Answer:

Step-by-step explanation:


Answer: 21
Step-by-step explanation:
Given : The scores on the midterm exam are normally distributed with

Let X be random variable that represents the score of the students.
z-score: 
For x=82

For x=90

Now, the probability of the students in the class receive a score between 82 and 90 ( by using standard normal distribution table ) :-

Now ,the number of students expected to receive a score between 82 and 90 are :-

Hence, 21 students are expected to receive a score between 82 and 90 .

Let's solve for value of values of x and y ~
According to Angle sum property of triangles :




Now, solve for y ~




Now, by the results we got, we can conclude that :
The two triangles are not similar because 70 + 58 + x = 180 means x = 52° and 70 + 49 + y=180 means y = 61°
Answer:
x = 29
Angle A = 46.4°
Angle B = 43.6°
Step-by-step explanation:
Since it is a right angle triangle, we can find x from pythagoras theorem;
x = √(20² + 21²)
x = √(400 + 441)
x = √841
x = 29
Using trigonometric ratios we can find angles A and B.
Opposite is 20
Adjacent is 21
Thus; opp/adj = tan B
20/21 = tan B
B = tan^(-1) 0.9524
B = 43.6°
Sum of angles in a triangle is 180°. Thus;
A = 180 - (90 + 43.6)
A = 46.4°