Between which two consecutive whole numbers does 42−−√ lie?
We can estimate the answer by thinking of which two whole numbers the square root of 42 is between. Since 6^2 = 36 and 7^2 = 49, we know that the square root of 42 is between 6 and 7.
To be more precise, we can use decimals:
42^0.5 = 6.48074069840786...
So, we know that the square root of 42 is greater than 6 and less than 7. Therefore, 42^0.5 lies between the consecutive whole numbers 6 and 7.
Answer:
Between 6 and 7.
A company ordered 328 pens with the company logo printed on them. The company returned 82 of the pens because the wrong logo was printed on them. What percent of the original order did the company keep?
To find the number of pens the company kept, we need to subtract the number of pens returned from the original order:
328 - 82 = 246
So the company kept 246 pens out of the original order of 328.
To find the percentage, we can use the formula:
percentage = (part/whole) x 100
In this case, the part is 246 (the number of pens the company kept) and the whole is 328 (the original order).
percentage = (246/328) x 100 = 75%
Therefore, the company kept 75% of the original order.
To find the two consecutive whole numbers between which 42−−√ lies, we need to find the integer values of both the smaller and larger numbers.
Step 1: Find the smaller whole number.
To find the smaller whole number, we can use the floor function or integer division. The floor function gives us the largest integer less than or equal to a given number. In this case, we want the largest whole number less than or equal to 42−−√.
Using the floor function, we get:
Smaller whole number = ⌊42−−√⌋
Step 2: Find the larger whole number.
To find the larger whole number, we can use the ceiling function or integer division. The ceiling function gives us the smallest integer greater than or equal to a given number. In this case, we want the smallest whole number greater than or equal to 42−−√.
Using the ceiling function, we get:
Larger whole number = ⌈42−−√⌉
Now, we can calculate the values:
Smaller whole number = ⌊42−−√⌋ = ⌊6.48⌋ = 6
Larger whole number = ⌈42−−√⌉ = ⌈6.48⌉ = 7
Therefore, 42−−√ lies between the consecutive whole numbers 6 and 7.