CD=8
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An office building casts a shadow that is 55 m long. At the exact same time, a 5 m tree casts a shadow that is 1.1 m long. Use s
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Answer and Step-by-step explanation:
This is a complete question
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the nullhypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The computation is shown below:
The null and alternative hypothesis is
= 0.7629
Now Test statistic = z
= -0.91
Now
P-value = 0.1804
So, it is Fail to reject the null hypothesis.
There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.
The cost of the least expensive fence is $3200
Step-by-step explanation:
The given is:
- A fence must be built to enclose a rectangular area of 20,000 ft²
- Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides
We need to find the cost of the least expensive fence
Assume that the length of each side opposite to North or South is x feet and the length of each other sides is y feet
∵ The length of the rectangle = x feet
∵ The width of the rectangle = y feet
∵ The rectangular area is 20,000 ft²
- Area of a rectangle = length × width
∴ x × y = 20,000
- Divide both sides by x to find y in terms of x
∴
The fence's length is equal to the perimeter of the rectangular area
∵ Perimeter of the rectangle = 2 length + 2 width
∴ Perimeter of the rectangle = 2x + 2y
∵ Fencing material costs $4 per foot for the two sides facing
North and South
∴ x costs $4 per foot
∵ The cost of the other two sides is $8 per foot
∴ y costs $8 per feet
The cost of the fence is the sum of the products of 4 , 2x and 8 , 2y
∵ The cost of the fence (C) = 4(2x) + 8(2y)
∴ C = 8x + 16y
- Substitute y by its value above
∴
∴
To find the least expensive differentiate C with respect to x and equate the answer by 0 to find the value of x
∵ can be written as
∴
∵
∴
- Equate by zero
∴
∵
∴
- Subtract 8 from both sides
∴
- Multiply both sides by x²
∴ - 320,000 = - 8x²
- Divide both sides by -8
∴ 40,000 = x²
- Take √ for both sides
∴ 200 = x
Substitute x in the equation of C to find the least cost of fence
∵
∴ C = 1600 + 1600
∴ C = 3200
The cost of the least expensive fence is $3200
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