Math Answers

Which of the following represent the solution of the differential equation d^2y/dx^2+4y=0

5tan2x+5cos2x
5sin2x+4cos2x
5sin2x−3cos2x
5sin^22x−3cos2x

If x=a*sinQ + b*cosQ and y=a*cosQ + b*sinQ

Prove that (x^2+y^2)(a^+y^2) - 4abxy = (a^2 - b^2)^2

At a party, you and your friend are both eying the last slice of pizza. To settle the matter, you agree on the following dice game: each of you is going to roll a die; if the highest number rolled by either one of you is a 1, 2, 3 or 4, then Player 1 wins. If the highest number is a 5 or a 6, then Player 2 wins. Assuming that you really want that last slice of pizza would you rather be Player 1 or Player 2 to maximize your chance of winning? Explain your choice.

Let X have a standard gamma distribution with
α=7
. Compute P(X<4 or X>6)
0.912
0.625
0.812
0.713

10 Let X = the time between two successive arrivals at the drive –up window of a bank. If X has a exponential distribution with h=1 ( which is identical to a standard gamma distribution with a=1). Compute the standard deviation of the time between successive arrivals
2
1
3
4

In a study of plants, five characteristics are to be examined. If there are six recognizable differences in each of four characteristics and eight, recognizable difference in the remaining characteristics. How many plants can be distinguished by these five characteristics?
120
150
80
70

8 Let X have a uniform distribution on the interval [A,B]. compute V(X)
B−A12−−√
A−B2√
B+A12−−√
BxA2√

Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation
0.132
0.121
0.112
0.651

4 The error involved in making a certain measurement is a continuous rv X with pdf
f(x)={0.09375(4−x2),−2≤x≤2
0,otherwise
compute P(-1<X
0.6875
0.3425
0.3662
0.5522

1 A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(B|A)?
0.027
0.064
0.072
0.083

2 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective.
0.677
0.512
0.578
0.617

Matti wants to cover a 6 mile course in 1 hour by running part of the course and walking the rest. he also wants to make a 5-minuet stop for water. He runs at 8mi/h and walks 3mi/h.
What is the minimum distance that mattwill need to run to complete the course in 1 hour?

cos55 degree ka solucation with proof giving the answer fast

Let (x1,x2,x3) and (y1,y2,y3) represent the coordinates with respect to the bases
B1 = {(1, 0, 0),(0, 1, 0),(0, 0, 1)}, B2 = {(1, 0, 0),(0, 1, 2),(0, 2, 1)}. If
Q(X) = 2x1^2+ 2x1x2 − 2x2x3 +x2^2+x3^2, find the representation of Q in terms of
(y1,y2,y3).