Container A is cylinder with a radius of 6 units and a height of 6 units. A right cone has been carved from its base and has a h
eight of 6 units. Container B has the same radius as container A. Which statement derives the formula to find the volume of container A?
1 over 3π(62)(6) − π(62)(6)
2[1 over 3π(62)(6) − π(62)(6)]
2[π(62)(6) − 1 over 3π(62)(6)]
π(62)(6) − 1 over 3π(62)(6)
1 over 3π(62)(6) − π(62)(6)
2[1 over 3π(62)(6) − π(62)(6)]
2[π(62)(6) − 1 over 3π(62)(6)]
π(62)(6) − 1 over 3π(62)(6)
1 answer:
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Answer:
(x-8)(x+7)
Step-by-step explanation:
using quadratic formula we have
x=
we have:
x^2-x-56=0
a= 1 b=-1 c=-56
so we have:
x=(-(-1)+-sqrt(1^1-4*(1)*(-56)))/(2*1)
x=1+-sqrt(1-4*(-56))/(2)
x=(1+-sqrt(225))/2
x=(1+-15)/2
so we have the roots:
x1=(1+15)/2 =8
x2=(1-15)/2=-7
so the answer is (x-8)(x+7)
Answer:
P(939.6 < X < 972.5) = 0.6469
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.
This means that
Sample of 57:
This means that
Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.
This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So
X = 972.5
By the Central Limit Theorem
has a pvalue of 0.6915
X = 939.6
has a pvalue of 0.0446
0.6915 - 0.0446 = 0.6469
So
P(939.6 < X < 972.5) = 0.6469