Math 15 questions

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timer Asked: Jun 15th, 2018
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Question description

"You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit."

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Please show all work on the exam. 1) Simplify the following expression: −3(5 − 7 ) − 2 (15 − 9 ) 3 2 2) Simplify the following expression:  7  −   6 2    +  − 1   5   2  3  3) Simplify the radical expression: 5 32 − 3 48 + 4 18 4) Evaluate the following expression for x = −5 and y = −6 Math 037 Midterm Exam Page 2 of 6 −2 x3 − 3 y 2 5) Solve the equation. Show all work and show the complete check of your answer: 5x −14 = −29 6) Solve the equation. Show all work and show the complete check of your answer: 5 − 4 ( 7 x + 2) = 5x − 6 (6x − 3) Math 037 Midterm Exam Page 3 of 6 1 bh , where A = area of the triangle, b = 2 length of the base of the triangle, and h = height of the triangle. 7) The formula for area of a triangle is given by A = a) Solve the formula for h. b) Use the new version of the formula you found in part (a) to find the height of a triangle that has an area of 28 square inches and a base length of 8 inches. Show all work and write a complete answer, including units. 8) Solve the inequality. Write the answer in set-builder notation and graph the solution set on a number line. 4x − 2  7 ( x +1) Math 037 Midterm Exam Page 4 of 6 9) In a sample of 2400 new iPhones, 18 were found to be defective. At this rate, how many defective iPhones would be expected in a sample of 10,000 new iPhones? Use a proportion to set up and solve this problem. 10) Student enrollment at a university was 8500 last year and 9200 this year. Find the percentage increase in enrollment, rounding your answer to the nearest tenth of a percent. Math 037 Midterm Exam Page 5 of 6 #11 - #15) You are an environmental scientist studying the causes of global warming, and you are using the data in the table below to determine the rate of increase in Global Carbon Emissions Per Capita (per person) over time. Use the data in the table to answer the questions that follow. Year (x) Global Carbon Emissions Per Capita (metric tons) (y) Year (x) Global Carbon Emissions Per Capita (metric tons) (y) 1751 0.00367 2000 1.104 1775 0.00442 2001 1.11651 1800 0.00808 2002 1.11386 1825 0.01532 2003 1.16641 1850 0.04277 2004 1.21308 1875 0.13091 2005 1.24238 1900 0.32364 2006 1.26948 1925 0.49942 2007 1.28366 1950 0.64683 2008 1.30048 1975 1.12896 2009 1.27876 2010 1.32544 Source: http://www.ourworldindata.org/data/resources-energy/CO2-emissions #11) By how much did global per capita carbon emissions change from 1775 to 1800? Show all work and write a complete answer, including units. #12) By how much did global per capita carbon emissions change from 1875 to 1900? Show all work and write a complete answer, including units. Math 037 Midterm Exam Page 6 of 6 #13) By how much did global per capita carbon emissions change from 1975 to 2000? Show all work and write a complete answer, including units. Percentage change from one number to another can be found by determining the difference in the two numbers, dividing that difference by the original number, and multiplying by 100. For example, the percentage change in carbon emissions from 1751 to 1775 would be given by: 0.00442 − 0.00367 100 0.00367 0.00075 = 100 0.00367  0.2044 100  20.4% Percentage increase = 14) Find the percentage increase in per capita carbon emissions from 1850 to 1900. Show all work and write a complete answer, including units. 15) Find the percentage increase of per capita carbon emissions from 1950 to 2000. Show all work and write a complete answer, including units.

Tutor Answer

mickeygabz
School: Duke University

See attached

Please show all work on the exam.
1) Simplify the following expression:

−3(5 − 7 ) − 2 (15 − 9 )
3

2

= -3(-2)3 -2(6)2
=-3* -8 -2(36)
=24-72
= -48

2) Simplify the following expression:

 7
 − 
 6

2



 

+  − 1   5 
 2  3 

49 - 5
6

= 36

= 49 - 30

36

36

= 19

36

3) Simplify the radical expression:

5 32 − 3 48 + 4 18

Math 037
Midterm Exam

Page 2 of 8

= 5√16 ∗ 2 - 3 √16 ∗ 3 + 4√9 ∗ 2
= 5√16 √2 - 3 √16 √3+ 4√9√2
= 5*4√2 - 3*4 √3+ 4∗ 3√2
=20√2 - 12 √3+ 12√2
=32√2 - 12 √3

4) Evaluate the following expression for

x = −5

and

y = −6

−2 x3 − 3 y 2
= -2(-5)3 -3(-6)2
= -2(-125) -3(36)
=250- 108
= 142

5) Solve the equation. Show all work and show the complete check of your answer:

5x −14 = −29
5x = -29 + 14
5x = -15
x= -15/5
x=-3

Math 037
Midterm Exam

Page 3 of 8

6) Solve the equation. Show all work and show the complete check of your answer:

5 − 4 ( 7 x + 2) = 5x − 6 (6x − 3)
5 -28x-8...

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