Answer:
Step-by-step explanation:
If k items out of 20 total items are defective, then the number of non-defective item is 20 – k. The probability of choosing 5 items where all of them are non-defective is
- For the 1st slot the chance is (20 – k)/20
- For the 2nd slot the chance is (20-k-1)/(20-1) = (19-k)/19
- For the 3rd slot: (18 – k)/18
- 4th : (17 – k)/17
- 5th: (16 – k)/16
The probability in total would be
So the probability of selecting at least 1 defective item is the inverse of this, which is
Answer:
Step-by-step explanation:
Remark
The two trains are travelling towards each other. That means that their total distance = 912 km. Neither one has gone that distance by itself. The effect this has on the question is that you add the two rates multiplied by time.
Givens
r1 = x
r2 = x + 12
t = 3 hours
d = 912 km
Equation
d = r * t
r1 * t + r2 * t = 912
Solution
3x + 3*(x + 12) = 912 Remove the brackets
3x + 3x + 36 = 912 Combine like terms
6x + 36 = 912 Subtract 36 from both sides
<u> -36 -36</u>
6x = 876 Divide both sides by 6
6x/6 = 876/6
x = 146 km/h
Answer
Slow train = 146 km/hr
Fast train = 146 + 12 = 158 km/hr
Answer:
a=-4
b=-4
Step-by-step explanation:
-0.113 blank =0.452x + 0.452
-0.113(a+bx) =0.452x + 0.452
-0.113a-0.113bx =0.452x + 0.452
so we have
-0.113a=0.452
a=-0.4520/0.113= -4
-0.113bx =0.452x
b=-0.452/0.113= -4
Answer:
b 14.5
Step-by-step explanation:
Ok 25+4=29 then half of 29 is 14.5
Answer:
D
Step-by-step explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant
Using the distance formula
= | y + 1 |
Squaring both sides
(x + 5)² + (y - 5)² = (y + 1)^2 , that is
(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides
(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify
y² + 2y + 1 - y² + 10y - 25 = (x + 5)²
12y - 24 = (x + 5)² ← factor left side
12(y - 2) = (x + 5)² ← divide both sides by 12
y - 2 = 
(x + 5)² ← add 2 to both sides
y = (x + 5)² + 2
or
f(x) = (x + 5)² + 2 → D
