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:
The algebraic expression for this problem is 
.
Step-by-step explanation:
Given:
15 students fit in a van and 3 students will be traveling in a car.
So we can say that;
Number of students travelling by van = 15
Number of students travelling by car = 3
Now Let the number of vans be 'x'.
also Let the number of cars be 'y'.
Let the Total number of students bayside middle school be 'T'.
Solution:
now we can say that;
Total number of students going on field trip is equal to sum of Number of students travelling by van multiplied by the number of vans and Number of students travelling by car multiplied by the number of cars.
framing in equation form we get;
Hence, The algebraic expression for this problem is .
Answer:
8.5 cm
Step-by-step explanation:
original length: x
3.5x = 29.75
divide both sides of equation by 3.5
x = 8.5 cm
4 3/10 because you can turn two over five into 4/10 so to make -1 3/10 to -2 you -7/10 then -3 to get -5 then -6/10 to get -5 4/10
