I have 3 questions:
1) If ABC and DEF are three- digit numbers, which of the following could be the number of digits in the product of ABC and DEF?
i. 4
ii. 5
iii. 6
I don't have the vaguest idea on how to do this and what type of math it is part of... My answer is 6 only but I am not sure.
2) How many of the integers from -10 to 10, inclusive, are even?
A. 9
B. 10
C. 11
D. 12
E. 13
Other than counting the numbers one by one to get B. 10, is there a way to do such questions algebraically?
3)(homework check) Every student from Mrs. C's sixth grade class is between 50 and 64 inches tall. If n inches is the height in inches of a student in her class, which of the following represent all possible values of n?
A. |50+n|<64
B. |50+n|>64
C. |57-n|<7
D. |57-n|=7
E. |64-n|>14
Is the answer B.?
1. Depending on the values of the numbers, it could be 5 or 6. Try 100^2 and 999^2. Are you searching for a maximum or minimum?
2. I don't know either.
3. Agree.
1) To determine the possible number of digits in the product of three-digit numbers ABC and DEF, we need to find the maximum and minimum values for their product.
The maximum value of ABC is 999 (the largest three-digit number), and the maximum value of DEF is also 999. To find the maximum value of their product, we multiply these two values: 999 * 999 = 998,001. Since 998,001 has 6 digits, option iii. 6 could be a possible number of digits.
The minimum value for ABC is 100 (the smallest three-digit number), and the minimum value for DEF is also 100. The minimum value of their product is 100 * 100 = 10,000. Since 10,000 has 5 digits, option ii. 5 could also be a possible number of digits.
Therefore, the possible number of digits in the product of ABC and DEF is either 5 or 6. Your answer of 6 is correct.
2) There is indeed a more efficient way to solve this question without counting one by one. We know that every second number is even, so we can use a formula to find the count of even numbers in the given range.
The formula to find the count of integers between two numbers (inclusive) can be calculated using the equation: (Highest number - Lowest number)/2 + 1.
In this case, the highest number is 10 and the lowest number is -10. Plugging these values into the formula, we get (10 - (-10))/2 + 1 = 20/2 + 1 = 10 + 1 = 11.
Therefore, there are 11 even integers between -10 and 10, inclusive. The answer is C. 11.
3) Let's analyze the options to find the correct representation for the possible values of n.
Option A. |50+n| < 64 means that the absolute value of 50 + n is less than 64. This represents all values of n between -114 and 14. However, this range is not within the given range of 50 to 64.
Option B. |50+n| > 64 represents all values of n outside the range from -14 to 14. This is the correct representation based on the given height range of 50 to 64 inches. Thus, the answer is B.
Therefore, your answer of B. is correct.