Answer:
36°
Step-by-step explanation:
By remote interior angle theorem:
b + 81° = 117°
b = 117° - 81°
b = 36°
Let KLMN be a trapezoid (see added picture). From the point M put down the trapezoid height MP, then quadrilateral KLMP is square and KP=MP=10.
A triangle MPN is right and <span>isosceles, because
</span>m∠N=45^{0}, m∠P=90^{0}, so m∠M=180^{0}-45^{0}-90^{0}=45^{0}.Then PN=MP=10.
The ttapezoid side KN consists of two parts KP and PN, each of them is equal to 10, then KN=20 units.
Area of KLMN is egual to

sq. units.
Answer:
The surface area is 78 unit square.
Step-by-step explanation:
Given : The surface area for a rectangular prism with a square base is
.
To find : What is the surface area if s=3 and h=5?
Solution :
The surface area for a rectangular prism with a square base is 
Substitute, s=3 and h=5




Therefore, The surface area is 78 unit square.
Answer:
a. 0.76
b. 0.23
c. 0.5
d. p(B/A) is the probability that given that a student has a visa card, they also have a master card
p(A/B) is the probability that given a student has a master card, they also have a visa card
e. 0.35
f. 0.31
Step-by-step explanation:
a. p(AUBUC)= P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)
=0.6+0.4+0.2-0.3-0.11-0.1+0.07= 0.76
b. P(AnBnC')= P(AnB)-P(AnBnC)
=0.3-0.07= 0.23
c. P(B/A)= P(AnB)/P(A)
=0.3/O.6= 0.5
e. P((AnB)/C))= P((AnB)nC)/P(C)
=P(AnBnC)/P(C)
=0.07/0.2= 0.35
f. P((AUB)/C)= P((AUB)nC)/P(C)
=(P(AnC) U P(BnC))/P(C)
=(0.11+0.1)/0.2
=0.21/0.2 = 0.31