Determine the number of subsets of 3,4,5,6,7,8,9,10,11,12,13,14,15
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Answer:
8192
Step-by-step explanation:
The number of subsets of an n-element set is 2^n.
Your set has 13 elements, so has 2^13 = 8192 subsets.
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This count includes the empty set and the full set.
Answer:
x = 10
Step-by-step explanation:
l n 20 + l n 5 = 2 l n x
ln (20×5) = ln x²
ln(100) = lnx²
100 = x²
x = +/- 10
Since logs of negative numebrs don't exist, we reject -10
Answer:
The answer is A. AB and AC are congruent
10000 digits can be used for 4 digit A.T.M code.
<u>Solution:</u>
Given that A.T.M required 4 digit codes using the digits 0 to 9.
Need to determine how many four digit code can be used.
We are assuming that number starting with 0 are also valid ATM codes that means 0789 , 0089 , 0006 and 0000 are also valid A.T.M codes.
Now we have four places to be filled by 0 to 9 that is 10 numbers
Also need to keep in mind that repetition is allowed in this case means if 9 is selected at thousands place than also it is available for hundreds, ones or tens place .
First digit can be selected in 10 ways that is from 0 to 9.
After selecting first digit, second digit can be selected in 10 ways that is 0 to 9 and same holds true for third and fourth digit.
So number of ways in which four digit number is created = 10 x 10 x 10 x 10 = 10000 ways
Hence 10000 digits can be used for 4 digit A.T.M code.
