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3 years ago

12

Solve for x: 4(3 - 2x) = 2(10 - 8x) Type only your solution, do not type x = *

1 answer:

velikii [3]3 years ago

7 0

The solution is x = 1

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USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

Write the polynomial as a product: p2q+r2–pqr–pr

Assoli18 [71]

${p}^{2} q + {r}^{2} - pqr - pr \\ = pq(p - r) - r(p - r) \\ = (pq - r)(p - r)$

6 0

3 years ago

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Dillon has 4 blue marbles and 3 times as many red marbles.Max has 8 times as many red marbles as Dillon.How much red marbles do

SCORPION-xisa [38]

Dillion has 4 blue marbles and 12 red marbles

And max has 96 red marbles

5 0

3 years ago

Hassan built a fence around a square yard. It took 48 m^2 of lumber to build the fence. The fence is 1.5 meters tall.

Gennadij [26K]

Answer:

Step-by-step explanation:

<u>Please check ones more because this might be incorrect.</u>

The area is in square meters...Let's change it

Square 48= 48*48 =2304

2304 divided by 4( 4 since the formula for the area of a sqaure is s*s and square has 4 sides)

2304 divided by 4 = 576

The formula for area of a square is S*S(side times side)

Let's apply the formula here.

so, 576 times 576

331776 square meters

Hope this is right and helps! :)

<u>( This just my point of view. Please check this onces again)</u>

8 0

3 years ago

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I need the formula can you please help me

Ahat [919]

Multiply the diagonals together and then divide by two

4 x 6 / 2

so the answer would be 12yd

5 0

3 years ago

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