For this exercise assume that the matrices are all nxn. The statement in this exercise is an implication of the form "If "statement 1", then "statement 2"." Mark an implication as True if the truth of "statement 2" always follows whenever "statement 1" happens to be true. Mark the implication as False if "statement 2" is false but "statement 1" is true. Justify your answer. If A is an nxn matrix, then the equation Ax = b has at least one solution for each b in R". Choose the correct answer below. A. The statement is true. By the Invertible Matrix Theorem, Ax = b has at least one solution for each b in R^ for all matrices of size nxn. B. The statement is false. By the Invertible Matrix Theorem, Ax = b has at least one solution for each b in R" only if a matrix is invertible. O C. The statement is true. By the Invertible Matrix Theorem, if Ax = b has at least one solution for each b in R", then the matrix is not invertible.

Q: 2) tan C B 28 21 35

A: In right angle triangle  tan thetha = perpendicular/Base

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Q: Question 20 ) dm: -2m cosh2m dm A) True B) False

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A: Let the random variable X be the number of times the fair six-sided die rolls the number 1 out of 10…

Q: Let a = (1,3,–2), b=(2,2, –1) . 2. Find la- 36| a) b) a•b c) The angle (in degrees) between a and b

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Q: XUIS I the exact value f touQx) tnd

A: Solution: The objective is to find the value of tan(2x)

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Q: 4) tan X Y_27 36 45

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Q: e) 27,9,3,1,_ How does it change

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Q: 8) Find the length of SB B 12. T 18 C 6. U

A: Finding BU and then SB

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A: As the question asking the value of M For different value of  r= 0.3 , 0.4, 0.5, 0.6, 0.7 and  n= 1,…

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Q: 5) x, x – 2 X, X

A: we know that L.C.M. of two prime number is given by product of numbers here, x and x-2 are prime…

Q: 20. If segment AC is 28, what is x? 3x + 2 2x - 4 B A Answer:

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A: Given Cot π We have to find the value

Q: Find m BAD C. E/62

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Q: Show that AC = BC, even though A ≠ B.

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Q: 11) Find mZB 101 27 ft 44 ft B)

A: Here we have to find angle B in the given figure.

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Q: Given the graph of y = 5* and the point (a, b) on the graph, describe b in terms of a. b =

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Q: A possible graphical representation of (x – 1)², (y + 2)² = 1 a With a> b > 0 A) B)

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Q: 10) 34, 26, 18, 10, ... 11) 29, 32, 35, 38, ...

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A: The slope of a function at a point is the rate of change of the function with respect to the change…

Q: Calculate             a)12/7 x  (-2 2/3) ÷ 13/7  + 11/3 =

A: Given system is: A=127×-223÷137+113 Simplifying it: A=97×-83÷107+43

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!