"Given: x = -30 (mod 12) Which of the following integers are valid solutions for x 18- O 30 20 36-
Q: Consider the equation where x1,x2,...,x9 € N. How many solutions are there if: a) b) c) Xi 9 for all…
A: As per the question we are given a linear equation : x1 + x2 + ... + x9 = 73 And we have to find the…
Q: Find the 5-1 mod 57 A) 4 B) 11 C) 12 D) 23
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Q: Prove the following:For any natural number n, if n 2 + 6 n is an even number, then n is an even…
A: To prve that n is an even integer under the given conditions
Q: Find all solutions to 17r = 14 (mod 21).
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Q: Given: x = -30 (mod 12) Which of the following integers are valid solutions for x? A) -18 B)…
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Q: Consider the congruence 4 a 2 (mod 3). Then the value of 'a' could be: O a. the solution does not…
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Q: Q2: Solve the following (if possible): 1. = 5x + 11 mod 37 3
A: Since you have asked multiple questions, we will solve the first question for you. If you need any…
Q: II. Give FIVE different answers for each of the following. 1. 49 = mod 10 2. 82 = mod 9 3. 100 = mod…
A: 1) Given expression is 49≡______ mod 10
Q: Find all integer solutions satisfying all the equations given. 5x =1 mod 39 3x =1 mod 25 4x =1 mod…
A: Concept :. * ax =6 mod n g (d (a,n) = d (let)…
Q: x is congruent to 43 mod 12. Then x is None of the option 91 75 89
A: Answer is 91.
Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 18 2
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Q: x is congruent to 27 mod 7. Then x is 54 55 None of the option 46
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Q: For which positive numbers a is it true that ax >= 1+x for all x?
A: Explanation of the solution is given below...
Q: 6. Solve 11x = 4 (mod 21) (a) 8. (b) 4 (c) 11 (d) has no solution
A: given 11x≡4 mod 21 since gcd11,21=1 thus, we can write 11x=4+21y for some y
Q: x is congruent to 31 mod 6. Then x is 40 54 55 None of the option
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Q: Which one of the following is correct? a. 30 쓰 3 (mod 5) O b. 25 3 (mod 4) O c. 31 3 (mod 7) Od 20 3…
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Q: 1. Find the value for q given: (a) 39 = 4( mod 5) (b) -43 = 1( mod 4)
A: Note: Hi! Thank you the question, As per the honor code, we'll answer the first question since the…
Q: Given a = 4( mod 9) and b = 5( mod 9), find c with 0<c<9 such that c = 5a + 3b ( mod 9)
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Q: Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by…
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Q: 4. The statement P-> Q is equivalent to -PA Q. 5. To prove the statement: If ab = 0 then a = 0 or b…
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Q: x is congruent to 43 mod 12. Then x is None of the option 89 91 75
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Q: (a) Find two integers satisfying the equation r³ + 24x² – 2 = 0 mod 23.
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Q: 22. Suppose c is an integer. If c mod 15 = 3, what is 10c mod 15? In other words, if division of c…
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Q: Consider: for any integers a and b, if (a3 + b3) mod 3 does not equal 0, then (a + b) mod 3 does not…
A: The contrapositive of A implies B is not B implies not A. We use this and solve this problem.…
Q: you Prove the " of 25nY-18n +7 =0 (mod4), then statement contradiction. is by "even
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Q: The value of 52003 mod 7 is? (3 (4 8) 9
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Q: i need to find the value of m 12 = (m*28)mod 113
A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows
Q: 4.2 Linear Congruences 161 6. For which integers c, 0 sc< 30, does the congruence 12x =c (mod 30)…
A: Q6 asked and answered.
Q: b) Determine whether or not x? = 85 (mod 97) has a solution.
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Q: Given 3 * 4.52 = x(mod 53), Here x is equal
A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…
Q: Find the value of x if any. Show your complete solution. 1. (13 + x) = 3 mod 16 x = 2. (3x +…
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Q: The value of 52003 mod 7 is? (3 4 8
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Q: The order of 2 mod 17 is: a) 2 b) 4 c) 8
A: The order of a modulo p then is the least positive integer n such that an ≡ 1(mod p) where p is a…
Q: One of the following is a solution of 81x = 54 (mod 108) 43 47 45 42 has no solution
A: We are given the Equation :
Q: What is the result of: 6(40 – 13) (mod 11) The result is 8
A: Given 6(40-13)(mod 11)
Q: 27=31 mod 5 True or false and how you work the problem
A: The value of a mod b is equal to the remainder from the division of a by b. Given: 27 = 31 mod 5.
Q: Find the integer a such that a ≡ 71( mod 47) and -46 ≤ a ≤ 0 I need a better understanding of how…
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Q: I. Determine whether each of these integers are congruent to 3 mod 7. 1. 37 2. -17 3. 86
A: We will find out the required solution.
Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.
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Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 60
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Q: Suppose b is any integer. If b mod 12 = 7, what is 6b mod 12? In other words, if division of b by 12…
A: To determine the value of 6b mod(12) if b mod(12) = 7.
Q: Which of the following is not a possible value for y ≡≡ 17 mod 8 in the equation ? Group of answer…
A: Consider the given equation.
Q: Deduce the following statements: i) an odd prime number p is the sum of two squares of integers if…
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Q: Find the whole number of (3+12) =7 mod 10
A: The given equation (3x+12) ≡7 mod 10. Consider the following congruence equation (3x+12) ≡7 mod 10.…
Q: x is congruent to 21 mod 8. Then x is None of the option 29 16 24
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Q: Which is the solution of 71x congruent to 5 mod 142. 38 57 85 None of the above
A: To determine which of the given is the solution of 71x≡5mod142.
Q: 1 of the above number n, or (65) = Note that the other number is Therefore, we conclude that the…
A: Given that, number is 15 of the given number n
Q: Which one of the following is correct? a. 30 3 (mod 5) O b. 25 3 (mod 4) Oc. 31 3 (mod 7) O d. 20 3…
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Q: x = 13 (mod 39) have a solution. Select one: O True 2.
A: True
Q: 1)For each of the following, find an integer value x which satisfies the equation, or explain why…
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- A machine shop has an order for 12,000 pcs. of a machine part that requires anti-corrosive properties. Chromium steel alloy that cost Php 95.00/ kg or Nickel steel alloy that cost Php 85.00 /kg may be used. The weight per piece, production per day and tool bit replacement cost for Cr-alloy are: 0.25 kg, 75 pcs and Php 1,600 every 400 pcs. Produced. The respective date for Ni-alloy are 0.3 kg, 50 pcs. And Php 1,800.00 for every 300 pcs. produced. If the charge for the labor and other operating cost is Php 450.00/day with all other expenses being the same, determine which material should be used.One of your duties is the selection and disposal of boxes of obsolete files. According to regulations, ordinary files become obsolete after 24 months, confidential files after 36 months and classified files after 48 months. Which of the following boxes of files can be disposed of: A box containing ordinary files dated 26 months ago and classified files dated 34 months ago. A box containing ordinary files dated 38 months ago and confidential files dated 28 months ago.Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, ρ, σ) for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. Group of answer choices H0 : p = 0.0016H1 : p > 0.0016 H0 : p > 0.0016H1 : p ≤ 0.0016 H0 : p < 0.0016H1 : p ≥ 0.0016 H0 : p = 0.0016H1 : p < 0.0016
- Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.04 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.4 machines per hour. Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours Each employee…A researcher wants to find the effect of a special diet on systolic blood pressure. A sample of 7 adults was selected to start them on this diet for 3 months. Based on this information, can it be stated that systolic blood pressure changes with the special diet? Based on the findings of the test carried out, it is possible to conclude that...... A. systolic blood pressure does not change with special diet B. systolic blood pressure changes with special diet C. systolic blood pressure is lower with the special diet D. systolic blood pressure is higher with the special diet E. It is not possible to conclude anything regarding systolic blood pressure with the special dietA company receives a large shipment of bolts. The bolts will be used in an application that requires a torque of 100 J. Before the shipment is accepted, a quality engineer will sample 12 bolts and measure the torque needed to break each of them. The shipment will be accepted if the engineer concludes that fewer than 1% of the bolts in the shipment have a breaking torque of less than 100 J. Assume the 12 values(107, 109, 111, 113, 113, 114, 114, 115, 117, 119, 122, 124) are sampled from a normal population, and assume the sample mean and standard deviation calculated in the previous question (mean: 114, standard deviation: 5) are actually the population mean and standard deviation. Compute the proportion of bolts whose breaking torque is less than 100 J. Will the shipment be accepted? Express the answer as a percentage.(Round the final answer to two decimal places.)
- A company receives a large shipment of bolts. The bolts will be used in an application that requires a torque of 100 J. Before the shipment is accepted, a quality engineer will sample 12 bolts and measure the torque needed to break each of them. The shipment will be accepted if the engineer concludes that fewer than 1% of the bolts in the shipment have a breaking torque of less than 100 J. a) If the 12 values are 107, 109, 111, 113, 113, 114, 114, 115, 117, 119, 122, 124 compute the sample mean and sample standard deviation. b) Assume the 12 values are sampled from a normal population, and assume the the sample mean and standard deviation calculated in part (a) are actually the population mean and standard deviation. Compute the proportion of bolts whose breaking torque is less than 100 J. Will the shipment be accepted? c) What if the 12 values had been 108, 110, 112, 114, 114, 115, 115, 116, 118, 120, 123, 140? Use the method outlined in parts (a) and (b) to determine whether the…The problem of traffic delay in a highway can be studied in the following way. Let us assume that the probability of no traffic delay in one period, given no traffic delay in previous period, is 0.85 and that the probability of finding a traffic delay in one period, given a delay in the previous period is 0.75. The period of time is 30 minutes.1. Define the approach that should be used to solve the problem and identify all your inputs of the model6 2. Verify if one important assumption of the model should be questioned. Explain why.3. Assume that you are entering the traffic with your care in that highway and you receive a radio report of no traffic delay. What is the probability that for the next period there will be a delay.4. Assume that you are entering the traffic with your care in that highway and you receive a radio report of traffic delay. What is the probability that for the next hour there will be a delay. Use a tree diagram to answer the question.5. What is the probability…Filipina’s 3-year-old daughter, Manila, was brought to a clinic. The doctor diagnosed Manila with a severe dry cough. A mucolytic solution was prescribed and to be administered for seven days. The prescription states, “Mucolytic, XYZ Brand, 60 ml, dosage-1 teaspoon 1 hour before a meal, 3x a day”. Now, Filipina is skeptical of the dosage mentioned in the prescription regarding the proper amount of medicine to be administered to her daughter. If you are Filipina, how are you going to make sure that your daughter will not have an overdose or underdose of the medicine prescribed? Apply the principle of accuracy and precision in the problem.
- An explosion at a construction site could haveoccurred as the result of static electricity, malfunctioningof equipment, carelessness, or sabotage. Interviews withconstruction engineers analyzing the risks involved ledto the estimates that such an explosion would occur withprobability 0.25 as a result of static electricity, 0.20 as aresult of malfunctioning of equipment, 0.40 as a result ofcarelessness, and 0.75 as a result of sabotage. It is alsofelt that the prior probabilities of the four causes of theexplosion are 0.20, 0.40, 0.25, and 0.15. Based on all thisinformation, what is(a) the most likely cause of the explosion;(b) the least likely cause of the explosion?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? explainApply Rolle's theorem