The riding stables just received an unexpected rush of registrations for the next horse show, and quickly needs to create some a
dditional paddock space. There is sufficient funding to rent 1200 feet of temporary chain-link fencing. The plan is to form two paddocks with one shared fence running down the middle. What is the maximum area that the stables can obtain, and what are the dimensions of each of the two paddocks?a. 100b. 150c. 200d. 220e. 250
1 answer:
Answer:
Maximum added area will be 60,000 ft²
Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.
Step-by-step explanation:
Consider the provided information.
There is sufficient funding to rent 1200 feet of temporary chain-link fencing.
The plan is to form two paddocks with one shared fence running down the middle.
The total length of fencing is 1200 feet that is same as the total perimeter including that shared line down the middle.
Therefore, the perimeter is
Solve for L
As we know the area of rectangle is A=L×W
Substitute the value of L in above formula.
The above equation makes a downward parabola.
In order to find the maximum, find the vertex of parabola as shown:
Hence, the width should be 200 ft in order to get maximum area,
Therefore, the length will be:
Now substitute the value of L and W in area formula.
A=300×200=60,000
Hence, maximum added area will be 60,000 ft²
Hence, the length should be 300 ft, and each paddock should then be 150 feet long.
Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.
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Answer:
Option (d) and (e)
Step-by-step explanation:
We are given that a sample survey interviews SRS of 500 female college students and 550 male college students. And Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer.
In all, 410 of the females and 484 of the males say they worked for pay last summer.
From this, Null Hypothesis, :
{means proportion of male and female college students who worked for pay last summer are same}
Alternate Hypothesis, :
{means there is a difference in the proportion of male and female college students who worked for pay last summer}
Now, since we know that results were statistically significant at the 1% level.
So, if p-value is less than the significance level ⇒ we will reject
if p-value is more than the significance level ⇒ we will not reject
From the options given it is sure that P-value is less than 1%,i.e.;
<em>P-value is less than the significance level, so we will reject null hypothesis and conclude that there is convincing evidence that the proportion of all male college students in the study who worked for pay last summer is different from the proportion of all female college students in the study who worked for pay last summer. </em>
Also, option (d) and (e) are same in my opinion.