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
Flauer [41]
3 years ago
14

Two Social Security numbers (see Exercise 8.12) match zeros if a digit of one number is zero iff the corresponding digit of the

other is also zero. In other words, the zeros in the two numbers appear in exactly the same position. For example, the Social Security numbers 120-90-1109 and 430-20-5402 have matching zeros.
Prove: Given a collection of 513 Social Security numbers, there must be two that match zeros.
Mathematics
1 answer:
Roman55 [17]3 years ago
8 0

Answer:

Proved

Step-by-step explanation:

From the given parameters, we have:

n = 9 i.e. the length of each security numbers

r = 2 i.e. 2 security numbers

Required

In 513 security numbers, 2 must have matching zeros

To do this, we make use of Pigeonhole principle.

First, we calculate the number of all security numbers not having matching zeros.

Each of the 9 digits can be selected in 2 ways.

2 ways implies that each digit is either 0 or not

So, total selection is:

Total = 2^9

Total = 512

Apply Pigeonhole principle

The principle states that: suppose there are n items in m containers, where n>m, then there is at least one container that contains more than 1 item.

This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.

512 + 1 = 513

You might be interested in
Solve the Equation.
IgorLugansk [536]
<h2>1.</h2>

Firstly, combine like terms: 7r-8=10+r

Next, subtract r on both sides of the equation: 6r-8=10

Next, add 8 onto both sides of the equation: 6r=18

Lastly, divide both sides by 6 and <em><u>your answer will be r = 3.</u></em>

<h2>2.</h2>

Firstly, multiply both sides by e: TE=3u

Lastly, divide both sides by 3, and <em><u>your answer will be \frac{TE}{3}=u</u></em>

4 0
3 years ago
Read 2 more answers
WILL GIVE BRAINLIEST<br> Solve for y in terms of w, x, and z.<br> x=zyw<br> y=
Advocard [28]

Answer:

y= x/zw

Step-by-step explanation:

Isolate the variable by dividing each side by the factors that dont contain the variable

x = zyw /zw

y=x/zw

3 0
3 years ago
What is the factor of 16
insens350 [35]
1x16
2x8
is the answer
3 0
3 years ago
Read 2 more answers
-9 divided by 5/8 equals
DedPeter [7]
<span>-9 divided by 5/8 equals
-9 / (5/8) <---</span><span>Turn the second </span>fraction<span> upside down, then multiply.

= -9 * 8/5
= -72/5
= -14 2/5
= -14.4</span>
4 0
3 years ago
Solve 7p - 4 + 12p = -3 (5 + p) Can you show the work please?
prisoha [69]
7p - 4 + 12p = -3(5 + p)
7p - 4 + 12p = -15 - 3p
        + 4              + 4
7p + 12p    = -11 - 3p
        + 3p                + 3p
22p             = -11

p = -1/2  Answer
7 0
3 years ago
Read 2 more answers
Other questions:
  • Use the expression 5(6 + 4x) to answer the following:
    5·1 answer
  • Two hundred billion four hundred million expanded form
    11·2 answers
  • Si asamos 2800 g de carne, solo obtendremos 1960 g de carne ya cocinada. ¿Qué porcentaje de carne se pierde durante la cocción
    10·1 answer
  • What is the explicit formula for the geometric sequence with this recursive formula?
    13·2 answers
  • Choose Yes or No to tell whether each number is rational.
    7·1 answer
  • Please help!! i don’t understand how to find mBOC
    7·1 answer
  • Bob's Shoe Emporium sold 5,787 shoes in March. In April they sold 6,245 shoes. How many more shoes did they sell in April than i
    13·1 answer
  • What is the mean of $29 $58 $15 $129 $75 $22
    10·2 answers
  • You deposit $750 into a savings account Thats pays 2.75% simple interest for 4 years. How much interest was earned?
    11·2 answers
  • 47/94 in lowest terms
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!