Answer:
if you mulitply (19*19*27*10*10) you get:
974700
Answer:
0 ≤ an ≤ bn
The series ∑₁°° bn converges
The series ∑₁°° an converges by comparison to ∑₁°° bn.
0 ≤ an ≤ bn
The series ∑₁°° bn diverges
The comparison test is inconclusive for our choice of bn.
Step-by-step explanation:
an = 1 / (n² + n + 3) and bn = 1 / n²
The numerators are the same, and the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p > 1, so it converges.
Since the larger function converges, the smaller function also converges.
an = (3n − 1) / (6n² + 2n + 1) and bn = 1 / (2n)
If we rewrite bn as bn = (3n − 1) / (6n² − 2n), we can tell that when the numerators are equal, the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p = 1, so it diverges.
The larger function diverges. We cannot conclude whether the smaller function converges or diverges.
Answer:
Step-by-step explanation:
In this binomial probability case, the success is to pick a burrito with hot peppers, there are 7 out of 17, the probability is p=7/17=0.4118. The formula is
Where n is the number of burritos taken at random, k is the number of success (burrito with hot peppers), p is the probability of success. denotes the number of combinations and its formula is:
At least two burritos have hot peppers means having two or three burritos, these two cases are calculated and sum to get the probability of at least two burritos that have hot peppers.
Round to three decimal places: P=0.369
No, the set of numbers cannot represent the sides of a triangle.
This can be proven by the Pythagorean Theorem. (a^2+b^2=c^2)