Answer:
The largest area will be 2812.5 square meters.
Step-by-step explanation:
The perimeter of rectangle is given as:
(L is the length and W is the width)
As one side is not to be fenced, so the formula here will be :
Perimeter is 150.
So, ;
Area of the rectangle is :
Plugging the value of L in the area formula;
Area =
This is a parabola or quadratic function whose maximum or minimum values occur at the average of the solutions.
So, Solving
=> Or
=>
=>
W = 75
So, the two solutions are zero and 75.
The average of them is
Now, the maximum area is at W=37.5
And
L = 75
The dimensions that maximize the area are L=75 and width W=37.5
And maximum area = = 2812.5 square meters
Hence, the largest area will be 2812.5 square meters.
Given:
w be the weight in pounds of a baby tigers.
To find:
The inequality if baby tigers can be no larger than 4 pounds.
Solution:
Baby tigers can be no larger than 4 pounds. It mean weight of baby tigers cannot be greater than 4. In other words, the weight of the baby tigers must be less than or equal to 4.
Let w represents weight in pounds and the weight of the baby tigers must be less than or equal to 4. So,
Therefore, the required inequality is .
Answer:
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.
Step-by-step explanation:
Data given and notation
Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5
We can begin calculating the sample mean given by:
And the sample deviation given by:
And we got:
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis.