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aalyn [17]
3 years ago
15

How many different ways can you make 82 cents using current u.s. currency

Mathematics
1 answer:
andrew11 [14]3 years ago
3 0
 <span>You can probably just work it out. 

You need non-negative integer solutions to p+5n+10d+25q = 82. 

If p = leftovers, then you simply need 5n + 10d + 25q ≤ 80. 


So this is the same as n + 2d + 5q ≤ 16 

So now you simply have to "crank out" the cases. 

Case q=0 [ n + 2d ≤ 16 ] 

Case (q=0,d=0) → n = 0 through 16 [17 possibilities] 
Case (q=0,d=1) → n = 0 through 14 [15 possibilities] 
... 
Case (q=0,d=7) → n = 0 through 2 [3 possibilities] 
Case (q=0,d=8) → n = 0 [1 possibility] 

Total from q=0 case: 1 + 3 + ... + 15 + 17 = 81 

Case q=1 [ n + 2d ≤ 11 ] 
Case (q=1,d=0) → n = 0 through 11 [12] 
Case (q=1,d=1) → n = 0 through 9 [10] 
... 
Case (q=1,d=5) → n = 0 through 1 [2] 

Total from q=1 case: 2 + 4 + ... + 10 + 12 = 42 

Case q=2 [ n + 2 ≤ 6 ] 
Case (q=2,d=0) → n = 0 through 6 [7] 
Case (q=2,d=1) → n = 0 through 4 [5] 
Case (q=2,d=2) → n = 0 through 2 [3] 
Case (q=2,d=3) → n = 0 [1] 

Total from case q=2: 1 + 3 + 5 + 7 = 16 

Case q=3 [ n + 2d ≤ 1 ] 
Here d must be 0, so there is only the case: 
Case (q=3,d=0) → n = 0 through 1 [2] 

So the case q=3 only has 2. 

Grand total: 2 + 16 + 42 + 81 = 141 </span>
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Answer:

1) A

2) min; min; max; max

3) y = x² + 5x - 3

Step-by-step explanation:

f(x) = x² + 2(x)(5) + 5² - 5² + 24

f(x) = (x + 5)² - 25 + 24

f(x) = (x + 5)² - 1

In ax² + bx + c,

if a > 0, it's a min

if a < 0, it's a max

y = ax² + bx + c

Using (0,-3)

-3 = a(0)² + b(0) + c

c = -3

y = ax² + bx - 3

Using (1,3)

3 = a + b - 3

a + b = 6

Using (-1,-7)

-7 = a(-1)² + b(-1) - 3

-7 + 3 = a - b

a - b = -4

b = a + 4

a + (a + 4) = 6

2a = 2

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b = 5

y = x² + 5x - 3

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3 years ago
Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?
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Answer:

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6 0
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The fuel efficiency in miles per gallon of all bmw 320i's is (approximately) normally distributed with a mean of 25 and a standa
grigory [225]
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The random variable is x = 24 mpg.

Part (i):  n = 1
σ/√n = 2
z = (24 -25)/2 = -0.5
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Part (ii): n = 4
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z = (24 -25)/1 = -1
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