Answer:
Step-by-step explanation:
1/10 * 1/4 = 1/14
1/2 because there is a 50/50% chance its either heads or tails
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
The slope is 1/6. y= mx + b
m is always to slope.
Answer:
12 boxes per hour.
Step-by-step explanation:
Jake's family packed 22 boxes in 1 5/6 hours (that is, 1 hour plus 5/6 of a hour: 1 + 5/6 = (6+5)/6 = 11/6 hours).
So, to know the average number of boxes packed per hour, we can do a rule of three: If in 11/6 hours they packed 22 boxes, in 1 hours they packed X boxes.
22 boxes -> 11/6 hours
X boxes -> 1 hour
22/X = 11/6
X = 6 * 22 / 11 = 12
So, they packed an average of 12 boxes per hour.
