Can someone please help me??
2 answers:
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Answer:
Dimensions:
Perimiter:
Minimum perimeter: [16,16]
Step-by-step explanation:
This is a problem of optimization with constraints.
We can define the rectangle with two sides of size "a" and two sides of size "b".
The area of the rectangle can be defined then as:
This is the constraint.
To simplify and as we have only one constraint and two variables, we can express a in function of b as:
The function we want to optimize is the diameter.
We can express the diameter as:
To optimize we can derive the function and equal to zero.
The minimum perimiter happens when both sides are of size 16 (a square).
Answer:
The customer can conclude that the company's claim is correct
Step-by-step explanation:
The percentage of lids that has a free yogurt coupon = 20%
The number of cups a loyal customer purchases = 85 yogurt cups
The number of cups that contained a coupon = 12 (14.1%)
The confidence interval performed = 99% confidence interval for the proportion of yogurt cups containing coupon codes
The interval obtained = (0.044, 0.238)
Therefore, the range of proportion within which the true proportion exists is 0.044 < < 0.238
The range of percentage within which the true percentage exist is therefore;
0.044 × 100 = 4.4% < × 100 < 0.238 × 100 = 23.8%
Given that the possible true percentage of lids that has a coupon is between 4.4% and 23.8% at 99% confidence level, the customer can conclude that only 12 of his yogurt cup contained coupon by chance and that the company's claim is correct.