Download Exam 1 with Resolutions - Introduction to Quantitative Reasoning | MATH 1030 and more Exams Mathematics in PDF only on Docsity!
Exam 1 Solutions
MATH 1030-008 Spring 2008
- (5 Points) You invest $1000 into a mutual fund. In 5 years, this investment is worth $2500. Describe your profit in both relative and absolute terms.
Absolute Change = N V − RV = 2500 − 1000 = 1500
Relative Change =
N V − RV
RV
= 1.5 or 150 %
- (5 points) The number of students at a local high school decreased by 15% one year and increased 8% the following year. By what percent, did the number of students change over the two year period?
Let S be the original number of students, S 1 be the number of students after year 1, and S 2 be the number of students after year 2. We have
S 1 = (100 − 15)% of S = 0. 85 × S and S 2 = (100 + 8)% of S 1 = 1. 08 × S 1.
Therefore, S 2 = 1. 08 × S 1 = 1. 08 × (0. 85 × S) = 0. 918 × S.
This tells us that the percentage change is
(0. 918 − 1) × 100 = − 8 .2 %
- (5 points) On Monday, the average temperature was reported to be 101◦^ F. On Tuesday, the average temperature was reported to be 40◦^ C. Which was the hotter of the two days?
We need to compare the two temperatures. So, we need to either convert the Monday temperature to Celsius or the Tuesday temperature to Fahrenheit.
C 1 =
F 1 − 32
≈ 38. 3 ◦C
F 2 = 1. 8 C 2 + 32 = 1.8(40) + 32 = 104◦F
From the above calculations, we can see that it was hotter on Tuesday.
- (5 points) Draw a Venn diagram that represents the following scenario and answer the questions that follow. A group of 120 people were polled to see whether they had a dog, a cat, or a tarantula
as a pet. The following results were obtained.
15 have a cat, but not a dog or a tarantula. 22 have a dog, but not a cat or a tarantula. 13 have a tarantula, but not a cat or a dog. 8 have a cat and dog, but not a tarantula. 45 have a dog and a tarantula, but not a cat. 5 have a tarantula and a cat, but not a dog. 8 have none of the three pets.
How many people have all three pets? How many people have a dog or a tarantula?
See Handout.
- (5 points) Determine whether the following deductive arguement is valid by using a Venn diagram. Is the arguement sound?
Premise: Everyone who gets their flu shot does not get the flu. Premise: Jackie got her flu shot. Conclusion: Jackie did not get the flu.
See Handout.
- (5 points) You are riding your bicycle at a speed of 5 miles per hour.
a) What is your speed in feet per minute? b) How long will it take you (in minutes) to travel 1000 feet?
a) First, recall that 5280 ft = 1 mile and 60 min = 1 hr. From these conversion factors, we can convert the 5 miles per hour as follows.
Speed = 5 miles hr
×
5280 ft 1 mile
×
1 hr 60 min
440 ft min
b) For this part, recall that distance = speed × time. This tells us that time = distance/speed. Therefore,
Time = distance speed
1000 ft 440 ft per min ≈ 2 .273 min
- (5 Points) At a market place in Brazil, you want to buy some apples. The apples are priced at 4.25 Brazilian Reals per kilogram. If you have 12 Canadian Dollars with you, can you buy 4 pounds of apples? Note that 1.745 Brazil Real = 1Canadian Dollar.
