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.
9700 is the answer which is correct
You have a rectangle and 2 triangles:
rectangle = 12 *6 = 72
larger triangle on left, find the base:
base = 6 / tan(45) = 6
area = 1/2 x b x h = 1/2 x 6 x 6 = 18
smaller triangle:
area = 1/2 x b x h
1/2 x 2 x 6 = 6
total area:
72 +6 +18 = 96 cm^2
Answer: he had 5 pounds.
Step-by-step explanation:
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