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D and E are points on sides of AB and BC respectively of ∆ABC such that AD:DB= 2:3 and BE=4÷3 EC. If DK||AE and AE and CD intersect at P, Find the ratio of CP:PD

if in the process of rubbing the lenses of the eyeglasses, 6.28 x 1010 electrons were tranferred.


A. What is the charge of the lenses and the nylon cloth?

B. What is the change in their masses?


How does an increase in the value of the pound sterling


affect American businesses?

4. Calculate the concentration of each ions remaining in the solution when 100.0mL of 0.20M Silver Nitrate solution reacts with 100.0mL of 0.15M Calcium Chloride solution. A. 0.050M CI,0.075M Ca ,0.100M NO. B. 0.075M CL,0.050M Ca²+ ,0.100M NO₂. C. 0.100M CI,0.075M Ca² ,0.050M NO


If p(A) = 0.6 and k is the number of successes of A in n trials


(A) Show that p {550<= k <= 650} = 0.999 , for n = 1000


(B) Find n such that p{0.59n <= k <= 0.61n} = 0.95

Solve the following initial value problem using Laplace transform. y''+16y = 2 sin 4t, y(0)=-1/2; y'(0)=0 


Does the sequence 3+ (-1)^n converge to 2. Justify

a, b, and c have units of meters, s = a, what is [s] ?

a, b, and c have units of meters, s = a + b, what is [s] ?

a, b, and c have units of meters, s = (2a + b)b, what is [s] ?

a, b, and c have units of meters, s = (a + b) 3/c, what is [s] ?

a, b, and c have units of meters, s = (3a + 4b) 1/2/9c2, what is [s] ?


Assuming a message “Exams!” is to be transmitted over a network. If the message is made up of strings with the given probability: e = 0.4, x = 0.1, a = 0.2, m = 0.1, s = 0.1, and ! = 0.1, derive:



a. The codeword using Arithmetic coding procedures



b. The original message by decoding the codeword in (a).




a, b, and c have units of meters, s = a, what is [s] ?


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