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2 years ago

Monday What time is 5 3/4 hours after 11:32 pm?

1 answer:

6 0

bearing in mind that the an hour has 15 + 15 + 15 + 15 = 60 minutes, so 15 minutes in 1/4 of an hour, thus 45 minutes is 3/4 of an hour.

now, from 11PM, if we add the 5 hours first, we'll be at 4AM, pass midnight of course.

now let's add the minutes, 32 and then 45, that gives us 77 minutes.

so the time will be 4AM plus 77 minutes, since 60 minutes is 1 hr, so 4AM plus 1 hr and 17 minutes, that'd be 5:17AM.

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3 years ago

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3 years ago

The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars

stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

= $253x-2x^2$

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

= 3*x

= 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= $253x-2x^2 - (3x + 6972)$

= $253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\$

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

$-2x^2+250x-6972=0\\$

now we have to solve the above equation for x

Dividing both sides by -2 we get

$x^2-125x+3486=0$

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

$x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\$

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

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3 years ago