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Nastasia [14]
3 years ago
5

Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric recei

ve (Disregard the $ sign when gridding your answer.)
Mathematics
1 answer:
babymother [125]3 years ago
5 0

Answer:

Abel receives $60, and Cedric receives $120

Step-by-step explanation:

Let Abel's share = A

Let Cedric's share = C

we are given the following

A + C = 180  - - - - - (1)   (Abel and Cedric will share a total of $180)

A = \frac{C}{2}\ - - - - - - - (2) (Abel will receive half as much as Cedric. )

from equation 2:

A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)

putting this value of C in eqn (3) into eqn (1)

A + (2A) = 180

3A = 180

∴ A = 180 ÷ 3 = 60

to find C, let us replace the value of A in eqn (3) with 60

C = 2A - - - - (3)

C = 2 × 60

C = 120

Therefore, Abel receives $60, and Cedric receives $120

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One number is five more than five times another. If their sum is decreased by four, the result is twenty-five. Find
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a=4 n=25

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5a+5=n

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Suppose you roll a fair die. Let X be the value of the roll. What is the Moment Generating Function of X?
Alex_Xolod [135]

Answer:

μ₁`= 1/6

μ₂=  5/36

Step-by-step explanation:

The rolling of a fair die is described by the binomial distribution, as  the

  1. the probability of success remains constant for all trials, p.
  2. the successive trials are all independent
  3. the experiment is repeated a fixed number of times
  4. there are two outcomes success, p, and failure ,q.

The moment generating function of the binomial distribution is derived as below

M₀(t) = E (e^tx)

        = ∑ (e^tx) (nCx)pˣ (q^n-x)

        = ∑ (e^tx) (nCx)(pe^t)ˣ (q^n-x)

        = (q+pe^t)^n

the expansion of the binomial is purely algebraic and needs not to be interpreted in terms of probabilities.

We get the moments by differentiating the M₀(t) once, twice with respect to t and putting t= 0

μ₁`= E (x) = [ d/dt (q+pe^t)^n]  t= 0

            = np

μ₂`=  E (x)² =[ d²/dt² (q+pe^t)^n]  t= 0

              = np +n(n-1)p²

μ₂=μ₂`-μ₁` =npq

in similar way the higher moments are obtained.

μ₁`=1(1/6)= 1/6

μ₂= 1(1/6)5/6

   = 5/36

4 0
3 years ago
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