Answer:
Option c
Step-by-step explanation:
given that limit x tending to 4 of the function (3x-4) is 8
This implies for all values of x such that for epsilon >0 arbitrary small ,
, we get
|f(x)-8|<3epsilon
this is equivalent to the option c.
Proof:
Consider

Hence it follows that option C is right.
Hello and Good Morning/Afternoon!
<u>Let's take this problem step-by-step</u>:
<u>What the problem asks for:</u>
⇒ to rationalize the denominator
⇒ rationalize means that you multiply the numerator and
demonimator by the denominator
<u>Let's put that into action</u>:
<== <u>Answer</u>
<u></u>
Hopefully that helps!
We have the following function:

So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for

as shown in the Figure. This is also true because of

where

must be greater (or equal) than zero.
Second. The range of the function are the values of

.
Third. If

creases then

always creases, too.
Answer: A) .1587
Step-by-step explanation:
Given : The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce.
i.e.
and 
Let x denotes the amount of soda in any can.
Every can that has more than 12.50 ounces of soda poured into it must go through a special cleaning process before it can be sold.
Then, the probability that a randomly selected can will need to go through the mentioned process = probability that a randomly selected can has more than 12.50 ounces of soda poured into it =
![P(x>12.50)=1-P(x\leq12.50)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{12.50-12.30}{0.20})\\\\=1-P(z\leq1)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587](https://tex.z-dn.net/?f=P%28x%3E12.50%29%3D1-P%28x%5Cleq12.50%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5Cleq%5Cdfrac%7B12.50-12.30%7D%7B0.20%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq1%29%5C%20%5C%20%5B%5Cbecause%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%3D1-0.8413%5C%20%5C%20%5C%20%5B%5Ctext%7BBy%20z-table%7D%5D%5C%5C%5C%5C%3D0.1587)
Hence, the required probability= A) 0.1587
Its 18....................................