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
melamori03 [73]
3 years ago
14

In another state, all license plates consist of from four to six symbols chosen from the 26 letters of the alphabet together wit

h the ten digits 0–9.
a. how many license plates are possible if repetition of symbols is allowed?
b. how many license plates do not contain any repeated symbol? h
c. how many license plates have at least one repeated symbol?
d. what is the probability that a license plate chosen at random has a repeated symbol?
Mathematics
1 answer:
fredd [130]3 years ago
3 0
A)
First note that the plates can have between 4 and 6 symbols so we will need to find the number of plates with 4 symbols, 5 symbols and 6 symbols. We add these to get the total. In this part repetition of symbols is allowed. Since there are 26 + 10 =36 possible symbols we look at each position on the plate and think of how many choices there are. We multiply the number f choices using the counting principal since the choices are each independent -- one symbol does not affect another. There are 36 choices for the first symbol, 35 for the second and so on. The number of plates is:
4-symbols = (36)(36)(36)(36)=36^4
5 symbols = (36)^5
6 symbols = 36^6
So the total here is: 36^4+36^5+36^6

B) Here we do not repeat symbols so there are 36 choices for the first symbol but only 35 for the next and 34 for the one after and so on.
4-symbols = (36)(35)(34)(33)
5 symbols = (36)(35)(34)(33)(32)
6 symbols = (36)(35)(34)(33)(32)(31)
So the total here is: (36)(35)(34)(33)+(36)(35)(34)(33)(32)+(36)(35)(34)(33)(32)(31)

c)
In order for there to be a repeated symbol we have 36 choices for the first symbol, 36 for the next and so on. However, for the last symbol we have to pick from one of the ones already selected so there are 3, 4 or 5 choices respectively.
4-symbols = (36)(36)(36)(3)
5 symbols = (36)(36)(36)(36)(4)
6 symbols = (36)(36)(36)(36)(36)(5)
So the total here is: (36^3)(3)+(36^4)(4)+(36^5)(5)

D)
The probability is given by (the number of plates with at least one repeated symbol)/(the total number of plates if repetitions are allowed) = (the answer to c) / (the answer to a)
You might be interested in
A numerical data set has 9 values. How many of these values does the data
Paraphin [41]
I think it’s D) 9 because when you find the mean of a set of values you are taking into account and adding all of the numbers, and then dividing them by how many numbers there is, so the mean would be summarizing all of them, hope this helps
5 0
3 years ago
A forester planted 3 acres in seedlings the first day, 5 acres the second day, and
Yanka [14]

Answer:

9 acres remain

Step-by-step explanation:

First day:

3 acres

Second day:

5 acres were planted. 5 + 3 = 8

Third day:

4 acres were planted. 4 + 8 = 12

If 3 acres were destroyed, we just subtract!

12 - 3 = 9.

9 acres of seedlings remain.

I hope this helped! :)

6 0
3 years ago
A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his brea
fgiga [73]
First break= 1/2
second break = 1/2 of half= 1/4
third break = half of 1/4 = 1/8
forth break = 1/2 of 1/8 = 1/16
fifth break = 1/2 of 1/16 =1/32
fraction painted = 1 -1/32 =31/32
portion painted = 150*31/32 = 145.3125 ft^2
3 0
3 years ago
Is 2/15 a repeating decimal or a terminating decimal?
lubasha [3.4K]
2/15 = 0.1333333333... It is a repeating decimal, because a terminarog decimal ends, and this doesn't end.
6 0
3 years ago
What is the answer to this question? If x=y, then 6x=6y
Sliva [168]

Answer:

This is a true statement. I think that's what you're asking.

Step-by-step explanation:

It is true because if x=y, than 6x=6y because both sides have a 6 and x=y

8 0
3 years ago
Other questions:
  • Which of these nonterminating decimals can be converted into a rational number? A 0.48907542... b 0.02020202... C 0.92589542...
    5·1 answer
  • (Affgfbwg I’m struggling) Find the value of x in the isosceles triangle shown below
    13·1 answer
  • Given ABCD and D = 145, what is the measure of B? A. 145 B.35 C. 90 D. 235 E. 10 F. 55 DEGREES
    13·2 answers
  • Mark has twice as many quarters as nickels and three more dimes than nickels. He has 4.20 in all. How many of each type of coin
    10·1 answer
  • How much does it cost to run a computer for 50 hours in a week if the monitor runs on 140 Watts and the tower runs on 260 Watts
    6·1 answer
  • The time required to complete a job varies inversely as the number of
    6·1 answer
  • Help is appreciated ❤<br><br> Simplify the radical expression -2 √250
    15·1 answer
  • 3x + 7y = 2 6x-5y=4 solve this by elimination method
    12·2 answers
  • PLEASE HELP!!! Worth 14 points (re do) (do not awnser is you dont know the questions please :/)
    9·1 answer
  • Can someone please help me ill mark you brainliest!!! !!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!