Sam scored 43, 48, and 42 points on three tests. How many points should he get on the fourth test to get an average score of 50?
(1 point) 83 points 67 points 45.75 points 44.33 points
2 answers:
So we know that an average is the sum of the scores divided by the number of scores that were added together. In this case we are going to be dealing with 4 tests. So let's say x is the score for our fourth test. We can create this equation:
So then we need to simplify the top:
Then multiply by 4 on both sides to get rid of the denominator:
Then solve for x:
So now we know that Sam needs to score a 67 on the fourth test to have an average score of 50.
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<h2>Hello!</h2>
The answers are:
First image:
The answer is the second option, the angles is
Second image:
The answer is the third option:
Third image:
The length of the adjacent leg is the first option:
Fourth image:
The answer is the fourth option,
Fifth image:
The answer is the fourth option, DF (hypothenuse) is equal to 25 units.
<h2>Why?</h2>To solve these problems, we need to use the following trigonometric identities and the Pythagorean Theorem, since we are working with right triangles.
Pythagorean Theorem:
So, solving we have:
First image:
We are given a right triangle that has the following lengths:
Then, calculating we have:
Hence, the answer is the second option, the angles is
Second image:
We are given a right triangle that has the following lengths:
Then calculating the sin ratio, we have:
Thence, the answer is the third option:
Third Image:
We are given the following information:
Then, calculating one of the angle legs, since both will have the same length, using the sine trigonometric identity, we have:
Hence, the answer is the first option the length of the adjacent leg is
Fourth image:
We are given the following information:
To calculate the angle at the B vertex, first, we need to calculate the angle at the C vertex, and then, calculate the B vertex by the following way:
Since the sum of all the interior angles of a triangle are equal to 180°, we have that:
So, calculating the angle at the C vertex, we have:
Then, calculating the angle at the B vertex, we have:
Hence, the answer is the fourth option,
Fifth image:
We are given the following information:
Now, to calculate the distance DF (hypothenuse) we need to use the Pythagorean Theorem:
Then, substituting we have:
Hence, the answer is the fourth option, DF (hypothenuse) is equal to 25 units.
Have a nice day!