Answer:
Step-by-step explanation:
In a given triangle, the sum of every angle is always 
. Here, we are given a right angle (
), as well as another 
angle. Simply subtracting from 180 will give us the answer.
Answer:
{-5, -2}
Step-by-step explanation:
In a case like this please use parentheses to remove ambiguities. If I were to take your "x+5/x+2" literally, I'd have to write x plus 5/x plus 2.
I suspect that you actually meant (x + 5) / (x + 2), and will start with that.
First of all, this function is not defined at x = -5 or at x = -2. Thus, -5 and -2 are critical points.
Secondly, there may be one or more critical points beyond this. To find out, we have to differentiate (x+5)/(x+2):
(x + 2)(1) - (x + 5)(1)
f '(x) = ------------------------------
(x + 2)
Here it's clear that x cannot = -2, which would cause division by zero.
Thus, our critical values are {-5, -2}.
Slope = 3.1
This is in y =mx + b
Where m = slope
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:
.0000111
Step-by-step explanation:
move the decimal five places to the left because the 5 is negative
