Answer:
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Step-by-step explanation:
We have the standard deviation for the differences, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 8 - 1 = 7
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of 
. So we have T = 1.8946
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.582 - 10.67 = -1.088
The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
The given pair of lines are not perpendicular.
<h3>What is a line?</h3>
The line is a curve showing the shortest distance between 2 points.
5x - 5y = -2 - - - - - (1)
Transform the equation into standard form,
5x + 2 = 5y
y = 5x /5 + 2/5
y = x + 2/5
The slope of equation 1 is 
and intercept c = 2 / 5
Similarly
x + 2y = 4 - - - - - - - -(2)
Transform it into standard form
y = -x/2 + 4 /2
y = -x / 2 + 2
Slope of the equation 2 
= -1 / 2 and intercept c = 2
Slope of line 1 * slope of line 2 = 1 * -1/2 = -1/2
Since the lines are not perpendicular because the pair of lines does not satisfy the property of perpendicular lines i.e
Thus, the given pair of lines are not perpendicular.
Learn more about lines here:
brainly.com/question/2696693
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Answer:
3:36PM
Step-by-step explanation:
Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.
Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at 
capacity, we can use the equation:
This shows of his tank's capacity (
) is equal to 
gallons. This means he will stop for gas when gallons are remaining.
Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.
This is a simple proportion, and now we know he uses 
gallons of gas per hour.
Now we can how many hours of gas Leon has left.
He has 
gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.
The 
is because Leon doesn't stop when his tank is empty, he stops gallons earlier. We are dividing by because that is how much gas he uses per hour, meaning the result of this division (
) is how many hours he has left.
Now we can solve for what time Leon will stop to get gas.
12PM + 
hours of driving + the remaining hours = 3:36PM
( hours is equal to 1 hour and 36 minutes)
Therefore, Leon will stop for gas at 3:36PM
2.95 * 10%=
2.95 * .1 =
.295
Subtract .295 from 2.95
2.95 - .295 = 2.655
$ 2.66
