Given:
Let x be the whole amount inherited.
1/2 * x - invested with Bernie Madoff
1/3 * x - lost due to identity theft
1/8 * x - lost in casino
40,000 - remainder
x - x/2 - x/3 - x/8 = 40,000
LCM:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
3: 3, 6, 9, 12, 15, 18, 21, 24
8: 8, 16, 24,
x * 24/24 = 24x / 24
x/2 * 12/12 = 12x / 24
x/3 * 8/8 = 8x / 24
x/8 * 3/3 = 3x / 24
40,000 * 24/24 = 960,000 / 24
24x/24 - 12x/24 - 8x/24 - 3x/24 = 960,000/24
(24x - 12x - 8x - 3x)/24 = 960,000/24
x/24 = 960,000/24
24 * x/24 = 24 * 960,000/24
x = 960,000
x = 960,000 initial inheritance
x/2 = 960,000/2 = 480,000 invested with Bernie Madoff
x/3 = 960,000/3 = 320,000 lost due to identity theft
x/8 = 960,000/8 = 120,000 lost in the casino
40,000 - remaining amount.
960k - 480k - 320k - 120k = 40k
40k = 40k
Answer and Step-by-step explanation:
(a) Since the student have to stop when he gets to w softcover book, then the sample space should always stop at either 3 or 4 or 5. If the students examines the books randomly and stops at a softcover book, here are the possible ways he could carry this out,
S = {3, 4, 5, 13, 14, 15, 23, 24, 25, 123, 124, 125, 213, 214, 215}
2. Since only one book is to be examined then the student must check only one softcover book and end the examining. To do this, either he examines just 3 or 4 or 5. Therefore,
A = {3, 4, 5}
3. We need to pick the possibilities from the sample space that shows that the examining ended at book 5. Therefore,
B = {5, 15, 25, 125, 215}
4. We need to pick possibilities from the sample space that shows that book 1 was not examined. Therefore,
C = {3, 4, 5, 23, 24, 25}
Answer:
cost was 252
Step-by-step explanation:
Show all work including equations
Answer:

Step-by-step explanation:
the volume of a cylinder is given by:

and the volume of a cone is given by:

since both have the same height and radius, we can solve each equation for
(because this quantity is the same in both figures) and then match the expressions we find:
from the cylinder's volume formula:

and from the cone's volume formula:

matching the two previous expressions:

we solve for the volume of a cone
:

substituting the value of the cylinder's volume 

If f(x) = 0 then it is a root
x + 3 = 0
x=-3
f(-3) = (-3)^4 + 10(-3)^3 + 23(-3)^2 - 34(-3) - 120 = 0
x - 2 = 0
x=2
f(2) = (2)^4 + 10(2)^3 + 23(2)^2 - 34(2) - 120 = 0