13. If 6 times the 6th term of an A.P. is equal to
1 answer:
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides
6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )
- 7a₁ + 30d = 156d ( subtract 30d from both sides )
- 7a₁ = 126d ( divide both sides by - 7 )
a₁ = - 18d
Now
a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required
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Answer:
40.1% probability that he will miss at least one of them
Step-by-step explanation:
For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
0.95 probaiblity of hitting a target
This means that
10 targets
This means that
What is the probability that he will miss at least one of them?
Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So
We want P(X < 10). So
In which
40.1% probability that he will miss at least one of them