Answer:
12 different ways
Step-by-step explanation:
1 to 23
2 to 22
3 to 21
4 to 20
5 to 19
6 to 18
7 to 17
8 to 16
9 to 15
10 to 14
11 to 13
12 to 12
Answer:
-4, 0, and 4
Step-by-step explanation:
Answer:
a) the probability that the minimum of the three is between 75 and 90 is 0.00072
b) the probability that the second smallest of the three is between 75 and 90 is 0.396
Step-by-step explanation:
Given that;
fx(x) = { 1/5 ; 50 < x < 100
0, otherwise}
Fx(x) = { x-50 / 50 ; 50 < x < 100
1 ; x > 100
a)
n = 3
F(1) (x) = nf(x) ( 1-F(x)^n-1
= 3 × 1/50 ( 1 - ((x-50)/50)²
= 3/50 (( 100 - x)/50)²
=3/50³ ( 100 - x)²
Therefore P ( 75 < (x) < 90) = ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx
= 3/50³ [ -2 (100 - x ]₇₅⁹⁰
= (3 ( -20 + 50)) / 50₃
= 9 / 12500 = 0.00072
b)
f(k) (x) = nf(x) ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k
Now for n = 3, k = 2
f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))
= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)
= 6/50³ ( 150x - x² - 5000 )
therefore
P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx
= 99 / 250 = 0.396
Answer:
1/216
Step-by-step explanation:
The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.
<h3>Linear scale factor</h3>
If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.
<h3>Volume scale factor</h3>
The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...
(1/6)³ = 1/216
The volume of the filled portion of the cup is 1/216 of the volume of the cup.
