Find the exact value of sin(x+y) if cos x = 8/17 and sin y= 12/37

621 /629

Step-by-step explanation:

The formula for sin (x+y) is sin x cosy + cos x sin y.

                                                      opposite side

If sin y  12/37 (which is equal to )  we can find the length

                                                        hypotenuse

of the adjacent side as follows.  Representing the adjacent side by x, we get

37^2 = x^2 + 12^2 (following the Pythagorean Theorem).

Then 1369 = x^2 + 144, or x^2 = 1225, so that x must be +√1225, or +35.

Thus, the cosine of y is (adj side) / (hypo) = 35/37.

                                                    √(17^2 - 8^2)       √225

Similarly, the sine of angle x is =   = 15/17

                                                             17                     17

In summary, sin x = 15/17; cos x = 8/17; sin y = 12/37 and cos y =35/37.

We now substitute these values into the formula

sin (x+y) is sin x cosy + cos x sin y:

sin (x+y) = (15/17)(35/37) + (8/17)(12/37)

                      525               96               621

              = + = = 621 /629

                      629              629              629

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560