Answer:
60 cm³
Step-by-step explanation:
Applying,
Volume (V) = Area of the base(A)×Height(h)
V = Ah................ Equation 1
From the diagram,
A = Area of Trapezium
A = 1/2(a+b)c............. Equation 2
Substitute equation 2 into equation 1
V = [1/2(a+b)c]h........... Equation 3
Given: a = 3 cm, b = 7 cm, c = 3 cm, h = 4 cm
Substitute these values into equation 3
V = [3(3+7)/2]4
V = (3×10/2)4
V = (3×5)4
V = 15×4
V = 60 cm³
Answer:
x = 3
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle:
15x + 5 + 22x + 4 = 120 add like terms
37x + 9 = 120 subtract 9 from both sides
37x = 111 divide both side by 37
x = 3 and to find the angles replace x with 3 in given expressions
Answer:
All you do is
Step-by-step explanation:
1/4 x 6
Then simplefiy your answer
Answer:
a.
![1 - P(A \cup B ) = 1 - 0.8 = 0.2](https://tex.z-dn.net/?f=1%20-%20P%28A%20%5Ccup%20B%20%29%20%3D%201%20-%200.8%20%3D%200.2)
b.
![P(A \cap B) = P(A) + P(B) - P(A \cup B ) = 0.5 + 0.45 - 0.8 = 0.15](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%20%3D%20P%28A%29%20%2B%20P%28B%29%20%20-%20P%28A%20%5Ccup%20B%20%29%20%20%20%3D%200.5%20%2B%200.45%20-%200.8%20%3D%200.15)
c.
![P(A \cap B^c ) = P(A) - P(A \cap B) = 0.5 - 0.15 = 0.35](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%5Ec%20%29%20%3D%20%20P%28A%29%20-%20P%28A%20%5Ccap%20B%29%20%3D%200.5%20-%200.15%20%3D%200.35)
d.
They are not, the intersection is not 0.
Step-by-step explanation:
a.
The probability that the shopper has neither type of card is the probability of the complement of the union, therefore it would be
b.
That's probability of the intersection of the events. For that we use the following formula
![P(A \cup B ) = P(A) + P(B) - P(A \cap B)](https://tex.z-dn.net/?f=P%28A%20%5Ccup%20B%20%29%20%20%3D%20P%28A%29%20%2B%20P%28B%29%20%20-%20P%28A%20%5Ccap%20B%29)
Therefore
![P(A \cap B) = P(A) + P(B) - P(A \cup B ) = 0.5 + 0.45 - 0.8 = 0.15](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%20%3D%20P%28A%29%20%2B%20P%28B%29%20%20-%20P%28A%20%5Ccup%20B%20%29%20%20%20%3D%200.5%20%2B%200.45%20-%200.8%20%3D%200.15)
c.
That's the probability of A intersection the complement of B.
For that, first of all remember that
![A = (A \cap B) \cup (A \cap B^c)](https://tex.z-dn.net/?f=A%20%3D%20%20%28A%20%5Ccap%20B%29%20%5Ccup%20%28A%20%5Ccap%20B%5Ec%29)
Therefore
![P(A) = P(A \cap B) + P(A \cap B^c)](https://tex.z-dn.net/?f=P%28A%29%20%3D%20P%28A%20%5Ccap%20B%29%20%2B%20P%28A%20%5Ccap%20B%5Ec%29)
Therefore
![P(A \cap B^c ) = P(A) - P(A \cap B) = 0.5 - 0.15 = 0.35](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%5Ec%20%29%20%3D%20%20P%28A%29%20-%20P%28A%20%5Ccap%20B%29%20%3D%200.5%20-%200.15%20%3D%200.35)
d.
They are not, the intersection is not 0.