Multiply the fractions. Select the answer that is in simplest form.
1 answer:
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Answer:
(a)
(b)
(c)
(d)
Step-by-step explanation:
Given
--- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
Selection of at least 13 =
Ways of selecting at most 12 =
--- Complement rule
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
Selection of at least 9 =
Ways of selecting at most 8 =
--- Complement rule
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
Selection =
Using inclusion/exclusion rule of two sets:
Answer:
The Sample Size Need To be at least 114
Step-by-step explanation:
According to the Question,
- Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.
The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.
- Now, For 99% Confident the level of value α is 0.01.
α/2 = 0.01/2 ⇒ 0.005
- Thus, From The table, We get that the value of
is 2.58.
Hence, the sample size n can be found as
n = {}²
n = {2.58 × 6.2}² / 1.5²
n = 113.72 .
So, The Sample Size Need To be at least 114.