Question

1. 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
2. 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
3. fuel consumed (gallons): 50 15 12 40 55 3 25 88 16, distance flown (miles): 403 99 85 290 511 5 120 700 101
4. 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?
5. 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

Explanation:

9.

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

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

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

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. \(a_n = 11n-32\)

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