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Smplify the following algebraic expression: 6(2y + 8) - 2(3y - 2)

Answers

Answer 1

Answer:

Answer:

6y +52

Step-by-step explanation:

6(2y + 8) - 2(3y - 2)

Distribute

12y + 48 - 6y +4

Combine like terms

6y +52

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Which statement best describes the areas and perimeters of the figures below?
Which box-and-whisker plot represents this data
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Assume f(x) = ax^2+ bx + c Which one is true? f is a parabola that opens sideways to the right. f is a parabola that opens sideways to the left. f is a parabola that opens downward. f is a parabola that opens upward.

Find the two numbers whose sum is 24 and whose product is as large as possible.(Please show your work, No guess)!!!

Answers

Let, the numbers are: x, (24-x)
Let, P(x) denote their products. Then, we have:
P(x) = x(24-x) = 24x - x²
P'(x) = 24-2x
P''(x) = -2

Now, P'(x) = 0 ⇒ x = 12
Also,
P''(12) = -2 < 0

So, By second derivative test, x = 12 is the point of local maxima of p. Hence the product of the numbers is the maximum when the numbers are 12 and (24-12) = 12

So, In short that numbers would be 12,12

Hope this helps!

Call a household prosperous if its income exceeds $100,000. Call the household educated if the householder completed college. Select an American household at random, and let A be the event that the selected household is prosperous and B the event that it is educated. According to the Current Population Survey, P(A)=0.138, P(B)=0.261, and the probability that a household is both prosperous and educated is P(A and B)=0.082. What is the probability P(A or B) that the household selected is either prosperous or educated?

Answers

Answer: 0.317

Step-by-step explanation:

Let A be the event that the selected household is prosperous and B the event that it is educated.

Given : P(A)=0.138, P(B)=0.261

P(A and B)=0.082

We know that for any events M and N ,

$\text{P(M or N)=P(M)+P(N)-P(M or N)}$

Thus , $\text{P(A or B)=P(A)+P(B)-P(A or B)}$

$\text{P(A or B)}=0.138+0.261-0.082\n\n\Rightarrow\text{ P(A or B)}=0.317$

Hence, the probability P(A or B) that the household selected is either prosperous or educated = 0.317

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference. a) How many delegations are possible?

b) How many of these delegations have all men?

c) How many of these delegations have at least one woman?

Answers

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

$n=(16!)/((16-6)!)=16*15*14*13*12*11\n n= 5765760$

b) How many of these delegations have all men?

$n_(men) = (9!)/((9-6)!)=9*8*7*6*5*4 \nn_(men) = 60480$

c) How many of these delegations have at least one woman?

$n_(women >0)=n-n_(men)\nn_(women >0) =5765760-60480\nn_(women >0) =5705280$

What is the quotient and remainder of 8 divided 25

Answers

the answer is 3 reminder 1

On a farm there are 50 sheep and a farmer how many feet are there in total

Answers

Answer:

200 sheep legs and 2 farmer legs, or 202 legs in total.

Step-by-step explanation:

One sheep has 4 legs. and there are 50 sheep. So, we have to multiply 50*4 to get 200. Then, we have to add the two legs the farmer has. 200 + 2 = 202. Therefore, there are 202 legs on the farm.

discrete random variable X has the following probability distribution: x 13 18 20 24 27 P ( x ) 0.22 0.25 0.20 0.17 0.16 Compute each of the following quantities. P ( 18 ) . P(X > 18). P(X ≤ 18). The mean μ of X. The variance σ 2 of X. The standard deviation σ of X.

Answers

Answer:

(a) P(X = 18) = 0.25

(b) P(X > 18) = 0.53

(c) P(X ≤ 18) = 0.47

(d) Mean = 19.76

(e) Variance = 22.2824

(f) Standard deviation = 4.7204

Step-by-step explanation:

We are given that discrete random variable X has the following probability distribution:

X P (x) X * P(x) $X^(2)$ $X^(2)$ * P(x)

13 0.22 2.86 169 37.18

18 0.25 4.5 324 81

20 0.20 4 400 80

24 0.17 4.08 576 97.92

27 0.16 4.32 729 116.64

(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25

Therefore, P(X = 18) = 0.25

(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53

(d) Mean of X, $\mu$ = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1

= 19.76

(e) Variance of X, $\sigma^(2)$ = ∑ $X^(2)$ * P(x) - $(\sum X * P(x))^(2)$

= 412.74 - $19.76^(2)$ = 22.2824

(f) Standard deviation of X, $\sigma$ = $√(variance)$ = $√(22.2824)$ = 4.7204 .

Final answer:

The probabilities for the given X values are calculated by summing the relevant given probabilities. The mean of X is computed as a weighted average, and the variance and standard deviation are calculated using formula involving the mean and the individual probabilities.

Explanation:

The probability P(18) is given as 0.25 according to the distribution. The probability P(X > 18) is the sum of the probabilities for all x > 18, so we add the probabilities for x=20, x=24, and x=27, giving us 0.20 + 0.17 + 0.16 = 0.53. The probability P(X ≤ 18) includes x=18 and any values less than 18. As 18 is the lowest value given, P(X ≤ 18) is just P(18), or 0.25.

The mean μ of X is the expected value of X, computed as Σ(xP(x)). That gives us (13*0.22) + (18*0.25) + (20*0.20) + (24*0.17) + (27*0.16) = 2.86 + 4.5 + 4 + 4.08 + 4.32 = 19.76.

The variance σ 2 of X is computed as Σ [ (x - μ)^2 * P(x) ]. That gives us [(13-19.76)^2 * 0.22] + [(18-19.76)^2 * 0.25] + [(20-19.76)^2 * 0.20] + [(24-19.76)^2 * 0.17] + [(27-19.76)^2 * 0.16] = 21.61. The standard deviation σ of X is the sqrt(σ^2) = sqrt(21.61) = 4.65.

Learn more about Probability and Statistics here:

brainly.com/question/35203949

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