Find the volume of the cone. Round your answer to the nearest tenth.
1 answer:
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The number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040
<h3>What is the rule of product in combinatorics?</h3>If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
We're specified that:
- The password needs to be 4 characters long
- It must have 3 letters and 1 of 10 special characters.
- Repetition is allowed.
So, each of 3 characters get 26 ways of being 1 letter. (assuming no difference is there between upper case letter and lower case letter).
And that 1 remaining character get 10 ways of being a special character.
So, by product rule, this choice (without ordering) can be done in:
ways.
Now, the password may look like one of those:
- L, L, L, S
- L, L, S, L
- L, S, L, L
- S, L, L, L
where S shows presence of special character and L shows presence of letter.
Those 175760 ways are available for each of those four ways.
Thus, resultant number of ways this can be done is:
Thus, the number of possibilities for constructing the 4 characters long password with specified conditions is given by: Option C: 703,040
Learn more about rule of product here:
To solve this problem you must apply the proccedure shown below:
1. You must apply the following formula:
Where is the future value,
is the present value,
is the interest rate and
is the time in years.
2. You have that the bank will double your money in years. Therefore:
3. Substitute values into the formula and solve for , as following:
4. By applying natural logarithm, you have:
%
The answer is: %