Hello:
ln(2e^3x) =ln2+lne^3x
<span> =ln2 +3xlne
= ln2+3x .....lne=1
</span><span>choice B</span>
Answer: 175V
Step-by-step explanation:
V112+V63=112v+63V
Add them together because the terms are like terms. Therfore, 112V+63V=175V
<span>From the message you sent me:
when you breathe normally, about 12 % of the air of your lungs is replaced with each breath. how much of the original 500 ml remains after 50 breaths
If you think of number of breaths that you take as a time measurement, you can model the amount of air from the first breath you take left in your lungs with the recursive function

Why does this work? Initially, you start with 500 mL of air that you breathe in, so

. After the second breath, you have 12% of the original air left in your lungs, or

. After the third breath, you have

, and so on.
You can find the amount of original air left in your lungs after

breaths by solving for

explicitly. This isn't too hard:

and so on. The pattern is such that you arrive at

and so the amount of air remaining after

breaths is

which is a very small number close to zero.</span>
Answer:
,
Explanation:2√2 sin(q) + 2 = 0
2√2 sin(q) = -2
sin(q) =

sin(q) =

Now, we know that:
sin (45) =

From the ASTC rule, we know that the sine function is negative in the third and fourth quadrant.
This means that:
either q = 90 + 45 = 135° which is equivalent to

or q = 270 + 45 = 315° which is equivalent to

Hope this helps :)
Answer: The professor was not accurate with his hypothesis.
Null hypothesis: P1 = 12.5%, P2 = 42.5%, P3 = 45%
The alternate hypothesis: At least one proportion of the student will differ from the others.
Step-by-step explanation: To check if the professors hypothesis were inaccurate.
What percentage of student bought a hard copy of the book.
(25 ÷ 200) × 100 = 12.5%
What percentage of the student printed it from the web.
(85 ÷ 200) × 100 = 42.5%
What percentage of the students read it online.
(90 ÷ 200) × 100 = 45%
This means that the professor was not accurate with his hypothesis. Because the proportion of student in his hypothesis was not the same in the actual.
Therefore; the null hypothesis are
P1 = 12.5%, P2 = 42.5%, P3 = 45%
The alternative hypothesis will state that at least one of the proportion will be different from the others.