35. the set, s consists of 900,000,000 whole numbers, each being the same number of digits long. howmany digits long is a number from s? (hint: use the fact that a whole number cannot start with the digit 0.)
1 answer:
Answer:
Let the number of digits be n and the number of elements in set be s .
<h3>When n = 1</h3>
The set contains 1-digit numbers, 1 through 9, The set consists of 10 - 1 = 9 numbers.
<h3>When n = 2</h3>
The set contains 2-digit numbers, 10 through 99, The set contains 100 - 10 = 90 numbers.
<h3>When n = 3</h3>
The set contains 3-digit numbers, 100 through 999, The set contains 1000 - 100 = 900 numbers.
The pattern we see helps us determine the relationship between s and n as follows.
When set contains n-digit numbers, the set contains:
s = 10ⁿ - 10ⁿ⁻¹ = 10ⁿ⁻¹(10 - 1) = 9*10ⁿ⁻¹ elements
We have s known , substitute it into equation above and solve for n :
900000000 = 9*10ⁿ¹ 100000000 = 10ⁿ⁻¹ 10⁸ = 10ⁿ⁻¹ n - 1 = 8 n = 9
The numbers in the set s are 9-digit long.
You might be interested in
As function is = 4x
<h2><em>
h≥60 </em></h2>
This is saying that your height has to be equal to or greater than 60 inches.
You need to add the number of blocks or lines are betweenhem.
Answer:
The expression equivalent to 486-9+6+3^*2 is 500-7+6+5^*2
Step-by-step explanation:
486-9+6+3^*2 = 500-7+6+5^*2
486-9+6+9 = 500-7+6+25
486-24 = 500-38
462 = 462
5 for $3.50 has the lowest unit price because 3 for $2.19 is $0.73 per item, 4 for $3.00 has a in it price at $0.75, 5 for $3.50 has a unit rate for $0.70 per item, and $0.72 per item is more expensive than $0.70 per item
