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Use inductive reasoning to predict the next number in the list

Math

1. Use inductive reasoning to predict the next number in the list.

6, 1, 5, 0, 4, −1, 3, ?

2. A store orders cases of tomato sauce from a warehouse. The following bar graph shows the number of cases of tomato sauce in the warehouse for the first four months of a year.

• A bar graph has "Months" on the horizontal axis and "Cases" on the vertical axis.
• In January the height of the bar is 22.
• In February the height of the bar is 19.
• In March the height of the bar is 16.
• In April the height of the bar is 13.

Using inductive reasoning, how many cases of tomato sauce will be in the warehouse in May?

3. Use inductive reasoning to predict the next image in the sequence. (See Example 2 in this section.)

• Four squares are arranged horizontally.
• In the first square, on the very left, one horizontal line divides the square into two rectangles of equal size.
• In the second square, to the right of the first, one horizontal line and one vertical line divide the square into four squares of equal size.
• In the third square, to the right of the second, three horizontal lines and one vertical line divide the square into eight rectangles of equal size.
• In the fourth square, on the very right, three horizontal lines and three vertical lines divide the square into sixteen squares of equal size.
4. Brianna, Ryan, Tyler, and Ashley were recently elected as the new class officers (president, vice president, secretary, treasurer) of the sophomore class at Summit College. From the following clues, determine which position each holds. (See Example 8 in this section.)

5. Ashley is younger than the president but older than the treasurer.
6. Brianna and the secretary are both the same age, and they are the youngest members of the group.
7. Tyler and the secretary are next-door neighbors.

Estimate the number of raspberries in the following photo. (See Example 3 in this section.)

The following bar graph shows the approximate number of millionaires in the United States for selected years. (See Example 6 in this section.)

A bar graph with 7 bars has the horizontal axis labeled "Year" and the vertical axis labeled "Millionaires (in Millions)". The bar labels followed by their heights are listed:

• 2014, 10.0
• 2015, 10.7
• 2016, 10.9
• 2017, 11.7
• 2018, 12.2
• 2019, 12.5
• 2020, 13.2

(a)

Between which two years did the number of millionaires increase the least?

2014 and 20152015 and 2016    2016 and 20172017 and 20182018 and 20192019 and 2020

(b)

Between which two years did the number of millionaires increase the most?

2014 and 20152015 and 2016    2016 and 20172017 and 20182018 and 20192019 and 2020

Use an Euler diagram to determine whether the argument is valid or invalid.

 All men behave badly. Some hockey players behave badly. ∴ Some hockey players are men.

Choose the Euler diagram that shows whether the argument is valid or invalid.

Determine the truth-value of the conditional.

If all frogs can dance, then the sun is cold.

Consider the following conditional statement.

If I were rich, I would quit this job.

(a)

Write the converse of the given statement.

If I quit this job, I would not be rich.If I quit this job, I would be rich.    If I were not rich, I would not quit this job.If I did not quit this job, I would not be rich.If I were not rich, I would quit this job.

(b)

Write the inverse of the given statement.

If I quit this job, I would not be rich.If I quit this job, I would be rich.    If I were not rich, I would not quit this job.If I did not quit this job, I would not be rich.If I were not rich, I would quit this job.

(c)

Write the contrapositive of the given statement.

If I quit this job, I would not be rich.If I quit this job, I would be rich.    If I were not rich, I would not quit this job.If I did not quit this job, I would not be rich.If I were not rich, I would quit this job.

Consider the following conditional statement.

Only if we take the train will we be able to take the entire family.

(a)

Write the converse of the given statement.

If we take the train, we will not be able to take the entire family.If we do not take the train, we will not be able to take the entire family.    If we will not be able to take the entire family, we will not take the train.If we will be able to take the entire family, we will take the train.If we will be able to take the entire family, we will not take the train.

(b)

Write the inverse of the given statement.

If we take the train, we will not be able to take the entire family.If we do not take the train, we will not be able to take the entire family.    If we will not be able to take the entire family, we will not take the train.If we will be able to take the entire family, we will take the train.If we will be able to take the entire family, we will not take the train.

(c)

Write the contrapositive of the given statement.

If we take the train, we will not be able to take the entire family.If we do not take the train, we will not be able to take the entire family.    If we will not be able to take the entire family, we will not take the train.If we will be able to take the entire family, we will take the train.If we will be able to take the entire family, we will not take the train.

State the premise, conclusion, and logical fallacy.

Student:Students need a greater voice when it comes to curriculum changes.Teacher:The teachers are the ones who need a greater voice. We don't ever have a say when it comes to budget issues.

premise

Teachers do not have a say in budget issues.Teachers do not need a greater voice when it comes to budget issues.    Teachers need to include students when discussing curriculum changes.Students need a greater voice when it comes to curriculum changes.Students do not need a greater voice when it comes to curriculum changes.

conclusion

Teachers do not have a say in budget issues.Teachers do not need a greater voice when it comes to budget issues.    Teachers need to include students when discussing curriculum changes.Students need a greater voice when it comes to curriculum changes.Students do not need a greater voice when it comes to curriculum changes.

logical fallacy

hasty generalizationappeal to emotion    red herringslippery slopeappeal to ignorance

State the premise, conclusion, and logical fallacy.

Surely my beautiful and intelligent sister wants to give me a ride to school.

premise

I need a ride to school.My sister is beautiful and intelligent    My sister goes to the same school as me.My sister owns a car.My sister wants to give me a ride to school.

conclusion

I need a ride to school.My sister is beautiful and intelligent    My sister goes to the same school as me.My sister owns a car.My sister wants to give me a ride to school.

logical fallacy

hasty generalizationappeal to ignorance    ad hominemcircular reasoningappeal to emotion

An automobile was driven 292.1 mi on 11.5 gal of gasoline. Find the number of miles driven per gallon of gas.

Convert one measurement to another.
7.4 dL =
Calculate the simple interest (in dollars) due on the following. (Round your answers to the nearest cent.)
(a)
5-year loan of \$2,350 if the annual interest rate is 7.75%
(b)
5-month loan of \$2,350 if the monthly interest rate is 0.7%

The simple interest charged on a 5-month loan of \$6,600 is \$206.25. Find the simple interest rate (in percent).

Calculate the compound amount (in dollars) when \$2,000 is deposited in an account earning 6.5% interest, compounded monthly, for 3 years. (Round your answer to the nearest cent.)

Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)

7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

The table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21.
PHT-34 CBX-21
43 56
49 47
47 43
38 45
47 46
45 49
50 47
45 59
46 53
45 50
45 48
43 51
Using the same scale, draw a box-and-whisker plot for each of the two data sets, placing the PHT-34 plot below the CBX-21 plot.

(a)

Which of the following scatter diagrams suggests a nearly perfect positive linear correlation between the x and y variables?

• Several points are shown on the x y plane.
• The points lie in a extremely narrow area.
• The y values increase as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a narrow area.
• The y values generally increase as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a narrow area.
• The y values generally decrease as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a extremely broad area.
• The y values may increase or decrease as the x values increase.

(b)

Which of the following scatter diagrams suggests little or no linear correlation between the x and y variables?

• Several points are shown on the x y plane.
• The points lie in a extremely narrow area.
• The y values increase as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a narrow area.
• The y values generally increase as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a narrow area.
• The y values generally decrease as the x values increase.

• Several points are shown on the x y plane.
• The points lie in a extremely broad area.
• The y values may increase or decrease as the x values increase.

During a 12-hour period, the temperature in a city dropped from a high of 70°F to a low of 23°F. What was the range of the temperatures during this period?
On a reading test, Shaylen's score of 455 was higher than the scores of 4274 of the 7246 students who took the test. Find the percentile, rounded to the nearest percent, for Shaylen's score.
A survey was given to 18 students. One question asked about the one-way distance the student had to travel to attend college. The results, in miles, are shown in the following table. Use the median procedure for finding quartiles to find the first, second, and third quartiles for the data.
Distance Traveled to Attend College
40 48 14 16 62 80 6 24 32
32 8 66 74 32 86 18 16 44
Q1=Q2=Q3=

Use an Euler diagram to determine whether the argument is valid.

All Italian villas are wonderful. Some wonderful villas are expensive. Therefore, some Italian villas are expensive.

Choose the Euler diagram that shows whether the argument is valid or invalid.

There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Expensive, Wonderful, and Italian Villas. The point is labeled V.
• The Italian Villas circle is completely inside the Expensive circle.
• The Wonderful circle partially overlaps the other two circles.
• Point V is located inside the intersection of all three circles.

There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Wonderful, Italian Villas, and Expensive. The point is labeled V.
• The Italian Villas circle is completely inside the Wonderful circle.
• The Expensive circle partially overlaps the Wonderful circle, but does not overlap the Italian Villas circle.
• Point V is located inside the intersection of the Expensive and Wonderful circles.

There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Expensive, Wonderful, and Italian Villas. The point is labeled V.
• The Expensive circle is completely inside the Wonderful circle.
• The Italian Villas circle partially overlaps the other two circles.
• Point V is located inside the Expensive circle, but not inside the Italian Villas circle.

There are three labeled circles and a single labeled point inside a rectangle. The three circles are labeled Wonderful, Italian Villas, and Expensive. The point is labeled V.
• The Wonderful circle is completely inside the Italian Villas circle.
• The Expensive circle partially overlaps the Italian Villas circle, but does not overlap the Wonderful circle.
• Point V is located inside the intersection of the Expensive and Italian Villas circles.

Is the argument valid or invalid?

validinvalid

Determine whether the sentence is a proposition.

Would you like coffee or tea?