how many positive four- digit integers have 3 as their tens digit and 5 or 9 as their ones digit?
i don't know where to begin
Start listing them. Four-digit numbers must be between 1000 and 9999. The last two numbers must be 35 or 39.
1035
1039
1135
1139
...etc., ending with
9935
9939.
There are 90 pairs of numbers, starting with 10 and ending with 99 as the first two digits.
90 pairs = 180
To find the number of positive four-digit integers with 3 as their tens digit and 5 or 9 as their ones digit, you can break down the problem into smaller steps:
Step 1: Determine the range of possible values for the thousands digit.
Since the integer is four digits long, the thousands digit can have any value from 1 to 9.
Step 2: Determine the possible values for the hundreds digit.
The hundreds digit can have any value from 0 to 9, except for 3 since it is already taken by the tens digit.
Step 3: Determine the possible values for the tens digit and the ones digit.
The tens digit is already specified as 3, and the ones digit can have either 5 or 9.
Step 4: Calculate the total number of possible combinations.
Multiply the number of possibilities for each digit to find the total number of positive four-digit integers with 3 as their tens digit and 5 or 9 as their ones digit.
Let's go through this step by step:
Step 1: The thousands digit:
Since the thousands digit can have any value from 1 to 9, there are 9 possibilities.
Step 2: The hundreds digit:
The hundreds digit can have any value from 0 to 9, except for 3 since it is already taken by the tens digit. So, there are 10 - 1 = 9 possibilities.
Step 3: The tens digit and the ones digit:
The tens digit is fixed as 3, and the ones digit can have either 5 or 9. So, there are 2 possibilities.
Step 4: Calculate the total number of possible combinations:
Multiply the number of possibilities for each digit: 9 (thousands) * 9 (hundreds) * 1 (tens) * 2 (ones) = 162.
Therefore, there are 162 positive four-digit integers with 3 as their tens digit and 5 or 9 as their ones digit.
To find the number of positive four-digit integers that have 3 as their tens digit and 5 or 9 as their ones digit, you can follow these steps:
Step 1: Determine the range of possible values for the thousands, hundreds, and ones digits.
- The thousands digit can be any digit from 1 to 9 (excluding 0 since it is a positive integer).
- The hundreds digit can be any digit from 0 to 9.
- The tens digit must be 3.
- The ones digit can be either 5 or 9.
Step 2: Count the number of options for each digit.
- Since the thousands digit can be any digit from 1 to 9, there are 9 possibilities.
- The hundreds digit can be any digit from 0 to 9, so there are 10 possibilities.
- Since the tens digit must be 3, there is only one possibility.
- The ones digit can be either 5 or 9, so there are 2 possibilities.
Step 3: Multiply the number of options for each digit to find the total number of four-digit integers.
- Multiply the number of options for the thousands, hundreds, tens, and ones digits:
9 × 10 × 1 × 2 = 180.
Therefore, there are 180 positive four-digit integers that have 3 as their tens digit and 5 or 9 as their ones digit.