Andrew is 12 years old and James is 52 years old. In how many years will James be three times as old as Andrew?
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The probability that an adult likes soccer is aged between 18–30 will be 44.4%.
We have an adult who likes soccer.
We have to determine the probability the adult is aged 18–30.
<h3>What is Probability?</h3>The formula to calculate the probability of occurrence of an event 'A' can be written as -
P(A) =
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes.
According to question, we have an adult likes soccer.
The answer to this question is based on the hypothesis that the adults between 18 - 30 are highly energetic. To be more precisely - the adults in the range 18 - 24 and 24 - 30 are highly energetic and full of stamina. Above the age 30, the number of adults who like soccer will start to decrease and will hit nearly zero between the age range of 55 - 65 as the adults in this age group found it very difficult to even walk.
Mathematically -
The probability of an event A = an adult likes soccer is aged between 18–30 will be the highest value among the ones mentioned in options.
Hence, the probability that an adult likes soccer is aged between 18–30 will be 44.4%.
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Answer:
Please find attached the required plot accomplished with an online tool
Part A:
1/4
Part B:
P''(-1, 0), Q''(0, -1), and R''(2, -1)
Part C:
Triangle PQR is similar to triangle P''Q''R'' but they are not congruent
Step-by-step explanation:
Part A:
Triangle ΔPQR has vertices P(4, 0), Q(0, -4), R(-8, -4)
Triangle ΔP'Q'R' has vertices P'(1, 0), Q'(0, -1), R'(-2, -1)
The dimensions of the sides of the triangle are given by the relation;
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates on the ends of the segment
For segment PQ, we place (x₁, y₁) = (4, 0) and (x₂, y₂) = (0, -4);
By substitution into the length equation, we get;
The length of segment PQ = 4·√2
The length of segment PR = 4·√10
The length of segment RQ = 8
The length of segment P'Q' = √2
The length of segment P'R' = √10
The length of segment R'Q' = 2
Therefore, the scale factor of the dilation of ΔPQR to ΔP'Q'R' is 1/4
Part B:
Reflection of (x, y) across the y-axis gives;
(x, y) image after reflection across the y-axis = (-x, y)
The coordinates after reflection of P'(1, 0), Q'(0, -1), R'(-2, -1) across the y-axis is given as follows;
P'(1, 0) image after reflection across the y-axis = P''(-1, 0)
Q'(0, -1) image after reflection across the y-axis = Q''(0, -1)
R'(-2, -1) image after reflection across the y-axis = R''(2, -1)
Part C:
Triangle PQR is similar to triangle P''Q''R'' but they are not congruent as the dimensions of the sides of triangle PQR and P''Q''R'' are not the same.
