Which set of points contains the solutions to the inequality y ≥ 1⁄4x + 5?
1 answer:
Answer:
B. {(4,6), (8,8), (–3,6)}
Step-by-step explanation:
You can graph the equation and plot the points, or you can try the points algebraically. For the latter, it is convenient to rearrange the inequality a bit.
y ≥ 1/4x + 5 . . . . . given
4y ≥ x + 20 . . . . . multiply by 4
You can use this form, or you can subtract x to get ...
4y -x ≥ 20
Trying the offered points, we want 4y-x to be at least 20. We get ...
A: 4(-17) -(-3) = -65 . . . . less than 20
B: 4(6)-4 = 20 . . . a solution
4(8) -8 = 24 . . . a solution
4(6)-(-3) = 27 . . . a solution . . . . set B contains solutions to the inequality
C: 4(4)+3 = 19 . . . . less than 20
D: 4(-1)-(-2) = -2 . . . . less than 20
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Answer:
a) 0.27% probability that the mean is less than 1995 milliliters.
b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.
Step-by-step explanation:
To solve this problem, it is important 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
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?
So
This probability is the pvalue of Z when X = 1995. So
By the Central Limit Theorem
has a pvalue of 0.0027
So 0.27% probability that the mean is less than 1995 milliliters.
B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?
This is the value of X when Z has a pvalue of 1-0.1 = 0.9.
So it is X when
2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.
Answer:
Step-by-step explanation:
The plot chart below best represents the relationship between stress and productivity in the workplace. As seen in the chart both high and low levels of stress equate to very low productivity levels for employees in the workplace. While just enough stress creates very productive employees. This tends to be because employees are worried about the possibility of losing their jobs so they work hard in order to keep the job but are not so worried that they think it will happen tomorrow and become burned out.
