Browse Math problems in the Studdy Learning Bank!

Problem 7801

16. Approximate $\sqrt{2}$ as 1.414. Find approximate values for: a) $\sqrt{200}$ b) $\sqrt{20000}$
17. Approximate $\sqrt[3]{2}$ as 1.260 and $\sqrt[3]{4}$ as 1.587. Find approximate values for: a) $\sqrt[3]{2000}$ b) $\sqrt[3]{4000000}$

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Problem 7802

Evaluate $u \odot v = 2u - v$ for $4 \odot (2 \odot 5)$ .

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Problem 7803

Find the number of psychology and history textbooks sold, given that the total sold was 290 and the number of psychology textbooks was 42 more than the number of history textbooks. Let $x$ be the number of history textbooks sold. Then the number of psychology textbooks sold is $x + 42$ . The total number of textbooks sold is $x + (x + 42) = 290$ . Solve for $x$ to find the number of textbooks of each type sold.

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Problem 7804

Solve for $y$ in the equation $-\frac{y}{8}=-23$ . Simplify the solution $y=$ .

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Problem 7805

Find the value of $x$ when $y = a + b \ln x$ , given $a = 12.3301088919$ and $b = -8.22097130319$ , and $y = -16$ .

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Problem 7806

Solve the trigonometric equation $\tan \theta = -\sqrt{3}$ using the unit circle.

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Problem 7807

Find the value of $x$ that satisfies the equation $\frac{83}{x+4}=10$ .

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Problem 7808

Solve the linear equation $x + 3.75 = 5.5$ to find the value of $x$ .

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Problem 7809

Determine if $(-1,29)$ is a solution to the quadratic equation $y=-2x^2-5x+22$ . Show your work.

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Problem 7810

Complete the exponential decay table: Original Amount: $19,000$ , Decay Rate: $13\%$ per year, Years: $18$ , Final Amount after $18$ years of decay.

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Problem 7811

Solve for $x$ in the equation $1.008165=\frac{2}{2-x}-\frac{1.008165 x}{2}$ .

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Problem 7812

Determine which term the negative sign belongs to in the expression $16 t-3 t$ compared to $3 t-16 t$ .

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Problem 7813

Solve the system of linear equations to find the common solution.
$x+y=20$ and $y=2x-1$ $y=2x$ and $y=-6x+4$

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Problem 7814

Solve for x in the linear equation $12-12x=-6x+48$ .

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Problem 7815

Simplify the expression $-8(-4x^3 + 5 - 2y^2)$ using the distributive property.

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Problem 7816

Find the product of two complex numbers and express the result in the form $a + bi$ .

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Problem 7817

Identify the levels of measurement: $\{$ Nominal Data, Ratio, Quantitative Data, Ordinal Data $\}$

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Problem 7818

Perform the indicated operation $2.6 + 2.1$ and use a calculator to verify the result.

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Problem 7819

Determine if the underlined value, $59\%$ of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

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Problem 7820

Calculate the exact value of the ${ }_{27} P_{4}$ permutation expression.

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Problem 7821

Find the demand function $D(p) = -2p^2 - 6p + 300$ and its rate of change w.r.t. price $p$ . Interpret the rate of change when $p = \$11$ .

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Problem 7822

Solve for height $h$ given area $A$ and base $b$ using the formula $A=bh$ . Options: B) $h=\frac{A}{b}$

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Problem 7823

Babies with low birth weight (< 2500 g) may have health issues. Mean birth weight is 3496 g, but 2646 g for babies born 1 month early. Find standardized score (z-score) for 2500 g birth weight for: a) all births, b) 1 month early births. Determine which group 2500 g is more common.
a. $z=-2.17$ b. $z=-0.32$ c. B. A birth weight of 2500 g is more common for all births in the country.

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Problem 7824

Find the ordered pair that satisfies the inequality $12 \geq 2x + 4y$ given the points $(6,0)$ , $(0,6)$ , $(3,6)$ , and $(-2,8)$ on the graph of $12 = 2x + 4y$ .

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Problem 7825

Find the time (in seconds) when Ana, who dives from a high springboard, hits the water given the height model $h(x) = -5(x+1)(x-3)$ .

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Problem 7826

Multiply the complex number $9-12i$ by its complex conjugate and simplify the result.

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Problem 7827

Solve the equation $\frac{8}{x}=2x$ graphically and numerically.

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Problem 7828

Simplify the numerical expression $8^{2}+7(-2-5)+3$ using the rules for order of operations.

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Problem 7829

Find the value of $12 t - 2 y$ given that $x = 3$ is a solution to the equation $2 t x - y = 4$ .

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Problem 7830

Evaluate $\lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{x-1}$ using the provided table of $x$ and $f(x)$ values.

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Problem 7831

Solve the polynomial inequality $x^{3} - x^{2} - 12x > 0$ using the test-point method.

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Problem 7832

Solve the equation $\pi x + 3 = 4\pi x$ for $x$ .

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Problem 7833

Determine if the linear equation $3x + 6y = 12$ represents a function.

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Problem 7834

Solve the equation $8^{2x-3} = \left(\frac{1}{16}\right)^{x-2}$ for the unknown variable $x$ .

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Problem 7835

Rewrite the problem statement: Find the frequency distribution and construct a histogram for the hottest recorded temperatures (in °F) across 16 North American cities.
$92.5-96.5$ : $\square$ $96.5-100.5$ : $\square$ $100.5-104.5$ : $\square$ $104.5-108.5$ : $\square$ $108.5-112.5$ : $\square$

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Problem 7836

Solve for time $t$ in the equation $r = r_0 + \frac{1}{2}at^2$ , where $r_0$ and $a$ are known constants.

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Problem 7837

Simplify the complex expression $-6 i(8+2 i)$ and write the result in standard form.

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Problem 7838

Differentiate the function $f(\theta) = \frac{\sec \theta}{5 + \sec \theta}$ .

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Problem 7839

Solve the subtraction $(-7)-(+7)$ and model at least 3 subtraction problems.

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Problem 7840

Solve for $q$ where the product of two linear expressions equals 0. Write the solutions as integers or simplified fractions.

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Problem 7841

Solve the inequality $3|x+1|-2<4$ and select the correct solution.
A) $-3<x$ or $x<1$ B) $-3<x$ or $x>1$ C) $-3<x<1$ D) $-3<x$ and $x>1$

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Problem 7842

Divide $8.8 \times 10^{-3}$ by $2.4 \times 10^{-7}$ and give the answer in scientific notation.

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Problem 7843

Solve for $w$ where $w^{2}-4=0$ . Write answers as integers or simplified fractions.

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Problem 7844

Simplify $\frac{x^{4}+7 x^{3}-10 x^{2}-63 x+9}{x^{2}-9}$ where $x^{2} \neq 9$ using long or synthetic division.

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Problem 7845

Solve the inequality $3(x-9)<15$ and select the correct answer.

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Problem 7846

Simplify the expression $\frac{5}{7 y} \times \frac{10}{3 y}$ .

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Problem 7847

Convert temperature from Fahrenheit to Celsius given $101^\circ F$ .

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Problem 7848

Solve for the unknown value $u$ given the equation $10.24 = 4u$ .

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Problem 7849

Find the ratio of roses to daisies and daisies to all flowers in a vase with 5 roses and 11 total flowers.
(a) Ratio of roses to daisies: $\frac{5}{11-5}$ (b) Ratio of daisies to all flowers: $\frac{11-5}{11}$

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Problem 7850

Describe the types of symmetry in the circle with equation $x^2 + y^2 = 1$ .

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Problem 7851

Determine the number of significant digits in the value $587,410$ .

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Problem 7852

Solve $\left(u-14\right)\left(u+10\right)=-104$ using the completing the square method. Answer: $u=\pm 2, \pm 12$

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Problem 7853

Find the derivative of $\sqrt{5 x^{2}-4}$ with respect to $x$ .

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Problem 7854

Calculate the total liabilities of White Cleaning Services on $31/12/2022$ given that total assets on $31/12/2022$ were $\$ 126,000$ , total assets on $1/1/2022$ were $\$ 85,000$ , total liabilities on $1/1/2022$ were $\$ 17,000$ , total revenue in 2022 was $\$ 61,000$ , total expenses in 2022 were $\$ 35,000$ , and Mr. Mansoor made an additional investment of $\$ 12,000$ to the business in 2022.
Response: 29000

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Problem 7855

Solve for the variable $v$ in the equation $3xy = v/4$ .

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Problem 7856

Solve for $x$ : $x+8=60$ , $\frac{x}{4}=50$ , $x^{2}=400$ , $54=9 x$ , $60=35+x$ .

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Problem 7857

Company bought a 3-year insurance policy for $\$25,200$ on $1/4/2020$ . Reported net income for 2020 was $\$63,000$ . If the accountant missed the insurance adjustment on $12/31/2020$ , the correct 2020 net income should be $\$56,700$ .

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Problem 7858

Find the 98th percentile of a standard normal distribution with mean 0 and standard deviation 1.

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Problem 7859

Solve for the value of $d$ in the equation $4d - 4 = 5d - 8$ .

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Problem 7860

Solve for $m$ in the equation $12.6+4m=9.6+8m$ .

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Problem 7861

Solve for $u$ where $(5u-2)(-3u+4)=0$ . Write the solutions as integers or simplified fractions.

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Problem 7862

Solve $\left(u+3\right)^{3/2} = 6$ for real number $u$ , and simplify the solution.

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Problem 7863

Find values of $x$ that cannot be solutions to the equation $\frac{7}{4x+1} - \frac{1}{x-2} = 0$ .

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Problem 7864

Compare the numbers. Pick the correct sign: $-7 ? 6$ , where the options are $>$ , $<$ , or $=$ .

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Problem 7865

Solve for $x$ , rounding to the nearest tenth if necessary. $\frac{9}{4}=\frac{7 x+6}{2}$

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Problem 7866

Determine if $t=-5$ is a solution to the equation $-2t^3 - 4t^2 + 4t - 3 = 127$ .

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Problem 7867

Calculate the range, variance, and standard deviation for the given samples. a. $34, 47, 45, 40, 48$ , b. $100, 3, 9160, 16207$ , c. $100, 35, 40, 6040, 447$ . a. The range is $\square$ .

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Problem 7868

Evaluate the definite integral of $\frac{4y}{e^{2y}}$ from 0 to 1.

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Problem 7869

Solve for $x$ in the equation $x \times -6.3 = -3$ .

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Problem 7870

Find the y-intercept of the line passing through the points $(8,6)$ and $(4,22)$ .

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Problem 7871

Compare the z-scores of a 45-year-old Best Actor and a 37-year-old Best Supporting Actor with $\mu_{BA}=44.0$ , $\sigma_{BA}=7.2$ , $\mu_{BSA}=54.0$ , and $\sigma_{BSA}=16$ .
Best Actor: $z=\frac{45-44.0}{7.2} = 0.14$ Best Supporting Actor: $z=\frac{37-54.0}{16} = -1.06$

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Problem 7872

Find the number of solutions for the system of linear equations: $x+y+z=66$ and $5x+10y+20z=730$ , where $x, y, z$ are integers.

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Problem 7873

Solve the equation $8-8x=(3x+1)(x-1)$ by factoring. The solution set is $x=1, -\frac{1}{3}$ .

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Problem 7874

Determine if $u$ values satisfy inequality $37 \leq 25+u$ and mark solution status.

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Problem 7875

Solve the linear equation $\frac{u}{4} + -2 = 2$ for $u$ .

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Problem 7876

Simplify the expression $16^{\frac{1}{4}} \div 16^{\frac{1}{2}}$ to an integer or fraction.

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Problem 7877

Write an equation to represent "57 is the difference of Hector's age $h$ and 10".

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Problem 7878

Expresar como desigualdad: $w - 5 \geq 26$

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Problem 7879

Classify variables as quantitative or categorical: (a) customer satisfaction (very/somewhat satisfied/dissatisfied), (b) weight (in lbs) needed to break bridge cable, (c) cell phone service provider.

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Problem 7880

Marcos' cell phone balance $B=25-0.1n$ where $n$ is minutes talked. a) Initial balance: $\$ 25$ . b) Minutes until balance is $0$ : 250 minutes. c) Slope: $-0.1$ minutes/ $\$$

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Problem 7881

Solve the following exponential equations: a. $e^{-0.2 t}=9$ , b. $e^{k t}=\frac{1}{5}$ , c. $e^{(\ln 0.4) t}=0.7$ .

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Problem 7882

Prove there is at least one negative solution to $e^{x} = -x$ using the Intermediate Value Theorem. Approximate this solution using the bisection method with error at most 0.01.

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Problem 7883

Find the coordinates of the points where the parabolas $y = x^2 + 1$ and $y = -x^2 + 3$ intersect.

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Problem 7884

Determine if the statement $|x| + |y| = |x + y|$ is true for all real numbers $x, y$ .

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Problem 7885

Find the mode of the sample scores $[4, 14, 56, 0.8, 14, 56, 14]$ .

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Problem 7886

Calculate the standard deviation of the distances (in miles) traveled to work by 5 employees: $10, 3, 14, 34, 9$ . Round the answer to two decimal places.

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Problem 7887

Find the ship's bearing from its starting point and the bearing back to the starting point, given the ship sailed $3 \mathrm{~km}$ west and $2 \mathrm{~km}$ south.

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Problem 7888

Find the quadratic parent function: $f(x)=x^{2}$

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Problem 7889

Convert a CD's 3.3 rotations/second to degrees/second and rotations/minute.
$3.3 \text{ rotations/s} \rightarrow \text{degrees/s and rpm}$

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Problem 7890

Solve for complex numbers and rational exponents without a calculator. Find the values of the variables a, b, c, d, and f that satisfy the given equations.
1. $x^{2}=16$ solutions: $\{4, -4\}$
2. a. $3^{4} \cdot 3^{2}=3^{a}$ , b. $\frac{5^{4}}{5^{3}}=5^{b}$ , c. $4^{c}=1$ , d. $2^{6} \cdot d^{6}=14^{6}$ , e. $6^{f}=\frac{1}{6}$

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Problem 7891

Find the value of $x$ that satisfies the equation $-5|3x| = -75$ .

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Problem 7892

Rewrite the fraction $\frac{5}{6}$ as a decimal.

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Problem 7893

Find the derivative of $f(x) = 5x^4(x^3 - 2)$ and identify the correct application of the product rule.

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Problem 7894

Determine if the equation $4x - 3 = 19$ is true, false, or open.

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Problem 7895

Diane bought $\$ 12,600$ in lab equipment, paying $\$ 1200$ down and taking out a loan for the rest. She paid $\$ 505.26$ monthly for 2 years to pay off the loan. (a) What was the total cost? (b) How much interest did she pay?

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Problem 7896

Solve for $x$ in the equation $12x - 12 = 4(5x - 5)$ .

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Problem 7897

Solve the quadratic equation $3x^2 + 7x + 4 = 0$ by factoring. List the solutions in ascending order.

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Problem 7898

Find the factored form of $x^{2}y^{3}-2y^{3}-2x^{2}+4$ .

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Problem 7899

Find the value of $x$ given the equation $HJ = 7x - 27$ .

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Problem 7900

Calculate the difference between $\frac{85}{100}$ and $\frac{49}{1000}$ , and simplify the result.

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Math

Problem 7801

16. Approximate 2\sqrt{2}2​ as 1.414. Find approximate values for: a) 200\sqrt{200}200​ b) 20000\sqrt{20000}20000​17. Approximate 23\sqrt[3]{2}32​ as 1.260 and 43\sqrt[3]{4}34​ as 1.587. Find approximate values for: a) 20003\sqrt[3]{2000}32000​ b) 40000003\sqrt[3]{4000000}34000000​

Problem 7802

Evaluate u⊙v=2u−vu \odot v = 2u - vu⊙v=2u−v for 4⊙(2⊙5)4 \odot (2 \odot 5)4⊙(2⊙5).

Problem 7803

Problem 7804

Solve for yyy in the equation −y8=−23-\frac{y}{8}=-23−8y​=−23. Simplify the solution y=y=y=.

Problem 7805

Find the value of xxx when y=a+bln⁡xy = a + b \ln xy=a+blnx, given a=12.3301088919a = 12.3301088919a=12.3301088919 and b=−8.22097130319b = -8.22097130319b=−8.22097130319, and y=−16y = -16y=−16.

Problem 7806

Solve the trigonometric equation tan⁡θ=−3\tan \theta = -\sqrt{3}tanθ=−3​ using the unit circle.

Problem 7807

Find the value of xxx that satisfies the equation 83x+4=10\frac{83}{x+4}=10x+483​=10.

Problem 7808

Solve the linear equation x+3.75=5.5x + 3.75 = 5.5x+3.75=5.5 to find the value of xxx.

Problem 7809

Determine if (−1,29)(-1,29)(−1,29) is a solution to the quadratic equation y=−2x2−5x+22y=-2x^2-5x+22y=−2x2−5x+22. Show your work.

Problem 7810

Complete the exponential decay table: Original Amount: 19,00019,00019,000, Decay Rate: 13%13\%13% per year, Years: 181818, Final Amount after 181818 years of decay.

Problem 7811

Solve for xxx in the equation 1.008165=22−x−1.008165x21.008165=\frac{2}{2-x}-\frac{1.008165 x}{2}1.008165=2−x2​−21.008165x​.

Problem 7812

Determine which term the negative sign belongs to in the expression 16t−3t16 t-3 t16t−3t compared to 3t−16t3 t-16 t3t−16t.

Problem 7813

Solve the system of linear equations to find the common solution.x+y=20x+y=20x+y=20 and y=2x−1y=2x-1y=2x−1 y=2xy=2xy=2x and y=−6x+4y=-6x+4y=−6x+4

Problem 7814

Solve for x in the linear equation 12−12x=−6x+4812-12x=-6x+4812−12x=−6x+48.

Problem 7815

Simplify the expression −8(−4x3+5−2y2)-8(-4x^3 + 5 - 2y^2)−8(−4x3+5−2y2) using the distributive property.

Problem 7816

Find the product of two complex numbers and express the result in the form a+bia + bia+bi.

Problem 7817

Identify the levels of measurement: {\{{Nominal Data, Ratio, Quantitative Data, Ordinal Data}\}}

Problem 7818

Perform the indicated operation 2.6+2.12.6 + 2.12.6+2.1 and use a calculator to verify the result.

Problem 7819

Determine if the underlined value, 59%59\%59% of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

Problem 7820

Calculate the exact value of the 27P4{ }_{27} P_{4}27​P4​ permutation expression.

Problem 7821

Find the demand function D(p)=−2p2−6p+300D(p) = -2p^2 - 6p + 300D(p)=−2p2−6p+300 and its rate of change w.r.t. price ppp. Interpret the rate of change when p=$11p = \$11p=$11.

Problem 7822

Solve for height hhh given area AAA and base bbb using the formula A=bhA=bhA=bh. Options: B) h=Abh=\frac{A}{b}h=bA​

Problem 7823

Problem 7824

Find the ordered pair that satisfies the inequality 12≥2x+4y12 \geq 2x + 4y12≥2x+4y given the points (6,0)(6,0)(6,0), (0,6)(0,6)(0,6), (3,6)(3,6)(3,6), and (−2,8)(-2,8)(−2,8) on the graph of 12=2x+4y12 = 2x + 4y12=2x+4y.

Problem 7825

Find the time (in seconds) when Ana, who dives from a high springboard, hits the water given the height model h(x)=−5(x+1)(x−3)h(x) = -5(x+1)(x-3)h(x)=−5(x+1)(x−3).

Problem 7826

Multiply the complex number 9−12i9-12i9−12i by its complex conjugate and simplify the result.

Problem 7827

Solve the equation 8x=2x\frac{8}{x}=2xx8​=2x graphically and numerically.

Problem 7828

Simplify the numerical expression 82+7(−2−5)+38^{2}+7(-2-5)+382+7(−2−5)+3 using the rules for order of operations.

Problem 7829

Find the value of 12t−2y12 t - 2 y12t−2y given that x=3x = 3x=3 is a solution to the equation 2tx−y=42 t x - y = 42tx−y=4.

Problem 7830

Evaluate lim⁡x→1x−1x−1\lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{x-1}limx→1​x−1x​−1​ using the provided table of xxx and f(x)f(x)f(x) values.

Problem 7831

Solve the polynomial inequality x3−x2−12x>0x^{3} - x^{2} - 12x > 0x3−x2−12x>0 using the test-point method.

Problem 7832

Solve the equation πx+3=4πx\pi x + 3 = 4\pi xπx+3=4πx for xxx.

Problem 7833

Determine if the linear equation 3x+6y=123x + 6y = 123x+6y=12 represents a function.

Problem 7834

Solve the equation 82x−3=(116)x−28^{2x-3} = \left(\frac{1}{16}\right)^{x-2}82x−3=(161​)x−2 for the unknown variable xxx.

Problem 7835

Problem 7836

Solve for time ttt in the equation r=r0+12at2r = r_0 + \frac{1}{2}at^2r=r0​+21​at2, where r0r_0r0​ and aaa are known constants.

Problem 7837

Simplify the complex expression −6i(8+2i)-6 i(8+2 i)−6i(8+2i) and write the result in standard form.

Problem 7838

Differentiate the function f(θ)=sec⁡θ5+sec⁡θf(\theta) = \frac{\sec \theta}{5 + \sec \theta}f(θ)=5+secθsecθ​.

Problem 7839

Solve the subtraction (−7)−(+7)(-7)-(+7)(−7)−(+7) and model at least 3 subtraction problems.

Problem 7840

Solve for qqq where the product of two linear expressions equals 0. Write the solutions as integers or simplified fractions.

Problem 7841

Solve the inequality 3∣x+1∣−2<43|x+1|-2<43∣x+1∣−2<4 and select the correct solution.A) −3<x-3<x−3<x or x<1x<1x<1 B) −3<x-3<x−3<x or x>1x>1x>1 C) −3<x<1-3<x<1−3<x<1 D) −3<x-3<x−3<x and x>1x>1x>1

16. Approximate $\sqrt{2}$ as 1.414. Find approximate values for: a) $\sqrt{200}$ b) $\sqrt{20000}$
17. Approximate $\sqrt[3]{2}$ as 1.260 and $\sqrt[3]{4}$ as 1.587. Find approximate values for: a) $\sqrt[3]{2000}$ b) $\sqrt[3]{4000000}$

Evaluate $u \odot v = 2u - v$ for $4 \odot (2 \odot 5)$ .

Solve for $y$ in the equation $-\frac{y}{8}=-23$ . Simplify the solution $y=$ .

Find the value of $x$ when $y = a + b \ln x$ , given $a = 12.3301088919$ and $b = -8.22097130319$ , and $y = -16$ .

Solve the trigonometric equation $\tan \theta = -\sqrt{3}$ using the unit circle.

Find the value of $x$ that satisfies the equation $\frac{83}{x+4}=10$ .

Solve the linear equation $x + 3.75 = 5.5$ to find the value of $x$ .

Determine if $(-1,29)$ is a solution to the quadratic equation $y=-2x^2-5x+22$ . Show your work.

Complete the exponential decay table: Original Amount: $19,000$ , Decay Rate: $13\%$ per year, Years: $18$ , Final Amount after $18$ years of decay.

Solve for $x$ in the equation $1.008165=\frac{2}{2-x}-\frac{1.008165 x}{2}$ .

Determine which term the negative sign belongs to in the expression $16 t-3 t$ compared to $3 t-16 t$ .

Solve the system of linear equations to find the common solution.
$x+y=20$ and $y=2x-1$ $y=2x$ and $y=-6x+4$

Solve for x in the linear equation $12-12x=-6x+48$ .

Simplify the expression $-8(-4x^3 + 5 - 2y^2)$ using the distributive property.

Find the product of two complex numbers and express the result in the form $a + bi$ .

Identify the levels of measurement: $\{$ Nominal Data, Ratio, Quantitative Data, Ordinal Data $\}$

Perform the indicated operation $2.6 + 2.1$ and use a calculator to verify the result.

Determine if the underlined value, $59\%$ of passes completed for 265 yards and 2 TDs, is a parameter or statistic.

Calculate the exact value of the ${ }_{27} P_{4}$ permutation expression.

Find the demand function $D(p) = -2p^2 - 6p + 300$ and its rate of change w.r.t. price $p$ . Interpret the rate of change when $p = \$11$ .

Solve for height $h$ given area $A$ and base $b$ using the formula $A=bh$ . Options: B) $h=\frac{A}{b}$

Find the ordered pair that satisfies the inequality $12 \geq 2x + 4y$ given the points $(6,0)$ , $(0,6)$ , $(3,6)$ , and $(-2,8)$ on the graph of $12 = 2x + 4y$ .

Find the time (in seconds) when Ana, who dives from a high springboard, hits the water given the height model $h(x) = -5(x+1)(x-3)$ .

Multiply the complex number $9-12i$ by its complex conjugate and simplify the result.

Solve the equation $\frac{8}{x}=2x$ graphically and numerically.

Simplify the numerical expression $8^{2}+7(-2-5)+3$ using the rules for order of operations.

Find the value of $12 t - 2 y$ given that $x = 3$ is a solution to the equation $2 t x - y = 4$ .

Evaluate $\lim _{x \rightarrow 1} \frac{\sqrt{x}-1}{x-1}$ using the provided table of $x$ and $f(x)$ values.

Solve the polynomial inequality $x^{3} - x^{2} - 12x > 0$ using the test-point method.

Solve the equation $\pi x + 3 = 4\pi x$ for $x$ .

Determine if the linear equation $3x + 6y = 12$ represents a function.

Solve the equation $8^{2x-3} = \left(\frac{1}{16}\right)^{x-2}$ for the unknown variable $x$ .

Solve for time $t$ in the equation $r = r_0 + \frac{1}{2}at^2$ , where $r_0$ and $a$ are known constants.

Simplify the complex expression $-6 i(8+2 i)$ and write the result in standard form.

Differentiate the function $f(\theta) = \frac{\sec \theta}{5 + \sec \theta}$ .

Solve the subtraction $(-7)-(+7)$ and model at least 3 subtraction problems.

Solve for $q$ where the product of two linear expressions equals 0. Write the solutions as integers or simplified fractions.

Solve the inequality $3|x+1|-2<4$ and select the correct solution.
A) $-3<x$ or $x<1$ B) $-3<x$ or $x>1$ C) $-3<x<1$ D) $-3<x$ and $x>1$

Divide $8.8 \times 10^{-3}$ by $2.4 \times 10^{-7}$ and give the answer in scientific notation.

Solve for $w$ where $w^{2}-4=0$ . Write answers as integers or simplified fractions.

Simplify $\frac{x^{4}+7 x^{3}-10 x^{2}-63 x+9}{x^{2}-9}$ where $x^{2} \neq 9$ using long or synthetic division.

Solve the inequality $3(x-9)<15$ and select the correct answer.

Simplify the expression $\frac{5}{7 y} \times \frac{10}{3 y}$ .

Convert temperature from Fahrenheit to Celsius given $101^\circ F$ .

Solve for the unknown value $u$ given the equation $10.24 = 4u$ .

Find the ratio of roses to daisies and daisies to all flowers in a vase with 5 roses and 11 total flowers.
(a) Ratio of roses to daisies: $\frac{5}{11-5}$ (b) Ratio of daisies to all flowers: $\frac{11-5}{11}$

Describe the types of symmetry in the circle with equation $x^2 + y^2 = 1$ .

Determine the number of significant digits in the value $587,410$ .

Solve $\left(u-14\right)\left(u+10\right)=-104$ using the completing the square method. Answer: $u=\pm 2, \pm 12$

Find the derivative of $\sqrt{5 x^{2}-4}$ with respect to $x$ .

Solve for the variable $v$ in the equation $3xy = v/4$ .

Solve for $x$ : $x+8=60$ , $\frac{x}{4}=50$ , $x^{2}=400$ , $54=9 x$ , $60=35+x$ .

Solve for the value of $d$ in the equation $4d - 4 = 5d - 8$ .

Solve for $m$ in the equation $12.6+4m=9.6+8m$ .

Solve for $u$ where $(5u-2)(-3u+4)=0$ . Write the solutions as integers or simplified fractions.

Solve $\left(u+3\right)^{3/2} = 6$ for real number $u$ , and simplify the solution.

Find values of $x$ that cannot be solutions to the equation $\frac{7}{4x+1} - \frac{1}{x-2} = 0$ .

Compare the numbers. Pick the correct sign: $-7 ? 6$ , where the options are $>$ , $<$ , or $=$ .

Solve for $x$ , rounding to the nearest tenth if necessary. $\frac{9}{4}=\frac{7 x+6}{2}$

Determine if $t=-5$ is a solution to the equation $-2t^3 - 4t^2 + 4t - 3 = 127$ .

Calculate the range, variance, and standard deviation for the given samples. a. $34, 47, 45, 40, 48$ , b. $100, 3, 9160, 16207$ , c. $100, 35, 40, 6040, 447$ . a. The range is $\square$ .

Evaluate the definite integral of $\frac{4y}{e^{2y}}$ from 0 to 1.

Solve for $x$ in the equation $x \times -6.3 = -3$ .

Find the y-intercept of the line passing through the points $(8,6)$ and $(4,22)$ .

Find the number of solutions for the system of linear equations: $x+y+z=66$ and $5x+10y+20z=730$ , where $x, y, z$ are integers.

Solve the equation $8-8x=(3x+1)(x-1)$ by factoring. The solution set is $x=1, -\frac{1}{3}$ .

Determine if $u$ values satisfy inequality $37 \leq 25+u$ and mark solution status.