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vovangra [49]
3 years ago
12

The ice cream shop has 7 types of toppings available, and you decide to add 4 toppings to your bowl of 5 scoops of ice cream. Ho

w many combinations of 5 scoops of ice cream and 4 toppings are possible
Mathematics
1 answer:
Slav-nsk [51]3 years ago
6 0

Answer: 35

Step-by-step explanation:

The number of combinations of r things selected out of n things is given by

^nC_r= \dfrac{n!}{r!(n-r)!}

Given , the total number of types of toppings available = 7

The number of toppings needed to be selected = 4

Then, the number of ways to do this would be

^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35

Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.

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Part A

The equation is b = 36*a or simply b = 36a

We take the size of the farm 'a' and multiply it by 36 to get the number of bushels of corn 'b'.

-----------------------------------

Part B

The 36 means there are 36 times more bushels of corn compared to the size of the farm in acres

For example, if the size is 2 acres then 
b = 36*a
b = 36*2
b = 72
yielding 72 bushels of corn

-----------------------------------

Part C

Along the first row you should have: 25 and 30 in the missing blanks (over 900 and 1080 respectively)

You find this by dividing the value of b over 36
eg: b/36 = 900/36 = 25

-------

Then along the bottom row you should have the following for the blanks: 0, 360, 1800

These values are found by multiplying the 'a' value by 36
eg: if a = 10 then b = 36*a = 36*10 = 360

-----------------------------------

Part D

Plot any two points you want from the table back in part C
So plot say (0,0) and (10,360). Then draw a straight line through those two points.

-----------------------------------

Part E

The point (30,1080) means a = 30 and b = 1080
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Notice how
b = 36*a
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And how this matches up with the fourth column of the table in part C. So you can use this part to get a hint of how to fill out the table (or at least know what one column looks like)


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