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
lesya692 [45]
3 years ago
6

Numeric passwords of length r consist of n digits from {0,1,2,…,9}. Digits may be not repeated (e.g., 1178 is a not a permissibl

e password of length 4). Find the smallest value of r such that the number of possible passwords of length r is greater than 2,000,000.
Mathematics
1 answer:
In-s [12.5K]3 years ago
8 0

Answer:

The smallest value of r such that there are more than 2,000,000 possible passwords is r=9.

Step-by-step explanation:

Given : Numeric passwords of length r consist of n digits from {0,1,2,…,9}. Digits may be not repeated (e.g., 1178 is a not a permissible password of length 4).

To Find : The smallest value of r such that the number of possible passwords of length r is greater than 2,000,000.

Solution :

Numeric passwords of length r consist of n digits from {0,1,2,…,9}

i.e. There are 10 possible digits : 0,1,2,3,4,5,6,7,8,9.

So, The first digit have 10 ways,

Second digit have 9 ways different from previous digit.

Third digit have 8 ways different from previous digit.

Similarly, r th digit have n-r+1 ways.

Applying fundamental counting principle,

If the first event occur in m ways and second event occur in n ways the the number of ways two events occur in sequence is m\cdot n

10\cdot 9\cdot 8\cdot ....\cdot (n-r+1) is the required ways.

But The smallest value of r such that the number of possible passwords of length r is greater than 2,000,000.

i.e. 10\cdot 9\cdot 8\cdot ....\cdot (n-r+1)\geq 2000000

The increasing value of r will obtain more than 2,000,000 possible passwords were,

If r=1

Number of passwords = 10

If r=2

Number of passwords = 10\cdot 9=90

If r=3

Number of passwords = 10\cdot 9\cdot8=720

If r=4

Number of passwords = 10\cdot 9\cdot8\cdot 7=5040

If r=5

Number of passwords = 10\cdot 9\cdot8\cdot 7\cdot 6=30240

If r=6

Number of passwords = 10\cdot 9\cdot8\cdot 7\cdot 6\cdot 5=151200

If r=7

Number of passwords = 10\cdot 9\cdot8\cdot 7\cdot 6\cdot 5\cdot 4=604800

If r=8

Number of passwords = 10\cdot 9\cdot8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3=1814400

If r=9

Number of passwords = 10\cdot 9\cdot8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2=3628800

For r = 9 the password length exceeds.

Therefore, The smallest value of r such that there are more than 2,000,000 possible passwords is r=9.

You might be interested in
Noah thinks the answers to these two questions will be the same. This year, a herd of bison had a 10% increase in population. If
Shalnov [3]

The answer to these two questions are not the same. We don't agree with Noah.

Reason:

Let's start with the first question.

1. Given: rate = 10% increase, base/original number = 550 bison

10% of 550 is:

.10\times550bison=55bison

10% of 550 is 55. Hence, there is an increase of 55 bison this year. This year, there are 550 + 55 = 605 bison in the herd.

2. Given: rate = 10% decrease, percentage/final number = 550 bison

Applying the concept of Percentage = Base x Rate, we can get the Base or the original number of bison before the decrease by dividing Percentage over Rate.

\text{Base}=\frac{\text{Percentage}}{\text{Rate}}

Filling in the formula with the given values in question 2, we have:

\text{Base}=\frac{550}{1-.10}=\frac{550}{.90}=611.11\approx611bison

Last year, there were 611 bison.

As we can see, the answer for number 1 is 605 bison while the answer for the number 2 is 611 bison. The answer of the two questions are not the same.

4 0
1 year ago
20.
sp2606 [1]

Answer: Smaller

Step-by-step explanation:

Multiplying a number by 1.25 increases it by a quarter

Multiplying a number by 0.75 decreases it by a quarter

1.25 / 0.75 = 0.9375

Thus, increasing something by a quarter then decreasing it by a quarter, you are effectively multiplying that number by 0.9375, which is less than 1, so the number will decrease.

4 0
3 years ago
Please help me with this question.
Mumz [18]

Answer:

Step-by-step explanatiobidvshzbxgsjsgsjGjmI don’t even know that

8 0
3 years ago
Brady recorded the number and color of cars in the parking lot. 45% of the cars in the parking lot were white. If Brady counted
MA_775_DIABLO [31]

Answer:

180 cars

Step-by-step explanation:

Like you can see in the picture, I like to set up a proportion, so 81 over X and 45 over 100. Then, you can cross multiply, so 81 x 100 = 8100 and then divide, 8100 ÷ 45 = 180, your answer!

4 0
3 years ago
Read 2 more answers
A soda machine takes 3 seconds to fill a 15-ounce cup. If t represents the time in seconds, which equation can you use to find h
Svet_ta [14]

Information we know:

a 15 ounce cup takes 3 second to fill

determine variables:

x=3

y=15

rate:

y/x=3/15= 0.2

fixture an equation:

y=kx

y=0.2x

plug in 40 for x:

y=0.2(40)

=8

Thus, it should take 8 seconds to fill a 40-ounce cup of soda.

8 0
3 years ago
Read 2 more answers
Other questions:
  • How many times can 21 go into 78,974
    5·2 answers
  • write an algebraic expression for the following problem next weekend a student wants to study for his four classes if he has h h
    10·1 answer
  • 22 divided by 179 equals ? ​
    6·2 answers
  • If I have 5 X's and I take 2 X's away, how many X's<br> will I have left?
    8·1 answer
  • Simplify: (2x - 4) - (6x + 6)
    12·2 answers
  • Product A is a 12 ounce bottle of generic mouthwash that sells for $1.39. Product B is a 24 ounce bottle of mouthwash that cost
    14·2 answers
  • Combine the like terms to create an equivalent expression:<br> −3x−6+(−1)
    9·2 answers
  • What is m∠C ? Anyone willing to help me (:
    6·1 answer
  • What is the greatest common factor of 30 and 36
    6·2 answers
  • Which equation can be used to find the volume of the cylinder?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!