All categories

3 years ago

Is - (- 1 1/2 ) located to the right or left of zero?

1 answer:

5 0

As the number -1 1/2 would be to the left because it is negative, if it is as the number's integer, then the new number would be 1 1/2 because 1 1/2 and -1 1/2 are integers.

Hope this helps, if not, comment below please!!!!

You might be interested in

PLZ Help

o-na [289]

I have This too sooo hard

5 0

3 years ago

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 t

Zinaida [17]

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 -

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 = $\frac{(63 - 60}{(79 - 80)} (x - 80)$

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

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

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = $\frac{285}{6}$

⇒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

5 0

2 years ago

A survey was conducted to determine the amount of time, on average, during a given week SCAD students spend outside of class on

fiasKO [112]

Answer:

Standard Deviation = 5.928

Step-by-step explanation:

a) Data:

Days Hours spent (Mean - Hour)²

1 5 61.356

2 7 34.024

3 11 3.360

4 14 1.362

5 18 26.698

6 22 84.034

6 days 77 hours, 210.834

mean

77/6 = 12.833 and 210.83/6 = 35.139

Therefore, the square root of 35.139 = 5.928

b) The standard deviation of 5.928 shows how the hours students spend outside of class on class work varies from the mean of the total hours they spend outside of class on class work.

5 0

3 years ago

What is the solution of quadratic system of equations ?

kobusy [5.1K]

Answer:

(- 1, 1) and (- 5, - 35)

Step-by-step explanation:

since both equations express y in terms of x, equate the right sides

x² + 15x + 15 = - x² + 3x + 5 ( subtract - x² + 3x + 5 from both sides )

2x² + 12x + 10 = 0 ( divide all terms by 2 )

x² + 6x + 5 = 0 ← in standard form

(x + 1)(x + 5) = 0 ← in factored form