What is the value of h? h = 20 h = 35 h = 55 h = 70
2 answers:
Answer:
The value of h is 55. Therefore the correct option is 3.
Step-by-step explanation:
In the given triangle the measure of two exterior angles are 2h°.
The interior angle of one of those exterior angles
The sum of two interior angles of a triangle is equal to the opposite exterior angle.
Add 2h on both the sides.
Divide both sides by 4.
The value of h is 55. Therefore the correct option is 3.
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Answer:
(A)
Step-by-step explanation:
Given the equations:
Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.
Substitution of y into gives us:
The correct option is A.
Answer:
78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value
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 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 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.
In this problem, we have that:
What is the probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value?
This is the pvalue of Z when X = 2 + 0.1 = 2.1 subtracted by the pvalue of Z when X = 2 - 0.1 = 1.9. So
X = 2.1
By the Central Limit Theorem
has a pvalue of 0.8944
X = 1.9
has a pvalue of 0.1056
0.8944 - 0.1056 = 0.7888
78.88% probability that the mean thickness in the sample of 100 points is within 0.1 mm of the target value