Caroline wants to compare the expressions 15-9 and 9 (-15) to determine which result is greater. How can she do this without fin
1 answer:
You might be interested in
Answer:
Null hypothesis:
Alternative hypothesis:
And we want to test this with a confidence interval:
The confidence interval for the mean is given by the following formula:
(1)
After conduct the interval of 95% for the true mean we got: (11.59, 13.31)
And for this case the confidence interval contains the value of 11.89, so then we have enough evidence to FAIL to reject the null hypothesis at 5% of significance that the true mean is 11.89.
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".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n=30 represent the sample size
Solution to the problem
For this case we want to test the following hypothesis:
Null hypothesis:
Alternative hypothesis:
And we want to test this with a confidence interval:
The confidence interval for the mean is given by the following formula:
(1)
After conduct the interval of 95% for the true mean we got: (11.59, 13.31)
And for this case the confidence interval contains the value of 11.89, so then we have enough evidence to FAIL to reject the null hypothesis at 5% of significance that the true mean is 11.89.
Answer:
Length of hypothenuse = 13 inches
Length of other leg = 5 inches
Step-by-step explanation:
A triangle has three sides and three angles. A right angle triangle has 90 degrees as one of the angles. The remaining two angles are complimentary. This means that the sum if the other two angles is 90 degrees.
The longest side is the hypotenuse. The shorter sides are the opposite and adjacent.
In this triangle, the hypotenuse is three inches more than twice the length of one leg. Let the length of one leg be x inches.
Hypothenuse = 2x + 3
The other leg is 12 inches.
The diagram is illustrated in the attached photo.
Applying Pythagoras theorem,
Hypothenuse ^2 = adjacent^2 + opposite ^2
(2x+3)^2 = 12^2 + x^2
(2x+3)(2x+3)= 144 + x^2
4x^2 + 6x + 6x + 9 = 144 + x^2
4x^2 - x^2 + 6x + 6x + 9 - 144 = 0
3x^2 +12x - 135 = 0
3x^2 +27x - 15x - 135 = 0
3x(x+9)-15(x+9)=0
(3x -15)(x+9) = 0
3x -15 = 0 or x+9= 0
3x = 15 or x = -9
x = 15/3 = 5
x = 5inches because it cannot be negative.
Length of hypothenuse = 2x + 3
= 2×5 + 3 = 10 + 3 = 13 inches
