Geoffrey is evaluating the expression StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript
2 answers:
The mathematical expression does not seem clear but I have made an attempt to make sense of what is implied.
Answer:
<em>a</em> = 4, <em>b</em> = 2, <em>c</em> = 16, <em>d</em> = 9
Step-by-step explanation:
Solving the first part of the question by indices,
Comparing the rightmost term with the second term in the question,
<em>a</em> = 4, <em>b</em> = 2
Solving on,
Comparing with the final term in the question,
<em>c</em> = 16 and <em>d</em> = 9
Therefore,
<em>a</em> = 4, <em>b</em> = 2, <em>c</em> = 16, <em>d</em> = 9
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Answer:
a) 0.0392
b) 0.4688
c) At least $39,070 to be among the 5% most expensive.
Step-by-step explanation:
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.
In this problem, we have that:
a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?
This is the pvalue of Z when X = 20000. So
has a pvalue of 0.0392.
So this probability is 0.0392.
b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?
This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.
X = 30000
has a pvalue of 0.5080.
X = 20000
has a pvalue of 0.0392.
So this probability is 0.5080 - 0.0392 = 0.4688
c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?
This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.
The wedding would have to cost at least $39,070 to be among the 5% most expensive.
Let the total cost of the item be represented by C and the price be represented by P, then given that t<span>he total cost of an item including sales tax is directly proportional to its price, thus</span>
where k is a constant.
Given that <span>the total cost of a $32 item is $33.60, thus
Therefore, the total cost on a $55 item is given by
</span>
where k is a constant.
Given that <span>the total cost of a $32 item is $33.60, thus
Therefore, the total cost on a $55 item is given by