Answer:
r = 4
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to 5
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (7, r ) and (x₂, y₂ ) = (8, 9)
m = =
= 9 - r = 5 ( subtract 9 from both sides )
- r = - 4 ( multiply both sides by - 1 )
r = 4
Answer:
The probability of finding a non-defective television is 0.9815.
Step-by-step explanation:
We are given that a television manufacturer has three locations where it is finally assembled. Plants A, B, and C supply 65%, 15%, and 20% respectively of the televisions used by the manufacture.
Quality control has determined that 1.5% produced by Plant A are defective, while plants B and C have 2.5% defective products.
Let Probability that Plant A supply televisions = P(A) = 0.65
Probability that Plant B supply televisions = P(B) = 0.15
Probability that Plant C supply televisions = P(C) = 0.20
<em>Also, let D = event that television is defective</em>
Probability that television is defective given that it is supplied by Plant A = P(D/A) = 0.015
Probability that television is defective given that it is supplied by Plant B = P(D/B) = 0.025
Probability that television is defective given that it is supplied by Plant C = P(D/C) = 0.025
<u>Now, to find the probability of finding a non-defective television firstly we will find the probability of a defective television.</u>
<em>Probability of a defective television is given by;</em>
= P(A) P(D/A) + P(B)
P(D/B) + P(C)
P(D/C)
= 0.65 0.015 + 0.15
0.025 + 0.20
0.025
= 0.00975 + 0.00375 + 0.005
= 0.0185
Now, <em><u>probability of finding a non-defective television</u></em> = 1 - Pro<em>bability of a defective television</em>
Probability of finding a non-defective television = 1 - 0.0185
= 0.9815
<em>Therefore, the probability of finding a non-defective television is 98.15%.</em>
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]
As in the question,
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]
As in the question,
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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