Answer:
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Step-by-step explanation:
We are given a linear regression model that relates daily high temperature, in degrees Fahrenheit and number of lemonade cups sold.
Where y is the number of cups sold and x is the daily temperature in Fahrenheit.
Residual value:
A residual value basically shows the position of a data point with respect to the regression line.
A residual value of 0 is desired which means that the regression line best fits the data.
The Residual value is calculated by
Residual = Observed value - Predicted value
The predicted value of number of lemonade cups is obtained as
So the predicted value of number of lemonade cups is 23 and the observed value is 21 so the residual value is
Residual = Observed value - Predicted value
Residual = 21 - 23
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
For this case we have a function of the form:
Where,
A: initial amount
b: growth rate (if b> 1)
n: time in hours
Substituting values we have:
We have then that the initial amount is:
If b = 1.85 then the growth percentage is:
Answer:
here were initially 20 bacteria.
The hourly percent growth rate of the bacteria would be 85%
Answer:
a. 
μ = $24.57
μ ≠ $24.57
b. 0.12
c. we fail to reject the null hypothesis since p ≈0.12 > 0.05
d. we fail to reject the null hypothesis since z ≈-1.6 > -1.96
Step-by-step explanation:
a)
μ = $24.57
μ ≠ $24.57
b)
To compute p value, we need to calculate z-score of $23.89 per hour. in the distribution assumed under null hypothesis
z-score can be calculated as follows:
where
- X= $23.89
- M is the mean value under null hypothesis ( $24.57)
- s is the sample standard deviation ($2.40)
- N is the sample size (30)
Putting the numbers in the formula we get
≈ −1,5518
The corresponding p-value is <em>two tailed </em>and ≈ 0.12
c)
since p ≈0.12 > 0.05 <em>we fail to reject the null hypothesis.</em>
d)
Critical value for the 0.05 significance level in two tailed test is :
c(z)=-1.96 Since z≈ −1,6 >-1.96, it is not in the critcal region, therefore <em>we fail to reject the null hypothesis. </em>
A.) .4 of a balloon is left
To Check:
what I did was divide 172 by 27 and it is 6.37 rounded to ........6 is an equal number so I kept it and .4 will be left over after sharing equally.
B.) 17 more balloons are needs
To Check:
what I was multiply 27 by 7 because each student needs seven balloons and I got 189 after that I subtracted 172 from 189 (189-172=17)
to see how many more balloons are needed.
Answer:
length = 6 feet
width = 4 feet
Step-by-step explanation:
To find the dimensions of the rectangle, you can set up a variable and an expression that will equal the perimeter of the figure. Given l = length, width is '8 feet less than twice the length' or w = 2l - 8.
The general formula for perimeter of a rectangle is:
2w + 2l = P, where w = width and l = length
Using the variable and expression from above and the perimeter of 20 feet:
2(2l - 8)+ 2l = 20
distribute: 4l - 16 + 2l = 20
combine like terms: 6l - 16 = 20
add 16 to both sides: 6l - 16 + 16 = 20 + 16 or 6l = 36
divide and solve for 'l': 6l/6 = 36/6, or l = 6 feet
solve for 'w': w = 2(6) - 8 or w = 12 - 8 = 4 feet
