The measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°
<u>Explanation:</u>
A polygon has three or more sides.
Example:
Triangle has 3 sides
Square has 4 sides
Pentagon has 5 sides and so on.
27)
In a quadrilateral ABCD, the measure of ZA, ZB, ZC and ZD are the ratio 1 : 2 : 3 : 4
We know,
sum of all the interior angles of a quadrilateral is 360°
So,
x + 2x + 3x + 4x = 360°
10x = 360°
x = 36°
Thus, the measure of four angles would be:
x = 36°
2x = 2 X 36° = 72°
3x = 3 X 36° = 108°
4x = 4 X 36° = 144°
Therefore, the measures of the four angles of quadrilateral ABCD are 36°, 72°, 108° and 144°
Answer:



Step-by-step explanation:
Given 
(A) 
We know that Sin(A + B) = SinA cosB + cosAsinB
Substituting in the above formula we get:


(B) Cos(A + B) = CosAcosB - SinASinB




(C) Tan(A + B) = 
From the above obtained values this can be calculated and the value is
.
X² - 4x + 4 = 0
(x-2)(x-2) = 0
the equation has one root mainly 2 with multiplicity 2
the answer is a
Answer: Required mean would be 15.
Step-by-step explanation:
Since we have given that
Number of girls G= 75
Number of boys B= 100
Probability that girls smoke = P₂ = 0.20
Probability that girls don't smoke = P'₂=1-0.20=0.80
Probability that boys smoke = P₁ = 0.30
Probability that boys don't smoke = P'₁=1-0.30=0.70
We need to find the mean of the sampling distribution of the difference in the sample proportion of girl smokers and boys smokers.
So, it becomes,
![E[P_1-P_2]=E[P_1]-E[P_2]\\\\=B\times P_1-G\times P_2\\\\=100\times 0.30-75\times 0.20\\\\=30-15\\\\=15](https://tex.z-dn.net/?f=E%5BP_1-P_2%5D%3DE%5BP_1%5D-E%5BP_2%5D%5C%5C%5C%5C%3DB%5Ctimes%20P_1-G%5Ctimes%20P_2%5C%5C%5C%5C%3D100%5Ctimes%200.30-75%5Ctimes%200.20%5C%5C%5C%5C%3D30-15%5C%5C%5C%5C%3D15)
Hence, required mean would be 15.