Please help! A hat has the following marbles in it: 5 gray, 3 red, 6 white, 2 yellow and 4 green.

Mathematics

1 answer:

abruzzese [7]3 years ago

5 0

Answer:

1/40

Step-by-step explanation:

Probability: (number of ways to achieve the desired result / number of possible results)

For example, if we want a coin to land on heads:

We know there is one way for it to land on heads and two possible outcomes. Thus, the possibility of flipping a head is 1/2.

Using this, we know that there are 5 grey marbles (the desired result) and there are (5 + 3 + 6 + 2 + 4) total possible outcomes. The probability of drawing a grey marble is then:

5 / (5 + 3 + 6 + 2 + 4) =

5/20 =

1/4

We also know that there are 2 yellow marbles, so the probability of drawing one would be: 2 / 20 = 1/10

To find the probability of both of these events happening right after each other, multiply the probability of them each happening together.

1/4 * 1/10 = 1/40 chance of picking a grey marble and then a yellow marble.

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Factor by grouping (sometimes called the ac-method).

lesya692 [45]

Answer:

Step-by-step explanation:

The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.

Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything. Now, a = 8, b = 2 and c = -3. a*c = -24 so now we want to find all the factors of that.

-1 and 24

1 and -24

-2 and 12

2 and -12

-3 and 8

3 and -8

-4 and 6

4 and -6

And after that they repeat. It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be and 12 as well as -1 and -12.

Now we want to look at all the factor pairs and find one that add together to equal 2 because b = 2. -4 + 6 does it, so there's our choice. Now we can rewrite the original quadratic as 8x^2-4x+6x-3. You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3. Anyway, now we can factor.

8x^2-4x+6x-3 You can imagine there being two sets of parenthesis.

( 8x^2-4x)+(+6x-3) Now from here we can factor something out of each parenthesis. e can factor out 4x fromt he first and 3 from the second.

4x(2x-1)+3(2x-3) Now, it may not be obvious but you can factor 2x-3 from each term. If that's not clear pretend 2x-3 = u

4xu + 3u Now hopefully it is clear you can factor out this u

u(4x+3) Then we know u = 2x-3 so

(2x-3)(4x+3) And it's factored.

I do want to mention you could have done this with 8x^2+6x-4x-3 with the +6 and -4 switched. I won't go through it here but it may help to do it yourself if you still don't quite understand. Let me know if there is something I can further explain though.

3 0

3 years ago

1 Which expression can be simplified as this?

maks197457 [2]

Answer and Step-by-step explanation:

The answer would be the last answer choice.

$(n^{-3} )^{6}$