Subtract 73 from both sides of the equation.
102x+7y=567-73
Subtract 7y from both sides of the equation.
102x=567-73-7y
Subtract 73 from 567
102x=494-7y
Divide each term by 102 and simplify
Divide each term 102x=494-7y by 102
Cancel the greatest common factor which is 102x/102
Divide x by 1
Cancel the common factor is 494 and 102
Factor 2 out of 494
Factor 2 out of 102
Cancel the common factor which is 2
Rewrite the expression.
Move the negative in front of the fraction
Answer:
Step-by-step explanation:
Given
(a): Write as additive inverse.
An additive inverse is of the form a + (-b)
In this case:
So, the expression can be represented as:
(b): Number line representation
When the expression in (a) is solved.
The result is:
This means that the number line must accommodate 7 and -1.
Having said that, options (b) and (c) are out because their range is 0 to 15 and this excludes -1.
Option (d) is a wrong representation of
Hence, (a) is correct
Answer:
a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.
b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.
Step-by-step explanation:
To solve this question, it is important to know the Normal probability distribution and the Central Limit Theorem
Normal probability distribution
Problems of normally distributed samples can be 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) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?
This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.
By the Central Limit Theorem, the formula for Z is:
X = 7.1
has a pvalue of 0.9962
X = 5.5
has a pvalue of 0.0038
So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.
B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.
This is the pvalue of Z when X = 6.7 subtracted by the pvalue of Z when X = 5.9
X = 6.7
has a pvalue of 0.9082
X = 5.9
has a pvalue of 0.0918.
So there is a 0.9082 - 0.0918 = 0.8164 = 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.