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
Veronika [31]
3 years ago
14

What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice?

Mathematics
1 answer:
Vladimir [108]3 years ago
4 0
For three fair six-sided dice, the possible sum of the faces rolled can be any digit from 3 to 18.
For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).

Thus, there are 16 possible sums when three six-sided dice are rolled.

Therefore, from the pigeonhole principle, <span>the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.

The pigeonhole principle states that </span><span>if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.

That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
</span>
You might be interested in
3^3 - 5 x 9 + 6 - 29
xxMikexx [17]

Answer:

-41

Step-by-step explanation:

3^3-5x9+6-29

calculate exponents 3^3=27

now write as; 27-5x9+6-29

now multiply and divide (left to right) 5x9=45

now rewrite as 27-45+6-29

now add and subtract(left to right) 27-45+6-29= -41

6 0
3 years ago
Read 2 more answers
A turtle can swim 20 meters in 4 seconds. At this rate, how many meters can the turtle swim in 10 minutes?
Snezhnost [94]

Answer:

3,000 meters

Step-by-step explanation:

10*60=600/4=150*20=3000 meters (I highly doubt a turtle can swim three kilometers in 10 min... especially if it's a box turtle).

7 0
3 years ago
ben is filling up his cylinder shaped pool up to 80% of its capacity . If his is 6 feet deep and has a diameter of 18 feet, how
vlada-n [284]

Answer:

You will put 1220.83ft³ of water in the pool

Step-by-step explanation:

radius = half of diameter

d = 18ft

r = 18ft / 2 = 9ft

To calculate the volume of a cylinder we have to use the following formula:

v = volume

h = height = 6ft

π = 3.14

r = radius = 9ft

v = (π * r²) * h

we replace with the known values

v = (3.14 * (9ft)²) * 6ft

v = (3.14 * 81ft²) * 6ft

v = 254.34ft² * 6ft

v = 1526.04ft³

The volume of the cylinder is 1526.04ft³

If it is filled to 80% then we have to multiply the volume by 80/100

1526.04ft³  * 80/100 = 1220.83ft³

You will put 1220.83ft³ of water in the pool

5 0
3 years ago
Please answer 6 and 7
nexus9112 [7]
Number 6 is 15 7 is 3
5 0
3 years ago
Select the correct answer.<br> Which equation represents a function?
inn [45]

Answer:

C

Step-by-step explanation:

'x=' create vertical lines which are not functions whereas

'y=' create horizontal lines which are functions

7 0
3 years ago
Other questions:
  • How do I solve this equation
    10·2 answers
  • 30) Find the 29th term of the following sequence. <br><br> 27, 24, 21, 18, . . .
    13·1 answer
  • Kai took five tests this semester. His scores are listed below.
    13·1 answer
  • A line has a slope of 2 and a y-intercept of -9, what is the equation of the line?
    12·1 answer
  • What is the length of SR in the parallelogram given?<br> A) 22 <br> B) 24 <br> C) 28 <br> D) 34
    11·1 answer
  • Melinda earns 5 minutes to play video games for every hour she spends on homework.
    5·2 answers
  • Write the scientific notation for 2,460,000
    9·1 answer
  • Which is the best stock you can invest now in 2021, or where I can learn to invest in stock market​
    7·1 answer
  • A hockey puck has a height of -2.5 cm. What is the height of 7 hockey pucks?
    12·1 answer
  • Which pair of angles are vertical angles?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!