One circular table has a diameter of 9 ft, and another circular table has a diameter of 14 ft. How much greater is the area of t
2 answers:
<h2>Answer:</h2>
The area of the larger table is greater by about 90 square feet.
<h2>Step-by-step explanation:</h2>The area of a circular table or circle is given as :
Table 1:
Diameter is 9 feet. So, radius is = 9/2 =4.5 feet
Area = square feet
Table 2:
Diameter is 14 feet. So, radius is = 14/2 =7 feet
Area = Area = square feet
Now the difference between both the areas = square feet
As the difference has to be converted to nearest whole number, it becomes 90 square feet.
Therefore, the area of the larger table is greater by about 90 square feet.
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Using the normal distribution, we have that:
- The distribution of X is
.
- The distribution of
is
.
- 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.
- 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.
The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
In this problem, the parameters are given as follows:
Hence:
- The distribution of X is
- The distribution of
The probabilities are the <u>p-value of Z when X = 58 subtracted by the p-value of Z when X = 55</u>, hence, for a single movie:
X = 58:
Z = 0.05.
Z = 0.05 has a p-value of 0.5199.
X = 55:
Z = -0.1.
Z = -0.1 has a p-value of 0.4602.
0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.
For the sample of 17 movies, we have that:
X = 58:
Z = 0.19.
Z = 0.19 has a p-value of 0.5753.
X = 55:
Z = -0.38.
Z = -0.38 has a p-value of 0.3520.
0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.
More can be learned about the normal distribution at brainly.com/question/4079902
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Answer:
The point of intersection
(0,-14,22/5), (2,0,24/5), (-22,-24,0).
Step-by-step explanation:
Check attachment for solution
