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
vlada-n [284]
3 years ago
9

A fair, six-sided die (numbered 1 to 6) is rolled eight times to form an eight-digit number. what is the probability that the re

sulting number is a multiple of 8? express your answer as a common fraction.
Mathematics
1 answer:
IgorC [24]3 years ago
8 0
A number is a multiple of 8 if the last 3 digits of it, form a number which is a multiple of 8.

For example: 45288, 16840, 90024 are all multiples of 8, because 288, 840 and 024, the last 2 digits, are multiples of 8.

The total number of 8-digit numbers that we can form using {1,2,3,4,5,6} is 6*6*6*6*6*6*6*6= 6^{8}, as we have 6 options for each digit.

The last 3 digits of multiple of 8, formed from the set {1,2,3,4,5,6}  can be one of the following:

{112, 136, 144, 152, 216, 224,232, 256, 264
 312, 336, 344, 352, 416, 424,432, 456, 464
 512, 536, 544, 552, 616, 624,632, 656, 664} ,

which is 27 of them.

For each of these 3 digits fixed in the end, we can form 6*6*6*6*6*1*1*1= 6^{5} numbers

so in total, there are 27*6^{5} numbers divisible by 8, whose digits are numbers in the set {1, 2, 3, 4, 5, 6}.


P(multiple of 8)=n(multiple of 8)/n(numbers that can be formed)= 

\frac{27*6^{5}}{6^{8}} =  \frac{27}{6^{3}}= ( \frac{3}{6} )^{3} =( \frac{1}{2} )^{3}=0.125

Answer: 0.125
You might be interested in
Select the equation that represents the following graph<br>​
stiks02 [169]

Answer:

there is nothing atttached or no options given

Step-by-step explanation:

3 0
3 years ago
A recipe requires ¾ cup of nuts for 1 batch of muffins. Write the number of batches of muffins that can be made using 7 ½ cups o
Ivahew [28]

Answer:

10 batches

Step-by-step explanation:

3/4 cups = 1 muffins

15/2 cups = x muffins

For x muffins,

3/4 × X = 15/2 × 1

3x × 2 = 15×4

6x = 60

Divide both sides by 6

6x/6 = 60/6

X = 10

Hence 10 batches of muffins will be made from 15/2 cups of nuts.

8 0
2 years ago
Can someone please help me??
Svet_ta [14]

Answer:

A= 153.86

A=49\pi

Step-by-step explanation:

You again....

4 0
3 years ago
Read 2 more answers
Question in the picture. PLS HELP!! THANKS + 30 POINTS + BRAINLIEST
Andrej [43]

Answer:

C.  Lincoln Forest is at sea level

Step-by-step explanation:

Elevation above sea level is indicated for several points in the table

Positive number indicates points <u>above</u>, negative number indicates points <u>below</u>, zero elevation indicated points <u>at </u>sea level

So, the answer for Lincoln Forest is:

  • C.  Lincoln Forest is at sea level
4 0
3 years ago
Please send help i really need it lol thank u
fgiga [73]

Answer:

i think it is B

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Richard has a rectangular plot of land that is 525 feet long and y feet wide. He decides to build a fence around the plot. If th
    15·2 answers
  • Pretend you have a sibling who is two years younger than you. He/she hears you working on triangle similarity and wants to know
    7·1 answer
  • How to a magic square decmals
    13·1 answer
  • Evaluate 3(2a-4/b^2) for a = 4 and b = 3.
    14·2 answers
  • A $1,000 TR Global bond at 80.5 pays 6% interest. Find the annual yield.
    13·1 answer
  • Select the equation that is equivalent to the equation: y+6=-4(X-2)
    13·2 answers
  • Complete the following <br> a) 3/5 = ?/20<br><br> b) ?/6 = 25=30
    7·1 answer
  • Diagram 1 shows a composite solid consisting of a cuboid and a right pyramid.
    6·1 answer
  • I GIVEEEEE BRAINLILST
    5·2 answers
  • What is the diameter of a circular swimming pool with a radius of 8 feet?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!