Answer:
α = 62°
β = 56°
gamma = 90°
Step-by-step explanation:
ΔAOB is isosceles, so m∠A = m∠ABO = 28
28 + 28 + m∠AOB = 180
m∠AOB = 180 - 28 - 28 = 124
β = 180 - 124 = 56
arcAB = 124
ΔBOC is isosceles. α = m∠BCO = 1/2(arc AB) = 1/2(124) = 62
∠D is inscribed in a semicircle
m∠D = gamma = 90°
Answer:
Mean = 75
Median = 73.5
Mode = 95
Range = 36
Step-by-step explanation:
Given:
Sort:
To find:
Mean:
![\displaystyle \large{\dfrac{1}{n}\sum_{i =1}^n x_i = \dfrac{x_1+x_2+x_3+...+x_n}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%20%3D1%7D%5En%20x_i%20%3D%20%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%2B...%2Bx_n%7D%7Bn%7D%7D)
Sum of all data divides by amount.
![\displaystyle \large{\dfrac{59+60+70+77+89+95}{6}=\dfrac{450}{6}}\\\\\displaystyle \large{\therefore mean=75}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B59%2B60%2B70%2B77%2B89%2B95%7D%7B6%7D%3D%5Cdfrac%7B450%7D%7B6%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%20%5Clarge%7B%5Ctherefore%20mean%3D75%7D)
Therefore, mean = 75
Median:
If it’s exact middle then that’s the median. However, if two data or values happen to be in <em>middle</em>:
![\displaystyle \large{\dfrac{x_1+x_2}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%7D)
From 59,60,70,77,89,95, since 70 and 77 are in middle:
![\displaystyle \large{\dfrac{70+77}{2} = \dfrac{147}{2}}\\\displaystyle \large{\therefore median = 73.5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B70%2B77%7D%7B2%7D%20%3D%20%5Cdfrac%7B147%7D%7B2%7D%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B%5Ctherefore%20median%20%3D%2073.5%7D)
Therefore, median = 73.5
Mode:
The highest value or/and the highest amount of data. Mode can have more than one.
From sorted data, there are no repetitive data nor same data. Consider the highest value:
Therefore, mode = 95
Range:
or highest value - lowest value
Thus:
![\displaystyle \large{95-59 = 36}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B95-59%20%3D%2036%7D)
Therefore, range = 36
Answer:723.202
Step-by-step explanation:
Answer:
Absolutely convergent
0.82
Step-by-step explanation:
Use the alternating series test.
lim(n→∞) (1/√n) = 0
1/√n > 1/√(n+1) for n > 0
It is absolutely convergent.
Use error estimation.
1/(n+1)² < 0.01
(n+1)² > 100
n+1 > 10
n > 9
n = 10
Sum the first 10 terms.
∑₁¹⁰ (-1)ⁿ⁻¹/n²
= 1/1² − 1/2² + 1/3² − 1/4² + 1/5² − 1/6² + 1/7² − 1/8² + 1/9² − 1/10²
≈ 0.82
Answer:
9/22
Step-by-step explanation:
=
1
/2
−
1
/11
=
1
/2
+
−1
/11
=
11
/22
+
−2
/22
=
11+−2
/22
=
9
/22
(Decimal: 0.409091)