Mai makes her favorite shade of green paint by using 5 cups of blue paint for every 3 cups of yellow paint. Priya makes her favo
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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
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Answer:
a) (<em>μ</em>) = $128
b) 0.9472
c) 0.6671
Step-by-step explanation:
Given that:
Allegiant Airlines charges a mean base fare of $89.
this implies that: mean base fare = $89.
The question proceeds by stating the additional charge on its website, checking bags, and inflight beverages.
so , additional charges turns out to be = $39 per passenger
Now, Suppose a random sample of 60 passengers is taken
random sample (n) = 60
The population standard deviation of total flight cost is known to be $40
standard deviation (σ) = 40
Question (a) says; we should find the population mean cost per flight
To determine that; we have to consider the total sum(<em>μ</em>) of the mean base fare with the mean additional charges.
Population mean cost per flight (<em>μ</em>) = mean base fare + mean additional charges
(<em>μ</em>) = $89 + $39
(<em>μ</em>) = $128
b)
What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?
To determine that; we have:
P(128 - 10 ≤ Х ≤ 128 +10)
= P(118 ≤ Х ≤ 138)
= (where
= <em>μ </em>and ∝ = σ )
=
=
Using Excel Command to approach this process, we have;
= 0.9736 - 0.0264
= 0.9472 (to four decimal places)
∴ the probability that the sample mean will be within $10 of the population mean cost per flight = 0.9472
c)
What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?
We wll have to go through the process like the one attempted above in question (b);
So;
P(128 - 5 ≤ Х ≤ 128 + 5)
= P(123 ≤ Х ≤ 133)
= (where
= <em>μ </em>and ∝ = σ )
=
=
Computing these data in Excel; we have
= 0.8335 -0.1665
= 0.6671 (to 4 decimal places)
∴ the probability that the sample mean will be within $5 of the population mean cost per flight.