Answer:
converges
Step-by-step explanation:
well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)
0 < 7 the series converges
Subtract 3 from both sides
simplify 12 - 3 to 9
break down the problem into these two equations
1 + p = 9 and -(1 + p) = 9
solve the first equation 1 + p = 9 and that would be 8 since 1 + 8 = 9 is true.
solve the second equation -(1 + p) = 9 and just simplify brackets and add 1 to both sides then add 9 + 1 and lastly multiply both sides by -1 and p = -10.
Gather both solutions
Answers: p = -10, 8
Answer:
13° , 29° , 138°
Step-by-step explanation:
let x be the smallest angle , then
2x + 3 is the middle angle and
2x + 3 + 109 is the largest angle
summing the 3 angles and equating to 180
x + 2x + 3 + 2x + 3 + 109 = 180 , that is
5x + 115 = 180 ( subtract 115 from 180 )
5x = 65 ( divide both sides by 5
x = 13
2x + 3 = 2(13) + 3 = 26 + 3 = 29
2x + 3 + 109 = 29 + 109 = 138
the 3 angles are 13° , 29° , 138°
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 ![p = 0.95](https://tex.z-dn.net/?f=p%20%3D%200.95)
10 targets
This means that ![n = 10](https://tex.z-dn.net/?f=n%20%3D%2010)
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
![P(X = 10) + P(X < 10) = 1](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%2B%20P%28X%20%3C%2010%29%20%3D%201)
We want P(X < 10). So
![P(X < 10) = 1 - P(X = 10)](https://tex.z-dn.net/?f=P%28X%20%3C%2010%29%20%3D%201%20-%20P%28X%20%3D%2010%29)
In which
![P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401](https://tex.z-dn.net/?f=P%28X%20%3C%2010%29%20%3D%201%20-%20P%28X%20%3D%2010%29%20%3D%201%20-%200.5987%20%3D%200.401)
40.1% probability that he will miss at least one of them