rarinstraw1195

67. 

This problem seems immensely tough, but it isn't. 

The measure of angle KJL is equal to the measure of angle KML.

12x+8=10x+16

First, get the x on one side.

12-10=2

2x+8=16

Now, subtract 8

2x=8

Now, divide both sides by 2.

x=4

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The book looked as dusty as the antique table it sat on in the attic, unkept and left to age until it was gone.

First section involving Cards

In the first section, the correct selections are that they are independent events, P(A)=1/2, P(B)=1/13, and P(A&B)=1/26

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Second section involving Chance

Given P(A)=0.15 and P(B)=0.2, determine P(A and B) if A and B are independent events. Round answer to the nearest hundredth.

This is just like finding probability between getting 2 types of cards in a 52 card deck. We're going to just multiply the decimals.

0.15*0.2

0.15*0.2 = 0.03

This is rounded to the nearest hundredth, so our answer is 0.03

This answer does not include the third section. Very sorry, I haven't done much on dependent probability :/

Part 1 involving the Spinner

Firstly, let's look at the first probability statement. We have an ample chance of landing the same spin again, so we won't be removing one blue for the next spin.

This fits the denominator 64, as that is 8*8. 

We first have a 5/8 chance to land on a blue, then we have a 3/8 chance to land on a red. 

\({5\over{8}}*{3\over{8}}\)is our equation (sorry for it being tiny, LaTeX is small)

In fraction multiplication, we multiply the top and bottom separately. 5*3 is 15, and as we said before 8*8 is 64

This leaves us with the fraction 15/64, which is true.

Finding this answer ALSO eliminates the third answer from being true, as it said that we remove a piece of the spinner if it is landed on, which is untrue.

Keep in mind that (red, blue) is the same as (blue, red)

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Now, let's look at the second option. 

The probability of (blue, blue) is \({5\over{8}}*{5\over{8}}\)

Now, let's multiply. 5*5 is 25, and 8*8 is 64. 

Therefore, this answer is true. 

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Finally, let's look at the fourth option. (Remember that the third option was not correct.)

The probability of (red, red) is \({3\over{8}}*{3\over{8}}\)

Now, let's multiply. 3*3 is 9, and 8*8 is 64.

9/64 does NOT reduce to 3/32. 

Therefore, this is a FALSE statement. 

The correct statements are Options 1 and 2.

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Part 2 involving Playing Cards

First, let's look at the part involving (Queen, Black Card)

First, this is a 4 in 52 or 1 in 13 chance of drawing a queen.

Then we draw a black card. 

The chance of this is 1 in 2.

We'll use the simplified numbers to form our equation.

\({1\over{13}}*{1\over{2}}\)

Now we multiply. 1*1=1, and 13*2=26

We now end with 1/26. 

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Now let's look at the probability of (Diamond, Ace)

First, the chance of drawing a Diamond in a set of 52 cards is 13 out of 52, or 1 in 4.

Then you have a 4 in 52 or 1 in 13 chance of drawing an Ace after the card is replaced.

Let's set up the equation: \({1\over{13}}*{1\over{4}} \)

Now, let's multiply. 1*1=1, and 13*4=52.

Therefore, our answer is 1/52.

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Thirdly, let's look at the probability of (Jack, 4)

First, the probability of drawing a Jack is 1 in 13.

Then, after replacement, the probability of drawing a 4 is 1 in 13.

We can make this easy on ourselves by squaring the fraction since they are the same. \({1\over{13}}^2\)

1^2=1, and 13^2=169

Therefore, our final answer is 1/169.

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Finally, let's look at the probability that we first draw a red card, and then a Club (Red card, Club)

The probability of drawing a red card is 1 in 2.

The probability of drawing a club is 1 in 4.

Now, let's set up the equation: \({1\over{2}}*{1\over{4}}\)

Now let's multiply. 1*1=1, and 2*4=8

Therefore, our answer is 1/8.

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Hope this helped and sorry for the long answer!

Increasing something by a ratio means to increase it by a scalar

put it like this (using your example)

\({6 \over1} = {x \over25}\)

Now, cross multiply

6*25=1*x

x=25*6

x=150

Hope this helped :)

The square root of 24 comes out to a complicated decimal, so the simplest it can be is square root of 24.

3^7625597484987 = infinity

4-(-3)=4+3=7

The reason it's like adding is because -1*-3=3, so -(-3) = 3

Let's make an example

20,000

This number is in standard notation

The easy explanation is to make this number look like this: x * 10^n

x cannot be greater than or equal to 10. n can be any whole number, including 0.

Now, let's try putting 20,000 into scientific notation!

We must make it so that x is less than 10, let's try making x=2

20000=2*10^n

Now, what value of n will make 2*10^n = 20000?

Let's put in 4

2*10^4=20000

2*10000=20000

20000=20000

Since 20000=20000 is a true statement, we know that 2*10^4 is the scientific notation. 

( If this is confusing, n equals the amount of times you move the decimal point until you make a number less than 10. 

Ex. 100

Move the point 2 times and you end up with 1.00

1*10^2=100)

Hope this helped!

(i) What is the probability that a randomly chosen employee prefers vegetarian meal and took lunch? 

Let's get our ratio set up:

237/1200

Plug that into the calculator

237/1200 = 0.1975

So, part (i) has an answer of 0.1975

(ii) What is the probability that a randomly chosen employee took dinner or prefers non-vegetarian meal?  

In this, someone that chooses dinner AND chooses non-vegetarian meals are included.

First, let's add 206+200+191+182

206+200+191+182 = 779

So, our ratio will be 779/1200

Let's plug that into our calculator

779/1200 = 0.6491666666666667

Shorten that to 4 decimals and you get 0.6492

So, the answer for (ii) is 0.6492

(iii)     What is the probability that a randomly chosen employee took breakfast given that he or she prefers vegetarian meal?

In this, anyone who chooses a non-vegetarian meal is NOT included.

First, add 184+237+182

184+237+182 = 603

This will be the denominator of the ratio

The amount of people who chose breakfast is 184 people.

So, the ratio is 184/603

Plug this into the calculator.

184/603 = 0.3051409618573798

Shorten it to 4 decimal points and it becomes 0.3051

So, the answer to (iii) is 0.3051

I hope this helped!