IT is c i checked using all the steps
6. 16-4=12 divided by 2 equals 6 ;)
Is x = 5/8 in the other way is x = 0.625
Let Xi be the random variable representing the number of units the first worker produces in day i.
Define X = X1 + X2 + X3 + X4 + X5 as the random variable representing the number of units the
first worker produces during the entire week. It is easy to prove that X is normally distributed with mean µx = 5·75 = 375 and standard deviation σx = 20√5.
Similarly, define random variables Y1, Y2,...,Y5 representing the number of units produces by
the second worker during each of the five days and define Y = Y1 + Y2 + Y3 + Y4 + Y5. Again, Y is normally distributed with mean µy = 5·65 = 325 and standard deviation σy = 25√5. Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X −Y > 0). It is a quite surprising fact that the random variable U = X−Y , the difference between X and Y , is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σU, where σ2 U = σ2 x+σ2 y = 400·5+625·5 = 1025·5 = 5125. It follows that σU = √5125. A reference to the above fact can be found online at http://mathworld.wolfram.com/NormalDifferenceDistribution.html.
Now everything reduces to finding P(U > 0) P(U > 0) = P(U −50 √5125 > − 50 √5125)≈ P(Z > −0.69843) ≈ 0.757546 .
Answer:
Since the legs of the right triangle measure x + 1 and x + 15, respectively, and since the hypotenuse measures x + 17, the Pythagorean Theorem can be used as follows: (x + 1)2 + (x + 15)2 = (x + 17)2. This equation becomes (x2 + 2x + 1) + (x2 + 30x + 225) = x2 + 34x + 289, which then becomes 2x2 + 32x + 226 = x2 + 34x + 289. When all the terms are moved to one side, the equation becomes x2 – 2x – 63 = 0, and when the left side of the equation is factored, it becomes (x – 9)(x + 7) = 0. At this point, it seems as if x can equal 9 or –7, but if x were –7, one of the legs would have a negative length, and this is impossible. For this reason x equals 9, and the legs of the triangle measure 10 and 24, respectively, while the hypotenuse measures 26. Since cosine is
length of adjacent leg
length of hypotenuse
, the cosine of angle C is
24
26
, or
12
13
.