Math Problem Statement
Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.
How many numbers are greater than 54? numbers
Solution
To determine how many two-digit natural numbers formed from the digits 0 through 9 are greater than 54, we can break down the problem as follows:
Step 1: Define the range of two-digit numbers
- The two-digit numbers range from 10 to 99.
Step 2: Identify numbers greater than 54
- We need to count the numbers from 55 to 99 (inclusive) because these are the numbers greater than 54.
Step 3: Count the numbers in this range
- The smallest number in this range is 55, and the largest is 99.
- To find the total count of numbers from 55 to 99, use the formula for the number of terms in an arithmetic sequence:
Final Answer:
There are 45 two-digit natural numbers greater than 54.
Would you like more details or have any questions?
Here are some related questions to explore further:
- How many two-digit numbers are less than or equal to 54?
- What is the probability of randomly selecting a number greater than 54 from the set of all two-digit numbers?
- How many two-digit numbers are divisible by 5 and greater than 54?
- If you form three-digit numbers instead, how many of them are greater than 554?
- How does the count change if the digits cannot be repeated?
Tip: When dealing with ranges of numbers, counting the terms using the arithmetic sequence formula can simplify the process.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Number Theory
Formulas
Formula for the number of terms in an arithmetic sequence
Theorems
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Suitable Grade Level
Grades 6-8
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