The height of the given trapezoid is 7.5 m.
Step-by-step explanation:
Step 1:
The trapezoid's area is calculated by averaging the base lengths and multiplying it with the trapezoid's height.
The trapezoid's area,
Here is the lower base length and
is the upper base length while h is the height.
Step 2:
In the given problem, and
. Assume the height is h m.
The trapezoid's area
So the height of the given trapezoid is 7.5 m.
Answer:
The degrees of freedom are given by:
The p value would be given by:
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
Step-by-step explanation:
Information given
60, 56, 60, 55, 70, 55, 60, and 55.
We can calculate the mean and deviation with these formulas:
Replacing we got:
represent the mean
represent the sample standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level
t would represent the statistic
represent the p value
Hypothesis to test
We want to test if the true mean is less than 60, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic would be given by:
(1)
Replacing the info we got:
The degrees of freedom are given by:
The p value would be given by:
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
Answer:
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.
Step-by-step explanation:
Given that all the boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over.
This implies that boxes are in multiples of 12
i.e. 12, or 24, or 36 or....
Let us say this as 12m for m an integer
Now additional boxes arrived =60
Total number of boxes now =
This when arranged in stacks of 14,nothing left out
Or this is multiple of 14
for some positive integer n.
By trial and error we find that if 60 is to be divided by 14, 24 should be added and 24 is a multiple of 12.
So we say originally 24 boxes were there now 84 boxes there.
Hence both options are right.
(1) There were fewer than 110 boxes in the warehouse before the 60 additional boxes arrived. (2) There were fewer than 120 boxes in the warehouse after the 60 additional boxes arrived.