Answer:
45.12%
Step-by-step explanation:
We have that l = 50
The probability density function of the exponential distribution is:
(1 / l) * e ^ (x * 1 / l) l> 0
f (X = x) = 0 otherwise
in this case X would come being the probability the road in 30 minutes or less to pick-up the children to go to school, it would come being:
P (X <= 30) = integral from 0 to 30 [1/50 e ^ (x / 50) dx]
It is integral as a result:
P (X <= 30) = (1/50) [e ^ (- x / 50) / (-1/50)]
We evaluate x = 0 up to x = 30
P (X <= 30) = (1/50) [e ^ (- 30/50) / (-1/50)] - (1/50) [e ^ (- 0/50) / (-1 / fifty)]
P (X <= 30) = -0.5488 - (-1)
P (X <= 30) = 0.4512
Therefore the probability is 45.12%
Answer:
(6, ∞)
(-∞, 6)
Step-by-step explanation:
x^2 + 36 > 12x
Subtract 12 x from each side
x^2 -12 x+ 36 > 12x-12x
x^2 -12 x+ 36 > 0
Factor
What 2 numbers multiply together to give us 36 and add together to give us 12
-6*-6 = 36
-6+-6 = 12
(x-6) ^2 > 0
Take the square root of each side
x-6 >0 or x-6 <0
x>6 or x < 6
Answer:
x = 0
y = -2
Step-by-step explanation:
to solve this simultaneous equation we are going to say
let
12x - 3y = 6 ............................ equation 1
2x - y = 2 ................................. equation 2
from equation 2
2x - y = 2 ................................. equation 2
2x - 2 = y
y = 2x - 2 ................................ equation 3
substitute the value of y into equation 1
12x - 3y = 6 ............................ equation 1
12x - 3( 2x -2) = 6
12x -6x + 6 = 6
6x + 6 = 6
6x = 6-6
6x = 0
divide both sides by 6
6x/6 = 0/6
x = 0
put the value of x = 0 into equation 3
y = 2x - 2 ................................ equation 3
y = 2(0) - 2
y = 0 - 2
y = -2
therefore from the solution the value of x is equal to zero(0) and the value of y is equal to -2 respectively.
I believe that a flat surface continuing in all directions is called a plane.
Answer:
a) 20 units
b) 2 √10 units
c) 2 √17 units
Step-by-step explanation:
The distance formula is;
D = √(y2-y1)^2 + (x2-x1)^2
a) D = √(-7-9)^2 + (-7-5)^2
D = √256 + 144
D = √400
D = 20
b) D = √(10-8)^2 + (9-2)^2
D = √(2)^2 + 6^2
D = √4 + 36)
D = √40
D = 2 √10 units
c) D = √(1 + 7)^2 + (-8+10)^2
D = √(64 + 4)
D = √68
D = 2 √17 units