$e^(2x) = ln 5$ (solve with explanation)

Answers

Answer 1

Answer: $e ^(2x) = ln5$

Solve for the real domain

$e ^(2x) = ln(5)$

if $f(x) =g(x),$ then $ln(f(x))= ln(g(x))$

$ln(e ^(2x) ) = ln(ln(5))$

Solve : $ln(e ^(2x) ) = ln(ln(5))$

use the logarithmic definition :

$ln(e^(f(x)) ) = f(x)$

$ln(e^(2x) ) = 2x$

$2x=ln(ln(5))$

Divide both sides by 2 :

$(2x)/(2) = (ln(ln(5)))/(2)$

$x= (ln(ln(5)))/(2)$

hope this helps!

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Find the difference.

(3−2x+2x^2)−(4x−5+3x^2)

Answers

Answer:

the difference is that there is (3-2x) at the start instead of (4x-5)

step explanation:

What is 1/8 in percentage

Answers

12.5%

I hope I helped please leave thanks

That would be 12.5%. All you have to do is divide 100 by 8.

It was 7 degrees below zero in the morning. By afternoon the temperature rose 15 degrees. How warm was it?

Answers

Answer:

8 degrees

Step-by-step explanation:

The temperature was -7 and then rose by 15, -7 +15 = 8

8 degrees

(-7) + 15 = 8

A card is chosen from a standard deck of cards. What is the probability that the card is a king, given that the card is black ? A. 1/26 B. 1/13 C. 1/2 D.2/13 And I have another question. A drawer contains 12 brown socks, 8 white socks, and 2 blue socks. One sock is selected at random. What is the probability that the sock is blue, given that it is NOT brown? A. 1/4 B. 1/5 C. 1/10 D. 1/11. Thank you sorry i'm a noob at this.

Answers

EVERY probability question uses this formula.
You should memorize it.

Probability =
   (number of ways it can happen the way you want it)
   divided by
   (total number of ways it can happen).

When a card is chosen from a standard deck of cards, it can turn out
in 52 different total ways.
If you're looking for a black king, there are 2 of those.
So the probability is

2 / 52 = 1 / 26 = about 3.85%

===============================

In the sock drawer . . .

-- There are 22 socks altogether.

-- What is the total number of ways you can draw a single sock ?
Normally it would be 22. But the question says the one you draw is
definitely NOT brown. So you can just toss the brown socks out of
the question entirely. You're actually working with the total number
of ways you can draw one sock that is not brown. There are 10 of those.

-- 2 of them are blue.

-- So the probability is . . .

   2 / 10 = 1 / 5 = 20% .

There are 26 black cards in a deck of cards.

There is a King Of Clubs and a King of Spades.

So, given that the card is black, the chances of it being a King is:

2/26 which is 1/13.

This can be proven:

P(Card Is Black (B)) = 26/52

P(Card Is King (K)) = 4/52

P(Card Is King And Black) = 2/52

$P\left( K|B \right) =\frac { P\left( K\cap B \right) }{ P\left( B \right) } \n \n =\frac { \frac { 2 }{ 52 } }{ \frac { 26 }{ 52 } } \n \n =\frac { 2 }{ 52 } * \frac { 52 }{ 26 } \n \n =\frac { 2 }{ 26 } \n \n =\frac { 1 }{ 13 }$

----------

Using Bayes' theorem and:

P(Brown Sock (B)) = 12/22

P(White Sock (W)) = 8/22

P(Blue Sock (L)) = 2/22

P(Not Brown Sock (N)) = 10/22

Had to use this to make sure I got the right answer. Second question was a tad confusing.

$P\left( L|N \right) =\frac { P\left( L \right) * P\left( N|L \right) }{ P\left( N \right) } \n \n =\frac { \frac { 2 }{ 22 } * 1 }{ \frac { 10 }{ 22 } } \n \n =\frac { 2 }{ 22 } * \frac { 22 }{ 10 } \n \n =\frac { 2 }{ 10 } \n \n =\frac { 1 }{ 5 }$

Which is the volume of a cylinder with a radius of 6 feet and a height of 10 feet? (Use 3.14 for .) A. 1,129.88 cubic feet B. 1,130.40 cubic feet C. 1,130.24 cubic feet D. 1,131.00 cubic feet