Evaluate 5x2−9 when x=−2
1 answer:
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Answer:
a)
b)
c)
Step-by-step explanation:
Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.
To find : The following probabilities by summing the probabilities of the appropriate sample points ?
Solution :
The sample space is
S={HHH,HHT,HTT,HTH,TTT,TTH,THH,THT}
n(S)=8
A: At least one head is observed
i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}
n(A)=7
B: At least two heads are observed
i.e. B={HHH,HTT,TTH,THT}
n(B)=4
C: The number of heads observed is odd.
i.e. C={HHH,HTT,THT,TTH}
n(c)=4
a) Probability of A, P(A)
b) P(A or B)
Using formula,
(c) P((not A) or B or (not C))
A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}
not A = {TTT} = 1
B={HHH,HTT,TTH,THT}
C={HHH,HTT,THT,TTH}
not C = {HHT,HTH,THH,TTT} = 4
So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5
Answer:
Area of Shaded Region = (25π - 24) cm²
Step-by-step explanation:
See attachment
From the attached, the following observations are made;
Radius, r = 5cm
Base of triangles = 6cm.
Required
Area of shaded region.
If the distance between the base of the triangle to the outline of the circle is 1cm then the height of the triangle is 1cm less than the radius
Height = 5cm - 1cm
Height = 4cm
To calculate the area of the shaded region, we first calculate the area of the circle.
Area = πr²
Substitute 5 for r
Area = π * 5²
Area = π * 25
Area = 25π cm²
Then we calculate the area of both triangles
Area of 1 triangle is calculated as follows.
Area = ½ * base * height
Substitute 4 for height and 6 for base.
Area = ½ * 4 * 6
Area = 2 * 6
Area = 12cm²
Since both triangles are equal.
Area of two triangles = 2 * Area of 1 triangle
Area = 2 * 12cm²
Area = 24cm²
Having calculated the area of the circle and that of both triangles.
Area of shaded region = Area of Circle - Area of Triangles
Area of Shaded Region = 25π cm² - 24 cm²
Area of Shaded Region = (25π - 24) cm²
