Write a linear function f with the values f(10)=5 and f(2)=-3
1 answer:
Answer:
Step-by-step explanation:
step 1
Find the slope m
The formula to calculate the slope between two points is equal to
we have the ordered pairs
(10,5) and (2,-3)
substitute the values
step 2
Find the equation of the line in slope intercept form
we have
substitute and solve for b
The linear function is equal to
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Answer:
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
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 diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Lesser than 207.9.
pvalue of Z when X = 207.9. So
By the Central Limit Theorem
has a pvalue of 0.2743
2*0.2743 = 0.5486
54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches
Answer:
see below
Step-by-step explanation:
dilation with a scale factor of 1/3 means the distances to the center shrink by 1/3
so for center (4,-2)
distance of (7,4) is 3 n 6 to center
1/3 of distance = 1 n 2
so (7,4) become (4+1, -2+2) = (5, 0) after the dilation
similarly u can find the other 2 pts
distance of (-2,4) is -6 n 6 to center
1/3 of distance = -2 n 2
so (-2,4) become (4-2, -2+2) = (2, 0) after the dilation
distance of (1, 10) is -3 n 12 to center
1/3 of distance = -1 n 4
so (1,10) become (4-1, -2+4) = (3, 2) after the dilation
plot the new triangle using the 3 pts
