Answer:
Step-by-step explanation:
<u>Given AP with:</u>
- a₁= 28, aₙ = 79, Sₙ = 963
<u>Use the formula:</u>
- Sₙ = 1/2n(a₁ + aₙ), sum of the first n terms
<u>Substitute given values and solve for n:</u>
- 963 = 1/2n(28 + 79)
- 963 = 1/2n(107)
- 1/2n = 963/107
- 1/2n = 9
- n = 9*2
- n = 18
<span>23s+56s=21
79s=21
/79 /79
s=</span><span>0.265823</span>
Notice that
![9](https://tex.z-dn.net/?f=9%3C10%3C16%5Cimplies%5Csqrt9%3C%5Csqrt%7B10%7D%3C%5Csqrt%7B16%7D%5Cimplies3%3C%5Csqrt%7B10%7D%3C4)
and given that 10 is closer to 9, it's clear that
![\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D)
is probably closer in value to 3 then to 4. (The actual value is indeed about 3.162.)
Answer: 20, 70, 90
====================================================
Work Shown:
Let x be some positive real number.
Multiply each part of the given ratio by x to get 2x:7x:9x
So we have the three angles 2x, 7x, and 9x.
For any triangle, the three angles must add to 180
2x+7x+9x = 180
18x = 180
x = 180/18
x = 10
This leads to
- 2x = 2*10 = 20
- 7x = 7*10 = 70
- 9x = 9*10 = 90
The three angles of this triangle are: 20, 70, 90
This is a right triangle due to the 90 degree angle.
Answer:
Step-by-step explanation:
From the information given,
p represents the probability of success.
x represents the number of success
n represents the number of samples
Therefore,
1) b(x|n,p): b(3|8, .35)
x = 3
n = 8
p = 0.35
From the binomial probability distribution calculator,
P(x = 3) = 0.28
1) b(x|n,p): b(5|8, .6)
x = 5
n = 8
p = 0.6
From the binomial probability distribution calculator,
P(x = 5) = 0.28
c) n = 7
p = 0.6
P(3 ≤ X ≤ 5)
P(x ≥ 3) = 0.904
P(x ≤ 5) = 0.841
P(3 ≤ X ≤ 5) = 0.904 - 0.841 = 0.063
d) n = 9
p = 0.1
P(1 ≤ X) = p(x ≥ 1)
p(x ≥ 1) = 0.61