Answer:
B
Step-by-step explanation:
A geometric series will only converge if the common ratio r meets the requirement
- 1 < r < 1
The n th term of a geometric sequence is
= a
where a is the first term and r the common ratio
All terms inside the summation are of this form
The only one with - 1 < r < 1 is B where r = = 0.75
Answer:
Part A:
Find the attached
Part B:
y = 23.875x + 279.625
Part C:
Total Sales increase from one week to the next by $23.875. Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
Part D:
The restaurant's sales for the Monday of the 20th week is expected to be $757.13
Step-by-step explanation:
Part A:
The scatter-plot can be obtained from stat-crunch by following the given steps below;
The first step is to enter the data given into any two adjacent columns of Stat-crunch application.
Next, click on Graph then Scatter plot
In the pop-up window that appears, select the week column as the X variable and the Total Sales column as the Y variable
Click Compute. Stat-crunch returns the scatter-plot as shown in the attachment below.
Part B:
The total sales for week 5 is given as 399 while that of week 13 is 590. Therefore, we shall determine the equation for the line of best fit using the points;
( 5, 399) and ( 13, 590)
The first step would be to determine the slope of this line;
slope = (590 - 399)/ (13 - 5)
= 23.875
The equation of the line in slope-intercept form is thus;
Sales = 23.875(Week) + c
We need to determine c, the y-intercept. We can use the point ( 5, 399);
399 = 23.875(5) + c
c = 279.625
The equation of the line of best fit is thus;
y = 23.875x + 279.625
Part C:
The slope of the equation for the lines of best fit was found to be 23.875. This value is positive which implies that the Total Sales increase from one week to the next by $23.875. The slope in regression is defined as the change in y for every unit change in x.
Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.
Part D:
The equation for the line of best fit was found to be;
y = 23.875x + 279.625
where y denotes the total sales and x the corresponding week. We are required to determine y when x is 20;
Y = 23.875(20) + 279.625
y = 757.125
Therefore, the restaurant's sales for the Monday of the 20th week is expected to be $757.13
