Answer:
The final equation is .
Step-by-step explanation:
To rewrite an equation in slope-intercept form, our equation must be in form. This means the <em>y</em>-variable must be on the left side of the equation and the slope and y-intercept must be on the right side of the equation. We can do this by moving the equation around.
And then, we're done! Our final answer is .
15 percent of 500 is 75, and 7.5 percent of 75 is 5.63. Is that what you're asking?
A) height of a cylinder: 7.96
b) height of come: 1.43
c) radius of cylinder: 4.07
d) radius of cone: 2.82
e) radius of sphere: 9
use the following formulas to solve:
a) volume= (pi)(radius^2)(height) and substitute what’s given
b) (1/3)(pi)(radius^2)(height) and substitute the given
c) volume= (pi)(radius^2)(height) and substitute what’s given
d) (1/3)(pi)(radius^2)(height) and substitute the given
e) volume= (4/3)(pi)(radius^2) and substitute the given
4 and 5 both go into 20
1/4 equals 5/20
2/5 equals 8/20
So 2 and 5/20 + 1 and 8/20 is
3 and 13/20
The probability of an event A occurring given that B has occurred is
P(A | B) = P(A and B) / P(B)
a. By the definition above,
P(spade | black) = P(spade and black) / P(black)
- P(black) = 26/52 = 1/2 because 26 of the 52 cards have a black suit
- All spade cards are black, so P(spade and black) = P(spade) = 13/52 = 1/4
Then P(spade | black) = (1/4) / (1/2) = 1/8.
b. We can do the same breakdown as in (a), or we can make use of the definition of conditional probability
P(A | B) = P(A and B) / P(B) = (P(B | A) * P(A)) / P(B)
Then
P(black | spade) = (P(spade | black) * P(black)) / P(spade)
- P(black) = 1/2
- P(spade) = 1/4
- P(spade | black) = 1/8
Then P(black | spade) = (1/8 * 1/2) / (1/4) = 1/64.
c. By definition,
P(7 | black) = P(7 and black) / P(black)
- P(7 and black) = 1/52 because this is a unique card
- P(black) = 1/2
Then P(7 | black) = (1/52) / (1/2) = 1/104.
d. By definition,
P(king | face) = P(king and face) / P(face)
- All kings are face cards, so P(king and face) = P(king) = 4/52 = 1/13
- P(face) = 12/52 = 3/13
Then P(king | face) = (1/13) / (3/13) = 1/3.