Answer: x= 1/2
4x+8=10 1. Subtract 8 from both sides
-8 -8
——————
4x=2 2. Divide each side by 4
/4 /4
—————— 3. Simplify fraction
x=1/2
Answer:

Step-by-step explanation:
So we have the function:

And we want to find the derivative using the limit process.
The definition of a derivative as a limit is:

Therefore, our derivative would be:

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

Place the 4 in front:

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

Distribute:

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

The numerator will use the difference of two squares. Thus:

Simplify the numerator:

Both the numerator and denominator have a h. Cancel them:

Now, substitute 0 for h. So:

Simplify:

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

Multiply across:

Reduce. Change √x to x^(1/2). So:

Add the exponents:

And we're done!

Answer:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of gallons of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the following difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
For every 6 apple pie, you need 2 pounds of apples.
So, how many pounds of apples do you need for 10 apple pies?
Well, first to figure out this question we first need to make a conversion factor.
I see in the fraction 6/3 we can simplify that to 2/1. Now we got our conversion factor.
We need to invert the fraction in order for the pie unit to cancel out.
1/2 * 10 = 5
You will need 5 pounds of apples to make 10 apple pies.
The conversion is
x = magnitude × cos(angle)
y = magnitude × sin(angle)
or
(x, y) = 120.2(cos(119°), sin(119°)) ≈ (-58.27, 105.13)
_____
A suitable graphing calculator handles this easily.