In this problem, we need to find the measures of all three angles in a triangle.
Let the angles be represented as p, q, and r.
Given that the measure of angle q is one-third of angle p, we have:
The measure of angle r represents the difference between angles p and q, which gives us:
(Equation 1)
Applying the triangle angle sum property, it is known that the cumulative angle measure in a triangle is 
p+q+r=
Substituting the value for r from Equation 1, we find:
p+q+p-q=
2p=
Thus, p=
Since
Since angle r is equal to p-q, we can conclude:
r =
Refer to the diagram illustrated below.
The specified constraints are
(a) y ≥ 24 ft
(b) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The shaded area represents the permissible region.
A (0, 33) meets all criteria
B (4, 36) does not satisfy condition (d)
C (4.8, 30.5) meets all criteria
D (9, 26) does not meet condition (c)
E (2, 22) does not satisfy condition (a)
Response:
The valid points are A and C.
This slope can be described as passing through the origin or more formally, the point (0,0).
The likelihood of observing a sample mean that is less than 18 hours is 0.0082. \nTo evaluate this probability, we calculate the z-score for a sample mean of 18. Accordingly, the probability of getting a sample mean below 18 hours becomes P(z<z(18)). \nThe z-score is calculated as follows: \nz(18) = [(X - M) / s] where: \n- X is the sample mean (18 hours) \n- M is the average hours dentists devote weekly to fillings (20 hours) \n- s is the standard deviation (10 hours) \n- N is the sample size (144) \nSubstituting the numbers leads to: \nz(18) = [(18 - 20) / (10/sqrt(144))]. Using the z-table, we find that P(z<z(18)) is 0.0082.
