josh had 6 containers of strawberry yogurt. he had 7 fewer containers of strawberry than blueberry yogurt. than he ate 2 contain
1 answer:
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Answer:
Now we can calculate the p value with the following probability:
The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.
Step-by-step explanation:
Information given
represent the mean for sample 1 (younger)
represent the mean for sample 2 (older)
represent the sample standard deviation for 1
represent the sample standard deviation for 2
sample size for the group 2
sample size for the group 2
t would represent the statistic
System of hypothesis
We want to test if that people under the age of forty have vocabularies that are different than those of people over sixty years of age, the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And the degrees of freedom are given by
Replacing the info given we got:
Now we can calculate the p value with the following probability:
The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.
Answer:
The room dimensions that will minimize the cost of the paint are 12 ft x 12 ft x 11 ft.
Step-by-step explanation:
We can find first the volume equation using the formula of the volume of a box.
Thus we get the constraint function
Then since we are asked to minimize the cost, we can write the cost function which is the area of each one of the walls and ceiling multiplied by the painting cost.
Lagrange Multipliers to find minimum cost.
We can continue finding the partial derivatives to build the system of equations required for Lagrange Multipliers method.
And the constraint function
So we get
We can multiply each side of each equation by the dimension which is missing to get the full volume on the right side.
Then we can set each the equations equal to each other, so from the first one and the second equation we get
We can subtract 0.11xy from both sides.
And we can divide both sides by 0.12z to get
We can repeat the process by setting the first and third equation equal to each other.
We can subtract 0.12 xz from both sides
And we can solve by z
So if we replace that as well y = x on the constraint for the volume euqation we get
We can then solve for x
And taking the cube root
So then we can use the equations we have found for y and z in terms of x
And
Then the dimensions of the room that will minimize the cost are 12ft x 12 ft x 11 ft. Since you have to enter using commas you can write 12, 12, 11, please check as well if you have to insert the units that are feet for each.