Q.34
The infinite geometric series is converges if |r| < 1.
We have r =1.002 > 1, therefore our infinite geometric series is Diverges
Answer: c. Diverges, sum not exist.
Q.35
The infinite geometric series is converges if |r| < 1.
We have r = 4/5 < 1, therefore our infinite geometric series is converges.
The sum S of an infinite geometric series with |r| < 1 is given by the formula :
We have:
substitute:
Answer: c. Converges, -25.
For this case we must simplify the following expression:
Simplifying the numerator, dividing all the terms by 4, we have:
We factor by looking for two numbers that when added together give -8 and when multiplied by 12. These are: -6 and -2
So, we have to:
Simplifying the denominator:
We rewrite -17x as -18x + x:
We factor the highest common denominator of each group:
We factor the polynomial by factoring the highest common denominator (x-6):
So, we have to:
Substituting in the original expression we have:
ANswer:
The probability of winning exactly 21 times is:-0.32
Given,
The probability of winning on an arcade game, p = 0.659
Number of times you play arcade game, n = 30
By assuming this as a normal distribution, we get
Mean=μ=30×0.659 =19.77
Standard deviation, σ =
=
≈ 2.60
Let X be a binomial variable
Then, the z score for x = 21 will be:
z = (x - μ) / σ =
≈ 0.47
Now, the probability of winning exactly 21 times
P (x ≥ z) = P (21 ≥ 0.47) = 0.32
Hence the probability of winning exactly 21 times is 0.32
Learn more about probability here:-brainly.com/question/13067945
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