Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the
1 answer:
Answer:
Step-by-step explanation:
2x + 5y = 16 ------------------(1)
-5x -2y = 2 ------------------(2)
<u>Multiplying (1) by 5 </u>
5(2x+5y) = 16*5
10x+25y = 80 ----------------(3)
<u>Multiplying (2) by 2</u>
2(-5x-2y) = 2*2
-10x - 4y = 4 -----------------(4)
Adding Eq. (3) and (4)
10x + 25y -10x -4y = 80 + 4
25y - 4y = 84
21y = 84
Dividing both sides by 21
y = 4
Now, Putting y = 4 in Eq. (1)
2x + 5(4) = 16
2x + 20 = 16
2x = 20 - 16
2x = 4
Dividing both sides by 2
x = 2
Ordered Pair = (x,y) = (a,b) = (2,4)
Hope this helped!
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Answer:
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 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 less than .2 inches?
This is the pvalue of Z when X = 200 + 0.2 = 200.2 subtracted by the pvalue of Z when X = 200 - 0.2 = 199.8. So
X = 200.2
By the Central Limit Theorem
has a pvalue of 0.8238
X = 199.8
has a pvalue of 0.1762
0.8238 - 0.1762 = 0.6476
64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches