Bill bought 4 pens for $12. Which of the following equations shows the relationship between the cost of pens, c, and the number
2 answers:
Answer:
The correct option is
, $60
Step-by-step explanation:
We start by assuming that exists a linear relationship between the price of the pens and the amount of pens that Bill bought.We also assume that this linear relationship is a direct linear relationship.This means that the price of the pens increases with the amount of pens. According to this we can calculate the price of one pen as :
Solving for ''x'' :
We find that one pen costs $3
If ''c'' is the cost of pens and ''x'' is the number of pens we can write the ''cost function'' multiplying the cost per pen by the amount of pens :
cost = (cost per pen).(amount of pens) ⇒
Because cost is the letter ''c'' and the amount of pens is represented by the variable ''x''
To know the cost of 20 pens we only need to replace in the cost function ''c'' the variable ''x'' by 20 ⇒
Finally, the cost function is
And the cost of 20 pens is $60. Therefore, the third option is the correct option.
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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.