WILL GIVE BRAINLIEST!

Alice wants to make a fruit salad using 10 pieces of fruit. She can buy three types of fruits at the supermarket: Apples (A), Ba

sasho [114]

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:

$0\leq A\ ,\ 0\leq B\ ,\ 0\leq C$ (she cannot choose a negative number of pieces)
$\ A\ ,\ B\ ,\ C\ \leq 10$ (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:

$A+B+C=10$

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:

${r+k-1\choose r}={r+k-1\choose k-1}$

We have that $k=3$ and that $r=10$ 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:

${10+3-1\choose 10}={12\choose 10}=\frac{12!}{10!\cdot (12-10)!}=\frac{12\cdot 11\cdot 10!}{10!\cdot 2!}=\frac{132}{2}=66$ .

8 0

3 years ago

A taxi cab charges an initial fee of $3.50. Each 1/8 mile costs $0.23. Write an equation for the total cost, c, depending on the

Sav [38]

Answer:

3.50 + 1.84m = c

Step-by-step explanation:

Multiply 0.23 by 8 to get 1.84, the cost per mile.

Multipy that my m, the miles you drove.

Then add the initial fee of 3.50.

6 0

4 years ago

Does every number have a decimal expansion? yes or no

Aleonysh [2.5K]

I’m pretty sure the answer is no

5 0

3 years ago

Which expression is equivalent to –12x – 1.50 –12x + 1.50 –12x – 2.50 –12x – 3.50

balu736 [363]

Answer:

-12x+1.50

Step-by-step explanation:

Through Distributing, the above solution is derived

7 0

3 years ago

Read 2 more answers

Use two unit multipliers to convert 600 miles to inches. ( Do not multiply out.)

Sphinxa [80]

Answer:

(600 mi) × (5280 ft/mi) × (12 in/ft)

Step-by-step explanation:

A "unit multiplier" is a multiplier that has a value of 1. That is, the numerator and denominator have the same value. For units conversion problems, the numerator quantity has the units you want, and the denominator quantity has the units you're trying to cancel.

You have units of miles. You know that ...

1 mile = 5280 feet

1 foot = 12 inches

You want to get to units of inches. With these conversion factors, you can do it in two steps (as the problem requests). The first conversion is from miles to feet using the unit multiplier (5280 feet)/(1 mile). This gives you a number of feet.

Then the second conversion is from feet to inches, so you use the one that lets you put inches in the numerator and feet in the denominator:

(12 inches)/(1 foot)

When you multiplie these all out, units of miles and feet cancel, and you're left with inches.

_____

With the above conversion factors, you can write unit mulipliers of either ...

(5280 ft)/(1 mi) . . . to convert to feet

or

(1 mi)/(5280 ft) . . . to convert to miles.

5 0

4 years ago