Last week Kiwi filled his 16-gallon tank with gas. On the average, his car burns 0.03 gallon of gas per mile. If Kiwi has 4 gall
2 answers:
Answer:
He has driven 400 miles.
Step-by-step explanation:
Total amount of gas = 16 gallons
Amount of gas left= 4 gallons
Amount of gas used = 16-4 = 12 gallons
No. of miles traveled in 0.03 gallons of gas = 1
No. of miles traveled in 1 gallon of gas =
No. of miles traveled in 12 gallon of gas =
=
Hence he has driven 400 miles.
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Answer:
The 95% confidence interval for the difference would be given by (-1.776;0.376)
We are 95% confidence that the true mean difference is between . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Let put some notation
x=test value before , y = test value after
x: 6.4 2.6 7.7 10.5 11.7 5.8 4.3 2.8
y: 6.7 2.4 7.4 8.1 8.6 6.4 3.9 2.7
The differences defined as and we got:
d: 0.3, -0.2, -0.3, -2.4, -3.1, 0.6, -0.4, -0.1
We can calculate the mean and the deviation for the sample with the following formulas:
represent the sample mean for the difference
population mean (variable of interest)
=1.32 represent the sample standard deviation
n=8 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value t we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval for the difference would be given by (-1.776;0.376)
We are 95% confidence that the true mean difference is between . Since the confidence interval contains the value 0, we don't have enough evidence to conclude that hypnotism appear to be effective in reducing pain.
Answer: left 7 units, up 4 units, and vertical compression
Step-by-step explanation:
Given
The function is
First shift it to the left by 7 units, so the function becomes
Now compress it to make it one-third
Now, sift the graph upward by 4 units
Thus , the conditions are left 7 units, up 4 units, and vertical compression.