Advanced Algebra Midterm Review

Walter starts with a paper that is 1 millimeter thick and folds it in half repeatedly, doubling its thickness with each fold. After a certain number of folds, the paper's thickness is 2 millimeters. How many more times, y, must Walter fold the paper to reach a thickness of x millimeters?

• Equation: y = log₂ x Solution: (4, 2); To reach a thickness of 4 millimeters, Walter needs to fold the paper 2 times.

• Equation: y = log₂ x Solution: (8, 3); To reach a thickness of 8 millimeters, Walter needs to fold the paper 3 times.

• Equation: y = log₂ (2x) Solution: (4, 1); To reach a thickness of 4 millimeters, Walter needs to fold the paper 1 times.

• Equation: y = log₂ (2x) Solution: (8, 2); To reach a thickness of 8 millimeters, Walter needs to fold the paper 2 times.

• The variable y must be negative.

• The term (1 + yt) must be positive.

• The term (1 + yt) must be increasing each year.

• The variable y must be greater than 0 but less than 1.

Two data sets with the same mean are given below.

Data set A

5, 5.5, 6, 6, 6.5, 6.5, 7, 7, 7, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 8, 8, 8, 8.5, 8.5, 9, 9, 9.5, 10

Data set B

4, 4.5, 5, 5.5, 5.5, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10.5, 10.5, 11, 11.5, 12

Which statement best describes the difference in standard deviations between the two data sets and the suitability of using standard deviation to compare their spread?

• The standard deviation of data set B is about 1.2 units greater than the standard deviation of data set A. Using the standard deviation to compare spread is appropriate for these data sets.

• The standard deviation of data set B is about 5.0 units greater than the standard deviation of data set A. Using the standard deviation to compare spread is appropriate for these data sets.

• The standard deviation of data set B is about 1.2 units greater than the standard deviation of data set A. Using the standard deviation to compare spread is not appropriate for these data sets.

• The standard deviation of data set B is about 5.0 units greater than the standard deviation of data set A. Using the standard deviation to compare spread is not appropriate for these data sets.

Thalia develops a new pesticide and tests it on tomato plants. In a controlled experiment, the tomatoes treated with the pesticide had an average size increase of 3 inches compared to the control group.

Thalia wants to assess if this increase in average size is statistically significant. The dot plot shows the results of 100 simulations of re-randomizing all of the data from the experiment into two groups and calculating the difference in average sizes.

Which of these best describes whether the increase in average size from the experiment is significant?

• significant; There is less than a 5% probability that the situation where the treatment group has sizes that are 3 or more inches greater than the control group occurs by chance.

• significant; There is greater than a 5% probability that the situation where the treatment group has sizes that are 3 or more inches greater than the control group occurs by chance.

• not significant; There is less than a 5% probability that the situation where the treatment group has sizes that are 3 or more inches greater than the control group occurs by chance.

• not significant; There is greater than a 5% probability that the situation where the treatment group has sizes that are 3 or more inches greater than the control group occurs by chance.

• An initial investment of ​$5000 will have a value of ​​$3646.52 more than an initial investment of ​$2000 after ​4 years. 

• It will take an additional ​​3646.52 more years to earn ​4 times the initial investment if the initial investment is ​$5000 than if the initial investment is ​$2000.

• It will take approximately ​​3646.52 more years for an initial investment of ​$4 to reach an investment value of ​$5000 than to reach an investment value of ​$2000

• It will take an additional ​​$3646.52 in initial investment to reach an investment value of ​$5000 in ​4 years than to reach an investment value of ​$2000 in ​4 years

• 81

• 100

• 300

• 243

Let m(x)=x²−2 and n(x)=(x−2)².

What is n(m(x))?

• A) x^4 - 16x^3 + 96x^2 - 256x + 256

• B) x^4 - 8x^2 + 16

• C) x^4 - 8x^3 + 16x^2

• D) x^4 - 4x^3 + 4x^2

A survey is conducted with 600 randomly selected individuals from a newsletter subscription list of a local bookstore to determine their planned spending at the bookstore over the next year.

Which TWO statements are TRUE regarding the conclusions that can be drawn from the survey data?

• The survey results can be used to make valid inferences about the spending plans of all individuals on the newsletter subscription list.

• The survey results should not be used to make inferences about the spending plans of all individuals on the newsletter subscription list because the entire list was not surveyed.

• The survey results can be used to make valid inferences about the spending plans of all customers who visit the bookstore.

• The survey results should not be used to make inferences about the spending plans of all customers who visit the bookstore because the sample is not representative of the entire customer base.

• The survey results should not be used to make inferences about the spending plans of individuals on the newsletter subscription list because the sample may not be representative of the entire list.

Which of the following best describes secondary data?

• data that is collected firsthand by researchers

• data that is primarily qualitative

• data that has been previously gathered and is available for use

• data that is always outdated