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mathematics
statistics
A Pathway To Introductory Statistics 1st Edition Jay Lehmann - Solutions
Y = 5 / 6 xDetermine the slope and the y-intercept. Use them to graph the equation by hand
Y = 2Determine the slope and the y-intercept. Use them to graph the equation by hand
Y = –2x + 3Determine the slope and the y-intercept. Use them to graph the equation by hand
Graphs of four equations are shown in Fig. 135. State whether m and b are positive, negative, zero, or undefined for the y = mx + b form of each equation.
The median compensation (including salary and bonus) of college presidents was $870 thousand in 2010 and increased by about $37 thousand per year during the period 2010–2014 (Source: IRS). Let C be the median annual compensation (in thousands of dollars) of college presidents at t years since
Use the graph of the relation in Fig. 136 to determine the relation€™s domain and range. Determine whether the relation is a function.
The percentages of tax returns in which individuals donated money to presidential elections by checking off boxes (for $1, $2, $3, or $6) on tax returns are shown in Table 66 for various years.Let p be the percentage of tax returns in which presidential-election donation boxes were checked off at t
The cooking times of a turkey in a 325°F oven are shown in Table 65 for various weights.For a 325°F oven, let T be the cooking time (in hours) of a turkey that weighs W pounds.a. Identify the explanatory and response variables.b. Construct a scatterplot by hand.c. Is the association positive or
The scatterplot and the model in Fig. 133 compare the years and the median square footages of newly built homes.a. Is the association positive, negative, or neither? What does that mean in this situation?b. Estimate the slope of the model. What does it mean in this situation?c. Estimate how much
When we write -1x + 52 as -x - 5, what number have we distributed? Show the missing steps.
Explain what law was used in each step to rearrange terms of a + b + c as follows: a + b + c = (a + b) + c = (b + a) + c = b + (a + c) = b + (c + a) = (b + c) + a = b + c + a
Use the distributive law a (b – c) = ab - ac and other laws to show that (a – b)c = ac - bc.
In Section 1.6, we learned that the product of two numbers with the same sign is positive. Explain what property or law was used in each step to show why 1-221-32 = 6: (-2) (-3) = (-1∙2) (-3) = –1 (2 ∙ (–3)) = –1 (–6) = – (–6) = 6
a. Pick a number. Next, subtract 3. Then double the result. Then subtract the original number. Finally, add 6. Compare your result with the original number.b. Pick another number and follow the instructions in part (a), including comparing your result with the original number.c. Let x be a number
Which of the following expressions are equivalent?– (2x – 3) 3 - 2x -(3 - 2x) -2x + 3– (3x – 2) + x + 1 -(x – 1) – (x – 2)
Y = 9x-4 – 7 xSimplify the right-hand side of the equation. Then graph the equation by hand.
Y = 4x + 3 – 6xSimplify the right-hand side of the equation. Then graph the equation by hand.
Y = 4(2x – 1) – 5xSimplify the right-hand side of the equation. Then graph the equation by hand.
Y = –2 (3x – 2) + 5xSimplify the right-hand side of the equation. Then graph the equation by hand.
Describe the meaning of equivalent expressions.
A student works 7 hours on Monday, 3 hours on Tuesday, and 6 hours on Wednesday. The student earns $10 per hour. Show two ways to compute the student’s total earnings. Use the distributive law to explain why both methods give the same result.
5 – x = 3 (2x – 1)Determine whether 2 is a solution of the equation.
A student tries to solve the equation 3/7x = 2: 3/7x = 2 7 ∙ 3/7 x = 7 ∙ 2 7/1 ∙ 3/7 x = 14 3x = 14 3x /3 = 14/3 x = 14/3 Is the work correct? If yes, show a way to solve the equation in fewer steps. If no, describe the student’s error(s) and then solve the equation correctly.
Are the equations 2x = 10 and x + 2 = 7 equivalent?
Are the equations x (x + 1) = 6 and 2x (x + 1) = 12 equivalent? Explain.
a. Solve 2x = 7. b. Solve 5x = 9. c. Solve mx = p, where m and p are constants and m is non- zero.
– 4 / 9x = – 5
– 8 = 2x /5
4 / 7 b = – 5/21
– 5x / 4 = – 15/8
– x = 2.
X + 7.5 = – 2.8
5.27 = x – 28.85
2 – x = – 9
8x – 5x – 4 = 11
–2x + 5 = 4.Determine whether 2 is a solution of the equation.
2x + 6 – 7x = – 4
4x + 3 – 9x = –22
1 = 3x – 5 – 9x
10 = 3x – 6 – 7x
5x + 4 = 3x + 16
7x + 5 = 4x + 17
–3r –1 = 2r + 24
–6w –3 = 4w + 17
8 – 2x – 2 = 3x + x
In 2013, the sales of Monster® energy drink were $3.1 billion, which was about 35% of all energy drink sales. What were the total sales of all energy drinks?
The Sun UltraSPARC processor has multiple register sets. Describe what happens when a context switch occurs if the new context is already loaded into one of the register sets. What happens if the new context is in memory rather than in a register set and all the register sets are in use?
In 2010, there were 223 thousand new cases of lung cancer, which was about 14.6% of the new cases of all types of cancer in that year. How many new cases of cancer were there in 2010?
– 3 (x – 2) = 0Determine whether 2 is a solution of the equation.
A student tries to solve the equation x + 6 = 9: x + 6 = 9 x+ 6 – 6 = 9 x + 0 = 9 x = 9 A student tries to solve the equation x + 6 = 9:
A student x – 4 = 7:x – 4 = 7x – 4 + 4 = 7 + 4x + 0 = 11x = 11
True or False: A key step in solving an equation that contains 17. fractions is to multiply both sides of the equation by the LCD so that there are no fractions on either side of the equation.
– 2 (5x + 3) – (4x – 1) = 5(x + 2)
The percentages of American adults who have earned an annual salary over $200,000 at least once in their lives are shown in Table 14 for various years. Let p be the percentage of American adults at age a years who have earned an an- nual salary over $200,000 at least once in their lives.a.
The percentages of elementary school children who receive free or reduced-fee lunches and the percentages of bicycle riders who wear helmets are shown in Table 15 for 13 Californian neighborhoods.Let L be the percentage of children who receive free or reduced-fee school lunches, and let H = f (L)
The maximum weights and mean life expectancies of dogs are shown in Table 16 for various dog breeds.Let L = f (W) be the mean life expectancy (in years) of a dog breed with maximum weight W pounds.a. Construct a scatterplot.b. Describe the four characteristics of the association. Compute and
A student tries to solve the equation 1 / 2x + 3 = 5/2:Describe any errors. Then solve the equation correctly.
Two students try to solve the equation 5x + 3 = 3x + 7:Compare the methods of solving the equation. Is one method better than the other? Explain.
Two students try to solve the equation 2x + 4 = 0:Did either student, both students, or neither student solve the equation correctly? Explain.
Two students try to solve the equation 3 / 4x €“ 5 / 6 = 1 / 3:Compare the methods of solving the equation. Is one method better than the other? Explain.
A student tries to simplify the expression 1/4x + 1/3x:Describe any errors. Then simplify the expression correctly.
Solve 5 (x – 2) = 2x - 1. Show that your result satisfies each of the equations in your work.
Solve 3 (x + 1) + 2 = x + 7. Show that your result satisfies each of the equations in your work.
x / 9 – 1 / 3 = 2 / 9
3x / 8 – 1 / 2 = 1
5/6 k = 3 / 6 k + 1 / 2
3 / 8t = 5 / 6 t – 1 / 4
3 / 8 t = 5 / 6t – 1 / 4
5 / 4 + 9 / 2x = 3 / 8 x – 1 / 4
4 / 3x – 2 = 3x + 5 / 2
2 / 5x –4 = 2x – 3 / 4
Solve the following 3 (x – 4) / 5 = – 2x
5 (x – 2) / 3 = – 4x
4x + 3 / 5 = 2x – 1 / 3
3x + 2 / 2 = 6x – 3 / 5
4m – 5 / 2 – 3m + 1 / 3 = 5/6
2p + 4 /3 –5p –7 /6 = 11/12
5.27x – 6.35 = 2.71 x + 9.89 Round the result to the second decimal place.
8.25x – 17.56 + 4.38x = 25.86 Round the result to the second decimal place.
0.4x – 1.6 (2.5 – x) = 3.1 (x – 5.4) –11.3 Round the result to the second decimal place.
3.2x + 0.5 (7.3 – 3) = 4.7 – 6.4 (x – 2.1) Round the result to the second decimal place.
3 (x – 2) – (7x + 2) – 4 (3x + 1) Simplify the expression or solve the equation, as appropriate.
5x – 4 = 3x + 16 Simplify the expression or solve the equation, as appropriate.
3(x – 2) – (7x + 2) = 4 (3x + 1) Simplify the expression or solve the equation, as appropriate.
2x/3 – 5x / 2 – 1 = 0 Simplify the expression or solve the equation, as appropriate.
7 / 2x – 5 / 6 = 1 / 3 + 3 / 4x Simplify the expression or solve the equation, as appropriate.
€“3/2x + 2 = €“ 4Solve the given equation by referring to the graphs of y = €“3/2x + 2 and y = 1/2 x €“ 2 shown in Fig.21.
1/2x €“ 2 = €“ 3Solve the given equation by referring to the graphs of y = €“3/2x + 2 and y = 1/2 x €“ 2 shown in Fig.21.
2 (x + 3) = 5x – 3
€“ 3/2x + 2 = 2Solve the given equation by referring to the graphs of y = €“3/2x + 2 and y = 1/2 x €“ 2 shown in Fig.21.
– 3 (x – 4) = 2x + 2
Find x when f(x) = 6. Let f (x) = -3x + 7
1 – 3 (5b – 2) = 4 – (7b + 3)
Find x when f(x) = 5/2. Let f (x) = -3x + 7
Find x when f (X) = 99.34. Let f (x) = -3x + 7
The number of Americans without health insurance was 46.7 million in 2010, and it increased by about 1.04 million per year until 2013 (Source: Centers for Disease Control and Prevention). Let n be the number (in millions) of Americans without health insurance at t years since 2010.a. Find an
The minimum salary for a hockey player in the National Hockey League was $500 thousand in 2010, and it increased by about $14 thousand per year until 2015 (Source: National Hockey League Players Association). Let s be the minimum salary (in thousands of dollars) at t years since 2010.a. Find an
Martha Stewart went to prison for selling nearly 4000 shares of ImClone Systems stock because she had inside information that the company was about to announce bad news that would result in the stock’s value plummeting. Surprisingly, the value of a share of Martha Stewart Living Omnimedia stock
3 – 4 (3p + 2) = 7 – (9p – 1)
The number of Radio Shack stores was 5.74 thousand in 2010, and it decreased by about 0.21 thousand stores per year until 2013. Let n be the number (in thou- sands) of Radio Shack stores at t years since 2010.a. Find an equation of a model.b. Estimate when there were 5.1 thousand Radio Shack
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