Twelve equally spaced holes are to be drilled in a 34 1/4 inch metal strip, after 2 inches are cut off on each end. What is the distance, to the nearest hundredth of an inch, from center to center of 2 consecutive holes? _______ inches

How do I start this?

You have a 30 1/4 inch strip after trimming the ends. You need to specify how close the holes can be to the end of the remaining strip. The diameter of the holes is also necessary, to make sure part of the hole does not go beyond an edge

If the holes are very small and can be drilled right to the edges, you need 11 gaps in 30.25 inches. That would be 2.75 inches between holes.

Well, I'm glad you came to me, a "Clown Bot" for help with this question. So, you want to drill some holes, huh? That's both exciting and dangerous at the same time. Let's see if I can help you out.

First, let's calculate the length of the metal strip after cutting off 2 inches from each end. So, we start with a 34 1/4 inch strip, but then we chop off 2 inches from both ends. That means we've lost a total of 4 inches. So, the new length of the metal strip is 34 1/4 inches minus 4 inches, which gives us 30 1/4 inches. Phew!

Now, we know that we have to drill 12 equally spaced holes along this new length. To find the distance between each hole, we divide the total length by the number of holes. So, 30 1/4 inches divided by 12 gives us the distance from center to center of two consecutive holes.

I'm going to pull out my handy calculator here. Yes, yes, Clown Bots need calculators too! Okay, let's do the math...

*Clown Bot takes a moment to calculate on a pretend calculator*

Well, looks like the distance from center to center of two consecutive holes is approximately 2.52 inches. Ta-da!

Now, please be careful with those drills, and remember, if things get boring, just make funny faces at your metal strip. Good luck drilling those holes!

To solve this problem, we can follow these steps:

Step 1: Determine the length of the metal strip after cutting off 2 inches on each end.
Length of the original strip = 34 1/4 inch
Length of the cut-off ends = 2 inch on each end
Length of the remaining strip = Length of the original strip - 2 inch on each end

Step 2: Calculate the remaining length of the strip.
Length of the remaining strip = 34 1/4 inch - (2 inch on each end) - (2 inch on each end)

Step 3: Calculate the distance between the centers of two consecutive holes.
Distance between the centers of two consecutive holes = Length of the remaining strip / (12 - 1)

Step 4: Round the distance to the nearest hundredth of an inch.

Let's perform these calculations step-by-step:

Step 1:
Length of the original strip = 34 1/4 inch
Length of the cut-off ends = 2 inch on each end
Length of the remaining strip = 34 1/4 inch - 2 inch - 2 inch
= 34 1/4 inch - 4 inch
= 30 1/4 inch

Step 2:
Length of the remaining strip = 30 1/4 inch

Step 3:
Distance between the centers of two consecutive holes = 30 1/4 inch / (12 - 1)
= 30 1/4 inch / 11

Step 4:
Rounding to the nearest hundredth of an inch gives us:
Distance between the centers of two consecutive holes = 2.75 inch

Therefore, the distance, to the nearest hundredth of an inch, from center to center of two consecutive holes is 2.75 inches.

To start solving this problem, we need to understand the given information and the steps involved.

Given:
- Length of the metal strip: 34 1/4 inches
- 2 inches are cut off from each end

To find:
- Distance from center to center of two consecutive holes after cutting the ends

Steps to follow:
1. Convert the mixed number length of the metal strip into a fraction or decimal.
2. Subtract the amount cut off from each end from the total length to get the remaining length of the metal strip.
3. Calculate the total distance between the remaining ends of the strip.
4. Divide the total distance by the number of equally spaced holes to find the distance from center to center.

Let's now work on each step to find the answer.

Step 1: Convert the mixed number length to fraction or decimal.
34 1/4 inches can be written as a fraction:
34 1/4 = (34 * 4 + 1)/4 = 137/4

Step 2: Subtract the amount cut off from each end.
Since 2 inches are cut off from each end, we subtract 4 inches from the total length:
Remaining length = 137/4 - 4

Step 3: Calculate the total distance between the remaining ends.
The remaining ends are the endpoints after cutting off 4 inches from both sides. Multiply the remaining length by 2 to get the total distance:
Total distance = (137/4 - 4) * 2

Step 4: Divide the total distance by the number of equally spaced holes.
As per the problem, there are 12 equally spaced holes. Divide the total distance by 12 to get the center-to-center distance:
Center-to-center distance = [(137/4 - 4) * 2] / 12

Now, you can calculate the center-to-center distance by evaluating the above expression.