Its is surprising that no one attempted this question for over a week.
As in all geometry problems, start with a diagram (shown).
Then we realize right away that AB=sqrt(8^2+2^2)=sqrt(68)=2sqrt(17)
BC=sqrt(4^2+1^2)=sqrt(17)
The perimeter is therefore twice the sum of AB+BC=2(2sqrt(17)+sqrt(17))
2(3sqrt(17))=6 sqrt(17) We can estimate sqrt(17)=4.125, so 6sqrt(17)=24.75 which is close enough to get the correct answer choice.
Have a good day.
I graphed this line below.
Start with an open dot on 7.
The reason we use an open dot is because x
does not equal 7, it is only greater than 7.
So from your open dot, draw an arrow to the right
to represent all numbers greater than 7.
Finally, state your answer in set notation if possible.
It is read as {x: x > 7}.
Answer:
If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 24 items are picked at random, 8% of the time their mean life will be less than how many years?
This is the value of X when Z has a pvalue of 0.08. So it is X when Z = -1.405.
By the Central Limit Theorem
If 24 items are picked at random, 8% of the time their mean life will be less than 5.156 years.