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vovikov84 [41]
3 years ago
15

Jayne has 3 quarters, 2 dimes, 1 nickel and 2 pennies in her pocket.how many different amounts of money can she make using some

or all of these coins?
Mathematics
1 answer:
Papessa [141]3 years ago
8 0

Upper limit: There is a logical maximum that it could be. You can have 0, 1, 2, 3 quarters, 0, 1, 2 dimes, 0, 1 nickels, and 0, 1, 2 pennies. This is a total of 4*3*2*3 = 72. Of course, not all of these are distinct; this is why the answer is smaller. Also, this problem isn't counting $0.00 as a valid combination. Now that we have an idea of how the problems works, lets simplify it a little.

 

Pennies. Since you can have 0, 1, 2 pennies, there will be NO conflicts. (It takes 5 pennies to cause a problem, since then it will conflict with the nickel). It means that for all combinations of quarters, nickels, and dimes, we can have 0, 1, or 2 pennies. This means we can handle the other three coins and handle the pennies later. This brings the upper limit down to 24.

 

One combination has no nickels and no dimes, and another, equivalent combination has one fewer quarters, one nickel, and two dimes. There are three ways for the first combination: 1, 2, 3 quarters only. It will bring down the total to 21.

 

The pennies we have 21*3=63 possibilities.

General process:

Simplify the problem. (Pennies didn’t cause any conflict so they just make 3 times as many combination)

Determine the maximum possible combinations. This is a few multiplications. Not very difficult

Count the duplicates. This is often simpler because there are usually not that many of them. In this case, just three.

 

Put it back together.

<span>Of course, sometimes there will be so many conflicts that anything short of listing them is unreasonable. This was quite a bit more difficult that it would have been to just list those 62 possibilities.  </span>

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insens350 [35]

Answer:

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3 0
2 years ago
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Pls need help
koban [17]
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4 0
3 years ago
Hello!!! i’ll give brainliest if you want but please answer correctly
gladu [14]

Answer:

Step-by-step explanation:

hope this helps!

5 0
2 years ago
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What does i^739 equal? explain how you found your answer.
Sophie [7]
<h3>Answer:   -i</h3>

========================================================

Explanation:

i = sqrt(-1)

Lets list out the first few powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.

For example, i^5 = i^1 because 5/4 leads to a remainder 1.

Another example: i^6 = i^2 since 6/4 = 1 remainder 2

Again, we only care about the remainder to find out which bin we land on.

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

Turning to the question your teacher gave you, we have,

739/4 = 184 remainder 3

So i^739 = i^3 = -i

<h3>-i is the final answer</h3>

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

Side notes:

  • if i^a = i^b, then a-b is a multiple of 4
  • Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.
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2 years ago
What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12? an = 4(−3)n
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The geometric sequence is given by:
an=ar^(n-1)
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hence the formula for this case will be:
an=4(-3)^(n-1)
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