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All strictly monotonically decreasing sequences are convergent.



True or false with full explanation

Using data from the Economic Report of the President, calculate velocity For the M2 definie of the money fupply in the past five years Does velocity appear to be constant


Determine whether each of the following statements is a proposition or not. If it is, give its truth value.


p: Mindanao is an island in the Philippines.


q: Find a number which divides your age.


r: My seatmate will get a perfect score in the Logic exam.


s: Welcome to the Philippines!

Jamylla and Janylla are on a hike. Both hikers begin a trip by walking, the first leg A: 2.65 km, 140° from their base


camp, on their second leg B: 4.77 km, 252° and to complete their final leg C: 3.18 km, 332°. What is the magnitude and


direction of their final position from their base camp? Apply polygon method and component method and compare their


results.


For all even integral value of n, lim (x+1)^-n


n to ∞


Exist or not


True or false with full explanation



if two varieties are tested in 5 different locations for their yeld proformance in (q/ha) with the follo results.Find out which variety which is more consistent over the location by comparing their CV value?


Variety A -12,8,10,11,14


Variety B - 15,9,7,12,12

The combination is connected to an external resistance of 24Ω.



Calculate;



a) the intensity of the current?




(2 mks)



b) the intensity of current if the cells are combined in parallel




(3 mks)



c) the intensity of current if the combination has two parallel series of two cells each.

From a population of 700 plants, 500 plants are healthy, rest are unhealthy. For a sample size of 10 plants, calculate the probabilities that—(a) Exactly 3 are unhealthy (b) at least 3 plants are unhealthy (c) at most 3 plants are unhealthy (d) Exactly 3 are healthy (e) None healthy?

Calculate the mean and the variance of the discrete random variable X which can take only values 1, 2, and 3, given that P(1) = 10/33, P(2) = 1/3, and P(3) = 12/33.




P(X) X-P(X) X²P(X)


























Solve for the mean and the variance of the discrete random variable X which can take only the values 2, 4, 5 and 9, given that P(2) = 9/20, P(4) = 1/20, P(5) = 1/5 and P(9) = 3/10.



X P(X) X∙P(X) X2∙P(X)




























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