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IgorC [24]
3 years ago
5

Find all solutions to the system

Mathematics
1 answer:
lara31 [8.8K]3 years ago
8 0

Answer:

x=-3\\y=5\\\\(-3,5)

Step-by-step explanation:

Make both equations equal, as following:

y=y\\x^{2}+12x+32=6x+23

Add like terms:

x^{2}+12x+32-6x-23=0\\x^{2}+6x+9=0

Factor it as following:

(x+3)^{2}=0

Then:

x=-3 (Double root)

Substitute this into the second equation to obtain y:

y=6(-3)+23\\y=5

Then the solution is:

x=-3\\y=5\\\\(-3,5)

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Use the Distributive Property<br><br> 1/2 (2n+6m)
Alik [6]

Answer:

n + 3m

Step-by-step explanation:

It will become 1/2 * 2n + 1/2 * 6m = n + 3n

4 0
3 years ago
A die is rolled. If you roll a 1, 2 or 3, you will toss 10 coins. If you roll a 4, 5 or 6, you will toss 20 coins. Let X denote
trasher [3.6K]

Answer:

a) The support of X is {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

b) The mean of X is 7.5

c) The variance of X is 10

Step-by-step explanation:

a) Since you can toss up to 20 coins, and from that you can obtain any number of heads from 0 to 20, then the support of X {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

b) To compute the mean of X, we need to see how is the <em>behavior</em> of X. Since 3 dices will gives 10 coins to toss and the other 3 will give us 20, then there is a probability of 1/2 that we tossed 10 coins and a probability of 1/2 that we tossed 20.

The random variable X, conditioned to the event 'The dice is 1,2 or 3' (or equivalently, 10 coins are tossed), will have a binomial distribution with paramenters n = 10, p = 1/2. The mean of X in this case is np = 5. If X is conditioned to the event 'The dice is 4,5 or 6', then X will have also binomial distribution, but this time with paramenters n = 20, p = 1/2. The mean of X in this case is 20*1/2 = 10.

Since each event we conditioned in had probability 1/2 to occur, then E(X) = 1/2 * 5 + 1/2 * 10 = 7.5.

c) Remember that V(X) = E(X²)- E(X)². Since we alredy know the mean of X, we just need to compute the mean of X squared.

The variance of a binomial distribution Z with paramenters n and p is

V(Z) = np(1-p)

since V(Z) = E(Z²)- E(Z)² = E(Z²)- n²p², then

E(Z²) = V(Z) + E(Z)² = np(1-p) + n²p² = p²(n²-n) + np

Therefore

E(X²) = E(X² | 10 coins are tossed) * 1/2 + E(X² | 20 coins are tossed) * 1/2 =

1/2*(0.5²(10²-10) + 5) + 1/2*(0.5²(20²-20) + 10) = 13.75 + 52.5 = 66.25

As a consecuence

V(X) = 66.25 - 7.5² = 10

The variance of X is 10.

5 0
3 years ago
Which is the best but?
garri49 [273]
12.60 / 7 = $ 1.80 per bottle
10.98 / 6 = $ 1.83 per bottle
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16.38 / 9 = $ 1.82 per bottle

best buy (cheapest) is : $ 12.60 for 7 bottles <==
4 0
3 years ago
Read 2 more answers
Corey deposits $300 in a bank that pays 4% annual interest. How much interest does Corey earn in one year? What would the intere
hammer [34]
$300/100= $3 1%=$3 $3x4=$12 $300+$12=4%$312
$3x6=$18 $300+$18=$318
5 0
3 years ago
If a sample of 64 golfers is taken from a population of 190 golfers, the
Alona [7]
Im going to guess B.

Explanation:
Its either tricky or I’m thinkin too hard on it, but I’m seeing that 64 golfers were TAKEN OUT the population of 190 golfers, so it can’t be either.
6 0
3 years ago
Read 2 more answers
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