EXPLANATION
The nth term of the sequence is given by
Where
is the first term and
is the constant difference.
We were given that,
S we just need the common difference to write the nth term.
We can get that from another information given to us.
We were also given that the 4th term is 6. This gives the equation.
We substitute
to obtain
Or
This implies,
We substitute these values into the general formula to obtain,
This gives us,
Hence the nth term of the sequence is,
Answer:
a = p/10 - (3 b)/10
Step-by-step explanation:
Solve for a:
p = 10 a + 3 b
p = 10 a + 3 b is equivalent to 10 a + 3 b = p:
10 a + 3 b = p
Subtract 3 b from both sides:
10 a = p - 3 b
Divide both sides by 10:
Answer: a = p/10 - (3 b)/10
Given:
p = 47% = 0.47, the probability that a man considers himself a professional baseball fan.
q = 1 - p = 0.53, the probability that a man does not consider himself a professional baseball fan.
n = 10, the number of men surveyed.
(a) Calculate the probability that exactly 5 of 10 men surveyed consider themselves as professional baseball fans.
P(5 of 10) = ₁₀C₅ p⁵q⁵ = 252*0.47⁵*0.53⁵ = 0.242
Answer: 0.242 or 24.2%
(b) Calculate the probability of at least 6 out of 10.
P(at least 6 of 10)
= ₁₀C₆ p⁶q⁴ + ₁₀C₇ p⁷q³ + ₁₀C₈ p⁸q² + ₁₀C₉ p⁹q + ₁₀C₁₀ p¹⁰ q⁰
= 0.1786 + 0.0905 + 0.0301 + 0.0059 + 0.0
= 0.3057
Answer: 0.3057 or 30.6%
(c) Calculate the probability of less than 4 of 10.
P(less than 4 of 10)
= ₁₀C₁ pq⁹ + ₁₀C₂ p²q⁸ + ₁₀C₃ p³q⁷
= 0.0155 + 0.0619 + 0.1464
= 0.2238
Answer: 0.2238 or 22.4%
Answer:
10626 ways
Step-by-step explanation:
Given
Number of students = 23
Prizes = 3
Required
Number of different outcomes for the top 3
This question will be solved using permutation formula because it implies selection of 3 students from 23
<em>Where n = 23 and r = 3</em>
The formula becomes
<em>Hence, there are 10626 ways</em>
To solve this problem you must apply the proccedure shown below:
1- You have the following radical expression given in the problem above:
(√7)(√(14)+√(3))
2- When you apply the distributive property, you obtain:
(√7)(√(14))+ (√7)(√(3))
3-Simpliying, you have:
(7√2)+(√21)
4- Therefore the answer is: (7√2)+(√21)