An experiment involves rolling a die and drawing a card from a standard deck of 52 cards.What is the probability that the die la
2 answers:
You might be interested in
Answer:
.
Step-by-step explanation:
Probability that the car encounters a green light on the first day: .
To meet the question's conditions, the car needs to encounter another green light on the second day. Given that the colors of the light on each day are "independent," the chance that there's a green light followed by another green light will be
.
- Condition is met on the first two days and green light on the third day:
.
- Condition is met on the first three days and green light on the fourth day:
.
To meet the condition on the fifth day, there needs to be a yellow light. The probability that the condition is met on the first four days and on the fifth day will be .
To meet the condition on the sixth day, all prior days should meet the conditions. Besides, there needs to be a red light on the sixth day.
- Seventh day:
- Eighth day:
- Ninth day:
- Tenth day:
The question asks that the condition be met on all ten days. As a result, the probability of meeting the condition will be equal to the probability on the tenth day: .
Question # 13
Answer:
The required equation for the given function is <em>y = 4sin(x/2+2π/3) -2 , as shown attached graph diagram.</em>
<em>Step-by-step explanation: </em>
As the general sine function is given by
.......[A]
- amplitude = a
- period = 2π ÷ b
- Phase shift = -c ÷ b
- Vertical shift = d
As in the question,
- amplitude = a = 4
- period = 4π
- phase shift = -4π/3
- Vertical shift = d = -2
As
period = 2π ÷ b
b = 2π/period
b = 2π/4π ∵ period = 4π
b = 1/2
Also
Phase shift = -c/b
-4π/3 = -c/b ∵ phase shift = -4π/3
4π/3 = c/b
c = b × 4π/3
c = 1/2 × 4π/3
c = 4π/6
c = 2π/3
So, putting Amplitude ⇒ a = 4, Vertical shift ⇒ d = -2, b = 1/2 ,
and c = 2π/3 in Equation [A] would bring us the required equation for the given function.
y = 4sin(x/2+2π/3)+(-2)
y = 4sin(x/2+2π/3) -2
<em>Note: The graph is also shown in attached diagram.</em>
Question # 14
<em>Answer:</em>
The required equation for the given function is y = cot(x+π/3)+2, as shown in attached graph diagram.
<em>Step-by-step explanation: </em>
As the general cotangent function is given by
.......[A]
- amplitude = a
- period = π ÷ b
- Phase shift = -c ÷ b
- Vertical shift = d
As in the question,
- period = π
- phase shift = -π/3
- Vertical shift = d = 2
As
period = π ÷ b
b = π/period
b = π/π ∵ period = 4π
b = 1
Also
Phase shift = -c/b
-π/3 = -c/b ∵ phase shift = -π/3
π/3 = c/b
c = b × π/3
c = 1 × π/3
c = π/3
So, putting vertical shift ⇒ d = 2, b = 1 and c = π/3 in Equation [A] would bring us the required equation for the given function.
y = cot(x+π/3)+2
<em>Note: The graph is also shown in attached diagram.</em>
Keywords: amplitude, period , phase shift , vertical shift
Learn more about trigonometric functions of equations from brainly.com/question/2643311
#learnwithBrainly
Answer:
D
Look at the picture. :)
