Answer:
The y intercept should be 2 lower than the original equation
Step-by-step explanation:
Answer:


or

Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the
intercept, then
is easy to find.
It is just the
coordinate of the
intercept is your value for
.
(Why? The
intercept happens when
. Replacing
with 0 gives
. This says when
.)
So
.
So our function so far looks like this:

Now to find
we need another point. We have two more points. So we will find
using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given
is a point on our curve.
So when
,
.


Divide both sides by 8:

Reduce the fraction:

So the equation if it works out for the other point given is:

Let's try it. So the last point given that we need to satisfy is
.
This says when
,
.
Let's replace
with 2 and see what we get for
:






So we are good. We have found an equation satisfying all 3 points given.
The equation is
.
Answer:
≈ 10.63
Step-by-step explanation:
Pythagorean Theorem... Possibly the most easy theory in math once you understood it.
Here's the formula.
AB would be the hypothenuse
BC would be the opposite
CA would be the Adjacent.
But let's not make it complicated though, the question is actually quite easy.
You are asked to find AB, the hypothenuse.
The hypothenuse would be C.
BC and CA would be A and B.
It doesn't matter where are you going to place the numbers.
So,
= 113
Now we would have to square root 113 since
is an irrational number, and the question asks you to round ro the nearest tenth.
=10.63014581
≈ 10.63
Your answer would be 10.63
Hope this answer helped :)
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.