Analyze

Problem 12001

Find (a)(fg)(x)(a)(f \circ g)(x) and its domain, and (b)(gf)(x)(b)(g \circ f)(x) and its domain for f(x)=x,g(x)=x+9f(x)=\sqrt{x}, g(x)=x+9.

See Solution

Problem 12002

Use the distance formula to check if AB\overline{AB} and CD\overline{CD} are congruent: (61)2+(11)2\sqrt{(-6-1)^{2}+(1--1)^{2}} and (154)2+(43)2\sqrt{(15-4)^{2}+(-4-3)^{2}}. Are they congruent?

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Problem 12003

In RST\triangle R S T, U divides TS\overline{T S} in a 2:32:3 ratio. M is the midpoint of RU\overline{R U}. Find RV:RS.

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Problem 12004

What three numbers between 0.68 and 0.69 could Mario have written? Choose the correct option.

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Problem 12005

Match decimals from Set A to Set B: 0.48, 1.20, 1.09, 0.046 with 1.200, 1.090, 0.046, 0.480.

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Problem 12006

Check if line segments AB\overline{AB} and CD\overline{CD} are congruent using points A(1,1)A(1,-1), B(6,1)B(-6,1), C(4,3)C(4,3), D(5,4)D(5,-4). Use distance formula: (x2x1)2+(y2y1)2\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

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Problem 12007

Check if (fg)(x)(f \circ g)(x) equals (gf)(x)(g \circ f)(x) for f(x)=7x2f(x)=7x-2 and g(x)=2x7g(x)=2x-7. Simplify (fg)(x)=((f \circ g)(x)=\square( )).

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Problem 12008

What three numbers did Mario write between 0.68 and 0.69? Choose the correct set: A. 0.686,0.693,0.6940.686,0.693,0.694 B. 0.693,0.694,0.6980.693,0.694,0.698 C. 0.682,0.686,0.6880.682,0.686,0.688 D. 0.682,0.688,0.6940.682,0.688,0.694

See Solution

Problem 12009

Check if the following domains are correct for functions q(x)=1/xq(x)=1 / \sqrt{x} and h(x)=x2h(x)=x^2: a. Domain of q(x)/h(x)q(x) / h(x): x>0,x5x>0, x \neq 5 b. Domain of q(h(x))q(h(x)): x>5|x|>5 c. Domain of h(q(x))h(q(x)): x>0x>0

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Problem 12010

Create a frequency distribution with 5 classes for the reading times. Identify the class with the highest and lowest frequency. Data: 4, 22, 2, 20, 4, 29, 0, 2, 26, 24, 3, 2, 4, 28, 25, 23, 9, 14, 7, 4.

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Problem 12011

Use the chart to answer questions 13-15. 13. What is the value of 5 in Alaska's area? 14. Which state has a digit 6 with a value of 60,000? 15. Which state has a 7 in the thousands place? Areas: Alaska: 587,878; Texas: 266,874; California: 158,648.

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Problem 12012

Given functions f(x)=xf(x)=\sqrt{x} and g(x)=x+3g(x)=x+3, find (a)(fg)(x)(a)(f \circ g)(x) and its domain, and (b)(gf)(x)(b)(g \circ f)(x) and its domain.

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Problem 12013

Given scores S={21,29,32,38,38,45,50,64,72,100}S = \{21, 29, 32, 38, 38, 45, 50, 64, 72, 100\}, find mean, median, mode. Then, adjust for errors and removal.

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Problem 12014

Find the value of f(1)f(1) for the piecewise function f(x)={cx+1,x<22x21,x2f(x)=\left\{\begin{array}{ll}c x+1, & x<2 \\ 2 x^{2}-1, & x \geq 2\end{array}\right. if it's continuous.

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Problem 12015

Estimate the length of a human stride, given it's about 1.44 m1.44 \mathrm{~m}. Choose: (A) 1100 m1 \cdot 10^{0} \mathrm{~m} or (B) 1101 m1 \cdot 10^{1} \mathrm{~m}.

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Problem 12016

Express 19 in scientific notation. Choose between 2×1012 \times 10^{1} and 1×1011 \times 10^{1}. Which is closer to 19?

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Problem 12017

Determine the type of interval represented by the inequality 1x<91 \leq x < 9.

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Problem 12018

What type of interval is represented by the inequality 10x<1-10 \leq x < 1?

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Problem 12019

Graph the solution for the inequality 3x9-3x \leq 9.

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Problem 12020

Given data on shopping habits by location, answer these:
A) Is living location "independent" or "dependent" of shopping choice?
B) Are observed values "same" or "different" from expected if dependent?
C) Expected urban shoppers at supermarket if independent? (Round to nearest tenth)
D) What is the pp-value for independence test? (Round to nearest tenth)
E) Is there evidence of a relationship between living location and shopping choice? "yes" or "no"

See Solution

Problem 12021

Solve the inequality 4x28-4 x \geq 28 and graph the solution.

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Problem 12022

Find the angle α\alpha coterminal with θ=π14\theta=\frac{\pi}{14} in the range 2π<α<0-2\pi < \alpha < 0.

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Problem 12023

Predict Sweden's population growth using data from 2010. Find aa, bb, correlation, population in 2030, and year for 12 million.

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Problem 12024

Graph the solution for the inequality 4x<20-4x < 20.

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Problem 12025

Find the slope of the line given by the equation y=2(x+3)+1y=-2(x+3)+1.

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Problem 12026

Find expressions equivalent to 2(h5)-2(h-5): 2(h5)-2(h-5), (h5)2(h-5) \cdot-2, 2h+10-2 h+10.

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Problem 12027

Determine if the given values represent a linear or quadratic function, then calculate bab-a.

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Problem 12028

Choose the equivalent expressions for 6(8w+5)+76(8 w+5)+7: 48w+1248 w+12, 48w+3748 w+37, 6(5+8w)+76(5+8 w)+7, 37w+4837 w+48.

See Solution

Problem 12029

Choose the equivalent expressions for 7(3p+2)8p7(-3 p+2)-8 p: - 11p+14-11 p+14 - 29p+14-29 p+14 - 3(7p+2)8p-3(7 p+2)-8 p - 7(4p+p+2)8p7(-4 p+p+2)-8 p

See Solution

Problem 12030

Find expressions equivalent to 6(5v+1)3-6(5 v+1)-3. Options include: 30v9-30 v-9, (5v+1)63(5 v+1) \cdot-6-3, 6(1+5v)3-6(1+5 v)-3, 9v30-9 v-30.

See Solution

Problem 12031

Find the slope of the line given by the equation y=2(x+3)+1y=-2(x+3)+1. What is the slope?

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Problem 12032

Solve lg(4y4)ylg2=lg3\lg(4^{y}-4)-y \lg 2=\lg 3 and (4k)lg5=(5k)lg7(4k)^{\lg 5}=(5k)^{\lg 7}.

See Solution

Problem 12033

Choose the equivalent expressions for 8(2s4)-8(-2 s-4). Options include:
1. 8(5s+3s4)-8(-5 s+3 s-4)
2. 8(8s+6s4)-8(-8 s+6 s-4)
3. (2s4)8(-2 s-4) \cdot-8
4. 16s+3216 s+32

See Solution

Problem 12034

Find expressions equivalent to 4(3m+6)+2m4(3 m+6)+2 m: 2(6m+12)+2m2(6 m+12)+2 m, 14m+2414 m+24, 4(6+3m)+2m4(6+3 m)+2 m, (3m+6)4+2m(3 m+6) 4+2 m.

See Solution

Problem 12035

Find the slope and a point on the line given by the equation y=2(x+3)+1y=-2(x+3)+1.

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Problem 12036

Profit function for a bracelet company is P(x)=2(x2000)P(x)=2(x-2000).
(a) Find P(1000)P(1000) and explain its meaning. (b) Solve P(x)=0P(x)=0 and explain its meaning. (c) Determine the yy-intercept of PP and explain its meaning.

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Problem 12037

Find equivalent expressions for 2(j+9)-2(j+9). Options: (j+9)2(j+9) \cdot-2, 2(9+j)-2(9+j), 2j18-2 j-18, 7j7 j.

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Problem 12038

What type of interval is represented by the inequality 3x<4-3 \leq x < 4?

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Problem 12039

Determine the y-intercept and slope of the equation 3x+12y=93x + 12y = 9.

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Problem 12040

Is 88%88\% greater than 1720\frac{17}{20}?

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Problem 12041

Find expressions equivalent to (4d1)+(7d6)(-4 d-1)+(-7 d-6).

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Problem 12042

Choose the expressions equivalent to 7(3n+5)+47(3 n+5)+4: (3n+5)7+4(3 n+5) 7+4, 21n+3921 n+39, 5(3n+7)+45(3 n+7)+4, 7(5n+3)+47(5 n+3)+4.

See Solution

Problem 12043

Find expressions equivalent to 8(2k+3)8(-2 k+3): - 2(3k+8)-2(3 k+8) - 24k1624 k-16 - 16k+24-16 k+24 - 2(8k+3)-2(8 k+3)

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Problem 12044

Choose the equivalent expressions for 2(6f+8)+32(6 f+8)+3:
1. 6(8f+2)+36(8 f+2)+3
2. 2(8f+6)+32(8 f+6)+3
3. 12f+1912 f+19
4. 19f+1219 f+12

See Solution

Problem 12045

Find expressions equivalent to (4d3)(9d+4)(-4 d-3)-(9 d+4). Options: 13d7-13 d-7, 7d13-7 d-13, 43+13d-4-3+-13 d, (3d4)(4d+9)(-3 d-4)-(4 d+9).

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Problem 12046

Choose the equivalent expressions for (7b3)(2b+3)(-7 b-3)-(2 b+3).

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Problem 12047

Use the table to find the equation for Y2\mathrm{Y}_{2}:
X: -3, -2, -1, 0, 1, 2, 3; Y₂: 0, -1, -2, -3, -4, -5, -6.
Options: A. y2=3xy_{2}=-3-x B. y2=23xy_{2}=2-3x C. y2=x3y_{2}=x-3 D. y2=x+2y_{2}=x+2.

See Solution

Problem 12048

Find expressions equivalent to 9(2g+4)+5g9(-2 g+4)+5 g. Options: 36g1336 g-13, 13g+4-13 g+4, (2g+4)9+5g(-2 g+4) 9+5 g, 3g+363 g+36.

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Problem 12049

Choose the equivalent expressions for 3(3v+1)+43(3 v+1)+4. Options include:
1. (3v+1)3+4(3 v+1) 3+4
2. 3(2v+v+1)+43(2 v+v+1)+4
3. 1(3v+3)+41(3 v+3)+4
4. 3(1+3v)+43(1+3 v)+4

See Solution

Problem 12050

Find intervals where cost C=50x+400C=50x+400 equals revenue R=70xR=70x for break-even points.

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Problem 12051

Find the intersection points of Y1Y_{1} and Y2Y_{2} from the table: (-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6).

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Problem 12052

Find expressions equivalent to (2z1)+(5z3)(-2 z-1)+(-5 z-3).

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Problem 12053

Choose the equivalent expressions for (2z1)+(5z3)(-2z - 1) + (-5z - 3).

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Problem 12054

Choose the equivalent expressions for (2z1)+(5z(2z1))(-2 z-1)+(-5 z-(-2 z-1)).

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Problem 12055

Find the intersection points of the graphs of Y1Y_{1} and Y2Y_{2} using the given table values. List as ordered pairs.

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Problem 12056

Un comerciante visitó tres ferias, gastando \$30, \$54 y \$72, y regresó con \$48. ¿Ganó o perdió dinero? ¿Cuánto?

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Problem 12057

A chlorine sample has isotopes Cl35\mathrm{Cl}-35 (75.8\%) and Cl37\mathrm{Cl}-37 (24.3\%). What is true about its atomic mass?

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Problem 12058

Un comerciante visitó 3 ferias. Comenzó con xx, terminó con \$48. ¿Cuánto ganó o perdió después de gastar en cada feria?

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Problem 12059

Which statement is false about the atoms 13 N,14 N,15 N^{13} \mathrm{~N}, \,^{14} \mathrm{~N}, \,^{15} \mathrm{~N}?

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Problem 12060

Un comerciante visitó 3 ferias, duplicó, triplicó y cuadruplicó su dinero, gastando \$30, \$54 y \$72. Regresó con \$48. ¿Ganó o perdió dinero?

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Problem 12061

Classify each expression as a rational function, equation, or inequality:
1. 5x+23+x4=15\frac{5 x+2}{3}+\frac{x}{4}=15
2. 2x+3<1232 x+3<123
3. a2+6a+5a+1=2a+4\frac{a^{2}+6 a+5}{a+1}=2 a+4
4. f(x)=x225xf(x)=\frac{x^{2}-25}{x}
5. 6x+486 x+4 \geq 8

See Solution

Problem 12062

Identify the example of potential energy from the following options: exercise bike, chewing food, burning wood, fan blade, or water in a reservoir.

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Problem 12063

Graph the equation y=7y=7 for x=3,2,1,0,1,2,3x=-3,-2,-1,0,1,2,3. Find yy-values and select the correct graph.

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Problem 12064

Find the 10%10\% trimmed mean for the data set: 248, 261, 267, 273, 275, 279, 282, 283, 285, 285, 287, 288, 290, 290, 294, 295, 296, 300, 311, 504. Identify outliers and compare mean, median, 10%10\%, and 20%20\% trimmed means.

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Problem 12065

Is it true or false that if the product of a point's coordinates is positive, the point is in quadrant I?

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Problem 12066

Determine if the polynomial 3x(x2+5x24)(2x+1)3 x(x^{2}+5 x-24)(2 x+1) is in factored, standard, or mixed form.

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Problem 12067

Determine if the polynomial x+9(x25x+4)x + 9 \cdot (x^{2} \cdot 5x + 4) is in factored, standard, or mixed form.

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Problem 12068

Count the significant figures in the number 1.006×1071.006 \times 10^{7}.

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Problem 12069

Determine the form of the polynomial: (x+2)7x(x+1)3x4(x8)(x+2) 7 x(x+1) 3 x^{4}(x-8) (factored, standard, or mixed).

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Problem 12070

Calculate the mean, median, 10%10\% trimmed mean, and 20%20\% trimmed mean for these values: 248, 261, 267, 273, 275, 279, 282, 283, 285, 285, 287, 288, 290, 290, 294, 295, 296, 300, 311, 504. Identify outliers.

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Problem 12071

Complete the frequency distribution for the following video game hours: 13, 16, 14, 12, 8, 14, 11, 15, 3, 5, 11, 16, 2, 10, 9, 0, 12, 16, 4, 5, 17, 3, 17, 2, 13, 9, 12, 4, 10, 13, 15, 13, 15, 10, 8, 4, 15, 6.

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Problem 12072

Find the set of numbers that are both rational and irrational. Choose the correct set: A. \varnothing B. {0}\{0\} C. {x,x}\{\sqrt{x}, \sqrt{-x}\} D. {0,1,2,3,4,5,}\{0,1,2,3,4,5, \ldots\}

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Problem 12073

Calculate the density of a liquid transferred using a 10.00 mL10.00 \mathrm{~mL} pipet with uncertainty +/0.02 mL+/-0.02 \mathrm{~mL}. Initial weight: 44.5912 g+/0.0002 g44.5912 \mathrm{~g} +/-0.0002 \mathrm{~g}; final weight: 45.2199 g+/0.0002 g45.2199 \mathrm{~g} +/-0.0002 \mathrm{~g}.

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Problem 12074

Calculate the drained liquid volume from 23.15 mL±0.03 mL23.15 \mathrm{~mL} \pm 0.03 \mathrm{~mL} to 15.22 mL±0.03 mL15.22 \mathrm{~mL} \pm 0.03 \mathrm{~mL}.

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Problem 12075

Identify natural numbers from the set: {35,1.4,2,0,414,12,15,π}\{-\frac{3}{5}, 1.\overline{4}, \sqrt{2}, 0, -4\frac{1}{4}, 12, -15, \pi\}. Options: A. 12, B. 414-4\frac{1}{4}, C. -15, D. 0, E. π\pi, F. 1.41.\overline{4}, G. 2\sqrt{2}, H. 35-\frac{3}{5}.

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Problem 12076

Find the unit rate (price per cup) for popcorn in the small, medium, and large combos at Carmike Cinema.

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Problem 12077

Is the function f(x)f(x), defined as f(x)=lnx+413+xf(x)=\ln \frac{\sqrt{x+4}-1}{3+x} for x3x \neq -3 and f(3)=2f(-3)=2, continuous at x=3x=-3?

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Problem 12078

Which graph has the narrowest parabola: y=2x2+x+3y=-2x^{2}+x+3 or f(x)=4x230xf(x)=-4x^{2}-30x?

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Problem 12079

Check if the function f(x)={ex/(x+1)if x1e1if x=1f(x)=\begin{cases} e^{x /(x+1)} & \text{if } x \neq-1 \\ e^{-1} & \text{if } x=-1 \end{cases} is continuous at x=1x=-1.

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Problem 12080

Is the piecewise function f(x)={x2if x33if x<3f(x)=\begin{cases} \sqrt{x^{2}} & \text{if } x \geqslant-3 \\ -3 & \text{if } x<-3 \end{cases} continuous at x=3x=-3?

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Problem 12081

Is the function f(x)={sinxx if x01 if x=0f(x)=\left\{\begin{array}{ll}\frac{\sin x}{x} & \text { if } x \neq 0 \\ 1 & \text { if } x=0\end{array}\right. continuous at x=0x=0?

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Problem 12082

Kerry and John want to compare their sales. Who has a bigger standard deviation: Kerry's 1.11.1 or John's 1.91.9?

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Problem 12083

Is the function f(x)f(x) continuous at x=1x=-1, where f(x)=x+2f(x)=|x+2| if x1x \neq -1 and f(1)=1f(-1)=-1?

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Problem 12084

Determine if you should use sample or population standard deviation for these pumpkin weights: 12, 18, 15, 12, 15.

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Problem 12085

Find the 70th percentile of the following data from 40 companies: 1, 5, 6, 7, 8, 17, 18, 18, 22, 29, 31, 39, 43, 46, 50, 50, 51, 55, 55, 57, 59, 62, 64, 67, 71, 72, 75, 77, 77, 82, 85, 92, 92, 92, 93, 93, 95, 98, 98, 100.

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Problem 12086

What is the 3rd quartile of the following 40 sorted data values: 3, 3, 4, 15, 16, 16, 20, 23, 23, 25, 25, 26, 28, 32, 36, 38, 45, 46, 53, 54, 55, 57, 58, 62, 62, 62, 63, 70, 72, 72, 72, 75, 83, 84, 88, 91, 95, 97, 97, 100?

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Problem 12087

Is the function f(x)={1lnxπ/2 if x>eπ0 if xeπf(x)=\left\{\begin{array}{ll}\frac{1}{\ln \sqrt{x}-\pi / 2} & \text { if } x>e^{\pi} \\ 0 & \text { if } x \leqslant e^{\pi}\end{array}\right. continuous at x=eπx=e^{\pi}?

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Problem 12088

Find the 70th percentile of the following data from 40 companies: 1, 5, 6, 7, 8, 17, 18, 18, 22, 29, 31, 39, 43, 46, 50, 50, 51, 55, 55, 57, 59, 62, 64, 67, 71, 72, 75, 77, 77, 82, 85, 92, 92, 92, 93, 93, 95, 98, 98, 100.

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Problem 12089

Find the sample standard deviation of the data set 9,12,9,14,69, 12, 9, 14, 6. Round your answer to one decimal place.

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Problem 12090

Find the standard deviation of the pumpkin weights: 12, 18, 15, 13, 17.

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Problem 12091

Check if the function f(x)f(x) is continuous at x=0x=0, where f(x)={arctan1xif x>0x+π2if x0f(x)=\begin{cases}\arctan \frac{1}{x} & \text{if } x>0 \\ x+\frac{\pi}{2} & \text{if } x \leq 0\end{cases}.

See Solution

Problem 12092

Is the function f(x)=elnxf(x)=e^{\ln x} continuous at x=0x=0?

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Problem 12093

Is the piecewise function f(x)={2xif x22xif x<2f(x)=\left\{\begin{array}{ll} 2|x| & \text{if } x \geqslant -2 \\ 2x & \text{if } x < -2 \end{array}\right. continuous at x=cx=c, where c=2c=-2?

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Problem 12094

Find the zz-scores for morning and evening flights that are 30 minutes late, using averages of 15 and 20 minutes late.

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Problem 12095

Find the largest domain for which f(x)=9xf(x)=9-x is one-to-one, then provide the inverse function for that domain. Use interval notation.

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Problem 12096

Is the function f(x)={sin2x+cos2x if x>11 if x1f(x)=\left\{\begin{array}{ll}\sqrt{\sin ^{2} x+\cos ^{2} x} & \text { if } x>1 \\ 1 & \text { if } x \leqslant 1\end{array}\right. continuous at x=1x=1?

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Problem 12097

Is the function f(x)={x+42x if x>0x0.25 if x0f(x)=\left\{\begin{array}{ll}\frac{\sqrt{x+4}-2}{x} & \text { if } x>0 \\ x-0.25 & \text { if } x \leqslant 0\end{array}\right. continuous at x=cx = c? Explain.

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Problem 12098

Check if the function f(x)={x+42xif x>0x0.25if x0f(x)=\begin{cases} \frac{\sqrt{x+4}-2}{x} & \text{if } x > 0 \\ x-0.25 & \text{if } x \leq 0 \end{cases} is continuous at x=0x=0.

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Problem 12099

Find the largest one-to-one domain for f(x)=1x2+1f(x)=\frac{1}{\sqrt{x^{2}+1}} and its inverse function equation.

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Problem 12100

Find the value of cc for the piecewise function f(x)={2x+c,x1;x2+3,x>1}f(x)=\{2x+c, x \leq 1; x^2+3, x>1\} to be continuous.

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