Which of the following is the convergence range of the given power series?
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Which of the following is the convergence range of the given power series?
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- Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .1. Due to the high incidence of crime, a company is giving its employees new and secured access to the company. Instead of leaving the doors open, they are installing a card system. To open the door, employees must insert a card into a slot. If a green light comes on, it is okay to turn the handle and open the door; if a yellow light comes on it indicates the door is locked from inside and you cannot enter. Suppose that 90% of the time when the card is inserted, the door should open because it is not locked from the inside. When the door should open, the system makes errors 2% of the time. That is, the green light will appear 98% of the time. When the door should not open, the system makes errors 5% of the time (green light appears). Suppose you inserted the card and the light is green, what is the probability the door will open?To inspect the quality of the screens for mobile phones produced by Company X, two separate inspection devices are used to test the screens for defects. Basically, a specific screen is tested once using the two inspection devices. Device 1 can detect the presence of defects 99.3% of the time, whereas Device 2 can detect defects 99.7% of the time. Assume that the 2 devices are operating independently from each other. One day, four defective screens were sent for inspection. Let X represent the number of screens that will be correctly tagged as defective by Device 1, while Y represents the number of screens that will be correctly tagged as defective by Device 2. Are X and Y independent? explain
- 1st blank: 0.6267, 0.5006, 33, 0.7843 2nd blank: 1.44, 2.25, 1.15, 1.80 3rd blank: 0.7843, 0.6267, 0.5006, 0.4 4th blank: 2.25, 1.80, 1.15, 1.44 5th blank: larger or smaller 6th blank: 0.2689, 0.1293, 0.0145, 0.0378 7th blank: 0.0378, 0.1293, 0.0100, 0.2612 8th blank: flatter and more spread out or more like the z distributionEstablishing A number 1-5onlySuppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…
- 7.) Several years ago, the US began running out of telephone numbers. Telephone companiesintroduced new area codes and numbers were used up, and eventually almost all area codes wereused up. (a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0or 1. How many such area codes are possible? (b) The actual number of area codes under this system was 152. What could be the cause of thediscrepancy between this number and your answer to part (a)? (c) A 7-digit telephone number that follows the area code cannot start with a 0 or 1. How manysuch 7-digit telephone numbers are possible in each area code?(d) Under the old area code system in part (a), how many total possibilities are there for areacode with telephone number?(e) The shortage of area codes was resolved by removing the restriction on the second digit of thearea code. (This resulted in problems for some older equipment which used the second digit todetermine that a long-distance call…According to U.S. government statistics, mononucleosis (mono) is four times more common among college students than the rest of the population. Blood tests for the disease are not 100% accurate. Assume that the following table of data was obtained regarding students who came to a certain school's health center complaining of tiredness, a sore throat, and slight fever. Has Mono Doesn't Have Mono Totals Positive Blood Test 19 44 63 Negative Blood Test 46 29 75 Totals 65 73 138 If a student is selected from this group, find the probability that the test is positive, given that the student has mono.1. Assume that a password must be at least 8 characters long and include at least 1 digit and at least 1 special character. If people form their password by taking an English word of exactly 6 letters (assume that this password is not case-sensitive) and then adding (in either order) a digit and a special character, how many passwords would be possible? 2. How does your answer change if we assume that we still have a 6 letter word, but now we assume that both the digit and the special character can be inserted into the word in any position?
- 4 Suppose we have 3000 identical sheets separated into packs of 25 sheets each. Use generating functions to calculate the number of ways in which you can distribute the packs of 25 sheets among four groups of students so that each group has at least 150 sheets and more than 1000 sheets. Express your answer using binomial coefficients and include the calculations made. Explain your solution in detail.PROVE 1.11+2.2! +3.3!+----n.n!=(n++)!-1 A n>=11. Pretend that in a certain city the number of new cases of COVID was reported to be 200 new cases on Sunday. Let’s pretend that the number of new cases grows by 22% on Monday, and then after that falls by 22% on Tuesday a. What will the number of new cases be on Monday and Tuesday? Don’t round for accuracy. (note: we are not talking about totals here, just daily new cases like in the news. So on Sunday there were 200 new cases. Ex: How many new cases did Monday have: Intuitively the answer should be more than 200 new cases bc the new cases grew by 22%.) Monday: Tuesday: