1) The outcomes for rolling two dice, the sample space, is as follows:
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5
We will traduce the sentences into equations.
Let x be the number of hours in the first job, and y be the number of hours in the second job.
Then the equations are:
The above system has many solution, we can select for example:
x = 1, y = 16. So we can work one hour at the first job and 16 hour at the second job.
Options
- (A)g(5) = 12
-
(B)g(1) = -2
- (C)g(2) = 4
- (D)g(3) = 18
Answer:
(D)g(3) = 18
Step-by-step explanation:
Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8
Then the following properties must hold
- The value(s) of x must be between -1 and 4
- The values of g(x) must be between 0 and 18.
- g(-1)=2
- g(2)=9
We consider the options and state why they are true or otherwise.
<u>Option A: g(5)=12</u>
The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.
<u>Option B: g(1) = -2
</u>
The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.
<u>Option C: g(2) = 4
</u>
The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.
<u>Option D: g(3) = 18</u>
This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.
Therefore, Option D could be true.
