We can treat each distance distance traveled by the four wheelers are vectors. Their sum must be zero since the last four wheeler truck ends up where the first four wheeler truck started
d1∠1 + d2∠2 + d3∠3 + d4∠4 + d5∠5 = 0
d5∠5 = - (d1∠1 + d2∠2 + d3∠3 + d4∠4)
Since we don't know the speed of the fifth wheeler, we just add the angles and equate it to 360
20 + 30 + 0 + -40 + ∠5 = 360
∠5 = 350 or -10
The fifth wheeler must travel at an angle of -10 degrees.
480700. The different combinations of students that could go on the trip with a total of 25 student, but only 18 may go, is 480700.
The key to solve this problem is using the combination formula 
. This mean the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
The total of students is n and the only that 18 students may go is r:
Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.
<h3>What is a slope?</h3>
The slope is given by the <u>vertical change divided by the horizontal change</u>, and it's also the tangent of the angle of depression.
In this problem:
- The vertical change is of 1 m.
- The horizontal change is the length l.
Hence:
tan(30º) = 1/l
l = 1/tan(30º)
l = 1.73.
More can be learned about the slope concept at brainly.com/question/18090623
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The probability that you will guess the first answer correctly = 1/2 = 0.5
The probability that you will guess the second answer correctly = 1/2 = 0.5
The probability that you will guess the third answer correctly = 1/2 = 0.5
The probability that you will guess all three answers correctly is
(0.5) x (0.5) x (0.5) = 0.125 = 12.5% .
============================
Here are all the ways your answer sheet could wind up:
(R = a right answer. W = a wrong answer.)
W W W
W W R
W R W
W R R
R W W
R W R
R R W
R R R
Number of possible ways to score 0 right out of 3 questions: 1 way
Number of possible ways to score 1 right out of 3 questions: 3 ways
Number of possible ways to score 2 right out of 3 questions: 3 ways
Number of possible ways to score 3 right out of 3 questions: 1 way
Statistically, if your answers are all pure guesses,
then on the average, the score you expect is
(0 + 33-1/3 + 33-1/3 + 33-1/3 + 66-2/3 + 66-2/3 + 66-2/3 + 100) / 8
= 400 / 8
= 50% .
If you're happy with that score, great !
Go to the movies the night before the test,
and start guessing.
