The area of any triangle is A = (1/2) (base) (height).
If the right triangle is not sitting
on its hypotenuse, then one leg
is the base, and the other leg is
the height: A = (1/2) (base leg) (height leg) .
If the triangle is isosceles, then
the legs are equal: A = (1/2) (either leg)²
You said the area is 18 in²: 18 in² = (1/2) (leg²)
Multiply each side by 2 : 36 in² = leg²
Square root each side: 6 in = leg
Answer:
Step-by-step explanation:
Sum of angles of a triangle = 180
So, 56 + 58 + x = 180
114 + x = 180
x = 116
Now ∠ 1 + ∠x = 180 [ straight line angles]
∠ 1 + 66 = 180
∠1 = 180 - 66 = 114°
OR
You can use the rule : Exterior angle = sum of 2 interior opposite angles.
56 + 58 = ∠1
114 = ∠1
If we consider that the figure is a square and the white region of the figure is a circle, the area of the shaded region is:
Answer:
a = 0.05
b = 0.028
c =0.014
Step-by-step explanation:
Given that;
inspector A visually inspected 1000 ceramic mugs and found flaws in 36 of them.
Let X represent Inspector A
P(X) =
= 0.036
inspector B visually inspected 1000 ceramic mugs and found flaws in 42 of them.
Let Y represent Inspector B
P(Y) =
= 0.042
A total of 950 mugs were found to be good by both inspectors.
i.e (X∩Y)' = 950
P (X∩Y)' =
= 0.095
We are tasked to find :
a) the probability that a flaw was found in this mug by at least one of the two inspectors [i.e P (X∪Y)]
b) the probability that flaws were found in this mug by both inspectors.
[i.e P ( X∩Y)]
c) the probability that a flaw was found by inspector B but not by inspector A. [i.e P (X) - P ( X∩Y)]
With a);
P (X∪Y) = 1 - P(A∩B)'
P (X∪Y) = 1 - 0.950
P (X∪Y) = 0.05
b)
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.036 + 0.042 + 0.05
P(X∩Y) = 0.028
c)
P (X) - P ( X∩Y) = 0.042 - 0.028
P (X) - P ( X∩Y) = 0.014
Therefore;
the probability that a flaw was found in this mug by at least one of the two inspectors = 0.05
the probability that flaws were found in this mug by both inspectors = 0.028; &
the probability that a flaw was found by inspector B but not by inspector A = 0.014