Answer:
8 π or
25.13 unit^3 to the nearest hundredth.
Step-by-step explanation:
(A)
The height of the shell is (2 + x - x^2) and the radius is (2 - x).
V = 2π ∫(2 - x)(x + 2 - x^2) dx between the limits x = 0 and x = 2.
= 2π ∫ (2x + 4 - 2x^2 - x^2 - 2x + x^3) dx
= 2π ∫ (x^3 - 3x^2 + 4 ) dx
= 2π [ x^4/4 - x^3 + 4x ] between x = 0 and x = 2
= 2 π [4 - 8 + 8 )
= 2 π * 4
= 8π
= 25.13 unit^3 to the nearest hundredth.
Part A:
Area of a circle is pi*radius^2
a=3.14*1^2
a=3.14
Part B:
Area of a rectangle is length*width
a=5*7
a=35
Part C:
Area of the shaded part would be the area of the rectangle - the area of the circle
a=35-3.14
a=31.86
434 rounded to the nearest ten is 430.
Hope this helps
Should be 5/6 if you balance it by making the denominator the same
Answer:
75%
88.89%
Step-by-step explanation:
Given :
Mean = 70
Standard deviation = 12
Since the data is said to be extremely skewed, we apply Chebyshev's theorem rather than the empirical rule :
The minimum proportion of observation between 46 and 94
Chebyshev's theorem :
1 - 1 / k²
k = number of standard deviations from the mean
k = (94 - 70) / 12 = 24 / 12 = 2
Hence, we have ;
1 - 1/2²
1 - 1/4
1 - 0.25 = 0.75
Hence, The minimum proportion of observation between 46 and 94 is 75%
Between 36 and 106 :
k = (106 - 70) / 12 ;
k = 36/12 = 3
Hence,
1 - 1/3² = 1 - 1/9 = 8/9 = 0.8888 = 88.89%
The minimum proportion of observation between 34 and 106 is 88.89%