<span>10x-3=6x+85
4x = 88
x = 22</span>
Domain: ( -infinity, infinity ) , { x|x € R }
Range: ( -infinity, infinity ) , { y|y € R }
Answer:
a) P(Y > 76) = 0.0122
b) i) P(both of them will be more than 76 inches tall) = 0.00015
ii) P(Y > 76) = 0.0007
Step-by-step explanation:
Given - The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches.
To find - (a) If a man is chosen at random from the population, find
the probability that he will be more than 76 inches tall.
(b) If two men are chosen at random from the population, find
the probability that
(i) both of them will be more than 76 inches tall;
(ii) their mean height will be more than 76 inches.
Proof -
a)
P(Y > 76) = P(Y - mean > 76 - mean)
= P(
) >
)
= P(Z >
)
= P(Z >
)
= P(Z > 2.25)
= 1 - P(Z ≤ 2.25)
= 0.0122
⇒P(Y > 76) = 0.0122
b)
(i)
P(both of them will be more than 76 inches tall) = (0.0122)²
= 0.00015
⇒P(both of them will be more than 76 inches tall) = 0.00015
(ii)
Given that,
Mean = 69.7,
= 1.979899,
Now,
P(Y > 76) = P(Y - mean > 76 - mean)
= P(
)) >
)
= P(Z >
)
= P(Z >
))
= P(Z > 3.182)
= 1 - P(Z ≤ 3.182)
= 0.0007
⇒P(Y > 76) = 0.0007
tl;dr Answer is C
Here we will have to calculate 3 different areas separately.
When calculating the area of the triangle we will use the formula
A = (h*b)/2
A = Area
h = height
b = base
To find the height we do X - Z
23 - 15 = 8 ft
To find the base we do Y - W
19 - 13 = 6 ft
Using the formula above we can now solve for A
A = (8*6)/2
A = (48)/2
A = 24 sq ft
Now we solve the two rectangles using the formula
A = wl
w = width
l = length
We will calculate the area of the left most rectangle first.
We know the length of the rectangle because it's Y - W and we are given the width of the triangle.
w = 15 ft
l = 6 ft
A = 15*6
A = 90 sq ft
Second Rectangle has the width of X and length of W
w = 23 ft
l = 13 ft
A = 23 * 13
A = 299 sq ft
Now we add all the areas to give us the total area of the warehouse.
24 + 90 + 299 = 413 sq ft
Therefore, the answer is C
Answer:
- $855,000
- Dividend per share of common stock = $1.06
Step-by-step explanation:
1. Preferred Share dividends.
There are 300,000 preference shares and each of them got $2.85. Total dividends are;
= 300,000 * 2.85
= $855,000
2. Total dividends = $3,500,000
Dividends left for Common Shareholders (preference gets paid first)
= 3,500,000 - 855,000
= $2,645,000
Common shares number 2,500,000
Dividend per share of common stock = 
= $1.06