Answer: 7.5 cups of sugar.
Step-by-step explanation:
Add all of the above:
2+1.5+0.5+3+1.5= <u>8.5 cups of sugar</u>
<u></u>
Since Zach only needs 1 cup of sugar, subtract 1 from 8.5.
Therefore, your answer is <u>7.5 cups of sugar.</u>
Answer:
x is all real numbers
Step-by-step explanation:
The domain is the values for the inputs
Since all values are allowed for the input
The domain is all real numbers
50 ounces of 15% saline solution contains 0.15*50 = 7.5 ounces of salt.
Let x be the amount of pure water you add to this solution. Then you end up with (x + 50) ounces of this new solution. The amount of salt stays the same.
You want the new solution to have a concentration of 10%. This means you need
7.5 / (x + 50) = 0.1
==> 7.5 = 0.1(x + 50)
==> 7.5 = 0.1x + 5
==> 2.5 = 0.1x
==> 2.5/0.1 = 0.1x/0.1
==> x = 25
Answer: The loser's card shows 6.
Explanation: Let's start by naming the first student A and the second student B.
Since the product of A and B are either 12, 15, or 18, let's list every single possibility, the first number being A's number and the second number being B's number.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
4 3
5 3
6 2
6 3
9 2
12 1
15 1
18 1
Now, the information says that A doesn't know what B has, so we can immediately cross off all of the combinations that have the integer appearing once and once ONLY off, because if it happened once only, A would know of it straight away. Now, our sample space becomes much smaller.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
6 2
6 3
Using this same logic, we know that we can cross off all of the digits that occur only once in B's column.
2 6
3 6
Now, A definitely knows what number B has because there is only one number left in B. Hence, we can conclude that the loser, B, has the integer 6.
