Cole is building a model rocket in science class. He selects the rocket parts from a set of solid cylinders and cones made from
metal. Cole wants to build a rocket with the dimensions shown. For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. Will Cole’s rocket meet the requirement for launch?
Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket. Use 3.14 for π. Explain.
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.
Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket. Use 3.14 for π. Explain.
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.
1 answer:
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Answer: 91/288
Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.
We can do this by multiplying the denominator by the whole number and then adding the numerator. Then, we put our new numerator over our old denominator.
So here, we can write 1 and 5/8 as the improper fraction 13/8 and we can write 5 and 1/7 as the improper fraction 36/7.
So here, we have 13/8 ÷ 36/7.
Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
So here, 13/8 ÷ 36/7 is the same as 13/8 × 7/36.
So now we are simply multiplying fractions and we do this by multiplying across the numerators and multiply across the denominators.
So now we have 91/288 which is in lowest terms.
This means that 1 and 5/8 divided by 5 and 1/7 is 91/288.
Answer:
a) 38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.
b) By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a. Find the probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.
This is 1 subtracted by the pvalue of Z when X = 200. So
has a pvalue of 0.6141
1 - 0.6141 = 0.3859
38.59% probability that a young man (aged 20 to 34) has a cholesterol level greater than 200 milligrams per deciliter.
b. Suppose you measure the cholesterol level of 100 young men chosen at random and calculate the sample mean. If you did this many times, i. what would be the mean of the distribution of the sample mean
By the Central Limit Theorem, the mean of the distribution of the sample mean would be 188 milligrams per deciliter