1. Explain the similarities and differences between the graphs of y = 5x and y = 3x. Include domain, range, intervals of increas
1 answer:
Answer:
1. Equal domain, range, interval of increase and lack of asymptotes
The difference is the difference in slope
2. Equal domain, range, no increase or decrease (constant value) and lack of asymptotes
The difference is the difference in the y-intercept
Step-by-step explanation:
1. The similarities between the functions, y = 5·x and y = 3·x are;
a. The domain of y = 5·x is the set of all real numbers and the range is (-∞; ∞)
b.There are no critical point and the interval of increase is (-∞; ∞)
There are no asymptotes the line crosses the origin
The x and y intercept are both zero
Similarly, The domain of y = 3·x is the set of all real numbers and the range is (-∞; ∞)
There are no critical point and the interval of increase is (-∞; ∞)
There are no asymptotes the line crosses the origin
The x and y intercept are both zero
The difference between the functions, y = 5·x and y = 3·x is that the slope of y = 5·x is 5 and the slope of y = 3·x is 3
2.
The similarities between the functions, y = 4 and y = (2) are;
a. The domain of y = 4 is the set of all real numbers (-∞; ∞), and the range is {4}
b.There are no critical point and no interval of increase or decrease
There are no asymptotes the line does not cross the origin
There are no x-intercept and y intercept is (0, 4)
Similarly, the domain of y = (2) is the set of all real numbers (-∞; ∞), and the range is {2}
There are no critical point and no interval of increase or decrease
There are no asymptotes the line does not cross the origin
There are no x-intercept and y intercept is (0, 2)
The difference between the functions, y = 4 and y = (2) is that the y-intercept of y = 4 is 4 and the y-intercept of y = (2) is 2
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Answer:
the probability the die chosen was green is 0.9
Step-by-step explanation:
Given that:
A bag contains two six-sided dice: one red, one green.
The red die has faces numbered 1, 2, 3, 4, 5, and 6.
The green die has faces numbered 1, 2, 3, 4, 4, and 4.
From above, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) =
P (4 | green dice) = =
A die is selected at random and rolled four times.
As the die is selected randomly; the probability of the first die must be equal to the probability of the second die =
The probability of two 1's and two 4's in the first dice can be calculated as:
=
=
=
=
=
=
The probability of two 1's and two 4's in the second dice can be calculated as:
=
=
=
=
=
∴
The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's in both die =
The probability of two 1's and two 4's in both die =
The probability of two 1's and two 4's in both die =
By applying Bayes Theorem; the probability that the die was green can be calculated as:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)
P(second die (green) | two 1's and two 4's ) =
P(second die (green) | two 1's and two 4's ) =
P(second die (green) | two 1's and two 4's ) = 0.9
Thus; the probability the die chosen was green is 0.9