Answer:
COMPLETE QUESTION:
To the right are drawings of a wide and a narrow cylinder. The cylinders have equally spaced marks on them. Water is poured into the wide cylinder up to the 4th mark (see A). This water rises to the 6th mark when poured into the narrow cylinder (see B). Both cylinders are emptied, and water is poured into the narrow cylinder up to the 11th mark. How high would this water rise if it were poured into the empty wide cylinder?
a)To the 7 1/2 mark b)To the 9th mark c)To the 8th mark d)To the 7 1/3 mark
e)To the 11th mark
ANSWER : Option D (To the 7 1/3 mark)
Step-by-step explanation:
First part of the question enables us to get the relationship between the radius of the wider cylinder (R) and the narrow cylinder(r) i.e
Volume of cylinders
π x R² x 4 = πxr²x 6
R²/r² = 6/4
after both cylinder were emptied
π x R² x h = π x r² x 11
R²/r² = 6/4 = 11/h
h = (4 x 11) /6 = 22/3 = 7 1/3 mark
Therefore, the height of the water in the wide cylinder is 7 1/3
Answer:
The answer is explained below
Step-by-step explanation:
We have the following formulas:
from binomial distibution: P (X = x) = (nCx) * (p) x * (1-p) n-x
from normal distribution: P (X <= x) = (x-np) / sqrT (np (1-p))
Now, n = 25 and p (0.5, 0.6, 0.8), we replace in the formulas and we are left with the following table:
P P(15<=X<=20) P(14.5<=X<=20.5)
0.5 0.2117 is less than 0.2112
0.6 0.5763 is less than 0.5685
0.8 0.5738 is greater than 0.5957
Answer:
2(x-2y)/(4x-y) = dy/dx
Step-by-step explanation:
2x^2+y^2=8xy
Take the derivative of each term, remembering that we take the 8xy as derivative by parts)
2 * 2x dx + *2y dy = 8 ( x dy + dx *y)
4x dx +2y dy = 8x dy + 8y dx
Subtract 2y dy from each side
4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx
4x dx = 8x dy - 2y dy + 8y dx
Subtract 8y dx from each side
4x dx -8y dx = 8x dy - 2y dy + 8y dx-8y dx
4x dx -8y dx = 8x dy - 2y dy
(4x-8y) dx = (8x-2y) dy
Factor out a 4 from the left side and a 2 from the right side
4(x-2y) dx = 2( 4x-y) dy
Cancel a 2
2(x-2y) dx = ( 4x-y) dy
Divide each side by (4x-y)
2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy
2(x-2y)/(4x-y) dx = dy
Divide by dx
2(x-2y)/(4x-y) dx/dx = dy/dx
2(x-2y)/(4x-y) = dy/dx
Answer: 40
Step-by-step explanation: 4 x 10 = 40
