A lighthouse is set 10 meters back from the edge of the shoreline, and it's beacon is 52 meters above sea level. Lucy can see the beacon from her ship, and the of elevation is 18 degrees. Her eyes are 12 meters above sea level. How far is the ship from the shoreline to the nearest meter?

The distance of the ship to the shoreline is 113 meters

Step-by-step explanation:

Here we have the following information

Location of lighthouse = 10 m back from the edge of the shoreline

Height of beacon above sea level = 52 m

Level of the eyes of Lucy above sea level = 12 m

Angle of elevation of the beacon from Lucy = 18°

Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °

Therefore, from

We have

0.325 =

Where the adjacent side is the distance of the ship from the lighthouse

Adjacent side = 40/0.325 = 123.107 meters

We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113  meters to the nearest meter.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.