Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
1 answer:
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
Rewriting the area as a function of x:
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
The value of y is:
Length = 29 m
Width = 29 m
You might be interested in
Answer:
And we can use the following excel code to find it:
"=NORM.DIST(-2.4,0,1,TRUE)"
Step-by-step explanation:
Data given and notation
n=100 represent the random sample taken
estimated proportion of interesst
is the value that we want to test
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion is lower than 0.5:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
And we can use the following excel code to find it:
"=NORM.DIST(-2.4,0,1,TRUE)"