Math 1030 Name Practice Final 1. A large cheese pizza at Tapa s Pizza costs $5.20 plus $0.85 for each topping. A large cheese pizza at Alfredo s Pizza costs $5.70 plus $0.60 per topping. a) If Charly wants five toppings on her large pizza, which pizzeria offers the better deal? Explain: b) Write an equation for the cost of a pizza from Tapa s using t to represent the number of toppings and C to represent the final cost. c) Write an equation for the cost of a pizza from Alfredo s using t to represent the number of toppings and C to represent the final cost. d) How many toppings can Charly order from Tapa s and know she is paying less than the same pizza from Alfredo s?
2. A Joe Garden wants to enclose a portion of his garden with fencing. The length of the shorter side is represented on the x- axis and the area of the enclosed portion of his garden is represented on the y-axis. The equation is: y = x 2 + 350x. a) Can Joe enclose 25,000 square feet of field? Circle the correct answer and explain. Explain: b) If the Joe wants the shorter side to be about 50 feet long, what will the corresponding area be? Area enclosed (feet squared) Length of the shorter side c) What is the greatest area Joe can enclose with the fence? d) What is the length of the shortest side that corresponds to the largest area?
3. A particular pesticide is toxic to a wide range of animals and plant life and is suspected to cause cancer in humans. We will assume the half-life of the pesticide is 8 years. This means that after 8 years, half of the initial amount of the pesticide is no longer toxic and in 16 years, half of the remaining pesticide is no longer toxic, etc. a) Let s say that 320 units of the pesticide were applied to a field in 1992. Do you anticipate more or less than 160 units still in the soil in 1998? Explain: b) How much of the pesticide that was initially applied in 1992 is still toxic in 2024? Show or explain how you arrived at your answer. c) If we assume that the pesticide is not harmful to humans at 40 units, when is the field no longer considered harmful? d) When is the pesticide completely gone? Explain.
4. Turkey prices are based on a constant price per pound. In 2009, the average price of a 15-pound holiday turkey was about $19.18 a) If someone purchased a 18-pound turkey in 2009, about how much would it have cost? b) In 2012, the average price for a 11-pound holiday turkey was about $17.09. In which year was the cost per pound of turkey lower? Explain: c) If the trend continues, what will the price per pound be in 2019? d) How much will a 17-pound turkey cost in 2019?
5. Tom and Julie, two recent high school graduates are thinking about their future. Tom feels like he can put away $1600 month. He puts the money into a savings account that earns 3% interest compounded monthly for 24 years. a) How much will Tom have in the savings account at the end of 24 years? Julie feels like her budget is currently tight, but promises herself to invest as soon as possible. Twelve years after high school, Julie invests $2000. Over the next 12 years Julie s savings account earns 3% interest compounded monthly. b) How much will Julie have in the savings account at the end of 12 years? c) At their 24 year reunion, Tom and Julie compare the amount of money in their respective savings accounts. Why does Tom have more money in his account than Julie? Explain:
6. You are interested in buying a 2016 Subaru Outback. You find one at a dealer for $14,600 with 5% interest, compounded monthly, on a five-year loan. a) You have to take out the loan from the dealer as described above. What will the minimum monthly payments be? b) Over the course of five years, how much money will you have paid the dealer for your car? c) If you paid an extra $100 dollars one time with your very first payment, what would happen to the total amount of money you ll pay the dealer for your car? Circle the correct answer and explain. Explain:
7. Three High schools participated in a track meet and tracked their times on the histograms below. Woods Cross High Viewmont High Bountiful High a) Which high school had more members participating in the track meet? b) Which running high school had the slowest individual finish time? c) Which running high school had the fastest average finish time? d) Which running high school has the smallest standard deviation? e) An error was discovered after the histograms were created. The time for one of the runners from Viewmont High school was accidentally recorded with the times for Bountiful High school. If the runner s time is correctly added to data for Viewmont High school, what will happen to the mean running time for Viewmont High school?
8. Students in Mr. Ruby s class listed their father s ages on the board: 38, 40, 42, 36, and 43 a) Compute the mean of the fathers ages. Show your work. b) Compute the standard deviation of the ages. Show your work. c) The mean age of Fathers in Mrs. Gray s class was 39 with a standard deviation of 1.7. Compare the standard deviations in Mrs. Gray s and Mr. Ruby s classes. Explain what that difference tells us in the context of the problem.
9. During the peak of summer, it has been observed that it takes an average of 15 days for a Monarch butterfly to emerge from a chrysalis. The time the butterfly spends in the chrysalis is normally distributed with a standard deviation of 2.3 days. Recall that a normal distribution is symmetric and follows the 68-95-99.7 rule a) About what percent of Monarch butterflies spend less than 17.3 days in their chrysalis? b) Between how many days would you anticipate the middle 95% of Monarch butterflies to stay in their chrysalis? c) You have been lucky enough to stumble on a freshly made Monarch chrysalis. After 18.9 days, the butterfly starts to emerge. Is that unusual? Please use math and a sentence or two to explain your answer. Math: Sentence:
10. Ryla really wants a regular watch and an Apple Watch for her birthday. Knowing her parents as she does, she thinks there is about a 55% chance they have already purchased a regular watch for her. Ryla estimates if her parents have already purchased a regular watch for her, there is a 30% chance they will purchase a Apple Watch. However, if they have not purchased a regular watch there is a 80% chance they will buy a Apple Watch. a) Draw a probability tree diagram illustrating the given information. b) What is the probability Ryla s parents have not purchased a regular watch and she does not receive a Apple Watch for her birthday? c) What is the probability Ryla does not receive a Apple Watch for her birthday? d) Given that Ryla s parents will not purchase a Apple Watch, what is the probability she does not receive a regular watch for her birthday?
11. Choose the correct answer to the questions below. Circle your answer. a) For a normal distribution, what proportion of the data falls between the mean and 2 standard deviation above the mean? i) 34% ii) 47.5% iii) 50% iv) 68% v) 95% b) Sets C and D have different cardinality. Additionally, the following sets all have different cardinality: C; D; C D; C D. Which set has the largest cardinality? i) C D ii) D C iii) Set D iv) Set C v) cannot tell from the given information c) Which account will have the most money in it at the end of 15 years? i) $50 deposited the beginning of each month earning 2% interest compounded monthly ii) $1,150 deposited at the beginning of each year earning 2% interest compounded monthly iii) $11,950 deposited once at the beginning of the 15 years earning 2% interest compounded monthly iv) $11,950 deposited once at the beginning of the 15 years earning 2% interest compounded annually v) $11,950 deposited once at the beginning of the 15 years earning 2% interest compounded daily d) One morning a gardener woke up to find a litter of five puppies in his barn. He knows that puppy populations double every 8 months. Which type of function should he use to model the number of dogs in his barn over time? i) Linear model ii) Quadratic model iii) Exponential model iv) Statistical model v) Financial model e) You flip a dime, a nickel and a half dollar. You record whether each coin landed heads-up or tails-up. How many different outcomes are possible? i) 8 ii) 4 iii) 6 iv) 3 v) 2
12. A study looked at the sleep patterns for high school students and found the following information: On weekdays, the number of hours a high school student sleeps at night is normally distributed with an average of 6.35 hours of sleep and a standard deviation of 0.25 hours On weekends, the number of hours a high school student sleeps at night is normally distributed with an average of 10.5 hours of sleep and a standard deviation of 0.95 hours. a) One weekday Jose slept 7.95 hours. Find the z-score for the number of hours Jose slept that night. Answer: b) If someone recorded getting about 8.64 hours of sleep per night, would that amount of sleep be more unusual for a weekday or a weekend? Explain your answer, you may use diagrams or mathematical equations to support your written explanation. c) Jose calculated his z-score for the number of hours he slept on a different weekend. It was positive. What do you know about the number of hours Jose slept that night?