Answer:
1) 120
2) E (Z) = 12 and Variance of Z = 90
a) 5 liters
Step-by-step explanation:
1. We can find this by suing combinations.
Here n= 10 and r= 3 so n C r
= 10 C 3= 120
2. E(X) = 8 and E(Y) = 3
Z = 2X - 3Y +5
E(Z ) = 2 E (X) - 3(E)(Y) +5 ( applying property for mean)
= 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12
V(X) = 9 and V(Y) = 6.
V(Z) = E(Z )²- V(X) *V(Y) (applying property for Variance for two variables )
= 144- 54= 90
3. 55 liters contain adulterated milk in 7: 4.
So it contains 4/ 11*55= 20 liters of water
But we want to make it a ratio of 7:6
the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water
So 25- 20 = 5 liters must be added to make it a ratio of 7:6
In this item, we are to supply for the missing term on one side of the equation. The left side is given to be composed of 62.834 x 0.45. The right hand side is given to be composed of 314170 along with a missing entity.
Translating the given to mathematical expression and letting A be the unknown,
62.834 x 0.45 = 314170 A
To determine the value of A, divide both sides of the equation by 314170.
(314170A)/(314170) = (62.834 x 0.45) / 314170
A = 0.00009
The missing value is 0.00009 or 9.0 x 10^-5.
<span>f(x)=x^2+6x+3
=(1/2.6)^2=3^2=9
f(x)=(x2^+6x+9)+3-9
=(x+3)^2-6</span>
2x-4=x^2-4
-4=x^2-2x-4 (start moving everything to one side)
x^2-2x=0 (the 4 cancel out)
x(x-2)=0 (factor out an x)
x=0 & x=2 (solved for x)
y=2x-4 (pick one of the equations)
y=2(0)-4 (plug in x)
y=-4
(0,-4)
y=2(2)-4 (plug in the second point)
y=0
(2,0)
The greatest possible value of s is 2. (2,0)
Answer:
$41,860.
Step-by-step explanation:
Weekly salary = 1610 / 2 = $805.
There are 52 weeks in a year so her annual salary
= 805 * 52 = $41,860.
