If there are 13 letters typed, the probability that no letters will be repeated can be found to be 1.05 x 10⁻²⁰
<h3>How to find the probability no letters are repeated?</h3>
First, find the number of possibilities of 13 letters from 26 letters in the alphabet as:
= 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26
= 6.156 x 10³⁶ possibilities
If the numbers are not to be repeated then the possibilities are:
= 26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14
= 64764752532480000 possibilities
The probability that no letters are repeated is:
= 64764752532480000 / 6.156 x 10³⁶
= 0.0000000000000000000105
= 1.05 x 10⁻²⁰
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Domik weights 30 pounds more than his sister
Together they weigh 330 pounds
Let "x" represent the weight of Dominik's sister, then his weight can be expressed as "x+30"
And their total weight can be calculated as:

From this expression you can calculate the value of x:

x=150 pounds
x+30=150+30=180 pounds
Dominik weights 180pounds and his sister 150 pounds
Answer:
the interest is $975
the total amount is $5975
Step-by-step explanation:
lets use tje formula
I=PRT
where I is interest earned
P is the principal amount(original amount)
R is the rate of interest
and T is the time in years
so
the principal amount is 5000 since it is the original amount
rate is
=0.065
time is 3 years
lets plug these values into our equation:
5000*0.065*3=I
5000*0.065*3=975
the interest is $975
the next part of the question is asking for the balance or the total amount which is principal+interest
5000+975=5975
the total amount or balance is $5975
hope this helps