Question

HEADWEAR is a company that is researching the cost of manufacturing special hats for mathematicians. The design consists of the first and last name of the buyer of the hat.

1. To be able to sell to anyone, they would like to stock all possible hats. how many combinations of initials are possible on a hat?

2. The manufacturer realizes that no store will stock that many hats. You are the store manager, and need to determine which initials most commonly occur. Describe how many you would collect the data to determine which hats to stock. Clearly describe your method to your employee.

Answer 1

What ideas do you have for this problem? @margejean

Answer 2

I am not really sure how to start?

Answer 3

Okay, let's discuss what an initial is.
What is an initial of a name?
(first initial for example)

Answer 4

an initial is the first letter of a person's name.
For instance, "M" is the initial of Mira. Does that make sense? :]

Answer 5

Yes it does.

Answer 6

This problem tells us to put the first and last initial on each hat.
Okay, we can find the total number of ways to put 2 initials on a hat
Let's draw a picture using two blank spaces
_ _
Each blank space represents an initial
How many choices do we have for the first initial?
(*Hint*) how many letters are there in the alphabet?

Answer 7

So their is 26 letters of the alphabet, but HEADWEAR is 8 letters.

Answer 8

That is correct. The name HEADWEAR has nothing to do with the initials on the hat. The initials on the hat belong to the potential buyer of the hat.

Answer 9

Okay then, that makes sense.

Answer 10

Great! :]

Answer 11

Are you ready to move on to the next step?

Answer 12

yes i am.

Answer 13

Okay, next we can find the total number of combinations initials possible.
To find the total number of choices we multiply : 26 * 26

Answer 14

26x26=?
:]

Answer 15

it is 676

Answer 16

Yes! 676 combinations is the answer to question #1

Answer 17

Okay that makes sense. Thanks for explaining number 1, you made it easier.
Number 2 it also ask to describe the method to my employer, who will conduct my study and report the results back to me.

Answer 18

What ideas do you have for Q2?

Answer 19

Okay, this question appears to be "open ended"
Do you know what that means?

Answer 20

Basically - There is more than one possible answer for this question.
Does that make sense?

So what would you do if you were in the position of the hat seller?
If you had to sell hats with initials on them, how would you find out which initials are most common?

Answer 21

Because it has different parts to the question it makes sense their will be more than one answer. How do I know which initials occur the most?

Answer 22

What do you think?

Answer 23

I will repeat my question: "So what would you do if you were in the position of the hat seller?
If you had to sell hats with initials on them, how would you find out which initials are most common?"

Answer 24

If I were a seller I would pick initials that usually in each word such as vowels or use initials that will stand out to customers.

Answer 25

Okay, there are a lot of different ways we could find that out.
We could go to the phone book and collect all of the names of people in the city the hat seller lives in .We could write down the initials of all the people in the phone book, and only make hats for the top ten most popular initials.
Can you think of a different method that involves a survey?
How about a mail in survey?
Can you think of how we could use a mail in survey?

Answer 26

how would you figure out which initials stand out to customers?

Answer 27

So you had a good idea, but now we need to develop your idea

Answer 28

How would you collect data to figure out which initials to put on the hats? @margejean

Answer 29

I would collect the data by doing a survey about what the customers want.

Answer 30

Okay, and what would you ask in your survey?

Answer 31

so you would ask them what initials they would want on a hat?

Answer 32

if you ask customers what they want, they might not respond about initials
Remember, the whole purpose of the survey is to find out what initials to put on the hats
So it is important to ask the customers about the *initials* they want on the hat.

Answer 33

okay that makes sense.

Answer 34

Okay, is this question written exactly as it appears in the original problem?
I am a little confused when it says "describe how many you would collect"
I think there might be a word missing.

"Describe how many _____ you would collect"?

Answer 35

It says describe how you would collect the data to determine which hats to stock?
I would collect 676??

Answer 36

Thanks for checking that.
You could do that. You could collect 676, but it is not necessary - You could collect more or less than 676 as well. It really is up to you in this problem. Generally, the more data you collect, the more information you will have to help you make your decision.

Answer 37

So it would probably be best to collect as much data as possible.

Answer 38

So, I like your idea of mailing surveys to every resident in an entire city
So I think you have formed an answer.
"I would collect the data by mailing a survey to residents of a city and ask what initials they want on a hat"

Answer 39

What would you do with that information?
So All the responses you get to the surveys you send out.
Say you get 1,000 residents who respond and tell you what initials they want on hats.
What do you do next?

Answer 40

I want to collect all that information.

Answer 41

Hai Sweet Friend, WeLcoMe to OpeN stuDy.. !!

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