4.8 is 10 times as much as _____?
2 answers:
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Answer:
The answer is below
Step-by-step explanation:
1)
mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65
Given that the confidence level (c) = 90% = 0.9
α = 1 - c = 0.1
α/2 = 0.05
The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65
The margin of error (E) is given as:
The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)
2)
mean (μ) = 23, SD(σ) = 12, sample size (n) = 45
Given that the confidence level (c) = 88% = 0.88
α = 1 - c = 0.12
α/2 = 0.06
The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56
The margin of error (E) is given as:
The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)
Answer:
The correct options, rearranged, are:
Options:
And the asnwer is the last option (D).
Explanation:
You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.
The difference of two perfect cubes may be represented by:
And it is, as a very well known special case:
Then, to prove, it you must divide the left side, , by the first factor of the right side,
Note that, to preserve the places of each term, you can write:
Then, you have:
By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:
That is the last option (D).