# Math 103

Math 103 Final Exam – June, 2021 Upload file(s) as “Last_Name final” etc

Open book (notes) examination, including the formula sheet PDFs. You may use a calculating device. FOR FULL CREDIT show work in each question, not just an answer. You do not need to show every step

but should include setting up each problem: filled-in formulas, initial calculations, organize info into tables or graphs, etc.

Upload the completed final, preferably as PDF, to the Assignments section of the LEO class site.

1) Solve: 8 – 4(2x + 7) = 9x – 3x – 4

2) The price of a home is $270,000. The bank requires a 15% down payment. After the down payment, the balance is financed with a 30-year fixed-rate mortgage at 6.5%. a) Determine the monthly mortgage payment. b) Find the total cost of interest over 30 years.

3) In a wildlife refuge 34 tigers are caught and tagged. Later 18 tigers are caught in the same wildlife refuge and 5 are found to have tags. Estimate the number of tigers in the wildlife refuge.

4) If the scores for a test are normally distributed with a mean of 58 and a standard deviation of 12, find the percentage of scores that are between 64 and 66.

5) Solve: 2x² + 3x – 6 = 0

6) Given the line y = –0.5x + 2 a) Find the slope of the line. b) Find the y-intercept of the line. c) Find the x-intercept of the line. d) Graph the line (label its scale).

1

7) Use this set of numbers: 9, 5, 6, 11, 6, 10, 7, 5 and find the: a) mean. b) mode. c) median. d) sample standard deviation.

8) The chart below shows the numbers of threatened species in the United States and abroad.

Species Mammals Birds Reptiles Amphibians USA 11 15 23 10

Not USA 22 7 16 3 If one threatened species is selected at random, find the probability that it is a) in the USA. b) an amphibian or is located outside the USA.

c) it is a reptile and is in the USA. d) a bird, given it is in the USA.

9) A bicycle manufacturer believes a company’s dollar profit P, is related to the number of bicycles produced and sold, x, by the function P(x) = –0.25x² + 850 – 75000. According to the function, what is the maximum profit the manufacturer can expect?

10) The ‘True Neapolitan Pizza Association’ puts tight conditions on a pizza that can be called a Neapolitan pizza. For instance, they have determined the ingredients for the dough and how long it should rise. Another condition is that the pizza should be baked at 475° F. The formula F = (9/5)C + 32 is one way to convert from Celsius to Fahrenheit. According to the TNPA’s rules, an oven with a Celsius scale should be set to what °C temperature?

11) A day care offers two options. Plan 1 allows a child to attend the day care any time during the work week for a cost of $231 per month. Plan 2 requires a $75 per month fee plus $3.25 per hour. After how many hours will the costs of the two plans be the same?

2

12) Given the function f(x) = – x² – 4x + 5 find the a) vertex, b) x-intercepts, c) y-intercept, and d) Graph the function (sketch a grid and indicate its scale).

13) A small pizzeria has mushrooms, pineapple, ham, pepperoni, olives, sausage, onions, anchovies, and tomatoes for pizza toppings. This pizzeria has 4 employees total.

a) In how many ways can five of the toppings be arranged on a shelf? b) This pizzeria is only open for four hours a day from 6pm to 10pm. Each day, only 2

employees work together. In how many ways can 2 of the employees be selected to work on a given night?

14) In 2020, Mexico’s population was approximately 130.1 million with a projected growth rate of 1.4% a year. The function P( x) = 104 . 9 e

0. 014 x models Mexico’s population P(x), in millions, x years after 2020. According to this model, what should Mexico’s population be in 2030?

15) You borrow $3500 from a friend and promise to pay back $7,100 in five years. What simple interest rate will you pay?

16) At age 25, to save for retirement, you decide to deposit $175 at the end of each month in an IRA that pays 3.5% compounded monthly. a) How much will you have from the IRA when you retire at age 65? b) Find the interest.

3

17) A food stand at a fourth of July celebration on an overseas American military base sells hot dogs and beer. To purchase three hot dogs and two beers costs $8.45. One beer and five hot dogs costs $10. How much does the food stand charge for one hot dog? How much does it charge for one beer?

18) To pass a course a student must have at least a 60 average after three exams, but the last test counts as 2 since it’s the final. Someone with scores of 47 and 72 on the first two regular tests needs what scores on the final to pass the course?

19) A jar has: five blue tokens numbered 1, 2, 3, 6, 9; three red tokens numbered 8, 9, 10; and two yellow tokens numbered 2 and 4. a) Two tokens are drawn from the jar. The first token is not replaced before drawing the second token. What is the probability that the two tokens are blue?

b) On one draw, what is the probability of drawing a yellow token or a #2 token?

20) Below are how many Math students attended a weekend math lab for weeks 1 through 7 of spring term, plus the mean scores of the weekly tests for that class.

a) Draw a scatter plot for this data (label its scale).

b) Does there appear to be a positive correlation, a negative correlation, or no significant correlation between the number of students and the weekly mean test scores for those 7 weeks? Support your answer with an explanation.

# of students x 7 4 8 5 9 12 6

Mean test scores y 89 90 84 86 72 66 80

4