Answer:
There is a total of 66 different fruit salads.
Step-by-step explanation:
One fruit salad differs from the other only in the amount of pieces of certain fruit put in it. In order to easier denote fruit pieces we introduce these notations:
A-how many apples are put into the salad;
B-how many bananas are put into the salad;
C-how many cranberries are put into the salad.
Since she can freely choose the number of pieces of each fruit, we have these conditions for the variables A, B and C:
-
(she cannot choose a negative number of pieces) 
(because she can get the total of 10 pieces of fruit)
Another condition for forming the salad is that the salad must consist of exactly 10 pieces of fruit, hence we have this equation to solve:
but we must obtain the non-negative integer solutions of this equation.
That is equivalent to calculating the number of r-combinations of the multi-set S with objects of k different types with infinite repetition numbers.
The formula for obtaining the number of such r-combinations is:
We have that 
and that 
and we can observe the repetition number as infinite since she can create a fruit salad with only one piece of fruit and the repetition number in such cases is the maximum 10. Finally, we have that the total number of fruit salads equals:
.
Answer:
$14 9/10
Step-by-step explanation:
Ruby had 30 dollars to spend on 3 gifts. She spent 9 7 10 dollars on gift A and 5 2 5 dollars on gift B. How much money did she have left for gift C?
From the above question,
$30 = Gift A + Gift B + Gift C
She spent 9 7/ 10 dollars on gift A and 5 2/5 dollars on gift B.
$30 = $9 7/10 + $5 2/5 + Gift C
Gift C = $30 - ( $9 7/10 + $5 2/5)
Lowest Common Denominator = 10
Gift C = $30 - $14+(7 + 4/10)
Gift C = $30 - $14+(7 + 4/10)
Gift C = $30 - $14+(11/10)
$30 - $14+(1 1/10)
$30 - $15 1/10
Gift C = $14 9/10
Therefore, the amount of money she had left for gift C is $14 9/10
Answer:
statement A
Step-by-step explanation:
If the ratio
= 
then TU is parallel to RS
= 
= 
= 
=
Since the ratios are equal then line segment TU is parallel to line segment RS
Answer:
18.
Step-by-step explanation:
If there were 90 runners, and in the first half 2/5 of them dropped out, here's how we get those who continued the race in the second half.
1. Firstly we need to calculate how many of them dropped out:
2/5 of 90 = 90 ÷ 5 × 2
2/5 of 90 = 18 × 2
2/5 of 90 = 36
2. Now we have to take away the number of dropped-out runners <u>from</u><u> </u><u>the total number of runners from the beginning of the race</u>:
90 - 36 = 54
Now we are left with 54 runners, 2/3 of which dropped out before the finish line.
1. In order to get the number of runners that finished the race, we first need to see how many of them gave up in the second half:
2/3 of 54 = 54 ÷ 3 × 2
2/3 of 54 = 18 × 2
2/3 of 54 = 36
2. Now we just take away the number of runners that dropped out in the second half <u>from the number on the beginning of the half</u>:
54 - 36 = 18
<em>18 runners finished the race.</em>
