Which inequality represents all values of x for which the product below is defined? 20 pts
1 answer:
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The question is incomplete. The complete question follows.
A company makes windows for use in homes and commercial builidings. The standards for glass thickness call for the glass to average 0.325 inch with a standard deviation equal to 0.065 inch. Suppose a random sample of n=44 windows yield a sample mean of 0.337 inch. Complete parts a and b.
a. What is the probability of x ≥ 0.337 if the windows meet the standards?
b. Based on your answer to part a, what would you conclude about the population of windows? Is it meeting the standards? (A result is unusual if it has a probability less than 0.05)
Answer and Step-by-step explanation: To answer this question, use <u><em>Central Limit Theorem</em></u>: it states regardless of the original population distribution, if the sample size is large enough, the sample mean distribution will approach a normal distribution.
The calculations for the CLT is given by normalizing the distribution, i.e.:
where
z is z-score
x is the sample mean
μ is population mean
σ is standard deviation of the population
n is the number of individuals in the sample
Calculating z-score for the window maker company:
z = 1.22
Using the z-score table, we found the probability:
P = 0.8888
As it is a "more than situation":
P(x≥0.337) = 1 - 0.8888
P(x≥0.337) = 0.1112 or 11.12%
a. Probability of x≥0.337 if the windows meet the standards is 11.12%.
b. Comparing results, probability of x≥0.337 is bigger than 0.05:
0.1112 > 0.05
So, we can conclude that the random sample of n=44 is meeting the standards estipulated.
2 Answers:
- B) The lines are parallel
- C) The lines have the same slope.
Parallel lines always have equal slope, but different y intercepts.
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Explanation:
Let's solve the second equation for y
3y - x = -7
3y = -7+x
3y = x-7
y = (x-7)/3
y = x/3 - 7/3
y = (1/3)x - 7/3
The equation is in y = mx+b form with m = 1/3 as the slope and b = -7/3 as the y intercept. We see that the first equation, where y was already isolated, also has a slope of m = 1/3. The two equations of this system have the same slope. Choice C is one of the answers.
However, they don't have the same y intercept. The first equation has y intercept b = -4, while the second has b = -7/3. This means that they do not represent the same line. They need to have identical slopes, and identical y intercepts (though the slope can be different from the y intercept of course) in order to have identical lines. So we can rule out choice D and E because of this.
Because the two equations have the same slope, but different y intercepts, this means the lines are parallel. Choice B is the other answer.
Parallel lines never touch or intersect, which in turn means there is no solution point. A solution point is where the lines cross. We can rule out choice A.
I recommend using your graphing calculator, Desmos, GeoGebra, or any graphing tool (on your computer or online) to graph each equation given. You should see two parallel lines forming. I used GeoGebra to make the graph shown below.
