9. which explicit formula describes the sequence -21, -10, 1, 12, 23, ...? a a_n = 11n - 32 b a_n = 11n + 32…

9. which explicit formula describes the sequence -21, -10, 1, 12, 23, ...? a a_n = 11n - 32 b a_n = 11n + 32 c a_n = 21n - 11 d a_n = -21n - 11\n10. each day at the bakery, jack bakes cakes and helps out at the counter. part a: make a scatter plot of the hours jack spends at the counter as a function of the number of cakes he bakes. cakes: 2 3 5 6 7, time (h): 4 4 1.5 2.5 1.5. part b: which equation models the trend line? a y = -1/2x + 5 c y = -1/2x - 5 b y = 1/2x + 5 d y = -2x + 5\n12. fuel consumed (gallons): 50 15 12 40 55 3 25 88 16, distance flown (miles): 403 99 85 290 511 5 120 700 101\n13. a. what would the correlation coefficient be if a scatter plot had no correlation? b. what would the correlation coefficient be if the scatter plot had a very strong positive correlation? c. what would the correlation coefficient be if the scatterplot had a very strong negative correlation?\n14. the table shows test scores for six students. grade: 76 79 83 86 91 92, height (in.): 85 87 89 90 93 93. part a: the data show a positive/negative correlation. (circle one) part b: the data in the table show a. correlation only b. causation only c. both correlation and causation d. neither correlation nor causation

9. which explicit formula describes the sequence -21, -10, 1, 12, 23, ...? a a_n = 11n - 32 b a_n = 11n + 32 c a_n = 21n - 11 d a_n = -21n - 11\n10. each day at the bakery, jack bakes cakes and helps out at the counter. part a: make a scatter plot of the hours jack spends at the counter as a function of the number of cakes he bakes. cakes: 2 3 5 6 7, time (h): 4 4 1.5 2.5 1.5. part b: which equation models the trend line? a y = -1/2x + 5 c y = -1/2x - 5 b y = 1/2x + 5 d y = -2x + 5\n12. fuel consumed (gallons): 50 15 12 40 55 3 25 88 16, distance flown (miles): 403 99 85 290 511 5 120 700 101\n13. a. what would the correlation coefficient be if a scatter plot had no correlation? b. what would the correlation coefficient be if the scatter plot had a very strong positive correlation? c. what would the correlation coefficient be if the scatterplot had a very strong negative correlation?\n14. the table shows test scores for six students. grade: 76 79 83 86 91 92, height (in.): 85 87 89 90 93 93. part a: the data show a positive/negative correlation. (circle one) part b: the data in the table show a. correlation only b. causation only c. both correlation and causation d. neither correlation nor causation

Answer

9.

Explanation:

Step1: Check the common - difference

For a sequence (a_n), if it is an arithmetic sequence, the common - difference (d=a_{n + 1}-a_n). Here, (d=-10-(-21)=11), (1 - (-10)=11), (12 - 1 = 11), (23 - 12 = 11). The general formula for an arithmetic sequence is (a_n=a_1+(n - 1)d), where (a_1=-21) and (d = 11).

Step2: Substitute values into the formula

(a_n=-21+(n - 1)\times11=-21 + 11n-11=11n-32).

Answer:

A. (a_n = 11n-32)

10.

Part A

To make a scatter - plot:

  1. On the x - axis, label the number of cakes.
  2. On the y - axis, label the counter time in hours.
  3. Plot the points ((2,4)), ((3,4)), ((5,1.5)), ((6,2.5)), ((7,1.5)) on the coordinate plane.
Part B

Explanation:

Step1: Calculate the slope and y - intercept

We can use the method of least - squares or just check the trend of the points. Let's assume two points ((x_1,y_1)=(2,4)) and ((x_2,y_2)=(6,2.5)). The slope (m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2.5 - 4}{6 - 2}=\frac{-1.5}{4}=-\frac{1}{2}). Using the point - slope form (y - y_1=m(x - x_1)) with ((x_1,y_1)=(2,4)) and (m =-\frac{1}{2}), we get (y-4=-\frac{1}{2}(x - 2)), which simplifies to (y=-\frac{1}{2}x+5).

Answer:

A. (y =-\frac{1}{2}x + 5)

13.

Explanation:

Step1: Recall the properties of the correlation coefficient (r)

The correlation coefficient (r) ranges from (- 1) to (1). If there is no correlation, the data points are scattered randomly and (r = 0). If there is a very strong positive correlation, the data points lie close to a straight - line with a positive slope and (r\approx1). If there is a very strong negative correlation, the data points lie close to a straight - line with a negative slope and (r\approx - 1).

Answer:

a. (r = 0) b. (r\approx1) c. (r\approx - 1)

14.

Part A

Explanation:

Step1: Observe the relationship between grade and height

As the grade increases, the height also generally increases. So, the data show a positive correlation.

Answer:

The data show a POSITIVE correlation.

Part B

Explanation:

Step1: Understand correlation and causation

Just because there is a positive correlation between grade and height does not mean that a higher grade causes a higher height. There could be other factors (such as age, nutrition, etc.) involved. So, the data show correlation only.

Answer:

A. Correlation only