Math Statement

Problem 14601

You wish to test the following claim (Ha)\left(H_{a}\right) at a significance level of α=0.02\alpha=0.02. Ho:μ=82.2Ha:μ<82.2\begin{array}{c} H_{o}: \mu=82.2 \\ H_{a}: \mu<82.2 \end{array}
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=18n=18 with mean M=78.3M=78.3 and a standard deviation of SD=18.2S D=18.2.
What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = \square What is the p-value for this sample? (Report answer accurate to four decimal places.) p -value == \square

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Problem 14602

A model helicopter takes off from a point OO at time t=0 st=0 \mathrm{~s} and moves vertically so that its height y cmy \mathrm{~cm}, above OO after time tt seconds is given by y=14t426t2+96t,0t4y=\frac{1}{4} t^{4}-26 t^{2}+96 t, \quad 0 \leq t \leq 4 a) Find (i) dydt\frac{d y}{d t} (ii) d2ydt2\frac{d^{2} y}{d t^{2}} b) Verify that yy has a stationary value when t=2t=2 and determine whether this stationary value is a maximum or a minimum value. c) Find the rate of change of yy with respect to tt when t=1t=1. d) Determine whether the height of the helicopter is increasing or decreasing at the instant when t=3t=3.

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Problem 14603

Consider the expression 2x3+5x2+5x3x3+1\frac{2 x^{3}+5 x^{2}+5 x}{3 x^{3}+1}.
Part: 0/30 / 3
Part 1 of 3 (a) Divide the numerator and denominator by the greatest power of xx that appears in the denominator. That is, divide each term in the numerator and denominator by x3x^{3}. Write your answers with positive exponents only. 2x3+5x2+5x3x3+1=+++\frac{2 x^{3}+5 x^{2}+5 x}{3 x^{3}+1}=\frac{\square+\square+\square}{\square+\square}

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Problem 14604

Simplify. 18w7w3w1518 w^{7} \sqrt{w}-3 \sqrt{w^{15}}
Assume that the variable represents a positive real numbe

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Problem 14605

Simplify. 18w7w3w1518 w^{7} \sqrt{w}-3 \sqrt{w^{15}}
Assume that the variable represents a positive real number.

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Problem 14606

Simplify the radical. Assume that all variables represent positive numbers 81a13\sqrt{81 a^{13}} 81a13=\sqrt{81 a^{13}}= \square (Type an exact answer in simplified form.)

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Problem 14607

Multiply. (3+46)(3+410)(3+4 \sqrt{6})(3+4 \sqrt{10})
Simplify your answer as much as possible. \square

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Problem 14608

Which function has the greatest maximum value? (a) y=2sin3(x+90)+5y=2 \sin 3\left(x+90^{\circ}\right)+5 b) y=3sin2(x+90)3y=3 \sin 2\left(x+90^{\circ}\right)-3 c) y=13sin3(x+90)1y=\frac{1}{3} \sin 3\left(x+90^{\circ}\right)-1 d) y=sin0.5(x90)y=\sin 0.5\left(x-90^{\circ}\right)

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Problem 14609

216÷(14)-2 \frac{1}{6} \div\left(-\frac{1}{4}\right)

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Problem 14610

ir welchen Wert des Paran sssene Fläche den Inhalt b) f(x)=x2g(x)=ax+2a2A=4,5\begin{array}{l} f(x)=x^{2} \\ g(x)=-a x+2 a^{2} \\ A=4,5 \end{array}

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Problem 14611

 solve: 2xyy=y2x2\text { solve: } 2 x y y^{\prime}=y^{2}-x^{2} the ODE

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Problem 14612

Find matrix PP and DD for the following Group 1: A=[204030006]A=\left[\begin{array}{lll}2 & 0 & 4 \\ 0 & 3 & 0 \\ 0 & 0 & 6\end{array}\right] Group 2: B=[120041007]B=\left[\begin{array}{ccc}-1 & 2 & 0 \\ 0 & 4 & 1 \\ 0 & 0 & 7\end{array}\right]

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Problem 14613

6x+2y=142x+5y=4(3)\begin{array}{l}6 x+2 y=-14 \\ 2 x+5 y=4(-3)\end{array}

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Problem 14614

3. Test for exactness. If exact, solve. If not, use an integrating factor to solve it. 2xydx+x2dy=02 x y d x+x^{2} d y=0

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Problem 14615

Determine the direction of the resultant of the following vectors with the xaxis(θx)\mathrm{x}-\operatorname{axis}\left(\theta_{\mathrm{x}}\right) : A=3ı^+7ȷ^+8k^B=4ı^5ȷ^+3k^C=2ı^+3ȷ^4k^\begin{array}{l} \boldsymbol{A}=3 \hat{\imath}+7 \hat{\jmath}+8 \hat{k} \\ \boldsymbol{B}=4 \hat{\imath}-5 \hat{\jmath}+3 \hat{k} \\ \boldsymbol{C}=2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k} \end{array} 9595^{\circ} b. 55.855.8^{\circ} 66.366.3^{\circ} 43.743.7^{\circ}

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Problem 14616

Suppose that the velocity v(t)v(t) (in meters per second) of a sky diver falling near the Earth's surface is given by the following exponential function, where time tt is the time after diving measured in seconds. v(t)=5555e0.26tv(t)=55-55 e^{-0.26 t}
How many seconds after diving will the sky diver's velocity be 41 meters per second? Round your answer to the nearest tenth, and do not round any intermediate computations. \square seconds

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Problem 14617

Given u=[1,2,1],v=[4,3,2]\vec{u}=[-1,2,-1], \vec{v}=[-4,3,-2] and w=[3,2,2]\vec{w}=[3,2,-2], find (i) u3v+2wu-3 \vec{v}+2 \vec{w} =[3(4);3(3);3(2)]=[12;9;6]=[3(-4) ; 3(3) ; 3(-2)]=[-12 ; 9 ;-6]

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Problem 14618

Solve for xx. log2(x+9)=log2(x6)+4\log _{2}(x+9)=\log _{2}(x-6)+4
If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". x=x= \square
No solution Explanation Check (C) 2024

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Problem 14619

اجتماع لترشيج لنادي الشطرنج Forms - Google Drive Google Translate Translate Micrometer Instructional Techno... ChatGPT C.E 123 مكهبة - Goo.. Dashboard | Pre (b) 1 (c) 2 (d) 3. (11) Which of the following is a subspace of P3P_{3} ? (a) S={pP3:p(1)=1}×S=\left\{p \in P_{3}: p(1)=1\right\} \times ax2+bx+ca x^{2}+b x+c (b) S={pP3:p(1)=0}S=\left\{p \in P_{3}: p(1)=0\right\} a+b+ca+b+c (c) β={pP3:p(0)=1}×\beta=\left\{p \in P_{3}: p(0)=1\right\} \times (少) S={pP3:p(x)=x2+ax+b,a,bR}S=\left\{p \in P_{3}: p(x)=x^{2}+a x+b, a, b \in \mathbb{R}\right\} (12) If the reduced row echelon form of AA is [122000]\left[\begin{array}{lll}1 & 2 & 2 \\ 0 & 0 & 0\end{array}\right] and a2=(2,2)Ta_{2}=(2,2)^{T}, (a) [122121]\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 2 & 1\end{array}\right] (b) [122020]\left[\begin{array}{lll}1 & 2 & 2 \\ 0 & 2 & 0\end{array}\right] 244241\begin{array}{lll} 2 & 4 & 4 \\ 2 & 4 & 1 \end{array} (c) [122122]\left[\begin{array}{lll}1 & 2 & 2 \\ 1 & 2 & 2\end{array}\right] (d) [422422]\left[\begin{array}{lll}4 & 2 & 2 \\ 4 & 2 & 2\end{array}\right]. Search

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Problem 14620

1. Which expression is equivalent to 4842\frac{4^{8}}{4^{2}} ? (A) 424^{2} (B) 464^{6} (C) 4104^{10} (D) 444^{4}

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Problem 14621

Find the nnth term of the sequence: (a) 21,32,43,54,\frac{2}{1}, \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \cdots (b) 12,14,18,116,132,-\frac{1}{2}, \frac{1}{4},-\frac{1}{8}, \frac{1}{16},-\frac{1}{32}, \cdots

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Problem 14622

Write the following numbers in standard form.
50. 3.95×10123.95 \times 10^{12} 51.9.8×10951.9 .8 \times 10^{-9}

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Problem 14623

Find dy/dxd y / d x in terms of xx and yy if x3yx4y2=0x^{3} y-x-4 y-2=0. dydx=\frac{d y}{d x}= \square

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Problem 14624

Express 240\frac{\sqrt{2}}{\sqrt{40}} as a fraction with a rational denominator. Give your answer in its simplest form.

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Problem 14625

Kuta Software - Infinite Calculus Slope at a Value Date \qquad Perio
For each problem, find the slope of the function at the given value. 1) y=x2+6x+7y=x^{2}+6 x+7 at x=2x=-2 2) y=x33x2+5y=x^{3}-3 x^{2}+5 at x=3x=3 3) y=x36x2+9x4y=x^{3}-6 x^{2}+9 x-4 at x=2x=2 4) y=x36x29x+1y=-x^{3}-6 x^{2}-9 x+1 at x=4x=-4

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Problem 14626

Solve the following equations
1. cos(4x)8=0\cos (4 x)-8=0 for the four smallest positive solutions.
2. cos(x)(2sin(x)+1)=0\cos (x) \cdot(2 \sin (x)+1)=0 on the interval [0,2π][0,2 \pi]
3. 2cos2(x)+3cos(x)+1=02 \cos ^{2}(x)+3 \cos (x)+1=0 on the interval [0,2π][0,2 \pi]

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Problem 14627

How many significant figures are there in 3,200.0003,200.000 * 1 significant figure 2 signiicant figure 3 signiicant figure 4 signiicant figure

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Problem 14628

Solve the rational equation. Express numbers as integers or simplified fractions. t+23t+65=0\frac{t+2}{3}-\frac{t+6}{5}=0
The solution set is \square \}.

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Problem 14629

p=5650,r=8.25%,t=60 days p=5650, r=8.25 \%, t=60 \text { days }
The simple interest is $\$ \square (Round to the nearest cent as needed.)

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Problem 14630

Solve the proportion. Express numbers as integers or simplified fractions. 1x3=x34\frac{1}{x-3}=\frac{x-3}{4}
The solution set is \square \}.

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Problem 14631

For the following exercises, determine whether the ordered pair is a solution to the system of equations.
2. 6x2y=243x+3y=18\begin{array}{l}6 x-2 y=24 \\ -3 x+3 y=18\end{array} and (9,15)(9,15)

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Problem 14632

log223log212\log _{2} \sqrt[3]{2} \cdot \log _{2} \frac{1}{2}

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Problem 14633

Simplify. 3z11z\sqrt{3 z} \cdot \sqrt{11 z}
Assume that the variable represents a positive real number. \square

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Problem 14634

1. Simplify the expressions to a single trigonometric function: a. csc2(t)1csc2(t)\frac{\csc ^{2}(t)-1}{\csc ^{2}(t)} b. cos(x)tan(x)+sin(x)\cos (x) \tan (x)+\sin (x)
2. Consider cot(x)=13\cot (x)=\frac{1}{\sqrt{3}} a. What quadrant is the angle located? b. Will the cosine of this angle be positive or negative? c. Will the sine of this angle be positive or negative?
3. Consider the function x9x2\frac{x}{\sqrt{9-x^{2}}}. Rewrite this expression by substituting x=3sinθx=3 \sin \theta, and simplifying completely.

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Problem 14635

3. Jika f(x)=2x3f(x)=2 x-3 maka f(1)+2f(x)+f(x1)=f(1)+2 f(x)+f(x-1)=\ldots

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Problem 14636

Determine whether the ordered triples listed are solutions of the system of linear equations. {x+y+2z=05x3y+2z=105x2y+3z=0\left\{\begin{array}{rr} x+y+2 z= & 0 \\ -5 x-3 y+2 z= & -10 \\ 5 x-2 y+3 z= & 0 \end{array}\right. (a) (1,1,1)(1,1,-1) (b) (3,1,2)(3,1,-2)

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Problem 14637

11. Given the functions f(x)=cosxf(x)=\cos x and g(x)=10+xg(x)=\sqrt{10+x}, determine the value of g(f(π))g(f(\pi)). a.
3 b. 9 c. 11\sqrt{11} d. π\sqrt{\pi}
12. If f(x)f(x) and g(x)g(x) are even functions, then what type of function is y=f(x)g(x)y=f(x)-g(x) ? a. odd b. even c. neither d. cannot be determined for sure
13. To solve the inequality f(x)>g(x)f(x)>g(x), a student could graph the combined function y=f(x)g(x)y=f(x)-g(x) and identify the portions of the graph that are below the xx-axis. a) True b) false
14. If f(x)f(x) and g(x)g(x) are both functions that are defined for all xRx \in \mathbb{R}, then f(g(x))=g(f(x))f(g(x))=g(f(x)). a) True b) false
15. If f(x)f(x) is a function that is defined for all xRx \in \mathbb{R}, then f(f1(x))=xf\left(f^{-1}(x)\right)=x. a) True b) false

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Problem 14638

11. Given the functions f(x)=cosxf(x)=\cos x and g(x)=10+xg(x)=\sqrt{10+x}, determine the value of g(f(π))g(f(\pi)). (a.) 3 b. 9 c. 11\sqrt{11} d. π\sqrt{\pi}
12. If f(x)f(x) and g(x)g(x) are even functions, then what type of function is y=f(x)g(x)y=f(x)-g(x) ? a. odd b. even c. neither d. cannot be determined for sure
13. To solve the inequality f(x)>g(x)f(x)>g(x), a student could graph the combined function y=f(x)g(x)y=f(x)-g(x) and identify the portions of the graph that are below the xx-axis. a) True b) false
14. If f(x)f(x) and g(x)g(x) are both functions that are defined for all xRx \in \mathbb{R}, then f(g(x))=g(f(x))f(g(x))=g(f(x)). a) True b) false
15. If f(x)f(x) is a function that is defined for all xRx \in \mathbb{R}, then ff1(x))=x\left.f f^{-1}(x)\right)=x. a) True b) false

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Problem 14639

Given that; Torque =Fr&a=r=\mathrm{F} * \mathrm{r} \& \mathrm{a}=\mathrm{r} * alpha (angular acceleration) Prove T=Inertia*Alpha (angular acceleration)

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Problem 14640

12. If f(x)f(x) and g(x)g(x) are even functions, then what type of function is y=f(x)g(x)y=f(x)-g(x) ? a. odd b. even c. neither d. cannot be determined for sure
13. To solve the inequality f(x)>g(x)f(x)>g(x), a student could graph the combined function y=f(x)g(x)y=f(x)-g(x) and identify the portions of the graph that are below the xx-axis. a) True b) false
14. If f(x)f(x) and g(x)g(x) are both functions that are defined for all xRx \in \mathbb{R}, then f(g(x))=g(f(x))f(g(x))=g(f(x)). a) True b) false
15. If f(x)f(x) is a function that is defined for all xRx \in \mathbb{R}, then f(f1(x))=xf\left(f^{-1}(x)\right)=x. a) True b) false

Part B - Thinking and Investigation Full marks will be given only for if all steps are shown[TI - 15 marks]

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Problem 14641

For the following exercises, use addition to solve the system of equations. 8. 8x+4y=26x5y=0.7\begin{array}{l} 8 x+4 y=2 \\ 6 x-5 y=0.7 \end{array}

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Problem 14642

Factor the polynomial g(x)=8x4+44x3128x2284x+168g(x)=8 x^{4}+44 x^{3}-128 x^{2}-284 x+168 into linear and irreducible quadratic factors.
You must algebraically determine what the polynomial fully factors to AND list the rational zeros.

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Problem 14643

Find the following matrices where A=[863083]A=\left[\begin{array}{rr}8 & 6 \\ 3 & 0 \\ -8 & 3\end{array}\right] and B=[830653]B=\left[\begin{array}{rr}-8 & 3 \\ 0 & 6 \\ -5 & -3\end{array}\right]. a. A+BA+B b. -4 A c. 8A+3B-8 A+3 B a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A+B=A+B= \square (Simplify your answers.) B. This matrix operation is not possible. b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice α0\alpha_{0} A. 4 A=-4 \mathrm{~A}= \square (Simplify your answers.) B. This matrix operation is not possible. c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\square A. 8A+3B=-8 A+3 B=\square (Simplify your answers.) B. This matrix operation is not possible.

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Problem 14644

Question Evaluate. Express your answer in scientific notation. 5.8×10733,000,0005.8 \times 10^{7}-33,000,000
Answer Attempt 1 out of 2
Answer: \square ×10\times 10 \square Submit Answer

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Problem 14645

Evaluate the following expression. Express your answer as a fraction or a decimal number rounded to four decimal places. 10P810C4\frac{{ }_{10} P_{8}}{{ }_{10} C_{4}}
Answer Tables How to enter your answer (opens in new window)

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Problem 14646

f(x)=x44x38x2+12x+15f(x)=x^{4}-4 x^{3}-8 x^{2}+12 x+15
Factor the polynomial completely.

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Problem 14647

f(x)=x46x3+x2+42x56f(x)=x^{4}-6 x^{3}+x^{2}+42 x-56
Find the zero(s) at which ff "flattens out". Express the zero(s) as ordered pair(s).

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Problem 14648

6) Given that sinπ6=12\sin \frac{\pi}{6}=\frac{1}{2}, use an equivalent trigonometric expression to show that cosπ3=12\cos \frac{\pi}{3}=\frac{1}{2}

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Problem 14649

Ex) If g(x)=x+4g(x)=x+4, and h(x)=4x1h(x)=4 x-1. find ff such that g(f(x))=h(x)g(f(x))=h(x) q(f(x))=f(a(x))=xq(f(x))=f(a(x))=x

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Problem 14650

f(x)=(x+1)2(x4)3(x3)f(x)=(x+1)^{2}(x-4)^{3}(x-3)
Find the zero(s) at which ff "flattens out". Express the zero(s) as ordered pair(s)

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Problem 14651

2sinxcosx=3sinx2 \sin x \cos x=3 \sin x

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Problem 14652

The domain of the function f(x)=6x+3f(x)=6^{x+3} is (Type your answer in interval notation.)

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Problem 14653

Given: ABBC,AC\overline{A B} \cong \overline{B C}, \angle A \cong \angle C and BD\overline{B D} bisects AC\overline{A C}. Prove: ABDCBD\triangle A B D \cong \triangle C B D.

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Problem 14654

Which expression is equal to 3332?3^{3} \cdot 3^{2} ?
Part A (A) 313^{1} (B) 353^{5} (C) 363^{6} (D) 393^{9}
Part B Evaluate the expression.

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Problem 14655

6. Evaluate 54545^{4} \cdot 5^{-4} (A) 0 (B) 1 (C) 5 (D) 5165^{-16}

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Problem 14656

er the following polynomial function. f(x)=x4+4x33x224x18f(x)=x^{4}+4 x^{3}-3 x^{2}-24 x-18 of 4 : Factor the polynomial completely.

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Problem 14657

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate log7(7x)log7(7x)=\begin{array}{c} \log _{7}(7 x) \\ \log _{7}(7 x)= \end{array} \square

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Problem 14658

f(x)=x4+4x33x224x18f(x)=x^{4}+4 x^{3}-3 x^{2}-24 x-18
Find the zero(s) at which ff "flattens out". Express the zero(s) as ordered pair(s).

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Problem 14659

Find the difference quotient and simplify. f(x)=2x22x+6f(x)=-2 x^{2}-2 x+6
The difference quotient of f(x)f(x) is \square

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Problem 14660

Use properties of logarithms to expand each logarithmic expression log4(c64)\log _{4}\left(\frac{\sqrt{c}}{64}\right) \square

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Problem 14661

25. Find the domain of the function f(x)f(x). f(x)=12xf(x)=\sqrt{1-2 x}

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Problem 14662

Solve: 2x+7402|x+7|-4 \geq 0 Express the answer in set-builder notation. {x5<x<6}\{x \mid 5<x<6\} {xx5}\{x \mid x \geq-5\} {xx9\{x \mid x \leq-9 or x5}x \geq-5\} {x9<x<5}\{x \mid-9<x<-5\} DONE

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Problem 14663

Use properties of logarithms to condense the logarithmic expression logarithmic expressions. lnx+ln11\ln x+\ln 11

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Problem 14664

Which compound inequality can be used to solve the inequality 3x+2>7|3 x+2|>7 ? 7<3x+2>7-7<3 x+2>7 7>3x+2>7-7>3 x+2>7 3x+2>73 x+2>-7 or 3x+2>73 x+2>7 3x+2<73 x+2<-7 or 3x+2>73 x+2>7

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Problem 14665

[X]. Graph this line using the slope and yy-intercept: y=15x+7y=-\frac{1}{5} x+7
Click to select points on the graph.

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Problem 14666

1)
Determine the first six terms of the sequence defined by t1=5t_{1}=-5 and tn=3xm1+8t_{n}=-3 x_{m-1}+8.

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Problem 14667

x2x2x+3x+4\frac{x^{2}-x-2}{x+3}-x+4

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Problem 14668

Question Evaluate the indefinite integral xx9dx\int x \sqrt{x-9} d x

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Problem 14669

2)
Consider the sequence 1,23,49,827,1,-\frac{2}{3}, \frac{4}{9},-\frac{8}{27}, \ldots. Determine s8s_{8}.

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Problem 14670

Find the domain of the function. g(x)=16+2xg(x)=\sqrt{16+2 x}
Write your answer using interval notation. \begin{tabular}{|c|} \hline \multirow[t]{3}{*}{(1.ㄴ]} \\ \hline \\ \hline \\ \hline \end{tabular}

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Problem 14671

7) Let z=cos(π/24)+isin(π/24)=eiπ/24z=\cos (\pi / 24)+i \sin (\pi / 24)=e^{i \pi / 24}. What is z0z^{0} in the standard form a+bia+b i ? (a) 12+12i\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} i (b) 12+12i-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} i (c) is (d) i-i (e) 1

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Problem 14672

f(x)=x+7x3f(x)=\frac{-x+7}{x-3} Encuentra el dominio de la función.

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Problem 14673

a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 35\frac{3}{5} as a terminating decimal is \square - (Type an integer or a decimal.) B. 35\frac{3}{5} cannot be written as a terminating decimal.

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Problem 14674

b. Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. 17200\frac{17}{200} as a terminating decimal is \square . (Type an integer or a decimal.) B. 17200\frac{17}{200} cannot be written as a terminating decimal.

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Problem 14675

c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 36\frac{3}{6} as a terminating decimal is \square . (Type an integer or a decimal.) B. 36\frac{3}{6} cannot be written as a terminating decimal.

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Problem 14676

Question Evaluate using integration by parts. xe4xdx\int x e^{-4 x} d x

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Problem 14677

Let A(t)=3000e0.03tA(t)=3000 e^{0.03 t} be the balance in a savings account after tt years. Complete parts (a) through ( ff ) below. (Kound to the nearest cent as needed.) (d) What differential equation is satisfied by y=A(t)y=A(t) ?
The differential equation that is satisfied by y=A(t)y=A(t) is A(t)=0.03A(t)A^{\prime}(t)=0.03 A(t). (e) Use the results from parts (c) and (d) to determine how fast the balance is growing after 11 years.
The balance is growing at approximately $\$ \square per year after 11 years. (Round to the nearest cent as needed.)

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Problem 14678

f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. 11915,625\frac{119}{15,625} as a terminating derimal is \square (Type an integer or a decimal.) B. 11915,625\frac{119}{15,625} cannot be written as a terminating decimal.

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Problem 14679

Find the inverse for each of the following functions. a) f(x)=9x+8f(x)=9 x+8 f1(y)=x989f^{-1}(y)=\frac{x}{9}-\frac{8}{9} b) g(x)=3x210g(x)=3 x^{2}-10, with domain x0x \geq 0 g1(y)=g^{-1}(y)= \square c) h(x)=9x+10h(x)=\frac{9}{x+10} h1(y)=10+9xh^{-1}(y)=-10+\frac{9}{x}

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Problem 14680

Question Evaluate xe5xdx\int x e^{5 x} d x. Choose u=xu=x and dv=e5xdxd v=e^{5 x} d x.

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Problem 14681

wy Apps
Radicals Simplifying a radical expression with an odd exponent
Simplify. 16u9\sqrt{16 u^{9}}
Assume that the variable represents a positive real number.

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Problem 14682

Evaluate each definite integral if it is known that 03f(x)dx=5, and 03g(x)dx=3\begin{array}{l} \int_{0}^{3} f(x) d x=-5, \text { and } \\ \int_{0}^{3} g(x) d x=3 \end{array}
Utilize properties of definite integrals to evaluate 03[2f(x)+3g(x)]dx\int_{0}^{3}[2 f(x)+3 g(x)] d x

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Problem 14683

Question
Evaluate 02(7f(x)6g(x))dx\int_{0}^{2}(7 f(x)-6 g(x)) d x given that 014f(x)dx=9,02f(x)dx=9,014g(x)dx=5\int_{0}^{14} f(x) d x=9, \int_{0}^{2} f(x) d x=-9, \int_{0}^{14} g(x) d x=5, and 02g(x)dx=3\int_{0}^{2} g(x) d x=3
Provide your answer below:

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Problem 14684

Tan601=x7=\frac{\operatorname{Tan} 60}{1}=\frac{x}{7}=

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Problem 14685

Tan60×7=\operatorname{Tan} 60 \times 7=

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Problem 14686

Find the cost function C. Determine where the cost is a minimum. (a) C(x)=14x2800C^{\prime}(x)=14 x-2800 (b) C(x)=20x8000C^{\prime}(x)=20 x-8000
Fixed cost =$4300=\$ 4300 Fixed cost =$500=\$ 500
Provide your answer below:

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Problem 14687

Four functions are given below. Perform the indicated compositions to determine which functions are inverse to each other. Be sure to simplify the results. f(x)=15x+19g(x)=x1519h(x)=x151915j(x)=15x+285\begin{array}{l} f(x)=15 x+19 \\ g(x)=\frac{x}{15}-19 \\ h(x)=\frac{x}{15}-\frac{19}{15} \\ j(x)=15 x+285 \end{array} f(g(x))=g(f(x))=f(g(x))=\square g(f(x))= \square Conclusion: ff and gg ? v^\hat{v} inverses. f(h(x))=h(f(x))=f(h(x))=\square h(f(x))= \square \square Conclusion: ff and h?h ? \approx inverses. j(g(x))=g(j(x))=j(g(x))=\square g(j(x))= \square \square Conclusion: gg and jj ? \square inverses.

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Problem 14688

Solve the following equation for uu. 8=auu=\begin{array}{l} 8=a \sqrt{u} \\ u=\square \end{array}

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Problem 14689

Solve the following equation for BB. 7B=kB=\begin{array}{l} \sqrt{7 B}=k \\ B=\square \end{array}

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Problem 14690

For each of the following sets of vectors, determine whether it is linearly independent or linearly dependent. If it is dependent, give a non-trivial linear combination of the vectors yielding the zero vector. Give your combination as an expression using u,vu, v, and ww for the vector variables u,v\mathbf{u}, \mathbf{v}, and w\mathbf{w}. a) u=[512]v=[511]w=[1021]\mathbf{u}=\left[\begin{array}{c}5 \\ 1 \\ -2\end{array}\right] \mathbf{v}=\left[\begin{array}{c}5 \\ 1 \\ -1\end{array}\right] \quad \mathbf{w}=\left[\begin{array}{c}10 \\ 2 \\ -1\end{array}\right] {u,v,w}\{\mathbf{u}, \mathbf{v}, \mathbf{w}\} is linearly dependent 0=00=0 b) u=[312]v=[905]w=[342]\mathbf{u}=\left[\begin{array}{l}3 \\ 1 \\ 2\end{array}\right] \quad \mathbf{v}=\left[\begin{array}{c}-9 \\ 0 \\ -5\end{array}\right] \quad \mathbf{w}=\left[\begin{array}{c}-3 \\ -4 \\ -2\end{array}\right] {u,v,w}\{\mathbf{u}, \mathbf{v}, \mathbf{w}\} is linearly independent SUBMIT AND MARK SAVE AND CLOSE

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Problem 14691

13x+12=14x+1\frac{1}{3} x+\frac{1}{2}=\frac{1}{4} x+1

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Problem 14692

The marginal cost of oil production, in dollars per barrel, is represented by C(x)\mathrm{C}^{\prime}(\mathrm{x}), where x is the number of barrels of oil produced. Report the units of 600C(x)dx\int_{600} \mathrm{C}^{\prime}(\mathrm{x}) \mathrm{dx} and interpret what the integral means.
The units of 600640C(x)dx\int_{600}^{640} C^{\prime}(x) d x are \square

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Problem 14693

Which statements are true? Check all that apply. The equation x4=8|-x-4|=8 will have two solutions. The equation 3.40.5x42.1=20.63.4|0.5 x-42.1|=-20.6 will have one solution. The equation 12x34=0\left|\frac{1}{2} x-\frac{3}{4}\right|=0 will have no solutions. The equation 2x10=20|2 x-10|=-20 will have two solutions. The equation 0.5x0.75+4.6=0.25|0.5 x-0.75|+4.6=0.25 will have no solutions. The equation 18x1=5\left|\frac{1}{8} x-1\right|=5 will have infinitely many solutions.

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Problem 14694

1) 34x=25\frac{3}{4} x=\frac{2}{5}

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Problem 14695

y=12x+4y=2x1\begin{array}{c} y=-\frac{1}{2} x+4 \\ y=2 x-1 \end{array}
Plot two lines by clicking the graph. Click a line to delete it.

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Problem 14696

13x+1=x+15\frac{1}{3} x+1=-x+\frac{1}{5}

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Problem 14697

Consider the following vectors: a=[1231]b=[1412]c=[22101]\mathbf{a}=\left[\begin{array}{c} 1 \\ 2 \\ -3 \\ -1 \end{array}\right] \quad \mathbf{b}=\left[\begin{array}{c} 1 \\ 4 \\ -1 \\ -2 \end{array}\right] \mathbf{c}=\left[\begin{array}{c} 2 \\ -2 \\ -10 \\ -1 \end{array}\right]
For each of the following vectors, determine whether it is in span{a,b,c}\operatorname{span}\{\mathbf{a}, \mathbf{b}, \mathbf{c}\}. If so, express it as a linear combination using a,ba, b, and cc as the names of the vectors above. v1=[24120]\mathbf{v}_{1}=\left[\begin{array}{c}2 \\ -4 \\ -12 \\ 0\end{array}\right] < Select an answer > v2=[2824]\mathbf{v}_{2}=\left[\begin{array}{c}-2 \\ -8 \\ 2 \\ 4\end{array}\right] \quad Select an answer > v3=[10266]\mathbf{v}_{3}=\left[\begin{array}{c}-10 \\ 2 \\ 6 \\ -6\end{array}\right] < Select an answer >

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Problem 14698

12x13=14x15\frac{1}{2} x-\frac{1}{3}=\frac{1}{4} x-\frac{1}{5}

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Problem 14699

Example 4: Prove cosx=1cosxsinxtanx\cos x=\frac{1}{\cos x}-\sin x \tan x
LS RS

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Problem 14700

If T:R2R3T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3} is a linear transformation and the action of TT on the special vectors u\mathbf{u} and v\mathbf{v} is as given, find a formula for T(x)T(\mathbf{x}), where x\mathbf{x} is any vector in R2\mathbb{R}^{2}. u=[34]v=[45]T(u)=[222]T(v)=[323]T[xy]=[000]\begin{array}{l} \mathbf{u}=\left[\begin{array}{l} -3 \\ -4 \end{array}\right] \quad \mathbf{v}=\left[\begin{array}{l} 4 \\ 5 \end{array}\right] \quad T(\mathbf{u})=\left[\begin{array}{c} -2 \\ -2 \\ 2 \end{array}\right] \quad T(\mathbf{v})=\left[\begin{array}{c} 3 \\ 2 \\ -3 \end{array}\right] \\ T\left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right] \end{array}

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