Answer:
The expected volume of the box is 364 cubic inches.
Step-by-step explanation:
Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have
- (When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)
- (When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)
- (When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)
- (When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)
- (When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)
- (When X = 6) Y = 6²*24 = 864, with probability 1/6 (the same than P(X=6)
As a consequence, the expected volume of the box in cubic inches is
E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364
Answer:
113.1
Step-by-step explanation:
Answer:
y > 11/2
Step-by-step explanation:
This is solved the same way a 3-step equation is solved.
<u>Step 1</u>: subtract the smaller variable term from both sides.
4y -2y +3 > 2y -2y +14
2y +3 > 14
<u>Step 2</u>: subtract the constant with the variable term.
2y +3 -3 > 14 -3
2y > 11
<u>Step 3</u>: divide by the coefficient of the variable.
2y/2 > 11/2
y > 11/2
_____
<em>Additional comment</em>
By choosing to subtract the smaller variable term in the first step (regardless of which side of the inequality it is on), we ensure that the remaining variable coefficient is positive. That means we can do step 3 without worrying about changing the direction of the inequality symbol, because we're dividing by a positive number.
Answer:
b. 11 apples; 1 orange
Step-by-step explanation:
We test each option, and see if the total is $3.50(what you spend). If the result is different, it is not a possible solution.
a. 1 apple; 11 oranges
1 apple for $0.20
11 oranges for $0.30 each
0.20 + 11*0.30 = $3.50
Possible solution
b. 11 apples; 1 orange
11 apples for $0.20 each
1 orange for $0.30
11*0.2 + 0.3 = 2.5
Not $3.5, so this is not a possible solution.
This is the answer
c. 7 apples; 7 oranges
7*0.2 + 7*0.3 = $3.5
Possible
d. 4 apples; 9 oranges
4*0.2 + 9*0.3 = $3.5
Possible
Answer:
1.) a. i) f(4) = 2, ii.) f(-3)= -5 b.) x = -5, x = 2, c.) choice(2) -3 < x < 5
Step-by-step explanation:
Each problem
1.) a.) i.) we see f(4) = 2 on the graph the line goes through point (4, 2)
a.) ii.) f(-3) = -5
1.) b.) There are only 2 zeros for f(x) which intersect the x-axis in only 2 points.
x = -5 and x = 2 are the only 2 zeros.
1.) c.) only for -3 < x < 5 is the function f(x) increasing.
choice (2.)
