diff --git a/.mapping.json b/.mapping.json index 837d990..33c2c6a 100644 --- a/.mapping.json +++ b/.mapping.json @@ -1 +1 @@ -{"src/frontmatter.ptx": ["frontmatter", "Notes"], "src/language_logic_rules.ptx": ["language_logic_rules"], "src/chap_one_problem_solving_percents.ptx": ["chap_one_problem_solving_percents"], "src/chap_one_proportional_reasoning.ptx": ["chap_one_proportional_reasoning"], "src/chap_one_logic_everyday_life.ptx": ["chap_one_logic_everyday_life"], "src/chap_one_sets_venn.ptx": ["chap_one_sets_venn"], "src/chap_one_review.ptx": ["chap_one_review"], "src/chap_one_language_logic.ptx": ["chap_one_language_logic"], "src/chap_one_arguments.ptx": ["chap_one_arguments"], "src/chap_one_fallacies.ptx": ["chap_one_fallacies"], "src/financial_math.ptx": ["financial_math"], "src/chap_two_intro_spreadsheet.ptx": ["chap_two_intro_spreadsheet"], "src/chap_two_simple_compound.ptx": ["chap_two_simple_compound"], "src/chap_two_savings_plan.ptx": ["chap_two_savings_plan"], "src/chap_two_loans.ptx": ["chap_two_loans"], "src/chap_two_income_taxes.ptx": ["chap_two_income_taxes"], "src/chap_two_review.ptx": ["chap_two_review"], "src/statistics.ptx": ["statistics"], "src/chap_three_statistical_process.ptx": ["chap_three_statistical_process"], "src/chap_three_describing_data.ptx": ["chap_three_describing_data"], "src/chap_three_measure_of_center.ptx": ["chap_three_measure_of_center"], "src/chap_three_measure_of_variation.ptx": ["chap_three_measure_of_variation"], "src/chap_three_review.ptx": ["chap_three_review"], "src/chap_three_normal_model.ptx": ["chap_three_normal_model"], "src/probability.ptx": ["probability"], "src/chap_four_contingency_tables.ptx": ["chap_four_contingency_tables"], "src/chap_four_theoretical_probability.ptx": ["chap_four_theoretical_probability"], "src/chap_four_expected_value.ptx": ["chap_four_expected_value"], "src/chap_four_review.ptx": ["chap_four_review"], "src/democracy.ptx": ["democracy"], "src/chap_five_apportionment.ptx": ["chap_five_apportionment"], "src/chap_five_voting_methods.ptx": ["chap_five_voting_methods"], "src/chap_five_popular_vote.ptx": ["chap_five_popular_vote"], "src/chap_five_gerrymandering.ptx": ["chap_five_gerrymandering"], "src/chap_five_review.ptx": ["chap_five_review"], "src/chap_five_budget_deficit_debt.ptx": ["chap_five_budget_deficit_debt"], "src/backmatter.ptx": ["backmatter"]} \ No newline at end of file +{"src/frontmatter.ptx": ["frontmatter", "Notes"], "src/language_logic_rules.ptx": ["language_logic_rules"], "src/chap_one_problem_solving_percents.ptx": ["chap_one_problem_solving_percents"], "src/chap_one_proportional_reasoning.ptx": ["chap_one_proportional_reasoning"], "src/chap_one_logic_everyday_life.ptx": ["chap_one_logic_everyday_life"], "src/chap_one_sets_venn.ptx": ["chap_one_sets_venn"], "src/chap_one_review.ptx": ["chap_one_review"], "src/chap_one_language_logic.ptx": ["chap_one_language_logic"], "src/chap_one_arguments.ptx": ["chap_one_arguments"], "src/chap_one_fallacies.ptx": ["chap_one_fallacies"], "src/backmatter.ptx": ["backmatter"]} \ No newline at end of file diff --git a/Notes.html b/Notes.html index 5267d91..75b6ee4 100644 --- a/Notes.html +++ b/Notes.html @@ -95,7 +95,7 @@ Skip to main content
Logo image
-

Math in Society: Quantitative tools for decision making

+

Math in Society: Tools for decision making

Portland Community College Math Department

-Example 1.1.6. +Example 1.1.7.

Change each fraction or decimal into percentage form.
@@ -817,7 +585,7 @@

Search Results:

Solution.
    -
  1. First we divide \(\frac{4}{5}\) to get \(0.80\) and then \(0.80(100\%) = 80\%\text{.}\) +
  2. First we divide \(\frac{4}{5}\) to get \(0.80\) and then multiply by 100%. \(0.80(100\%) = 80\%\text{.}\)
  3. \(1.25(100\%)\) or moving the decimal two places to the right gives 125%.
    4. @@ -828,73 +596,131 @@

    Search Results:

Subsection 1.1.6 Calculating Percents

-
If two co-workers make the same hourly rate then it would be easy to compare their raises. But if they make different amounts then a percentage can be more useful. To compare unlike amounts, we can divide each part by the whole amount to find the percentage. The whole amount is also called the base of the percentage. First we will look at how to calculate percents and then how to calculate an amount.
+
When calculating percents, we divide the part by the whole amount. The whole amount is also called the base of the percentage. First we will look at how to calculate percents and then how to calculate a part.

Calculating Percents.

-
Percent = \(\frac{\text{part}}{\text{whole}}\) -
-
Part = percent \(\cdot\) whole

-Example 1.1.7. -

-
Iryna makes $22 an hour and got a raise of $3 per hour. Sundar currently makes $19 an hour and got a raise of $2.85. Who got a larger raise relatively?
Using the formula percent = \(\frac{\text{part}}{\text{whole}}\text{,}\) we can compare the two raises.
-
Iryna:
\(\frac{\$3}{\$22} \approx 0.136 \text{ or } 13.6\%\text{.}\)
Iryna’s raise was about 13.6% of her wage.
-
Sundar:
\(\frac{\$2.85}{\$19} = 0.15 \text{ or } 15\%\text{.}\)
Sundar’s raise was 15% of his wage.
-
Iryna had a bigger raise in terms of dollar amount, but in terms of percentage, Sundar’s raise was bigger.

+
+\begin{equation*} +\text{Percent} = \frac{\text{part}}{\text{whole}} +\end{equation*} +
+
+\begin{equation*} +\text{Part} = \text{percent} \cdot \text{whole} +\end{equation*} +

We can also think of these formulas as sentences. The word is means equals, per means divide, and of often means multiplication. So we can also say, “Percent is part per whole,” and, “Part is percent of whole.”
+

Example 1.1.8.

-
+
In a survey of 1,031 randomly chosen adults, 577 said they would feel better if they got more sleep (source
 1 
news.gallup.com/poll/642704/americans-sleeping-less-stressed
). What percent is this?
+
Solution.
+
First, we need to identify the part and the whole. The whole is the total number of adults surveyed. The part is the 577 adults who said they would feel better if they got more sleep.
+
Using the formula
+
+\begin{equation*} +\text{Percent} = \frac{\text{part}}{\text{whole}} +\end{equation*} +
+
we can calculate:
+
+\begin{equation*} +\frac{577}{1013} \approx 0.570 \text{ or } 57\%\text{.} +\end{equation*} +
+
About 57% of the adults surveyed said they would feel better if they got more sleep.
+

+Example 1.1.9. +

+
First estimate which quantity is the larger percentage. Then calculate both percentages.
    -
  1. A quiz score of 8/10 or 11/15.
    2. -
  2. A cereal with 2 grams of sugar in a 28 gram serving size or 3 grams of sugar in a 32 gram serving size.
    3. +
  3. A quiz score of 8 out of 10 or 11 out of 15.
    4. +
  4. A cereal with 2 grams of sugar in a 28 gram serving size or 3 grams of sugar in a 32 gram serving size.
-
Solution.
    -
  1. -
    We are estimating that 8/10 seems larger compared to 11/15 because missing 2 out of 10 is less than 4 out of 15.
    -
    \(\frac{8}{10} = 0.80 \text{ or } 80\%\)
    -
    \(\frac{11}{15} \approx 0.733 \text{ or } 73.3\%\)
    -
    The score of 8 out of 10 is a higher percentage.
    +
    Solution.
      +
    1. +
      We are estimating that 8 out of 10 seems larger compared to 11 out of 15 because missing 2 out of 10 seems like less than 4 out of 15.
      +
      +\begin{equation*} +\frac{8}{10} = 0.80 \text{ or } 80\%\text{.} +\end{equation*} +
      +
      +\begin{equation*} +\frac{11}{15} \approx 0.733 \text{ or } 73.3\%\text{.} +\end{equation*} +
      +
      The score of 8 out of 10 is a higher percentage.
      2. -
    2. -
      We are estimating that 3/32 is a higher percentage than 2/28 because the added gram of sugar seems high compared with only a 4 gram increase in serving size.
      -
      \(\frac{2\text{ g}}{28\text{ g}} \approx 0.07 \text{ or about } 7\%\)
      -
      \(\frac{3\text{ g}}{32\text{ g}} \approx 0.09 \text{ or about } 9\%\)
      -
      The cereal with 3 grams of sugar out of 32 grams has a higher percentage of sugar.
      +
    3. +
      We are estimating that 3 out of 32 is a higher percentage than 2 out of 28 because the added gram of sugar seems high compared with only a 4 gram increase in serving size.
      +
      +\begin{equation*} +\frac{2\text{ g}}{28\text{ g}} \approx 0.07 \text{ or about } 7\%\text{.} +\end{equation*} +
      +
      +\begin{equation*} +\frac{3\text{ g}}{32\text{ g}} \approx 0.09 \text{ or about } 9\%\text{.} +\end{equation*} +
      +
      The cereal with 3 grams of sugar out of 32 grams has a higher percentage of sugar.
      4. -
Another useful tool is finding the part when we know the percentage and the whole amount.
-

-Example 1.1.9. -

-
For example, say you have a high yield online savings account that pays an annual interest rate of 4.5%. If you have $3000 in the account for your emergency fund, how much interest will you earn in a year? What would your total balance be with the interest?
To perform calculations with percents, we change them into decimal form first. So we divide 4.5 by 100 or move the decimal two places to the left and we get 0.045.
Then, using the formula part = percent \(\cdot\) whole, we have
\(0.045(\$3000) = \$135\)
You would earn $135 in interest. Interest is added to your account so we will add to find the total balance.
-\(\$3000+135 = \$3,135\text{.}\) Your total balance is $3,135 after one year.
Note, most interest is compounded daily or monthly so we simplified the example above. We will come back to this and learn how to calculate compund interest in the financial math chapter.
-

+

Another useful tool is finding the part when we know the percentage and the whole amount.
+

Example 1.1.10.

-
-
Find each amount described and the total or ending amount.
+
For example, say you have a high yield online savings account that pays an annual interest rate of 4.5%. If you have $3000 in the account for your emergency fund, how much interest will you earn in a year? What would your total balance be with the interest?
+
Solution.
+
To perform calculations with percents, we change them into decimal form first. So we divide 4.5 by 100 or move the decimal two places to the left and we get 0.045.
+
Then, using the formula
+
+\begin{equation*} +\text{part} = \text{percent} \cdot \text{whole} +\end{equation*} +
+
we have:
+
+\begin{equation*} +0.045(\$3000) = \$135\text{.} +\end{equation*} +
You would earn $135 in interest. Interest is added to your account so we will add to find the total balance.
+
+\begin{equation*} +\$3000+135 = \$3,135\text{.} +\end{equation*} +
+
Your total balance is $3,135 after one year.
+
+
Note, most interest is compounded daily or monthly so we simplified the example above. We will come back to this and learn how to calculate compound interest in the financial math chapter.
+

+Example 1.1.11. +

+
+
Find each part described and the total or ending amount.
    -
  1. A stock valued at $83 went down by 15%. Find the amount it decreased by and the ending value.
    2. -
  2. The sales tax in Vancouver, Washington is currently 8.7%. How much tax would you pay on TV that costs $399 and what is the total price?
    3. +
  3. A smartphone’s battery life of 12 hours decreased by 20% after a year of use. Find the amount it decreased by and the current battery life.
    4. +
  4. The sales tax in Vancouver, Washington is currently 8.7%. How much tax would you pay on TV that costs $399 and what is the total price?
-
Solution 1.
    -
  1. -
    First we will find 15% of $83 by multiplying by the decimal form of the percentage:
    +
    Solution 1.
      +
    1. +
      First we will find 20% of 12 hours by multiplying by the decimal form of the percentage:
      \begin{equation*} -\$83(0.15)=\$12.45 +12(0.20)=2.4\text{ hours} \end{equation*}
      -
      Then we will subtract since the stock price went down.
      +
      Then we will subtract since the battery life went down.
      \begin{equation*} -\$83-12.45=\$70.55 +12-2.4=9.6\text{ hours}\text{.} \end{equation*}
      -
      The stock went down by $12.45 to $70.55.
      +
      The phone battery life went down by 2.4 hours to 9.6 hours.
      2. -
    2. +
    3. We will find 8.7% of $399 by multiplying the amount by the decimal form of the percentage:
      \begin{equation*} @@ -907,28 +733,31 @@

      Search Results:

      \$399+34.71=\$433.71 \end{equation*}
      -
      The tax on the TV is $34.71 for a total price of $433.71.
      +
      The tax on the TV is $34.71, which gives a total price of $433.71.
      4. -
    Solution 2.
      -
    1. There is a shorter way to go about this type of problem. If we look at a 15% decrease as the stock retaining 85% of its value (100-15=85)%, we can calculate the stock price directly.
      +
    Solution 2.
    +
    There is an optional shorter way to go about this type of problem if you are interested.
    +
      +
    1. If we look at a 20% decrease as the battery retaining 80% of its life (100-20=80)%, we can calculate the new battery life directly:
      \begin{align*} -\$83(1-0.15) \amp= \$83(0.85)\\ -\amp= \$70.55 +12(1-0.20) \amp= 12(0.80)\\ +\amp= 9.6\text{ hours.} \end{align*}
      2. -
    2. We can also do this with the TV price using addition for an increase (100+8.7=108.7)%.
      +
    3. We can also do this with the TV price using addition for an increase (100+8.7=108.7)%:
      \begin{align*} \$399(1+0.087)\amp=\$399(1.087)\\ -\amp=\$433.71 +\amp=\$433.71. \end{align*}
      4. -
    +
+

Subsection 1.1.7 Absolute and Relative Change

-
As we saw in the shirt sale prices and the raise comparisons, we can talk about a difference in absolute terms or relative terms. Absolute change is the actual amount of the change in dollars, people, etc. The change is positive if the value goes up or negative if it goes down. Relative change is the amount of change as a percentage of the starting amount.
+
As we saw in the shirt sale prices, we can talk about a difference in absolute terms or relative terms. Absolute change is the actual amount of the change in dollars, people, etc. The change is positive if the value goes up or negative if it goes down. Relative change is the amount of change as a percentage of the starting amount.
For example, Portland Community College recently increased its tution from $128 to $133 per credit hour. The absolute change is the dollar increase of
@@ -945,35 +774,69 @@

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or about 3.9%.

Absolute and Relative Change.

-
Absolute Change = Ending Amount - Starting Amount
-
Relative Change = \(\frac{\text{Ending Amount - Starting Amount}}{\text{Starting Amount}}\) or \(\frac{\text{Absolute Change}}{\text{Starting Amount}}\) -
The base of a percentage is very important and relative change is calculated as a percentage of the original amount because that was the amount before the change.
+
+\begin{align*} +\text{Absolute Change} \amp= \text{Ending Amount} - \text{Starting Amount}\\ +\\ +\text{Relative Change} \amp= \frac{\text{Ending Amount} - \text{Starting Amount}}{\text{Starting Amount}} = \frac{\text{Absolute Change}}{\text{Starting Amount}} +\end{align*} +
The base of a percentage is very important and relative change is calculated as a percentage of the original amount because that was the amount before the change.

-Example 1.1.11. +Example 1.1.12.

-
The U.S. population was 332 million people in 2021 and 333.3 million people in 2022. What is the absolute and relative change?
+
Maria has been thinking about selling her car. The value went from $7400 to $6800 over the last year. What is the absolute and relative change in the car’s value?
Solution.
-
First we will subtract to calculate the absolute change:
-
-\begin{equation*} -333.3 - 332\text{ million people} = 1.3\text{ million people} -\end{equation*} +
+
First we will subtract to calculate the absolute change:
+
+\begin{align*} +\text{Absolute Change} \amp= \text{Ending Amount} - \text{Starting Amount}\\ +\amp=\$6800 - \$7400\\ +\amp=-\$600 +\end{align*}
-
The population increased by 1.3 million people.
-
Now we can calculate the relative change:
-
-\begin{equation*} -\frac{\text{Absolute Change}}{\text{Starting Amount}}=\frac{1.3\text{ million people}}{332\text{ million people}} \approx 0.0039 -\end{equation*} +
The absolute change is a decrease of $600.
+
Now we can calculate the relative change:
+
+\begin{align*} +\text{Relative Change} \amp= \frac{\text{Absolute Change}}{\text{Starting Amount}}\\ +\amp= \frac{-\$600}{\$7400}\\ +\amp\approx -0.081 +\end{align*}
-
The U.S. population increased by about 0.39%.
+
The relative change in the price of the car was a decrease of about 8.1%.
+
Notice in the last example we either used the negative sign or the word decrease to show the direction of the change. We could say the car’s value changed by -8.1% or decreased by 8.1%. We wouldn’t use both at the same time because that would be a double negative. Let’s look at another example.
+

+Example 1.1.13. +

+
After raises, Iryna’s wage went from $22 to $25 per hour. Sundar’s hourly wage went from $19 to $21.85. Calculate their absolute and relative raises. Who got a larger absolute raise? Who got a larger relative raise?
+
Solution.
+
First we will calculate the absolute raises:
+
+
Iryna:
+
\(\$25 - \$22 = \$3\text{.}\)
+
+
+
Sundar:
+
\(\$21.85 - \$19 = \$2.85\text{.}\)
+
+
Iryna got a larger absolute raise of $3 per hour compared with $2.85 for Sundar. Now we will calculate the relative raises.
+
+
\(\frac{\$3}{\$22} \approx 0.136 \text{ or } 13.6\%\text{.}\)
+
Iryna’s raise was about 13.6% of her pay.
+
+
+
\(\frac{\$2.85}{\$19} = 0.15 \text{ or } 15\%\text{.}\)
+
Sundar’s raise was 15% of his pay.
+
+
Sundar had a relative raise of 15% of his pay and Iryna’s raise was about 13.6% of her pay. Iryna had the larger absolute raise but Sundar had the larger raise relative to their starting wages.

Subsection 1.1.8 Multiple Percent Changes

-
We can also calculate values with multiple percent increases and decreases. We must be careful in this case because the base changes with each change. For example, if a stock price drops by 60% in one week and increases by 75% the next week, this is not the same as an increase of 15%. The base for the drop is the original price and the base for the increase is the price after the drop. Let’s look at this more closely in the next example.
+
We can also calculate values with multiple percent increases and decreases. We must be careful here because the base changes each time. For example, if a stock price drops by 60% in one week and increases by 75% the next week, this is not the same as an increase of 15%. The base for the drop is the original price and the base for the increase is the price after the drop. Let’s look at this more closely in the next example.

-Example 1.1.12. +Example 1.1.14.

A stock valued at $100 dropped in value by 60% one week, then increased in value the next week by 75%. Is the value higher or lower than where it started? What is the ending value and what is the relative change?
Solution.
@@ -1002,383 +865,111 @@

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Exercises 1.1.9 Exercises

1.

-
These have not been updated yet
    -
  1. Pigs can fly.
    2. -
  2. What?
    3. -
  3. I don’t know.
    4. -
  4. I like tofu.
    5. -

2.

-
Which of the following are propositions?
    -
  1. How far?
    2. -
  2. Portland is not in Oregon.
    3. -
  3. Portland Community College.
    4. -
  4. It is raining.
    5. -

3.

-
Write the negation of each proposition.
    -
  1. I ride my bike to campus.
    2. -
  2. Portland is not in Oregon.
    3. -

4.

-
Write the negation of each proposition.
    -
  1. You should see this movie.
    2. -
  2. Lashonda is wearing blue.
    3. -

5.

-
Write a proposition that contains a double negative.

6.

-
Write a proposition that contains a triple negative.

7.

-
For each situation, decide whether the “or” is most likely exclusive or inclusive.
    -
  1. An entrée at a restaurant includes soup or salad.
    2. -
  2. You should bring an umbrella or a raincoat with you.
    3. -

8.

-
For each situation, decide whether the “or” is most likely exclusive or inclusive.
    -
  1. We can keep driving on I-5 or get on I-405 at the next exit.
    2. -
  2. You should save this document on your computer or a flash drive.
    3. -

9.

-
For each situation, decide whether the “or” is most likely exclusive or inclusive.
    -
  1. I will wear a sweater or a jacket.
    2. -
  2. My next vacation will be on the Oregon Coast or Mount Hood.
    3. -

10.

-
For each situation, decide whether the “or” is most likely exclusive or inclusive.
    -
  1. While in California I will go to the beach or Disneyland.
    2. -
  2. The insurance agent offers car or boat insurance.
    3. -

11.

-
Rewrite the statement in the conditional form if p, then q. -
    -
  1. Whenever it is sunny, I go swimming.
    2. -
  2. I go see a movie on Fridays.
    3. -

12.

-
Rewrite the statement in the conditional form if p, then q. -
    -
  1. I always carry an umbrella when it rains.
    2. -
  2. On the weekend I like to hang out with friends.
    3. -

13.

-
Translate each statement from symbolic notation into English sentences. Let A represent “Elvis is alive” and let K represent “Elvis is the King”.
    -
  1. Not A
    2. -
  2. A or K
    3. -
  3. Not A and K
    4. -
  4. If K, then not A
    5. -

14.

-
Translate each statement from symbolic notation into English sentences. Let A represent “It rains in Oregon” and let B represent “I own an umbrella”.
    -
  1. Not B
    2. -
  2. A and not B
    3. -
  3. If A, then B
    4. -
  4. If not B, then A
    5. -

15.

-
Translate each statement from English sentences into symbolic notation. Let A represent “I will protest” and let B represent “There is injustice.”
    -
  1. There is injustice and I will protest.
    2. -
  2. If there is injustice, then I will protest.
    3. -
  3. I will protest if there is injustice.
    4. -
  4. If there is not injustice, then I will not protest.
    5. -

16.

-
Translate each statement from English sentences into symbolic notation. Let A represent “It’s time to eat” and let B represent “I am hungry.”
    -
  1. It’s time to eat and I’m not hungry.
    2. -
  2. It’s not time to eat.
    3. -
  3. If it’s time to eat, then I’m hungry.
    4. -
  4. If I’m not hungry then it’s not time to eat.
    5. -

17.

-
Determine if the entire statement is true or false.
    -
  1. An apple is a vegetable, or an apple is a fruit.
    2. -
  2. Portland is not a city in Oregon.
    3. -

18.

-
Determine if the entire statement is true or false.
    -
  1. Fish can walk and birds can swim.
    2. -
  2. If it is warm outside, then it is sunny.
    3. -
+
Determine which operation(s) you would use for each situation. There may be more than one correct answer.

2.

+
Determine which operation(s) you would use for each situation. There may be more than one correct answer.

3.

+
Estimate a reasonable range of values for each situation.

4.

+
Estimate a reasonable range of values for each situation.

Exercise Group.

-
Complete the truth table for each statement and write the meaning of each statement in the third column.
+
Use the problem solving process to solve these problems. Document your steps and thinking.
-
19.
-
Let A be: I live in Oregon.
Let B be: I go to Portland Community College
- - - - - - - - - - - - - - - - - - - - - - - - - -
ABA and B
T
T
F
F
20.
-
Let A be: I am a psychology major
Let B be: I’m planning to transfer to Portland State
- - - - - - - - - - - - - - - - - - - - - - - - - -
ABA or B
T
T
F
F
+
5.
+
6.
7.
8.
9.
10.
-
+

Exercise Group.

-
Complete the truth table for each statement.
+
Use the problem solving process to solve these problems. For this set of questions, after you identify the information you need, go to the end of the exercises to find that information. The details may be imprecise; answer the question the best you can with the provided information. Document your steps and thinking.
-
21.
-
A and not B
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ABNot BA and not B
T
T
F
F
22.
-
Not (not A or B)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ABNot ANot A or BNot (not A or B)
T
T
F
F
23.
-
Not (A and B and C)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ABCA and B and CNot (A and B and C)
T
T
T
T
F
F
F
F
24.
-
Not A or (not B and C)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
ABCNot ANot BNot B and CNot A or (Not B and C)
T
T
T
T
F
F
F
F
+
11.
12.
13.
14.
15.
16.
-
+

Exercise Group.

-
Create a complete truth table for each statement.
+
For this set of questions, research or make educated estimates for any unknown information needed to answer the question. Document your steps and thinking.
-
25.
-
Not(A and B) or C
26.
-
(A or B) and (A or C)
27.
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If (A and B), then C
28.
-
If (A or B), then not C
29.
-
If (A and C), then not A
30.
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If (B or C), then (A and B)
-
-
+
17.
18.
19.
20.
21.
22.
+ + +

23.

+
Convert each percent into decimal form.
    +
  1. 15.6%
    2. +
  2. 9.1%
    3. +
  3. 0.07%
    4. +
  4. 135.6%
    5. +

24.

+
Convert each percent into decimal form.
    +
  1. 1.25%
    2. +
  2. 230%
    3. +
  3. 7%
    4. +
  4. 0.1%
    5. +

25.

+
Change each fraction or decimal into percentage form.
    +
  1. 0.89
    2. +
  2. 0.043
    3. +
  3. \(\displaystyle \frac{3}{4}\)
    4. +
  4. 1.05
    5. +

26.

+
Change each fraction or decimal into percentage form.
    +
  1. 0.029
    2. +
  2. \(\displaystyle \frac{5}{6}\)
    3. +
  3. 1.804
    4. +
  4. 0.72
    5. +
+

Exercise Group.

+
For this set of questions, calculate the percent(s) and/or part(s).
+
+
27.
+
Out of 230 racers who started a marathon, 212 completed the race. What percentage is that? Round your percentage to 1 decimal place if needed.
28.
+
A customer left a tip of $9 tip on a $50 restaurant bill. What percent tip is that?
29.
+
To help aleviate homelessness, voters in the Portland Metro area approved a personal income tax for individuals who make over $125,000 in taxable income. Miguel has a taxable income of $180,000 and the rate for that level of income is 1.5%. How much will Miguel owe for this tax?
30.
+
Employees pay 7.65% of their gross earning towards Social Security tax (FICA) and employers pay the same amount. James earns $5,100 per month. How much will be deducted from his monthly paycheck for FICA tax?
31.
+
Vancouver, Washington has a sales tax of 8.7% Find the tax amount on a clothing purchase of $120. What is the total cost of the purchase?
32.
+
Safa managed a company to reduce it’s carbon emissions by 18.3%. The company originally emitted 920 tons of carbon dioxide anually. How much was the reduction and what are the new emmissions?
+
+
+

33.

+

34.

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35.

+
    +
    2. +
    3. +
    4. +
    5. +

36.

+
    +
    2. +
    3. +
    4. +
    5. +

37.

+
    +
    2. +
    3. +
    4. +
    5. +

38.

+
    +
    2. +
    3. +
    4. +
    5. +

39.

+
    +
    2. +
    3. +

40.

+
    +
    2. +
    3. +

41.

+
    +
    2. +
    3. +

42.

+
    +
    2. +
    3. +
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Math in Society: Quantitative tools for decision making

+

Math in Society: Tools for decision making

Portland Community College Math Department