1.
Identify whether each of the following is a proposition.
- Airplanes are the safest form of travel.
- Portland is a city in Oregon and Maine.
- Is it raining outside?
- Say what?
- I’m going on vacation on Monday.
- Everyone is addicted to technology.
Exercises 1.6 Chapter 1 Review
2.
Write the negation of each proposition.
- I take public transportation to get to class.
- I went to a movie on Friday.
- I don’t want to go golfing today.
- I love watching basketball.
- Breylynn’s favorite color is green
- Mirriam is a theater major.
3.
For each situation, decide whether the “or” is most likely exclusive or inclusive.
- I like watching soccer or basketball.
- You should pack shorts or capris for our vacation.
- We should take the train or bus to Portland to Eugene.
- I would like to paint the room grey or blue.
- The best reality TV show is Amazing Race or Big Brother.
4.
Express in the form of if p, then q.
- Doing homework helps increase your grade in class.
- Riding public transportation will help you save money.
- Squirrels, bury their food.
- You will get sick if you eat too much candy.
- Go to the doctor if you think you have the flu.
5.
Determine whether the compound statement is true or false.
- A rectangle has four sides or 5 is an even number.
- If a square has five sides then a rabbit is a mammal.
- A rabbit is not a mammal.
- Rabbits can fly and a rectangle has four sides.
- If rabbits are mammals, then squares have 3 sides.
6.
Write the converse, inverse and contrapositive of the statement: "If it is raining outside, then I will take an umbrella." Identify which statements are logically equivalent.
7.
The following Venn Diagram shows how 70 customers at the local coffee shop like their coffee.
- How many people only like cream in their coffee?
- How many people put sugar in their coffee?
- How many people put sugar or cream in their coffee?
- How many people don’t like cream in their coffee?
8.
In a group of 30 students at PCC, 21 have Biology this term, 12 have Math 105 and 7 are studying both Biology and Math 105.
- Create a two-circle Venn diagram that summarizes the results of the survey.
- How many students are not taking either course?
9.
The following data was collected at a local coffee shop. 120 customers were asked if they like coffee and chocolate. The results are in the table below.
| Liked coffee | Disliked coffee | Total | |
|---|---|---|---|
| Liked chocolate | 23 | 37 | 60 |
| Disliked chocolate | 42 | 18 | 60 |
Create a two-circle Venn diagram that summarizes the results of the survey.
10.
A 120 people were surveyed and it reveals the following results about how people learn about news events happening around the world.
- Twitter 35
- Websites 55
- Newspapers 10
- Newspaper and Website 5
- Newspaper and Twitte 4
- Website and Twitter 25
- All three sources 3
- Create a three-circle Venn diagram that summarizes the results of the survey.
- How many people get their news from Twitter or a Website?
- How many people do not get their news from any of the three sources?
- How many people use only Twitter?
- How many people use Twitter or a Website but not a Newspaper?
11.
Calculate the percent or part.
A nutrition label states that a serving of cereal contains 25% of the recommended daily value of iron. If the daily recommended intake of iron is 18 mg, how much is in one serving of cereal.
12.
Calculate the absolute and relative change. Include the direction of the change in words or symbols.
The population of the city of Astoria, Oregon was 10,169 in 2022 and 9,986 in 2023.
13.
A line of coats were marked up by 250% and then placed on sale for 30% off. If the owner of the store purchased the jackets wholesale for $70 each, find the sale price and the combined relative change from the wholesale price.
14.
Find the unit rate for each and determine which is more cost effective.
One brand of toothpaste comes in a 6-ounce package for $5.99. Another brand comes in a 4.3-ounce package for $4.99
Exercise Group.
Solve each proportion problem.
15.
If you like your coffee strong with 3 ounces of ground coffee to make 4 cups, how much would you need to make a pot of 10 cups?
16.
A 5-gallon container of paint says it will cover 1,750 square feet in one coat. How many gallons of paint would you need to cover 3,200 square feet per coat?
Exercise Group.
Use the problem solving process with a combination of operations, unit conversions and/or geometric formulas to solve the problem. Document your steps and thinking.
17.
You are planning to have your bathroom floor tiled with 8 inch by 8 inch tiles, that cost $17.54 per box of 12 tiles. The tiled area is approximately 8 feet by 10 feet and the tiler charges a base fee of $100 and $12 per square foot. The grout and other materials are estimated at $10 per square foot. About how much will the project cost? Add 10% to the number of tiles for partial tiles needed.
18.
One stick of butter is 8 tablespoons or half a cup. Your cookie recipe calls for one cup of butter to make 3 dozen cookies. You want to make 10 dozen cookies for a cookie exchange party. In your fridge you have 1 1⁄2 sticks of butter. Butter is sold for $4.29 per pound which is 4 sticks. How many sticks of butter do you need? How many pounds of butter should you buy and how much will it cost? How much will you have left over?
19.
A pediatrician prescribes 15 mg/kg/day of a liquid medication to be given in three equal doses. If the child weighs 44 pounds and the medication concentration is 10 mg/mL, how many milliliters should be given per dose? If the parent lost the dropper and only has a set of teaspoons, how much should they give in each dose? (1T=15ml)
20.
You just got a circular above ground pool with a 15-foot diameter and a height of 48 inches. You want to know the cost of the water to fill it up to 6 inches from the top and how much chlorine to put in. The package says to use two 3-inch tablets per 10,000 gallons of water. City of Portland water is measured and billed at a rate of $7.559 per 100 cubic feet(ccf). One ccf is 748 gallons.
