Exercises

Set 1: State the pattern and then find the next number in the sequence.

1. [latex]\left\{17,26,35,…\right\}[/latex]
2. [latex]\left\{-1,5,-25,125,…\right\}[/latex]
3. [latex]\left\{-1,2,5,…\right\}[/latex]
4. [latex]\left\{-32,-16,-8,-4,…\right\}[/latex]
5. [latex]\left\{40,60,80,…\right\}[/latex]
6. [latex]\left\{12,17,22,…\right\}[/latex]
7. [latex]\left\{10,-3,0.9,-0.27,…\right\}[/latex]
8. [latex]\left\{-15,-7,1,…\right\}[/latex]
9. [latex]\left\{0.61,1.83,5.49,16.47,…\right\}[/latex]
10. [latex]\left\{8.9,10.3,11.7,…\right\}[/latex]
11. [latex]\left\{-0.52,-1.02,-1.52,…\right\}[/latex]
12. [latex]\left\{-32,-16,-8,-4,…\right\}[/latex]
13. [latex]\left\{14,56,224,896,…\right\}[/latex]

Set 2: Solve each problem.

1. How many outcomes are possible from tossing a pair of coins?
2. How many outcomes are possible from tossing a coin and rolling a 6-sided die?
3. How many two-letter strings—the first letter from [latex]A[/latex] and the second letter from [latex]B-[/latex] can be formed from the sets [latex]A=\left\{b,c,d\right\}[/latex] and [latex]B=\left\{a,e,i,o,u\right\}?[/latex]
4. How many ways are there to construct a string of 3 digits if numbers can be repeated?
5. How many ways are there to construct a string of 3 digits if numbers cannot be repeated?
6. Compute [latex]P\left(5,2\right)[/latex]
7. Compute [latex]P\left(8,4\right)[/latex]
8. Compute [latex]P\left(3,3\right)[/latex]
9. Compute [latex]C\left(8,5\right)[/latex]
10. Compute [latex]C\left(12,4\right)[/latex]
11. Compute [latex]C\left(26,3\right)[/latex]
12. In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1st place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?
13. A wholesale T-shirt company offers sizes small, medium, large, and extra-large in organic or non-organic cotton and colors white, black, gray, blue, and red. How many different T-shirts are there to choose from?
14. Hector wants to place billboard advertisements throughout the county for his new business. How many ways can Hector choose 15 neighborhoods to advertise in if there are 30 neighborhoods in the county?
15. An art store has 4 brands of paint pens in 12 different colors and 3 types of ink. How many paint pens are there to choose from?
16. How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?
17. How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the team?
18. A conductor needs 5 cellists and 5 violinists to play at a diplomatic event. To do this, he ranks the orchestra’s 10 cellists and 16 violinists in order of musical proficiency. What is the ratio of the total cellist rankings possible to the total violinist rankings possible?
19. A motorcycle shop has 10 choppers, 6 bobbers, and 5 café racers—different types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 café racers for a weekend showcase?
20. A skateboard shop stocks 10 types of board decks, 3 types of trucks, and 4 types of wheels. How many different skateboards can be constructed?

Set 3: Solve each problem.

1. Out of 230 racers who started the marathon, 212 completed the race, 14 gave up, and 4 were disqualified. What percentage did not complete the marathon?
2. Patrick left an $8 tip on a $50 restaurant bill. What percent tip is that?
3. Ireland has a 23% VAT (value-added tax, similar to a sales tax). How much will the VAT be on a purchase of a €250 item?
4. Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax), while employers paid another 6.2%. How much will someone earning $45,000 a year pay towards social security out of their gross wages?
5. A project on Kickstarter.com was aiming to raise $15,000 for a precision coffee press. They ended up with 714 supporters, raising 557% of their goal. How much did they raise?
6. Another project on Kickstarter for an iPad stylus raised 1,253% of their goal, raising a total of $313,490 from 7,511 supporters. What was their original goal?
7. A company wants to decrease their energy use by 15%.
   • If their electric bill is currently $2,200 a month, what will their bill be if they’re successful?
   • If their next bill is $1,700 a month, were they successful? Why or why not?
8. A store is hoping an advertising campaign will increase their number of customers by 30%. They currently have about 80 customers a day.
   • How many customers will they have if their campaign is successful?
   • If they increase to 120 customers a day, were they successful? Why or why not?
9. An article reports “attendance dropped 6% this year, to 300.” What was the attendance before the drop?
10. An article reports “sales have grown by 30% this year, to $200 million.” What were sales before the growth?
11. A store has clearance items that have been marked down by 60%. They are having a sale, advertising an additional 30% off clearance items. What percent of the original price do you end up paying?
12. Find a unit rate:   You bought 10 pounds of potatoes for $4.
13. Find a unit rate: Joel ran 1500 meters in 4 minutes, 45 seconds.
14. A crepe recipe calls for 2 eggs, 1 cup of flour, and 1 cup of milk. How much flour would you need if you use 5 eggs?
15. An 8ft length of 4 inch wide crown molding costs $14. How much will it cost to buy 40ft of crown molding?
16. Four 3-megawatt wind turbines can supply enough electricity to power 3000 homes. How many turbines would be required to power 55,000 homes?
17. A highway had a landslide, where 3,000 cubic yards of material fell on the road, requiring 200 dump truck loads to clear. On another highway, a slide left 40,000 cubic yards on the road. How many dump truck loads would be needed to clear this slide?
18. Convert 8 feet to inches.
19. Convert 6 kilograms to grams.
20. A wire costs $2 per meter. How much will 3 kilometers of wire cost?
21. Sugar contains 15 calories per teaspoon. How many calories are in 1 cup of sugar?
22. A car is driving at 100 kilometers per hour. How far does it travel in 2 seconds?
23. A chain weighs 10 pounds per foot. How many ounces will 4 inches weigh?
24. The Deepwater Horizon oil spill resulted in 4.9 million barrels of oil spilling into the Gulf of Mexico. Each barrel of oil can be processed into about 19 gallons of gasoline. How many cars could this have fueled for a year? Assume an average car gets 20 miles to the gallon, and drives about 12,000 miles in a year.
25. During the landing of the Mars Science Laboratory Curiosity, it was reported that the signal from the rover would take 14 minutes to reach earth. Radio signals travel at the speed of light, about 186,000 miles per second. How far was Mars from Earth when Curiosity landed?
26. It is estimated that a driver takes, on average, 1.5 seconds from seeing an obstacle to reacting by applying the brake or swerving. How far will a car traveling at 60 miles per hour travel (in feet) before the driver reacts to an obstacle?
27. The grocery store has bulk pecans on sale, which is great since you’re planning on making 10 pecan pies for a wedding. Your recipe calls for 1¾ cups pecans per pie. However, in the bulk section there’s only a scale available, not a measuring cup. You run over to the baking aisle and find a bag of pecans, and look at the nutrition label to gather some info. How many pounds of pecans should you buy?
28. Soda is often sold in 20 ounce bottles. The nutrition label for one of these bottles is shown to the right. A packet of sugar (the kind they have at restaurants for your coffee or tea) typically contain 4 grams of sugar in the U.S. Drinking a 20 oz soda is equivalent to eating how many packets of sugar?^[1]

Set 4: First identify the information you need to answer the question, and then turn to the end of the section to find that information. The details may be imprecise; answer the question the best you can with the provided information. Be sure to justify your decision.

1. You’re planning on making 6 meatloafs for a party. You go to the store to buy breadcrumbs, and see they are sold by the canister. How many canisters do you need to buy?
2. Your friend wants to cover her car in bottle caps, like in this picture. How many bottle caps will she need?
3. You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.99 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.79 a pound.   Is it worth the extra drive?
4. I have an old gas furnace, and am considering replacing it with a new, high efficiency model. Is upgrading worth it?
5. Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money?
6. Marcus is considering going car-free to save money and be more environmentally friendly. Is this financially a good decision?

Information for Breadcrumbs Question (#1)

How much breadcrumbs does the recipe call for?

It calls for 1½ cups of breadcrumbs.

How many meatloaves does the recipe make?

It makes 1 meatloaf.

How many servings does that recipe make?

It says it serves 8.

How big is the canister?

It is cylindrical, 3.5 inches across and 7 inches tall.

What is the net weight of the contents of 1 canister?

15 ounces.

How much does a cup of breadcrumbs weigh?

I’m not sure, but maybe something from the nutritional label will help.

How much does a canister cost?

$2.39

Info for Furnace Question (#4)

How efficient is the current furnace?

It is a 60% efficient furnace.

How efficient is the new furnace?

It is 94% efficient.

What is your gas bill?

Here is the history for 2 years:

How much do you pay for gas?

There is $10.34 base charge, plus $0.39097 per Therm for a delivery charge, and $0.65195 per Therm for cost of gas.

How much gas do you use?

Here is the history for 2 years:

How much does the new furnace cost?

It will cost $7,450.

How long do you plan to live in the house?

Probably at least 15 years.