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.
Answer:
1. m∠CGB=120
3. m∠AGD=90
5. m∠CGD=150
2. m∠BGE=60
4. m∠DGE=30
6. m∠AGE=120
Step-by-step explanation:
Sorry that they are out of order.
Answer:
we could buy 43 party favors
Step-by-step explanation:
initially we have an amount of $380
if we already spend an amount of $272 this we have to subtract it from the total
$380 - $272 = $108
if each party favor comes out $ 2.50 and we have $ 108 we have to divide what we have by what each one comes out to know how many we can buy
$108 / $2.50 = 43.2
this means we could buy 43 party favors
Answer:
5x^2 + 4x - 8 Hope this helps! I think this is right, but it's hard to tell from the problem.
Step-by-step explanation:
