed, then enter the value on Zearn.

See Solution

Problem 399

Find $T_2$ given $t_2 \cdot \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ .

See Solution

Problem 400

Solve the equation $0.5 x = 16$ for $x$ using the division property of equality.

See Solution

1 2 3 4 5 6 7 ...28

Natural Numbers

Problem 301

Interpret 3−(−5)3-(-5)3−(−5): A) 5 left of 3 B) 5 right of 3 C) 3 left of -5 D) 3 right of -5

Problem 302

Find the value of the expression ∣−6∣−∣6∣−(−6)|-6|-|6|-(-6)∣−6∣−∣6∣−(−6).

Problem 303

Find rrr given 4r−2=r4r-2=r4r−2=r, then calculate 27r27r27r.

Problem 304

Find the roots of the equation 5x−1=2x+5\sqrt{5x-1} = \sqrt{2x+5}5x−1​=2x+5​ using algebraic methods.

Problem 305

Find the value of xxx that satisfies the equation 1=x21=\frac{x}{2}1=2x​.

Problem 306

Find the height of a radio antenna given the horizontal distance, angles of elevation to the roof and antenna top, and eye height. Use tan⁡(θ)=opposite/adjacent\tan(\theta) = \text{opposite}/\text{adjacent}tan(θ)=opposite/adjacent to solve for the antenna height.

Problem 307

Solve the absolute value equation ∣4−2x∣=7|4-2x| = 7∣4−2x∣=7 and find the value of xxx. If no roots exist, enter NA. (Round to 3 decimal places)

Problem 308

Find the exact value of tan⁡(arctan⁡(55))\tan (\arctan (55))tan(arctan(55)) using inverse function properties. Enter the answer in radians or UNDEFINED if it is undefined.

Problem 309

Solve the linear equation −15x−14=−104-15x-14=-104−15x−14=−104 by applying the Addition and Division Properties of Equality.

Problem 310

Select equations that reasonably estimate 2.83−1.192.83-1.192.83−1.19, such as (B) 3−1.25=1.753-1.25=1.753−1.25=1.75 and (E) 2.75−1.25=1.52.75-1.25=1.52.75−1.25=1.5.

Problem 311

Find the values of aaa, bbb, y-intercept, and domain for the function f(x)=2(34)xf(x)=2\left(\frac{3}{4}\right)^{x}f(x)=2(43​)x.

Problem 312

Complete the proportion: 101010 apartments on 222 floors = □\square□ apartments on 111 floor.

Problem 313

Solve for RRR in the equation 5R−1=R5 R - 1 = R5R−1=R, then find the value of 32R32 R32R.

Problem 314

Solve the equation 3.9x−10.6=1.13.9x-10.6=1.13.9x−10.6=1.1 using equality properties. Select all applicable: A. Addition, B. Multiplication, C. Division, D. Subtraction.

Problem 315

Evaluate the indefinite integral ∫x29x−7dx\int x \sqrt{29 x-7} d x∫x29x−7​dx.

Problem 316

Solve the system of linear equations to find the values of xxx and yyy. Substitute yyy from the second equation into the first equation to get the resulting equation. Determine the values of xxx and yyy.

Problem 317

Find the number of cupcakes in 8 boxes if there are 10 cupcakes in 1 box.

Problem 318

What is the y-intercept of the exponential function F(x)=a⋅bxF(x) = a \cdot b^{x}F(x)=a⋅bx?

Problem 319

Find the positive solution of the equation 7x6/5−12=50917 x^{6/5} - 12 = 50917x6/5−12=5091.

Problem 320

Ahmad bought bbb books online for $5\$ 5$5 each, paid $4\$ 4$4 for shipping, and the total cost was $89\$ 89$89. Find the number of books bbb he bought.

Problem 321

Evaluate the expression −84-8^{4}−84.

Problem 322

Find the value of ppp that satisfies the equation −0.65p−3=0.35p-0.65 p - 3 = 0.35 p−0.65p−3=0.35p.

Problem 323

Solve the expression 4[9+3(6⋅3−4)]4[9+3(6 \cdot 3-4)]4[9+3(6⋅3−4)] to find the missing value.

Problem 324

Which of the following statements about a normal distribution are true? μ=mode=median\mu = \text{mode} = \text{median}μ=mode=median

Problem 325

Find the least common multiple of 16u8x7y216 u^{8} x^{7} y^{2}16u8x7y2 and 6u5x66 u^{5} x^{6}6u5x6.

Problem 326

Solve for y in the equation 3(4y−1)=2(5y+1/2)3(4y-1) = 2(5y+1/2)3(4y−1)=2(5y+1/2). The solution is y=y=y=

Problem 327

Find and correct the error in the step-by-step solution to the linear equation x−5(x+1)=3x+2x-5(x+1)=3x+2x−5(x+1)=3x+2.

Problem 328

Evaluate the integral of tan⁡2xsec⁡x\tan^2 x \sec xtan2xsecx with respect to xxx.

Problem 329

Problem 330

Convert the angle α=81∘19′30′′\alpha = 81^{\circ} 19^{\prime} 30^{\prime \prime}α=81∘19′30′′ to decimal degrees.

Problem 331

Problem 332

Find the common denominator for 56+18\frac{5}{6} + \frac{1}{8}65​+81​ and simplify the expression.

Problem 333

Simplify the expression 5x+x5x + x5x+x.

Problem 334

Simplify the expression 35×5\frac{3}{5} \times 553​×5.

Problem 335

Use remainder theorem to determine if x=2x=2x=2 is a zero of p(x)=x3+21x2+74x−240p(x)=x^{3}+21 x^{2}+74 x-240p(x)=x3+21x2+74x−240. Find quotient and remainder.

Problem 336

Simplify the expression 5⋅12\sqrt{5} \cdot \sqrt{12}5​⋅12​ using positive exponents.

Problem 337

Solve the linear equation 1.5z+4=2.2z+7.51.5 z + 4 = 2.2 z + 7.51.5z+4=2.2z+7.5 by first subtracting a constant from both sides, then subtracting a variable term, and finally dividing to find zzz.

Problem 338

Find the exact value of yyy or state that yyy is undefined. y=tan⁡−133y=\tan^{-1}\frac{\sqrt{3}}{3}y=tan−133​​. Select the correct choice: A. y=π6y=\frac{\pi}{6}y=6π​ B. The answer is undefined.

Problem 339

Find the value of (h/g)(3)(h/g)(3)(h/g)(3) where g(x)=2xg(x)=2xg(x)=2x and h(x)=x−9h(x)=x-9h(x)=x−9.

Problem 340

Simplify the expression −3×(8−5)-3 \times (8 - 5)−3×(8−5).

Problem 341

Interpret $3-(-5)$ : A) 5 left of 3 B) 5 right of 3 C) 3 left of -5 D) 3 right of -5

Find the value of the expression $|-6|-|6|-(-6)$ .

Find $r$ given $4r-2=r$ , then calculate $27r$ .

Find the roots of the equation $\sqrt{5x-1} = \sqrt{2x+5}$ using algebraic methods.

Find the value of $x$ that satisfies the equation $1=\frac{x}{2}$ .

Find the height of a radio antenna given the horizontal distance, angles of elevation to the roof and antenna top, and eye height. Use $\tan(\theta) = \text{opposite}/\text{adjacent}$ to solve for the antenna height.

Solve the absolute value equation $|4-2x| = 7$ and find the value of $x$ . If no roots exist, enter NA. (Round to 3 decimal places)

Find the exact value of $\tan (\arctan (55))$ using inverse function properties. Enter the answer in radians or UNDEFINED if it is undefined.

Solve the linear equation $-15x-14=-104$ by applying the Addition and Division Properties of Equality.

Select equations that reasonably estimate $2.83-1.19$ , such as (B) $3-1.25=1.75$ and (E) $2.75-1.25=1.5$ .

Find the values of $a$ , $b$ , y-intercept, and domain for the function $f(x)=2\left(\frac{3}{4}\right)^{x}$ .

Complete the proportion: $10$ apartments on $2$ floors = $\square$ apartments on $1$ floor.

Solve for $R$ in the equation $5 R - 1 = R$ , then find the value of $32 R$ .

Solve the equation $3.9x-10.6=1.1$ using equality properties. Select all applicable: A. Addition, B. Multiplication, C. Division, D. Subtraction.

Evaluate the indefinite integral $\int x \sqrt{29 x-7} d x$ .

Solve the system of linear equations to find the values of $x$ and $y$ . Substitute $y$ from the second equation into the first equation to get the resulting equation. Determine the values of $x$ and $y$ .

What is the y-intercept of the exponential function $F(x) = a \cdot b^{x}$ ?

Find the positive solution of the equation $7 x^{6/5} - 12 = 5091$ .

Ahmad bought $b$ books online for $\$ 5$ each, paid $\$ 4$ for shipping, and the total cost was $\$ 89$ . Find the number of books $b$ he bought.

Evaluate the expression $-8^{4}$ .

Find the value of $p$ that satisfies the equation $-0.65 p - 3 = 0.35 p$ .

Solve the expression $4[9+3(6 \cdot 3-4)]$ to find the missing value.

Which of the following statements about a normal distribution are true? $\mu = \text{mode} = \text{median}$

Find the least common multiple of $16 u^{8} x^{7} y^{2}$ and $6 u^{5} x^{6}$ .

Solve for y in the equation $3(4y-1) = 2(5y+1/2)$ . The solution is $y=$

Find and correct the error in the step-by-step solution to the linear equation $x-5(x+1)=3x+2$ .

Evaluate the integral of $\tan^2 x \sec x$ with respect to $x$ .

Convert the angle $\alpha = 81^{\circ} 19^{\prime} 30^{\prime \prime}$ to decimal degrees.

Find the common denominator for $\frac{5}{6} + \frac{1}{8}$ and simplify the expression.

Simplify the expression $5x + x$ .

Simplify the expression $\frac{3}{5} \times 5$ .

Use remainder theorem to determine if $x=2$ is a zero of $p(x)=x^{3}+21 x^{2}+74 x-240$ . Find quotient and remainder.

Simplify the expression $\sqrt{5} \cdot \sqrt{12}$ using positive exponents.

Solve the linear equation $1.5 z + 4 = 2.2 z + 7.5$ by first subtracting a constant from both sides, then subtracting a variable term, and finally dividing to find $z$ .

Find the exact value of $y$ or state that $y$ is undefined. $y=\tan^{-1}\frac{\sqrt{3}}{3}$ . Select the correct choice: A. $y=\frac{\pi}{6}$ B. The answer is undefined.

Find the value of $(h/g)(3)$ where $g(x)=2x$ and $h(x)=x-9$ .

Simplify the expression $-3 \times (8 - 5)$ .

Find $x$ and $y$ where $2x + 3y = 5$ and $x - y = 5$ . Graph the solutions: $y = 4, -2, 2, -1$ .

Find all values of $t$ where the parametric curve $x=4t^3-2t^2+4t, y=2t^3+4t^2-2$ has a horizontal tangent.

Find the energy efficiency of a system with energy output of 25 units and energy input of 100 units.
$Energy\,Efficiency = \frac{Energy\,Output}{Energy\,Input} \times 100$

Order the numbers $7.19, \frac{157}{20}, 7 \frac{8}{9}, 7.886$ from least to greatest.

Simplify the expression $y^{\frac{50}{56}}$ where $y$ is a positive real number.

Find the value of $m$ that makes the system of linear equations $y=mx-6$ and $8x-4y=12$ have no solution.

Find the equation of the tangent line to $f(x) = \sqrt{5x-1}$ at the point $(1,2)$ in slope-intercept form.

Evaluate the compound interest formula $A=P\left(1+\frac{r}{n}\right)^{n t}$ with $P=2000, r=0.05, n=12, t=5$ . Round the result to the nearest cent and show the exact calculation.

Find the value of $n$ that satisfies $\sqrt[4]{3n-11}=3$ .

Find the value of $v$ that satisfies the quadratic equation $v^2 + 18v + 9 = -8$ .

Interpret the slope of the regression equation $\text{Salary} = \$95,000 + \$1,280 \cdot (\text{Years})$ in the context of professor salaries.

Find the value of $Z$ in the equation $8Z=64$ .

Find the value of $2k$ when $k$ more than 7 subtracted from 18 results in 2.

Calculate the standard error of the sample proportion $\hat{p}$ for $n=100$ and various values of $p$ . Observe how the standard error changes as $p$ approaches 0 or 1.

Solve the polynomial $9x^3 - 12x^2 - 8x - 1 = 0$ using Rational Zero Theorem and Descartes's Rule of Signs. The solution set is { $-1, \frac{1}{3}, 1$ }.

Find $dy/dt$ when $x^2 + y^2 = 36$ and $dx/dt = 3$ , for $y > 0$ and (a) $x = 0$ , (b) $x = 2$ , (c) $x = 3$ .

Find the value of $x$ given a parallelogram DECK with $DE=x+y, EC=12, CK=2x-y$ , and $KD=3x-2y$ .

Simplify the expression $7(-6+8)+8(-4+5)$ using the order of operations rule.

Find the product of coefficients a, b, and c when the expression $x^{-\frac{5}{4}} y^{-\frac{8}{3}} \sqrt{25 x^{4} y^{2}}$ is written in the form $a x^{b} y^{c}$ .

Solve and round to the nearest hundredth: a) $\frac{26}{b+5}=1+\frac{3}{b-2}$ , b) $\frac{c}{c+2}-3=\frac{-6}{c^{2}-4}$

If $4p=16$ , find the value of $8p+5$ .

Find the equations where $x=-26$ . Options: A. $-1.5(x+12)=21$ , B. $\square-1.2(x-9)=42$ , C. $\square-1.5(x+6)=-21$ , D. $1.25(x+7)=30$ .

Find the real number $x$ such that $x^{1/3} = -5$ . The solution is $x = -125$ .

Solve for $x$ in the equation $-15 = -\frac{5}{3}x$ . Simplify the solution.

Find the degrees of freedom, critical values $\chi_{L}^{2}$ and $\chi_{R}^{2}$ , and $\sigma$ confidence interval for a normal distribution sample with $n=149, s=1.95$ (1000 cells/ $\mu \mathrm{L}$ ) at 99% confidence.

Solve for the variable $m$ in the equation $4-\frac{m}{2}=10$ .

Find the value of $n$ in the equation $\frac{6^{8}}{6^{n}}=6^{2}$ .

Find the basic function $r(x) = (x+7)^3$ is derived from, and how it has been transformed.

Find the middle value $m$ and distance $E$ of the interval $6<\mu<24$ , then write the interval as $m \pm E$ .

Find the inverse function of $y=6^{x}$ . Options: $y=\log_{6} x$ , $y=\log_{x} 6$ , $y=\log \frac{1}{6} x$ , $y=\log_{6} 6x$ .

Solve for $x$ given the equation $10=8x$ .