Tom and some friends went to a movie the show started at 2: 30 pm and ended at 4: 15 pm how long is the movie last

1 hour and 45 mins

Step-by-step explanation:

As mentioned,

Starting time = 2:30 PM

Ending time = 4:15 PM

The given time is in hours and minutes, to calculate the duration of movie, time should be converted into a same unite minutes.

1 hour = 60 minutes

Therefore,

2:30 = 2 hours and 30 mins = 2*60 + 30 mins = 150 mins

4:15 = 4 hours and 15 mins = 4*60 + 15 mins = 255 mins

The duration = Ending time - Starting time

=> 255 - 150

=> 105 mins

or

60 + 45

1 hour and 45 mins

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47