Math

Problem 63401

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

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Problem 63402

Calculate $-\frac{3}{4}+\frac{5}{6}$ .

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Problem 63403

Calculate the grams of Sodium carbonate (Na2CO3) needed for a 1.1\% w/v solution in 50 mL of water.

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Problem 63404

Solve the initial value problem $y' = 9ty^2$ , $y(0) = y_0$ , and find how the solution interval depends on $y_0$ .

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Problem 63405

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

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Problem 63406

David's total pay is given by $P = 1800 + 80N$ . What is his pay if he sells 27 copies?

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Problem 63407

Identify the sequence type: 4, 9, 16, ... Is it Arithmetic, Geometric, or Neither?

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Problem 63408

Simplify 20 - 6 + 8 ÷ 2^{3}. What is the result?

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Problem 63409

Find the derivative $f^{\prime}(x)$ of $f(x)=\frac{12}{x}$ and evaluate $f^{\prime}(-2), f^{\prime}(0), f^{\prime}(5)$ .

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Problem 63410

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

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Problem 63411

Write an equation for water in a pond: $W = 300 + 28T$ . Find $W$ after 17 minutes.

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Problem 63412

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

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Problem 63413

Write an equation for Susan's savings: starts with \$550, adds \$60 each week. Find total after 13 weeks.

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Problem 63414

Find the derivative $f^{\prime}(x)$ for $f(x)=\frac{48}{x}$ and calculate $f^{\prime}(-4)$ , $f^{\prime}(0)$ , $f^{\prime}(3)$ .

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Problem 63415

Solve $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ . Options: $-0.45$ , $-0.25$ , $0.25$ , $0.45$ .

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Problem 63416

Find the grams of NaOH required for a $0.1 \, \text{M}$ solution in a $50 \, \text{ml}$ flask with deionized water.

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Problem 63417

Find the derivative $g^{\prime}(x)$ for $g(x)=\sqrt{7 x}$ , then calculate $g^{\prime}(-3), g^{\prime}(0), g^{\prime}(4)$ .

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Problem 63418

Solve the initial value problem $y^{\prime}+7 y=g(t)$ with $y(0)=0$ , where $g(t)=1$ for $0 \leq t \leq 1$ and $g(t)=0$ for $t>1$ .

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Problem 63419

The Sugar Sweet Company has a total cost equation $C = 4500 + 150S$ . Find the cost to transport 14 tons of sugar. Total cost: \$.

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Problem 63420

Let $y$ be the total cost of publishing a book and $x$ the number of copies printed, related by $1250 + 25x = y$ .
1. What is the change in cost per book printed?
2. What is the initial cost before printing?

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Problem 63421

Solve the equation $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ .

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Problem 63422

Find the best grading parameters for a score of $X=65$ :
1. $\mu=60$ , $\sigma=5$
2. $\mu=60$ , $\sigma=10$
3. $\mu=70$ , $\sigma=5$
4. $\mu=70$ , $\sigma=10$

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Problem 63423

Find slopes and lengths for points $I(5,0)$ , $J(-2,2)$ , $K(-4,-5)$ , $L(3,-7)$ to identify the quadrilateral type.

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Problem 63424

Find the derivative $g^{\prime}(x)$ of $g(x)=\sqrt{15 x}$ , then compute $g^{\prime}(-3)$ , $g^{\prime}(0)$ , and $g^{\prime}(3)$ .

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Problem 63425

A pond's water amount $y$ in liters after $x$ minutes is given by $y=500+32x$ . Find the starting amount and change per minute.

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Problem 63426

Calculate Michael Phelps' resultant velocity swimming North at $14 \mathrm{~m/s}$ against a $5 \mathrm{~m/s}$ South current.

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Problem 63427

Chang drives to Miami. Let $y$ be his distance from Miami (miles) and $x$ be driving time (hours). The equation is $-60x + 375 = y$ .
1. What was Chang's initial distance from Miami?
2. What is the distance change per hour he drives?

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Problem 63428

Find the resultant velocity when crossing a river with a current of $15 \mathrm{~m/s}$ downstream and crossing at $2 \mathrm{~m/s}$ north.

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Problem 63429

Find the value of $\frac{4 x-y}{2 y+x}$ for $x=3$ and $y=3$ .

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Problem 63430

Find the derivative $f^{\prime}(x)$ of $f(x)=4x^{3}+10$ using the limit definition, then calculate $f^{\prime}(-1)$ , $f^{\prime}(0)$ , and $f^{\prime}(4)$ .

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Problem 63431

Find the value of $2x + 11y$ for $x = 4$ and $y = 2$ . Choices: 30, 38, 48, 136.

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Problem 63432

Prepare a 100 ppm NaCl solution from a 1000 ppm stock using $M1V1 = M2V2$ . Find the volume of stock needed.

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Problem 63433

Find the equivalent expression for $36 \div 3 + 3$ .

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Problem 63434

Alice has $\frac{3}{4}$ of a chocolate bar. How much does each of the 4 people get when shared equally?

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Problem 63435

Find slopes and lengths for quadrilateral with points Q(1,3), R(3,-4), S(9,-7), T(7,0). Identify its type.

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Problem 63436

Chau has 18 shirts. Let $N$ be shirts left after folding $F$ . Find $N$ after folding 13 shirts.

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Problem 63437

Solve for $b$ in the equation $(2b + 88) + (-6b + 74) = 170$ .

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Problem 63438

The admission fee is \ $20 per person. Let$ C $be the cost for$ P $people. Find the equation and calculate$ C$ for 13 people.

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Problem 63439

Find the value of $x$ in the equation $x - 3x = 2(4 + x)$ .

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Problem 63440

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

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Problem 63441

In a race, a turtle has a 7 km head start and runs at 2 km/hr. A rabbit runs at 7 km/hr. How long until the rabbit catches the turtle?
1. The distance that the rabbit travels is $d_r = 7 + 7t$ .
2. The distance that the turtle travels is $d_t = 2t$ .
The rabbit races a distance of $d_r$ at 7 km/hr for time $t$ .

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Problem 63442

Jean has \$280 in savings. She deposits \$30 weekly. Find total savings after 1, 2, 3, and 4 weeks:
Total after week $n$ : \$280 + \$30n.

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Problem 63443

Find the midpoints of the murder rate classes given the frequency distribution for U.S. populations in 2011.

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Problem 63444

Find the constant of proportionality for Rocko's and Louisa's game ticket purchases.

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Problem 63445

A plant is 43 cm tall and grows 1 cm/month. Find the equation for height $H$ after $M$ months and $H$ after 34 months.

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Problem 63446

Martina has 21 cars. If she rents $R$ cars, how many cars $C$ does she have left? Find $C$ after renting 14 cars.

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Problem 63447

Find the constant of proportionality in minutes per cupcake for 40 cupcakes in 70 minutes and 28 cupcakes in 49 minutes.

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Problem 63448

Given the demand $p=900-10q$ and supply $p=20q$ , find: a. Price when demand is 0. b. Price when demand is 40 units. c. Supply at \$400. d. Demand at \$400. e. Surplus or shortage at \$400? f. Graph the curves. g. Equilibrium price and quantity.

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Problem 63449

Find the constant of proportionality for the runner's distance and time: $d = 4.55, 13.65, 22.75, 31.85$ miles; $t = 0.5, 1.5, 2.5, 3.5$ hours.

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Problem 63450

Find the constant of proportionality for dietary fiber in bananas with values: 9.3, 18.6, 27.9, 37.2 g for 3, 6, 9, 12 servings.

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Problem 63451

Find the secant line equation for $y=f(x)=x^{2}+x$ at $x=-3$ and $x=-1$ , and the tangent line at $x=-3$ . Which slope formula is correct?

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Problem 63452

Find the equation for the number of vans (4 wheels) and trucks (6 wheels) given 25 vehicles and 120 wheels.

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Problem 63453

Rewrite $x^{-3}$ as a fraction.

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Problem 63454

What is the value of $(\sqrt[3]{x})^{0}$ ?

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Problem 63455

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 63456

Calculate midpoints for class intervals using the formula $\frac{{\text{{lower limit}} + \text{{upper limit}}}}{2}$ .

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Problem 63457

A plant is 11 cm tall and grows 1 cm/month. Find the equation for height $H$ after $M$ months and graph it.

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Problem 63458

Amanda has 14 cars for rent. Write the equation $C = 14 - R$ for cars left after renting $R$ . Graph it.

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Problem 63459

Which is a better central tendency measure for right-skewed salary data: mean or median? A. Median, B. Mean?

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Problem 63460

Analyze the function $R(x)=\frac{8x+8}{7x+21}$ for domain, vertical asymptote, and horizontal asymptote.

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Problem 63461

Find the lower and upper fences for outliers using the five-number summary: $55, 68, 75, 82, 98$ . Choose the correct option.

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Problem 63462

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

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Problem 63463

Identify resistant measures for describing distributions with extreme values: A. median & IQR B. mean & SD C. mean & IQR D. median & SD

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Problem 63464

Find the secant line for $y=f(x)=x^{2}+x$ at $x=3$ and $x=7$ , and the tangent line at $x=3$ .

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Problem 63465

Find the maximum height of a projectile launched at $30^{\circ}$ with an initial speed of $50 \mathrm{~m/s}$ . Use $h(t)=v_{0} \sin (\theta) t-\frac{1}{2} g t^{2}$ , where $g=9.81 \mathrm{~m/s}^{2}$ .

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Problem 63466

1. $5x + 8y \geq 100$
2. $x + y \leq 15$ Where $x$ is hours as a cashier and $y$ is hours as a lifeguard.

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Problem 63467

Find the slope of the secant line for $y=f(x)=x^{2}+x$ at $x=-3$ and $x=-1$ . Also, find the tangent line at $x=-3$ .

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Problem 63468

Find the midpoints for these classes: $0.0-4.9$ , $5.0-9.9$ , $10.0-14.9$ , $15.0-19.9$ , $20.0-24.9$ , $25.0-29.9$ , $30.0-34.9$ , $35.0-39.9$ , $40.0-44.9$ , $45.0-49.9$ , $50.0-54.9$ .

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Problem 63469

Simplify $(\sqrt[3]{x})^{6}$ .

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Problem 63470

Two cell phone companies have different pricing.
a. Write equations for Company A: $A(x) = 34 + 0.05x$ and Company B: $B(x) = 40 + 0.04x$ .
b. Compare costs for 1,160 minutes.
c. Compare costs for 420 minutes.
d. Find minutes for equal costs.

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Problem 63471

Find the proportion of bass fish lengths between 7.1 and 15.9 inches, given mean = 11.5 and SD = 2.2. Choices: A. 0.997 B. 0.95 C. 0.68 D. 0.815

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Problem 63472

Two phone companies offer plans: A: \$34 + \$0.05/min and B: \$40 + \$0.04/min. Find equations, compare costs for 1,160 and 420 mins, and find equal minutes.

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Problem 63473

Find the monthly expenses for ABC electronics as a function of units produced, given \$2.50 per unit, \$350 utilities, and \$3,300 salaries.

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Problem 63474

Find the secant line between $x=3$ and $x=7$ for $y=f(x)=x^{2}+x$ , and the tangent line at $x=3$ .

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Problem 63475

Convert $79^{\circ} \mathrm{C}$ to Fahrenheit and $90^{\circ} \mathrm{F}$ to Celsius using $y=\frac{5}{9}(x-32)$ .

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Problem 63476

Calculate $\left(\left(-6+\frac{5}{6}\right)-\left(2-\frac{4}{5}\right)\right):\left(\frac{5}{3}-0.5\right)-\frac{1}{35}$ .

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Problem 63477

A new trainee scored 74 on a test with mean 77 and standard deviation 2. How does this score compare to others?

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Problem 63478

Create a frequency distribution for 65 vehicle emissions (g/gal) using a class width of 0.75 and starting at 0.00.

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Problem 63479

Analyze the function $f(x)=(x+8)(x-2)^{2}$ : find end behavior, intercepts, zeros, turning points, and sketch the graph.

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Problem 63480

A baseball travels 302 ft at 54 mph and 386 ft at 82 mph. Find the line model and determine the distance per mph increase.

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Problem 63481

Analyze the function $H(x)=\frac{2x-6}{9-x^{2}}$ for its domain, vertical, and horizontal asymptotes.

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Problem 63482

Analyze the function $R(x)=\frac{x^{2}-100}{x^{4}-81}$ : Find its domain, vertical asymptotes, and horizontal asymptote.

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Problem 63483

Estimate the CPI for 2014 and 2015 using the line from the points (11, 225.9) and (16, 230.5).

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Problem 63484

Find the equivalent expression for $x^{6} x^{2}$ . Options: $x^{4} x^{3}$ , $x^{5} x^{3}$ , $x^{7} x^{3}$ , $x^{9} x^{3}$ .

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Problem 63485

Determine the end behavior of $f(x)=-5 x^{2}(x^{2}-11)$ and find its real zeros and their multiplicities.

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Problem 63486

What is the probability that a General Manager works at a seafood restaurant, expressed as $P(S \mid G)$ ?

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Problem 63487

Solve for real solutions of $2 x^{4}-23 x^{3}+89 x^{2}-129 x+45=0$ . A: $\mathrm{x}=$ (exact answers); B: No real solutions.

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Problem 63488

Find the probability that a student studies daily given they passed the math test: $P(S | M)$ .

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Problem 63489

You earn \$5/hour as a cashier and \$8/hour as a lifeguard. You want to work ≤15 hours and earn ≥\$100 weekly.

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Problem 63490

What defines an event in probability? Choose the correct answer: all outcomes, a subset, a planned activity, or a single execution.

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Problem 63491

Paul rolls two dice. If $A=$ both dice are odd and $B=$ at least one die is even, how do $A$ and $B$ relate? Select two: Mutually Exclusive, Not Mutually Exclusive, Independent, Dependent.

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Problem 63492

Analyze the polynomial $f(x)=(x+7)^{2}(4-x)$ . Find end behavior, intercepts, zeros, turning points, and sketch the graph.

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Problem 63493

Graph the function $f(x)=-x^{2}+4x+1$ and find its vertex, max/min, axis of symmetry, intercepts, domain, and range.

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Problem 63494

Simplify the expression $15 \times 10^{2}$ .

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Problem 63495

Analyze the polynomial $f(x)=x^{3}+x^{2}-42x$ . Answer parts (a) to (e) including intercepts and turning points.

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Problem 63496

Find the probability of a cancer patient having elective surgery given they received chemotherapy: $P(E|C)$ .

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Problem 63497

Find the line equation through points $(1,5)$ and $(-6,-3)$ . $y=$

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Problem 63498

Convert $617 \times 10^{3}$ to standard notation.

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Problem 63499

Solve for $x$ in the equation: $8 - 2x = -8x + 14$ . Options: $x = -1$ , $x = -\frac{3}{5}$ , $x = \frac{3}{5}$ , $x = 1$ .

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Problem 63500

Solve the inequality: $9x - 9 \geq -4x^2$ . Provide the solution in interval notation.

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1 ...632 633 634 635 636 637 638 ...661

Math

Problem 63401

Match the recursive definition h(1)=1,h(n)=2∗h(n−1)+1h(1)=1, h(n)=2 * h(n-1)+1h(1)=1,h(n)=2∗h(n−1)+1 with the correct sequence: A. 80,40,20,10,580,40,20,10,580,40,20,10,5 B. 1,2,4,8,161,2,4,8,161,2,4,8,16 C. 1,3,7,15,311,3,7,15,311,3,7,15,31

Problem 63402

Calculate −34+56-\frac{3}{4}+\frac{5}{6}−43​+65​.

Problem 63403

Calculate the grams of Sodium carbonate (Na2CO3) needed for a 1.1\% w/v solution in 50 mL of water.

Problem 63404

Solve the initial value problem y′=9ty2y' = 9ty^2y′=9ty2, y(0)=y0y(0) = y_0y(0)=y0​, and find how the solution interval depends on y0y_0y0​.

Problem 63405

Identify the sequence type: 25,19,13,…25, 19, 13, \ldots25,19,13,… Is it Arithmetic, Geometric, or Neither?

Problem 63406

David's total pay is given by P=1800+80NP = 1800 + 80NP=1800+80N. What is his pay if he sells 27 copies?

Problem 63407

Identify the sequence type: 4, 9, 16, ... Is it Arithmetic, Geometric, or Neither?

Problem 63408

Simplify 20 - 6 + 8 ÷ 2^{3}. What is the result?

Problem 63409

Find the derivative f′(x)f^{\prime}(x)f′(x) of f(x)=12xf(x)=\frac{12}{x}f(x)=x12​ and evaluate f′(−2),f′(0),f′(5)f^{\prime}(-2), f^{\prime}(0), f^{\prime}(5)f′(−2),f′(0),f′(5).

Problem 63410

Calculate nnn using the formula n=A⋅B×ACn = A \cdot B \times A Cn=A⋅B×AC and the determinant ∣3112−1−3∣\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|∣∣​32​1−1​1−3​∣∣​.

Problem 63411

Write an equation for water in a pond: W=300+28TW = 300 + 28TW=300+28T. Find WWW after 17 minutes.

Problem 63412

Identify the sequence: 50,60,70,…50, 60, 70, \ldots50,60,70,…. Is it Arithmetic, Geometric, or Neither?

Problem 63413

Write an equation for Susan's savings: starts with \$550, adds \$60 each week. Find total after 13 weeks.

Problem 63414

Find the derivative f′(x)f^{\prime}(x)f′(x) for f(x)=48xf(x)=\frac{48}{x}f(x)=x48​ and calculate f′(−4)f^{\prime}(-4)f′(−4), f′(0)f^{\prime}(0)f′(0), f′(3)f^{\prime}(3)f′(3).

Problem 63415

Solve 2.25−11j−7.75+1.5j=0.5j−12.25 - 11j - 7.75 + 1.5j = 0.5j - 12.25−11j−7.75+1.5j=0.5j−1. Find the value of jjj. Options: −0.45-0.45−0.45, −0.25-0.25−0.25, 0.250.250.25, 0.450.450.45.

Problem 63416

Find the grams of NaOH required for a 0.1 M0.1 \, \text{M}0.1M solution in a 50 ml50 \, \text{ml}50ml flask with deionized water.

Problem 63417

Find the derivative g′(x)g^{\prime}(x)g′(x) for g(x)=7xg(x)=\sqrt{7 x}g(x)=7x​, then calculate g′(−3),g′(0),g′(4)g^{\prime}(-3), g^{\prime}(0), g^{\prime}(4)g′(−3),g′(0),g′(4).

Problem 63418

Solve the initial value problem y′+7y=g(t)y^{\prime}+7 y=g(t)y′+7y=g(t) with y(0)=0y(0)=0y(0)=0, where g(t)=1g(t)=1g(t)=1 for 0≤t≤10 \leq t \leq 10≤t≤1 and g(t)=0g(t)=0g(t)=0 for t>1t>1t>1.

Problem 63419

The Sugar Sweet Company has a total cost equation C=4500+150SC = 4500 + 150SC=4500+150S. Find the cost to transport 14 tons of sugar. Total cost: \$.

Problem 63420

Let yyy be the total cost of publishing a book and xxx the number of copies printed, related by 1250+25x=y1250 + 25x = y1250+25x=y. 1. What is the change in cost per book printed?2. What is the initial cost before printing?

Problem 63421

Solve the equation 2.25−11j−7.75+1.5j=0.5j−12.25 - 11j - 7.75 + 1.5j = 0.5j - 12.25−11j−7.75+1.5j=0.5j−1. Find the value of jjj.

Problem 63422

Find the best grading parameters for a score of X=65X=65X=65: 1. μ=60\mu=60μ=60, σ=5\sigma=5σ=5 2. μ=60\mu=60μ=60, σ=10\sigma=10σ=10 3. μ=70\mu=70μ=70, σ=5\sigma=5σ=5 4. μ=70\mu=70μ=70, σ=10\sigma=10σ=10

Problem 63423

Find slopes and lengths for points I(5,0)I(5,0)I(5,0), J(−2,2)J(-2,2)J(−2,2), K(−4,−5)K(-4,-5)K(−4,−5), L(3,−7)L(3,-7)L(3,−7) to identify the quadrilateral type.

Problem 63424

Find the derivative g′(x)g^{\prime}(x)g′(x) of g(x)=15xg(x)=\sqrt{15 x}g(x)=15x​, then compute g′(−3)g^{\prime}(-3)g′(−3), g′(0)g^{\prime}(0)g′(0), and g′(3)g^{\prime}(3)g′(3).

Problem 63425

A pond's water amount yyy in liters after xxx minutes is given by y=500+32xy=500+32xy=500+32x. Find the starting amount and change per minute.

Problem 63426

Calculate Michael Phelps' resultant velocity swimming North at 14 m/s14 \mathrm{~m/s}14 m/s against a 5 m/s5 \mathrm{~m/s}5 m/s South current.

Problem 63427

Chang drives to Miami. Let yyy be his distance from Miami (miles) and xxx be driving time (hours). The equation is −60x+375=y-60x + 375 = y−60x+375=y. 1. What was Chang's initial distance from Miami?2. What is the distance change per hour he drives?

Problem 63428

Find the resultant velocity when crossing a river with a current of 15 m/s15 \mathrm{~m/s}15 m/s downstream and crossing at 2 m/s2 \mathrm{~m/s}2 m/s north.

Problem 63429

Find the value of 4x−y2y+x\frac{4 x-y}{2 y+x}2y+x4x−y​ for x=3x=3x=3 and y=3y=3y=3.

Problem 63430

Find the derivative f′(x)f^{\prime}(x)f′(x) of f(x)=4x3+10f(x)=4x^{3}+10f(x)=4x3+10 using the limit definition, then calculate f′(−1)f^{\prime}(-1)f′(−1), f′(0)f^{\prime}(0)f′(0), and f′(4)f^{\prime}(4)f′(4).

Problem 63431

Find the value of 2x+11y2x + 11y2x+11y for x=4x = 4x=4 and y=2y = 2y=2. Choices: 30, 38, 48, 136.

Problem 63432

Prepare a 100 ppm NaCl solution from a 1000 ppm stock using M1V1=M2V2M1V1 = M2V2M1V1=M2V2. Find the volume of stock needed.

Problem 63433

Find the equivalent expression for 36÷3+336 \div 3 + 336÷3+3.

Problem 63434

Alice has 34\frac{3}{4}43​ of a chocolate bar. How much does each of the 4 people get when shared equally?

Problem 63435

Find slopes and lengths for quadrilateral with points Q(1,3), R(3,-4), S(9,-7), T(7,0). Identify its type.

Problem 63436

Chau has 18 shirts. Let NNN be shirts left after folding FFF. Find NNN after folding 13 shirts.

Problem 63437

Solve for bbb in the equation (2b+88)+(−6b+74)=170(2b + 88) + (-6b + 74) = 170(2b+88)+(−6b+74)=170.

Problem 63438

The admission fee is \20perperson.Let20 per person. Let 20perperson.LetCbethecostfor be the cost for bethecostforPpeople.Findtheequationandcalculate people. Find the equation and calculate people.FindtheequationandcalculateC$ for 13 people.

Problem 63439

Find the value of xxx in the equation x−3x=2(4+x)x - 3x = 2(4 + x)x−3x=2(4+x).

Problem 63440

Match the recursive definition $h(1)=1, h(n)=2 * h(n-1)+1$ with the correct sequence: A. $80,40,20,10,5$ B. $1,2,4,8,16$ C. $1,3,7,15,31$

Calculate $-\frac{3}{4}+\frac{5}{6}$ .

Solve the initial value problem $y' = 9ty^2$ , $y(0) = y_0$ , and find how the solution interval depends on $y_0$ .

Identify the sequence type: $25, 19, 13, \ldots$ Is it Arithmetic, Geometric, or Neither?

David's total pay is given by $P = 1800 + 80N$ . What is his pay if he sells 27 copies?

Find the derivative $f^{\prime}(x)$ of $f(x)=\frac{12}{x}$ and evaluate $f^{\prime}(-2), f^{\prime}(0), f^{\prime}(5)$ .

Calculate $n$ using the formula $n = A \cdot B \times A C$ and the determinant $\left| \begin{array}{ccc} 3 & 1 & 1 \\ 2 & -1 & -3 \end{array} \right|$ .

Write an equation for water in a pond: $W = 300 + 28T$ . Find $W$ after 17 minutes.

Identify the sequence: $50, 60, 70, \ldots$ . Is it Arithmetic, Geometric, or Neither?

Find the derivative $f^{\prime}(x)$ for $f(x)=\frac{48}{x}$ and calculate $f^{\prime}(-4)$ , $f^{\prime}(0)$ , $f^{\prime}(3)$ .

Solve $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ . Options: $-0.45$ , $-0.25$ , $0.25$ , $0.45$ .

Find the grams of NaOH required for a $0.1 \, \text{M}$ solution in a $50 \, \text{ml}$ flask with deionized water.

Find the derivative $g^{\prime}(x)$ for $g(x)=\sqrt{7 x}$ , then calculate $g^{\prime}(-3), g^{\prime}(0), g^{\prime}(4)$ .

Solve the initial value problem $y^{\prime}+7 y=g(t)$ with $y(0)=0$ , where $g(t)=1$ for $0 \leq t \leq 1$ and $g(t)=0$ for $t>1$ .

The Sugar Sweet Company has a total cost equation $C = 4500 + 150S$ . Find the cost to transport 14 tons of sugar. Total cost: \$.

Let $y$ be the total cost of publishing a book and $x$ the number of copies printed, related by $1250 + 25x = y$ .
1. What is the change in cost per book printed?
2. What is the initial cost before printing?

Solve the equation $2.25 - 11j - 7.75 + 1.5j = 0.5j - 1$ . Find the value of $j$ .

Find the best grading parameters for a score of $X=65$ :
1. $\mu=60$ , $\sigma=5$
2. $\mu=60$ , $\sigma=10$
3. $\mu=70$ , $\sigma=5$
4. $\mu=70$ , $\sigma=10$

Find slopes and lengths for points $I(5,0)$ , $J(-2,2)$ , $K(-4,-5)$ , $L(3,-7)$ to identify the quadrilateral type.

Find the derivative $g^{\prime}(x)$ of $g(x)=\sqrt{15 x}$ , then compute $g^{\prime}(-3)$ , $g^{\prime}(0)$ , and $g^{\prime}(3)$ .

A pond's water amount $y$ in liters after $x$ minutes is given by $y=500+32x$ . Find the starting amount and change per minute.

Calculate Michael Phelps' resultant velocity swimming North at $14 \mathrm{~m/s}$ against a $5 \mathrm{~m/s}$ South current.

Chang drives to Miami. Let $y$ be his distance from Miami (miles) and $x$ be driving time (hours). The equation is $-60x + 375 = y$ .
1. What was Chang's initial distance from Miami?
2. What is the distance change per hour he drives?

Find the resultant velocity when crossing a river with a current of $15 \mathrm{~m/s}$ downstream and crossing at $2 \mathrm{~m/s}$ north.

Find the value of $\frac{4 x-y}{2 y+x}$ for $x=3$ and $y=3$ .

Find the derivative $f^{\prime}(x)$ of $f(x)=4x^{3}+10$ using the limit definition, then calculate $f^{\prime}(-1)$ , $f^{\prime}(0)$ , and $f^{\prime}(4)$ .

Find the value of $2x + 11y$ for $x = 4$ and $y = 2$ . Choices: 30, 38, 48, 136.

Prepare a 100 ppm NaCl solution from a 1000 ppm stock using $M1V1 = M2V2$ . Find the volume of stock needed.

Find the equivalent expression for $36 \div 3 + 3$ .

Alice has $\frac{3}{4}$ of a chocolate bar. How much does each of the 4 people get when shared equally?

Chau has 18 shirts. Let $N$ be shirts left after folding $F$ . Find $N$ after folding 13 shirts.

Solve for $b$ in the equation $(2b + 88) + (-6b + 74) = 170$ .

The admission fee is \ $20 per person. Let$ C $be the cost for$ P $people. Find the equation and calculate$ C$ for 13 people.

Find the value of $x$ in the equation $x - 3x = 2(4 + x)$ .

Solve for $x$ : $x^{\frac{1}{3}}=2$ .

Jean has \$280 in savings. She deposits \$30 weekly. Find total savings after 1, 2, 3, and 4 weeks:
Total after week $n$ : \$280 + \$30n.

A plant is 43 cm tall and grows 1 cm/month. Find the equation for height $H$ after $M$ months and $H$ after 34 months.

Martina has 21 cars. If she rents $R$ cars, how many cars $C$ does she have left? Find $C$ after renting 14 cars.

Given the demand $p=900-10q$ and supply $p=20q$ , find: a. Price when demand is 0. b. Price when demand is 40 units. c. Supply at \$400. d. Demand at \$400. e. Surplus or shortage at \$400? f. Graph the curves. g. Equilibrium price and quantity.

Find the constant of proportionality for the runner's distance and time: $d = 4.55, 13.65, 22.75, 31.85$ miles; $t = 0.5, 1.5, 2.5, 3.5$ hours.

Find the secant line equation for $y=f(x)=x^{2}+x$ at $x=-3$ and $x=-1$ , and the tangent line at $x=-3$ . Which slope formula is correct?

Rewrite $x^{-3}$ as a fraction.

What is the value of $(\sqrt[3]{x})^{0}$ ?

Simplify $(\sqrt[3]{x})^{6}$ .

Calculate midpoints for class intervals using the formula $\frac{{\text{{lower limit}} + \text{{upper limit}}}}{2}$ .

A plant is 11 cm tall and grows 1 cm/month. Find the equation for height $H$ after $M$ months and graph it.

Amanda has 14 cars for rent. Write the equation $C = 14 - R$ for cars left after renting $R$ . Graph it.

Analyze the function $R(x)=\frac{8x+8}{7x+21}$ for domain, vertical asymptote, and horizontal asymptote.

Find the lower and upper fences for outliers using the five-number summary: $55, 68, 75, 82, 98$ . Choose the correct option.

Simplify the expression $\left(\frac{y^{5}}{8 x^{6} y^{8}}\right)^{-\frac{1}{3}}$ .

Find the secant line for $y=f(x)=x^{2}+x$ at $x=3$ and $x=7$ , and the tangent line at $x=3$ .

Find the maximum height of a projectile launched at $30^{\circ}$ with an initial speed of $50 \mathrm{~m/s}$ . Use $h(t)=v_{0} \sin (\theta) t-\frac{1}{2} g t^{2}$ , where $g=9.81 \mathrm{~m/s}^{2}$ .

1. $5x + 8y \geq 100$
2. $x + y \leq 15$ Where $x$ is hours as a cashier and $y$ is hours as a lifeguard.

Find the slope of the secant line for $y=f(x)=x^{2}+x$ at $x=-3$ and $x=-1$ . Also, find the tangent line at $x=-3$ .

Simplify $(\sqrt[3]{x})^{6}$ .

Two cell phone companies have different pricing.
a. Write equations for Company A: $A(x) = 34 + 0.05x$ and Company B: $B(x) = 40 + 0.04x$ .
b. Compare costs for 1,160 minutes.
c. Compare costs for 420 minutes.
d. Find minutes for equal costs.

Find the secant line between $x=3$ and $x=7$ for $y=f(x)=x^{2}+x$ , and the tangent line at $x=3$ .