Answer:
The Estimate the number of students who took the scores between 82 and 98 = 16
Step-by-step explanation:
<u><em>Explanation</em></u>:-
Given data The scores on a math test are normally distributed with a mean μ = 74
standard deviation of Population
S.D (σ) = 8
Let 'x' be the random variable of Normal distribution
<u><em>case(i)</em></u>:- when x = 82
<u><em>case(ii)</em></u>:- when x = 98
The probability that test scores between 82 and 98.
P(82≤x≤98) = P(1≤z≤3)
= P(z≤3) - P(z≤1)
= 0.5+A(3)-(0.5+A(1))
= A(3) -A(1)
= 0.4986 - 0.3413
= 0.1573
<u><em>Final answer</em></u>:-
The Estimate the number of students who took the scores between 82 and 98
= 100 X 0.1573 = 15.73 ≅16
Given:
Consider the below figure attached with this question.
Angles of a triangle are x, y and z.
To find:
The values of x, y and z.
Solution:
If two angles are linear pair, then their sum is 180 degrees.
Similarly,
According the the angle sum property, the sum of all angles of a triangle is 180 degrees.
Divide both sides by -5.
The value of x is 36.
Now,
Therefore, the values of x, y and z are 36, 67 and 77 respectively.
Answer:
Identity (a) can be re-written as
which we already proven in another question, while for idenity (b)
step A is simply expressing each function in terms of sine and cosine.
step B is adding the terms on the LHS while multiplying the one on RHS.
step C is replacing the term on the numerator with the equivalent from the pithagorean identity