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
Answer:
It would be option two: Bill's Electric Company charges 6 dollars per hour plus a flat rate of 15 dollars for a service call. If Monica has at least 100 dollars to spend, how many hours can the service man work?
Step-by-step explanation:
6 dollars an hour means it would be 6x.
A flat rate of 15 means there would be just 15 as a number, no x's.
And the sign is less than or equal to, so she has over a hundred dollars to spend.
Answer:
Sally is 42 in. tall, and Jack is 48 in. tall.
Step-by-step explanation:
There are some words missing in the problem.
Perhaps the problem was meant to read:
"The ratio of Sally's height to Jack's height is 7:8. If the sum of their heights is 90 inches, how tall are Sally and Jack?"
Solution:
The ratio of the heights is 7:8.
Sally could measure 7 inches and Jack 8 inches, but then when you add the heights, 7 in. + 8 in. = 15 in. which is not 90 inches.
If you multiply both numbers in a ratio by the same number, the new numbers are still in the same ratio.
Multiply 7 and 8 by 2. You get 14 and 16. Maybe Sally is 14 in. tall and Jack is 16 in. tall. Add the heights, 14 in. + 16 in. = 30 in. This is also not 90 in.
We can keep on guessing what number to multiply by 7 and 8 by so their sum is 90, but we can use algebra to write an equation and not have to go through many guesses.
There is a number, x, that when you multiply 7 and 8 by x, the sum of the products is 90. We don't know what x is, but we can write an equation and solve for x.
The numbers in the ratio are 7x and 8x.
7x and 8x are still in the ratio 7:8.
Now we add the numbers 7x and 8x and set the sum equal to 90. Then we solve for x.
7x + 8x = 90
15x = 90
x = 6
We get x = 6. Now we know we need to multiply both 7 and 8 by 6 to get the heights we need.
7 in. * 6 = 42 in.
8 in. * 6 = 48 in.
Check: 42 in. + 48 in. = 90 in.
Answer: Sally is 42 in. tall, and Jack is 48 in. tall.
The original square has the area (8 in)^2 = 64 in^2.
If we mult. this area by 36, we get the area of a larger square 2304 in^2.
The new side length is sqrt(2304 in^2), or 48. In other words, the original square has side length 8 in, but the 'new' square has side length 48 in.
