Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. Two causes of poor power
1 answer:
Answer:
a
b
Step-by-step explanation:
From the question we are told that
The sample size is n = 103
The sample mean of sag is
The sample mean of swells is
The standard deviation of sag is
The standard deviation of swells is
The number of swell for a randomly selected transformer is k = 100
The number of sag for a randomly selected transformer is c = 400
Generally the z-score for the number of swells is mathematically represented as
=>
=>
Generally the z-score for the number of sags is mathematically represented as
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Jenny won the race as she finished the race much more quickly and has greater average speed than Lester.
Jenny: distance/time = 100/15.2 = 6.58 m/s = 6.6 m/s
Lester: distance/time = 100/15.7 = 6.37 m/s = 6.4 m/s
Answer:
a) p(x) = 300 - 3
b) P(x) = -3 x² + 285 x
c) Price of per room per day = $ 157.5
when Number of rooms occupied , x = 47.5
Step-by-step explanation:
Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.
To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.
b) Find the profit function P(x).
c) Find the price of per room per day the motel should charge in order to maximize its profit.
Proof -
a)
Let
(x, y) be the point
where x represents number of rooms occupied
and y represents price of room per day.
Now,
Given that,
a room is priced at $60 per day, all 80 rooms of the motel are occupied.
So, point becomes (80, 60)
And given that For every $3 rise in the charge per room per day, one more room is vacant.
So, point becomes (79, 63)
Now, we have two points (80, 60), (79, 63)
Let us assume that,
p(x) be the price charged for each room per day
Now,
By using point - slope formula , we get
p -60 =
⇒p -60 = (-3)(x-80)
⇒p-60 = 240 -3 x
⇒p(x) = 240 + 60 -3 x
⇒p(x) = 300 - 3 x
b)
Given that,
Each occupied room costs an additional $15 per day to maintain.
Let C(x) be the cost function,
Then C(x) =15 x
now,
Revenue function,
R(x) =x*p
= x*(300 -3 x )
= 300 x - 3 x²
⇒R(x) = 300 x - 3 x²
Now,
We know
Profit function = Revenue function - Cost function
⇒P(x) = R(x)-C(x)
⇒P(x) = (300 x -3 x²) -15 x
⇒P(x) = -3 x² + 285 x
c)
P'(x) = -6 x +285
For Maximize profit , Put P'(x) = 0
⇒-6 x+ 285 =0
⇒6 x= 285
⇒x =
⇒x= 47.5
∴ we get
Maximize profit is when price, p = 300 - 3x
= 300 -3(47.5)
= $157.5
⇒Price of per room per day = $ 157.5
when Number of rooms occupied , x = 47.5
Answer:
The length of each rope is 9.93 feet (Approx).
Step-by-step explanation:
As given
Emma, Brandy, and Damian will cut a rope that is 29.8 feet long into 3 jump ropes.
Each of the three jump ropes will be the same length.
Thus
Therefore the length of the each rope is 9.93 feet (Approx).