16x² - 49
= (4x)² - 7²
Identity =》 a² - b² = (a + b) (a - b)
(4x)² - 7²
= (4x + 7) (4x - 7) [3rd option]
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Hope it helps ⚜
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The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours.
If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?
Given Information:
standard deviation = σ = 30 hours
confidence level = 99%
Margin of error = 6 hours
Required Information:
sample size = n = ?
Answer:
sample size = n ≈ 165
Step-by-step explanation:
We know that margin of error is given by
Margin of error = z*(σ/√n)
Where z is the corresponding confidence level score, σ is the standard deviation and n is the sample size
√n = z*σ/Margin of error
squaring both sides
n = (z*σ/Margin of error)²
For 99% confidence level the z-score is 2.576
n = (2.576*30/6)²
n = 164.73
since number of bulbs cannot be in fraction so rounding off yields
n ≈ 165
Therefore, a sample size of 165 bulbs is needed to ensure a margin of error not greater than 6 hours.
Answer:
[-4,0) ∪ [2, ∞)
Step-by-step explanation:
For piecewise function domain and range, we need to understand the difference between "(" and "[" or ")" and "]"
- The parenthesis ( "(" and ")" ) are used for "open circles" in the graph.
- The brackets ( "[" and "]" ) are use for "closed circles" in the graph.
Range is the set of y-values for which the function is defined.
Now,
The upper part of the function shows the graph going from y = 2 towards infinity (arrow). At y = 2 , there is closed circle, so this part range would be
[2, ∞) (infinity is always with parenthesis)
Now, looking at bottom part, the function is defined from 0 (open circle) to -4 (closed). so we can write:
[-4,0)
This is the range, 2nd answer choice is correct.
[-4,0) ∪ [2, ∞)
