<h3>
▄▄▄▄▄▄▄▄▄▄▄▄▄▄</h3>
We know that, Two angles are said to be complementary, if the sum of their measures is 90°.
<u>According to the Question</u>,
⇒ ∠ABD + ∠DBC = 90°
⇒ (2x + 30)° + (3x + 20)° = 90°
⇒ 2x + 30° + 3x + 20° = 90°
⇒ 5x + 50° = 90°
⇒ 5x = 90° - 50°
⇒ 5x = 40°
⇒ x = 40°/5
⇒ x = 8
<u>So</u>, <u>t</u><u>he measure of each angle will be</u>,
⇒ ∠ABD = (2x + 30)°
= 2 × 8 + 30°
= 16 + 30°
= 46°
⇒ ∠DBC = (3x + 20)°
= 3 × 8 + 30°
= 24 + 30°
<h3>
= 54° ▄▄▄▄▄▄▄▄▄▄▄▄▄▄</h3>
Answer:
a) p=0.2
b) probability of passing is 0.01696
.
c) The expected value of correct questions is 1.2
Step-by-step explanation:
a) Since each question has 5 options, all of them equally likely, and only one correct answer, then the probability of having a correct answer is 1/5 = 0.2.
b) Let X be the number of correct answers. We will model this situation by considering X as a binomial random variable with a success probability of p=0.2 and having n=6 samples. We have the following for k=0,1,2,3,4,5,6
.
Recall that 
In this case, the student passes if X is at least four correct questions, then
c)The expected value of a binomial random variable with parameters n and p is ![E[X] = np](https://tex.z-dn.net/?f=E%5BX%5D%20%3D%20np)
. IN our case, n=6 and p =0.2. Then the expected value of correct answers is 
First we calculate 20% of the price:
20% of 30$ is 0.2*30$=6$.
Then we subtract 6$ (that is 20% of the price) from 30$, and get 24$.
Thus, the sale price is 24$
You need to give us a picture of the slope
