5.43 x 10 to the 6th power
Answer:
0.200
Step-by-step explanation:
∑ₓ₌₁⁴⁰ (1 + i)⁻ˣ = 5
∑ₓ₌₁⁴⁰ ((1 + i)⁻¹)ˣ = 5
This is a geometric series. The sum of the first n terms of a geometric series is:
S = a₁ (1 − rⁿ) / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = (1 + i)⁻¹, r = (1 + i)⁻¹, and n = 40. For simplicity, let's write both a₁ and r in terms of r. So a₁ = r and r = r.
5 = r (1 − r⁴⁰) / (1 − r)
5 (1 − r) = r (1 − r⁴⁰)
5 − 5r = r − r⁴¹
r⁴¹ − 6r + 5 = 0
Solving with a calculator, r ≈ 0.8334.
Therefore:
(1 + i)⁻¹ = 0.8334
1 + i = 1.200
i = 0.200
For this problem, we use the repeated trials equation:
P = n!/r!(n-r)!*p^(n-r)*q^r
where
P is the total probability of having r successful trials out of the total n trials. p is equal to 13/58, while q is equal to 1 - 13/58.
P = 4!/4!(4-4)!*(13/58)^(4-4)*(1 - 13/58)^4
P = 0.362 or 36.2%
Answer:
12/51 or 0.2353
Step-by-step explanation:
There are 13 spades in a deck of 52 cards.
If the first card drawn is a spade and it is not replaced, we will have 51 cards, of which 12 are spades.
So the probability of drawing a spade for the second card is 12/51 ~ 0.2353
Divide 72 by 4which would give u 18
