A lot of water because it has to fill a barrel!!
Answer:
336.7 yards away from the cabin....
Step-by-step explanation:
The angle 30.7° is also the angle of the upper interior angle of the triangle (near the cabin)
Use the tan function:
opposite = 200 yards
adjacent = x
tan(30.7°) = (opposite / adjacent)
tan(30.7°) = 200 yards/x
x * tan(30.7°) = 200 yards
x = 200 yards/ tan(30.7°)
x= 200/ 0.594
x = 336.7 yards.
336.7 yards away from the cabin....
Answer:
The third score must be larger than or equal to 72, and smaller than or equal 87
Step-by-step explanation:
Let's name "x" the third quiz score for which we need to find the values to get the desired average.
Recalling that average grade for three quizzes is the addition of the values on each, divided by the number of quizzes (3), we have the following expression for the average:

SInce we want this average to be in between 80 and 85, we write the following double inequality using the symbols that include equal sign since we are requested the average to be between 80 and 85 inclusive:

Now we can proceed to solve for the unknown "x" treating each inaquality at a time:

This inequality tells us that the score in the third quiz must be larger than or equal to 72.
Now we study the second inequality to find the other restriction on "x":

This ine
quality tells us that the score in the third test must be smaller than or equal to 87 to reach the goal.
Therefore to obtained the requested condition for the average, the third score must be larger than or equal to 72, and smaller than or equal 87:
Answer
The distance from the house to the lake is (2.5 hr)*(48 mi/hr) = 120 miles. The rerurn trip would take (120 mi)/(40 mi/hr) = 3 hours. Distance equals rate times time, so the distance to the lake is 2 1/2 hours times 48 miles per hour.
I hope this helps