Algebra 1 HW 13-1

1. Several students at Rufus King High School were debating whether males or females were more involved in afterschool activities. There are three organized activities in the afterschool program – intramural basketball, chess club, and jazz band. Due to budget constraints, a student can only select one of these activities. The students were not able to ask every student in the school whether they participated in the afterschool program or what activity they selected if they were involved.

a. Write what the survey would look like (Hint: there should be 2 questionsand options to select for an answer!).

b. Rufus King High School has approximately 1500 students. Sam suggested that the first 100 students entering the cafeteria for lunch would provide a random

sample to analyze. Janet suggested that they pick 100 students based on a school identification number. Who has a better strategy for selecting a random sample? How do you think 100 students could be randomly selected to complete the survey?

c. Consider the following results from 100 randomly selected students:

Of the 60 female students selected, 20 of them played intramural basketball, 10 played chess, and 10 were in the jazz bland. The rest of them did not participate in the afterschool program.

Of the male students, 10 did not participate in the afterschool program, 20 played intramural basketball, 8 played in the jazz band, and the rest played chess.

Finish the table. What label is needed in the table cell identified with a “???”

2. Here is a two-way frequency table like we saw in the notes. There were another 100 people surveyed on their preferred super powers. Help fill in the rest of the table and answer the questions below.

To Fly Freeze Time

Invisibility

Super Strength

Telepathy

Total

Females 17 12 (a) 4 13 57

Males 16 (b) 6 18 2 (c)

Total (d) 13 17 22 (e) 100

a. Determine the frequencies of (a), (b), (c), (d), and (e).

b. Of the cells (a), (b), (c), (d), and (e), which cells represent joint frequencies?

c. Of the cells (a), (b), (c), (d), and (e), which cells represent marginal frequencies?

d. Why is it not fair to say that females like the super power “to fly” better than males in this survey?

3. Find three consecutive odd integers such that three times the second is five more than twice the third.

Algebra 1 HW 13-2

Juniors and seniors were asked if they plan to attend college immediately after graduation, seek full-time employment, or choose some other option. A random sample of 100 students was selected from those who completed the survey. Scott started to calculate the relative frequencies to the nearest thousandth.

a. Complete the calculations of the relative frequencies for each of the blank cells. Round your answers to the nearest thousandth.

b. A school website article indicated that “A Vast Majority of Students from our School Plan to Attend College.” Do you agree or disagree with that article? Explain why agree or why you disagree.

c. Why are the relative frequencies for the juniors and seniors misleading?

2. Solve, graph, and write your solution in interval notation.

–2(x + 7) ≥ –3x + 11

3. Here is the table that you helped fill in on last night’s homework.

To Fly Freeze Time

Invisibility

Super Strength

Telepathy

Total

Females 17 12 11 4 13 57

Males 16 1 6 18 2 43

Total 33 13 17 22 15 100

Calculate the relative frequencies for each of the cells to the nearest hundredth. Place the relative frequencies in the cells of the following table. (The first cell has been completed as an example.)

To Fly Freeze Time

Invisibility

Super Strength

Telepathy

Total

Females = .17

Males

Total

a. When selecting a student at random, what is the likelihood that you will select a male student that picked “super strength?” Is this a joint or marginal relative frequency?

b. When selecting a student at random, what is the likelihood that you will select a student who picked “freeze time?” Is this a joint or marginal relative frequency?

c. When selecting a student at random, what is the likelihood that you will select a female student? Is this a joint or marginal relative frequency?

d. Why is it not fair to say that females prefer the super power “to fly” compared to males?

Algebra 1 HW 13-3

Recall this table from last night’s homework: Juniors and seniors were asked if they plan to attend college immediately after graduation, seek full-time employment, or choose some other option. A random sample of 100 students was selected from those who completed the survey. Scott started to calculate the row conditional relative frequencies to the nearest thousandth.

1. Fill in the remaining cells with their row conditional relative frequencies, rounding to the nearest thousandth.

2. Are the row conditional relative frequencies for juniors and seniors similar, or are they very different?

3. Corey and Rachel had lunch at the mall. Corey ordered three slices of pizza and two

colas. Rachel ordered two slices of pizza and three colas. Corey’s bill was $6.00, and Rachel’s bill was $5.25. What was the price of one slice of pizza? What was the price

of one cola?

4. What is the mean of the data in the accompanying table? Scores Frequency

25 320 211 510 4

Here is the super power table from the last two homeworks. Let’s look one last time!! Don’t forget the survey asked 100 random people what they would pick to be their super power.

To Fly Freeze Time

Invisibility

Super Strength

Telepathy

Total

Females 17 12 11 4 13 57

Males 16 1 6 18 2 43

Total 33 13 17 22 15 100

Calculate the row conditional relative frequencies for each of the cells below to the nearest hundredth.

To Fly Freeze Time

Invisibility

Super Strength

Telepathy

Total

Females

Males

Total

5. Who prefers the super power “to fly” more? Males or females? Why?

6. Which is the more popular super power regardless of gender, “invisibility” or “freeze time?” Why?

7. Why are conditional relative frequencies better to compare than relative frequencies?

Algebra 1 HW 13-4

1. Consider the following scatterplot. It shows the finishing times and ages of 6 people in the 2003 NYC Marathon.

a. Is there a relationship between age and finish time for the race? If so, describe it.

b. Is there a linear relationship, or something else?

2. For 10 days, Romero kept a record of the number of hours he spent listening to music. The information is shown in the table.

Which scatter plot shows Romero’s data graphically?

3. John is trying to buy a Frosty at Wendy’s but forget his wallet. Luckily, he has exactly $2.14 (the total cost of his Frosty with tax) in change on the floor of his car. If John had twice as many nickels as dimes, and 4 more pennies than dimes, how many of each coin did he have?

4. Solve the following system GRAPHICALLY:

y – 2x = 12y = 5x + 4

5. Given the equation 2y – 8 = –3x

a. Write the equation of a line that is parallel to the given equation and has a y – intercept of 3

b. Write the equation of a line perpendicular to the given equation and has a y – intercept –7

Algebra 1 HW 13-5

Biologists conducted a study of the nesting behavior of a type of bird called a flycatcher. They examined a large number of nests and recorded the latitude for the location of the nest and the number of chicks in the nest.

1. What type of model (linear, quadratic or exponential) would best describe the relationship between latitude and mean number of chicks?

2. One model that could be used to describe the relationship between mean number of chicks and latitude is: y = 0.175 + 0.21x − 0.002x2, where x represents the latitude of the location of the nest and y represents the number of chicks in the nest. Use the quadratic model (equation) to complete the following table. Then plot the points you come up with and sketch a graph of the quadratic curve through those points on the scatterplot.

3. Based on this quadratic model, what is the best latitude for hatching the most flycatcher chicks? Justify your choice.

Suppose that social scientists conducted a study of senior citizens to see how the time (in minutes) required to solve a word puzzle changes with age. The scatter plot below displays data from this study.

Let x equal the age of the citizen and y equal the time (in minutes) required to solve a word puzzle for the seven study participants.

4. What type of model (linear, quadratic, or exponential) would you use to describe the relationship between age and time required to complete the word puzzle?

5. One model that could describe the relationship between age and time to complete the word puzzle is: y = 10 −1.01 + 0.017x. This exponential curve is shown on the scatter plot below. Does this model do a good job of describing the relationship between age and time to complete the word puzzle? Explain why or why not.

6. Based on this exponential model (equation), what time would you predict for a person who is 78 years old?

Algebra 1 HW 13-6

1. Consider again a data set giving the shoe lengths and heights of 10 adult men. This data set is shown in the table below.

a. Use your calculator to construct the scatter plot of this data set. Include the least-squares line in your graph. What is the slope of your equation and what does the slope of the least-squares line indicates about shoe length and height?

b. Use your calculator to construct the residual plot for this data set.

c. Make a sketch of the residual plot on the axes given below. Does the scatter of points in the residual plot indicate a linear relationship in the original data set? Explain your answer.

2. Suppose that after fitting a line, a data set produces the residual plot shown below. An incomplete scatter plot of the original data set is also shown below. The least-squares line is shown, but the points in the scatter plot have been erased. Estimate the locations of the original points and create an approximation of the scatter plot below:

3. For each of the following residual plots, what conclusion would you reach about the relationship between the variables in

the original data set? Indicate whether the values would be better represented by a linear or a non-linear relationship. Justify your answer.

a.

b.

c.

4. As a waiter at a restaurant, Joe earns $2.25 an hour plus tips. If he made $55 in tips and his total earnings were did not exceed $70, how many hours could he have worked?

5. Find the slope of a line that goes through (-3, 2) and (-9, -10).

Algebra 1 HW 13-7

1. The scatter plot below displays the elevation and mean number of clear days per year of 14 U.S. cities. Two lines are shown on the scatter plot. Which represents the least-squares line? Explain your choice.

2. From the notes, we saw Kendra looked at the relationship between shoe length and height for men. She wondered if the relationship might be different for women. To investigate, she collected data on shoe length (in inches) and height (in inches) for 12 women. a. Construct a scatterplot from the data.

b. Is there a relationship between shoe length and height for these 12 women?

c. The equation of the least-squares line for this data is y = 32.68 + 3.15x. What are the slope and y-intercept? Describe what this slope value means in the situation.

d. Using the least-squares line, y = 32.68 + 3.15x, fill in the rest of the table below.

e. Calculate the sum of the residuals. What does this value tell us?

f. Calculate the sum of the squared residuals. Why is this value better to look at when choosing a least-squares line for your data?

g. Below are dot plots of the shoe lengths for women and the shoe lengths for men. Suppose that you found a shoe print and that when you measured the shoe length, you got 10.8 inches. Do you think that a man or a woman left this shoe print? Explain your choice.

h. Describe how the data is distributed for the men on the dot plot above. Algebra 1 HW 13-8

x = shoe length (in)

y = height (in) Predicted height

Residual

8.9 61 60.72 0.289.6 61 62.929.8 66 2.45

10.0 64 64.1810.2 6410.4 65 -0.4410.6 65 66.0710.6 6710.5 66 65.76 0.2410.8 6711.0 67 -0.3311.8 70 69.85

1. The time spent in surgery and the cost of surgery was recorded for six patients. The results and scatter plot are shown below.

a. Calculate the equation of the least-squares line (regression equation), rounding all coefficients to the nearest hundredth.

b. Draw the least-squares line on the graph above. (Hint: Substitute x = 30 into your equation to find the predicted y-value. Plot the point (30, your answer) on the graph. Then substitute x = 180 into the equation and plot the point. Join the two points with a straightedge.)

c. What does the least-squares line predict for the cost of a surgery that lasts 118 minutes? (Calculate the cost to the nearest cent.)

d. How much do you have to add to your answer to question (c) to get the actual cost of surgery for a surgery lasting 118 minutes? What is this value called?

e. Show your answer to question (d) as a vertical line between the point for that person in the scatter plot and the least-squares line.

f. Remember that the residual is the actual y-value minus the predicted y-value. Calculate the residual for the surgery that took 149 minutes and cost $8,855 by using the least-squares line (regression equation) from part a. Then fill out the rest of the table below.

g. Suppose that a surgery took 100 minutes.

What does the least-squares line predict for the cost of this surgery?

Would you be surprised if the actual cost of this surgery were $9000? Why or why not?

What is the slope of the least-squares line and what does in mean in the situation?

2. What is the equation of a line that:

a. has an undefined slope and goes through the point (-3, 5).

b. is perpendicular to the y-axis and goes through the point (7, 1).

c. has a zero slope and goes through the point (-2, 3).

d. is parallel to the y-axis and goes through the point (4, -4).Algebra 1 extra…. HW 13-8

1. Four athletes on a track team are comparing their personal bests in the 100 meter and 200 meter events. A table of their best times, is shown below. A scatter plot of these results (including the least-squares line) is also shown below.

a. Use your calculator to find the equation of the least-squares line. Round all coefficients to the nearest tenth.

b. Use your equation to find the predicted 200-meter time for the runner whose 100-meter time is 12.95. What is the residual for this athlete?

c. Calculate the other three residuals and write them all in the given table. Then, using the axes provided below, construct a residual plot for this data set.

2. Solve the following system algebraically: y – 2x = 1

(same answer as #4 in HW 6-4)2y = 5x + 4

3. Graph the system of inequalities. Put an “S” on the graph to indicate the solution set.

x ≤ 1y > -2

4. Graph and write the equation of a line that goes through the point (3, 1) and has a slope of – .

Algebra 1 HW 13-9

1. The scatter plot below displays data on the number of defects per 100 cars and a measure of customer satisfaction (on a scale from 1 to 1000, with higher scores indicating greater satisfaction) for the 33 brands of cars sold in the United States in 2009.

x

y

a. Which of the following is the value of the correlation coefficient for this data set:

𝑟 = −0.95, 𝑟 = −0.24, 𝑟 =0.83, or 𝑟 = 1.00?

b. Explain why you selected this value.

2. Which of the three scatter plots below shows the strongest linear relationship? Which shows the weakest linear relationship?

3. Consumer Reports published data on the price (in dollars) and quality rating (on a scale of 0 to 100) for 10 different brands of men’s athletic shoes.

a. Construct a scatterplot of the data using the grid above.

b. Using your calculator, find the least-squares line (regression equation). Round all coefficients to the nearest hundredth.

c. Calculate the value of the correlation coefficient between price and quality rating and interpret this value. Round to the nearest hundredth.

d. Does it surprise you that the value of the correlation coefficient is negative? Explain why or why not.

e. According to the correlation coefficient, the correlation between price and quality is that as price increases, quality goes down. Does this mean that there is a causal relationship between the two variables?

4. Define causation.