Answer: 1. 0.0256
2. 0.4096
Step-by-step explanation:
Binomial probability formula , to find the probability of getting x successes:
, where n= Total number of trials
p= Probability of getting success in each trial.
Let x be the number of customers will make purchase.
As per given , we have
p= 0.20
n= 4
1. The probability that 3 of the next 4 customers will make a purchase will be:-
![P(x=3)=(4)(0.20)^3(0.80)^{1}\ \ [\because\ ^nC_{n-1}=n]](https://tex.z-dn.net/?f=P%28x%3D3%29%3D%284%29%280.20%29%5E3%280.80%29%5E%7B1%7D%5C%20%5C%20%5B%5Cbecause%5C%20%5EnC_%7Bn-1%7D%3Dn%5D)
Hence, the probability that 3 of the next 4 customers will make a purchase = 0.0256
2. The probability that none of the next 4 customers will make a purchase will be :
![P(x=0)=(1)(0.80)^{4}\ \ [\because\ ^nC_{0}=1]](https://tex.z-dn.net/?f=P%28x%3D0%29%3D%281%29%280.80%29%5E%7B4%7D%5C%20%5C%20%5B%5Cbecause%5C%20%5EnC_%7B0%7D%3D1%5D)
Hence, the probability that none of the next 4 customers will make a purchase= 0.4096
19 is a prime number so 1, 19
hope this helps!
Answer:
m < A = 60º
m < B = 30º
Step-by-step explanation:
The given sides on this triangle are: 6, 
, and 12
Any triangle with the angles of 30º - 60º - 90º always has side lengths in this proportion:
x, 
, 2x
We can line this up with the given sides. If x is 6, then 2x would be 12.
x : : 2x = 6 : : 12
Angle B is across from 6, the shortest side. That also means that it corresponds to x, or the smallest angle in the proportion, 30º.
m < B = 30º
Solving for < A:
Method 1) Sum of Angles in a Triangle
Since we already know that one angle is right and therefore 90º and m < B is 30º, we can subtract these from the total sum of angle measures in a triangle to get the last angle, < A.
180º - 90º - 30º = 60º
m < A = 60º
Method 2) Using the second part of the proportion
Since m < A is across from the second largest side, we know that it is equal to ( in this question) or 60º in the angle proportion.
This means that m < A = 60º
Let me know if you have any questions!
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
