You arrive at a bus stop at 10 o’clock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If, at 10:15, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

A) 2/3

B) 1/3

Step-by-step explanation:

A) Since the bus arrives uniformly at the bus stop between 10 and 10:30.Let X denote the arrival of a bus at a bus stop. Thus X is a uniform tandom variable having a density function;

f(x) = 1/30 : x ∈ [0,30]

Now, probability that a passenger arriving at the bus stop between 10 and 10:30 will have to wait more than 10 minutes can be expressed as;

P[x > 10] = ∫f(x)•dx at boundary of 30 and 10

Thus,

∫(1/30)•dx at boundary of 30 and 10

P[x > 10] = (1/30)•x at boundary of 30 and 10

P[x > 10] = (1/30)(30) - (1/30)(10)

P[x > 10] = 1 - 1/3 = 2/3

B) The probability that the passenger will have to wait additional 10 minutes is given as;

P[X > 25 | X > 15] =P[X > 25 ∩ X > 15]

= (P[X > 25])/(P[X > 15])

= [∫(1/30)•dx at boundary of 30 and 25]/ [∫(1/30)•dx at boundary of 30 and 15]

= [(1/30)•x at boundary of 30 and 25]/[(1/30)•x at boundary of 30 and 15]

= [(30/30) - (25/30)]/[(30/30) - (15/30)]

= (1 - 5/6)/(1 - 1/2)

= 1/6 ÷ 1/2 = 1/3

∩

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

change of stock price/initial stock price on friday * total stock value = change of stock value

0.89/73.73 *x = 42.72

x=3539.04 = total stock value at initial stock price on friday .

total stock value at initial stock price on friday/ initial stock price on friday = number of shares

3539.04/73.73 = 48 shares

they own 48 shares of this stock