1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Keith_Richards [23]
3 years ago
10

You are given 1000 one dollar bills and 10 envelopes. Put the bills into the envelopes in such a way that someone can ask you fo

r any amount of money from $1 to $1000 (examples - $532, $619, $88, etc.) and you can give it to them through a combination of the envelopes.
Mathematics
1 answer:
taurus [48]3 years ago
4 0

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

  • Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

  1. 1+2+4+8+16+32+64+128+256+489=1000
  2. Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
  3. If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since x-489\leq511, by 2) we know that this would be possible.

You might be interested in
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.50.
Marta_Voda [28]

Answer:

$9

Step-by-step explanation:

If you do 13x1.50= 19.5

28.50 - 19.5 = 9

7 0
3 years ago
The figure is made up of a square and a rectangle. Find the area of the shaded region.
inn [45]

Answer:

10 \:  { \: m}^{2}

Step-by-step explanation:

area of the shaded region = Area of triangle formed in rectangle with base (10 - 6 = 4) 4m and height 2 m + Area of triangle formed in square with base 2 m and height 6 m

=  \frac{1}{2}  \times 4 \times 2 +\frac{1}{2}  \times 2\times 6 \\  \\  = 4+6  \\  \\  = 10 \:  { \: m}^{2}

8 0
2 years ago
Read 2 more answers
Write the following using negative exponents: 1/x5
stira [4]
1/(x^5) is equal to x^-5, by the definition of negative exponents.
3 0
3 years ago
Please helllppppp ....thx if u do​
soldier1979 [14.2K]
Answer

Complete the sentence

There were 240 more people shopping in 2019 than 2020
7 0
3 years ago
Help please asap................
iren2701 [21]

Answer:

Linear pair

Step-by-step explanation:

<1 and <2 lie on a straight line.

Angles that lie on a straight line are considered as linear pair angles.

Linear pair angles sum up to 180°, which is the measure of a straight line angle.

7 0
2 years ago
Other questions:
  • If the drama club collected 25,915 points and gave away 71 shirts, how many shirts would be given away when 33,580 points are co
    5·1 answer
  • Part A. The tee shirts for the fundraiser will cost $10 to make and there is a $25 delivery fee to have the shirts delivered. 1)
    14·1 answer
  • Find the perimeter of the larger Octagon.
    7·1 answer
  • Light travels at the speed of approximately 3.0 × 108 meters per second. Find the time in minutes required for light to travel f
    12·1 answer
  • 4 + 2x2(3x-5)<br> number of terms
    6·1 answer
  • What is the SST for the data set (1,4), (2,6),(4,11)?
    8·2 answers
  • The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that bes
    9·2 answers
  • Solved my bad<br>.................
    10·1 answer
  • brenda runs 3 miles every morning.What is the time taken to complete her daily jogging if she jogs one mile in 6 mins
    10·1 answer
  • The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … is formed by summing two consecutive numbers to get the next number.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!