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Important Instruction In every question You will find the colored area in yellow (with three numbers) and red box with arTow The red box will tell You which digit o...

Question

Important Instruction In every question You will find the colored area in yellow (with three numbers) and red box with arTow The red box will tell You which digit of your ID You have to check Out of three numbers in yellow; you have to identify the number for the question based on your ID. Examples are aS shown below:digit ofIDIf the numbers is given as &/ b/ c: To identify which data is related to yours check digit of your ID as mentioned in the red box.If your digit is in between (0-3) the

Important Instruction In every question You will find the colored area in yellow (with three numbers) and red box with arTow The red box will tell You which digit of your ID You have to check Out of three numbers in yellow; you have to identify the number for the question based on your ID. Examples are aS shown below: digit ofID If the numbers is given as &/ b/ c: To identify which data is related to yours check digit of your ID as mentioned in the red box. If your digit is in between (0-3) then select *a' Ifit is (4-6) then select *b . Ifit is (7-9) then select Once you select the data, cancel the remaining data For example if my ID is 125858 and: Third digit of ID if the given no is 35/ 40/ 45 Third digit of my ID is $: [ will select 40 and cancel remaining data as shown 35/40/ 45 Fourth digit of Similarly, if the given no is 10%/129//[4% ID Fourth digit of my ID is 8: [ will select 14% and cancel remaining data as shown ]0%/12%/14%



Answers

Telephone Number Problem: When 10 -digit telephone numbers were introduced into the United States and Canada in the 1960 s, certain restrictions were placed on the groups of numbers: Area Code: 3 digits; the first must not be 0 or $1,$ and the second must be 0 or 1 Exchange Code: 3 digits; the first and second must not be 0 or 1 Line Number: 4 digits; at least one must not be 0 a. Find the possible numbers of area codes, exchange codes, and line numbers. b. How many valid numbers could there be under this numbering scheme? c. How many 10-digit numbers could be made if there were no restrictions on the three groups of numbers? d. What is the probability that a 10 -digit number dialed at random would be a valid number under the original restrictions? e. The total population of the United States and Canada is currently about 300 million. In view of the fact that there are now area codes and exchange codes that do not conform to the original restrictions, what assumption can you make about the number of telephones per person in the United States and Canada?

In question Number 11 were given a situation where we have a sample. We have to sample high school students and we have a total of 40 students. So we want to use table D in our textbook to choose five different students to sample. Well, we're also explain clearly the method that we would use to use their table of random digits to select those five students. So whenever you're asked to explain how to use the table of random digits, you need to be so detailed that whoever can read your writing can copy your method and get the exact same results. So here we go. All right. Since there are 40 students, we're gonna assign each student a number between 01 and 40. Now, it's important here that we assign each student a two digit number because there's 40 total students, 40 being a two digit number. We should also treat the single digit values one through nine. I'm sorry. Zero through not actually as two digit numbers. Now you can start at 00 If you would like and go through 39 you could start a 01 and go through 40 either one is okay, As long as you have 40 values that you can choose from, then we're gonna be detailed here saying, moving left to right on table d. Look at H two digit value. If the value is within the range of 012 40 we're going to select the number and continue until four other values between 01 and 40 are selected. This also brings up the idea of repeated values. Um, in any other numbers that aren't in our range and we have to mention what we're gonna do with those values. So I'm gonna say skip repeated numbers, which means we're sampling without replacement. We're also going to skip 00 because we're not including that one 41 through 99. This is gonna take care of any two digit number that's not in our range. When five numbers air selected figure out which students were assigned those numbers in order to create the sample in Part B, were asked to use Line 107 on Table D, which is the table of random digits to select the sample were given the list of students in our textbook. We're gonna label those students zero went through 40 just like the instructions above, say, and they're labeled, um, they're listed alphabetically, so we're gonna number them also alphabetically. So, uh, I'm sorry, numerically. So, um, the very first student alphabetically is gonna be the very first student numerically, and that's how we're gonna label it. So I've recorded the random numbers that were in table D here and starting that line 107 We're gonna look at every two digit number, so 82 is not in a range. Eso We're gonna skip that 73. Skip, we're gonna connect the night in the five because we're not gonna skip any number. We can't use 95 can't you? 78 Nanny, We're gonna go through this process until we confined five numbers that we can actually use. So 20 there we go. There's one 80. Cannot use no. 74 no. 75. We can use 11. No, 2 81 67 or 65? No, 2 53. Now there's a 00 If you started with that, you could use it. We did not start with that. No. 94 38 38. Looks good. We can use 38 here. There's also a 31 kind of looks strange being separated, but we can use the 31 40 eight's outside of our range 93 outside of the range. So now we've reached the end of line 107 Whenever we reached the end of 1107 we can go down the line 108 and continued the same process 60 No. 24 07 which should be our fifth value. And we can use that. So, using this process, we selected values 20 11, 38 31 and 07 And these five numbers correspond to students Johnson, Drezen, Washburn writer and Calloway.

So we're testing out some number of tricks you could call him, so we'll start by taking a five digit number. Will take a very creative number of 12345 and reverse it to become 54321 or then asked to subtract thes from each other. And this will give 41 976 as a result and then were asked to add the flip of the numbers again. Don't we do this. We will end up getting 109,000 890 and then where you want to test this out again with a four digit number and a six digit number. So we'll do that again with the same thing. But 4321 Just cutting off to five verses. 1234 4321 minus 1234 is equal to 3087. And when we add the flip side of it, 7803 we end up getting 10. 89. 10,890. And then to test this with a six digit number, I will raise this 12345 We'll do this with a six digit number, Um, and that will just be adding on six. So 654321 minus 123456 and then plugging this really quick. Well, give us 530,000 865. So when we add the you reverse the digits. 568035 We end up getting one million 98,900 and the results of this is always going to be some combination of eight and nine, with some zeros thrown in. There's a really nice theory behind this. If you want to look farther into it, it's, um, thesis attraction of reverse numbers can probably find it on Google just by doing that, Um, essentially the If you assign the variables letters and solve, you'll find that, um, the variables must be a multiple of nine and nine. And 18 is where the 989 owes come from. So, yes, the number will always be some combination of 10 and then either 99 rate. And so then we're told that's weekend represent a number on a number line by making it have a length equal number of units that we have by in general. Um, you know, knows that with these problems that there is actually a lot of cool theory behind it. And it's part of why other problems you're seeing are going to touch upon, uh, solving for variables. Because if you were to assign variables, this problem and solve there actually is a cool math reason for why this always works out. And in general, that's how this looks with the 45 and six.

For this problem. We are given data in parts A and B. We want to find the equation of the best fit line for each of these data sets and we want to answer the questions that follow 1st Empire. They were given data X. Y as follows to find Y. Hot. We proceeded in normal procedural steps first finding the means of X and Y Expires 2.66. Why is three next? We have to find the slope and intercept with the best fit line. Remember the slope B is given by the equation listed here, which requires as input the sums listed as well. The sample size end, which is three to calculate these sums, we simply compute the equation exactly. So some X is one plus three plus four or eight. Some Y is two plus one plus six on nine. Some X Y is some of the products. So two plus three plus 24 29 and some X squared is some one plus nine plus 16 or 26 plugging in. These values gives B equals 1.71 plug E. And Y. Barbie an expert to eh give us our intercept 0.143 And from this we're able to compute our best fit line. Why had he goes .143 plus 1.071 x. Next in part B will follow identical statute. These data points X. Y. To find my hat again Expires three and wine bar is 2.66 being A. Are given the idea by identical formulas be we have to compute the sum slightly differently because X and Y have been changed. But now we get B equals 0.357 ugly. And and and our sons for a wee plug in Y bar B and expire To get intercept 1.595 giving us why had equals 1.595 point 357 X. Next apart. See we make a note that in A and B we swapped X and Y. So our explanatory in response variables were swapped and these two data sets, what part do you want to answer? Solve Y equals 0.143 plus 1.71 X for X. So we want to isolate X on one side of the equation. We'll subtract our constant .143 from both sides. Then we'll divide by the 1.07. Wanted to get x equals .934, Y -133. And we note that this is not the best fit line from part B with X and Y swapped. So finally party were asked if we swap X and Y. Does Y hat for X. Y solve for X equal to the white hat for Y X. In the first place. Our results from paris A through D suggests that, obviously no, this is not the case.

The question is what Mazda columns first in the C 65 CH, two 36, that's five seniors, too. Still going to be yeah. Own reaction with they will go to the to do reaction. Both reacted the same rate. Yes. So even goes without you media to the comma s seen are Obama's. And is that because in the B but all the island is not degree. And to realize that side we live in favor even reaction, and also first reaction and even reaction is a first reaction is already they. So this will be the correct color match that I have explained. Okay, thank you.


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