Express 7/40 as a percent
1 answer:
Answer: 17.5%
Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100.
So to write 7/40 as a percent, we need to find a fraction equivalent to 7/40 that has a 100 in the denominator.
We can do this by setting up a proportion.
Now we can use cross products to find the missing value.
=
700 = 40n
Next, dividing both sides of the equation by 40, we have <em>17.5 = n</em>.
So, 7/40 is equal to 17.5/100 or 17.5%.
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Answer:
b=7
Step-by-step explanation:
We want to determine the positive base b in which:
The easiest way to approach this is to convert all the numbers to base 10.
Next, we factorize the resulting expression.
The positive value of b for which the equality hold is 7.
Consider the set of all (not-all-zero) decimal strings of length 6. This is the set of strings
000001
000002
...
099998
099999
100000
There are obviously 100,000 strings in this set, so we have a one-to-one correspondence to the integers between 1 and 100,000. Think of any string starting with 0s as the number with the leading 0s chopped off.
There are two choices for the first digit, either 0 or 1, but a number can only contain a 6 if the first digit is 0; otherwise, the number would exceed 100,000. For every digits place afterward, if a given digits place contains a 6, then the remaining four places have 9 possible choices each, choosing from 0-9 excluding 6. If we fix the 6 in, say, the second digits place, then the number of integers between 1 and 100,000 containing exactly one 6 is
where the first 1 refers to the only choice of 0 in the first digits place, the second 1 refers to the unique 6 in the next place, and the remaining four places are filled with one of 9 possible choices.
Now, notice that we can permute the digits of such a number in 5 possible ways. That is, there are 5 choices for the placement of the 6 in the number, so we multiply this count by 5.
000001
000002
...
099998
099999
100000
There are obviously 100,000 strings in this set, so we have a one-to-one correspondence to the integers between 1 and 100,000. Think of any string starting with 0s as the number with the leading 0s chopped off.
There are two choices for the first digit, either 0 or 1, but a number can only contain a 6 if the first digit is 0; otherwise, the number would exceed 100,000. For every digits place afterward, if a given digits place contains a 6, then the remaining four places have 9 possible choices each, choosing from 0-9 excluding 6. If we fix the 6 in, say, the second digits place, then the number of integers between 1 and 100,000 containing exactly one 6 is
where the first 1 refers to the only choice of 0 in the first digits place, the second 1 refers to the unique 6 in the next place, and the remaining four places are filled with one of 9 possible choices.
Now, notice that we can permute the digits of such a number in 5 possible ways. That is, there are 5 choices for the placement of the 6 in the number, so we multiply this count by 5.