As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
a. Write the expression for total cost per month. Assume 30 days per month.
b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
c. If there are 12 guest rooms available, can they break even? What would be the profit with 12 rooms?
d. What percentage of rooms would need to be occupied, on average, to break even?

x = 12

5x + 15 = 75

5x = 75 - 15

5x = 60

x = 60 : 5

x = 12

Answer:

2. w = -90

4. b = 8

Step-by-step explanation:

Multiply both sides by the reciprocal of the number multiplying the variable.

2.

[tex] -\dfrac{2}{3}w = 60 [/tex]

[tex] -\dfrac{3}{2} \times (-\dfrac{2}{3}w) = -\dfrac{3}{2} \times 60 [/tex]

[tex] w = -\dfrac{180}{2} [/tex]

[tex] w = -90 [/tex]

4.

[tex] 9.6 = 1.2b [/tex]

[tex] \dfrac{1}{1.2} \times 9.6 = \dfrac{1}{1.2} \times 1.2b [/tex]

[tex] 8 = b [/tex]

[tex] b = 8 [/tex]

Answer:

The answer is below

Step-by-step explanation:

Given that f(x)=x(22-x)

a) f(x)=x(22-x)

f(x + h) = (x + h)(22 - (x + h))

f(x + h) = (x + h)(22 - x - h)

f(x + h) = (22x - x² - xh + 22h - xh - h²)

f(x + h) = (-x² + 22x - h²+ 22h - 2xh)

b) f(x)=x(22-x) = 22x - x²

f(x + h) = (-x² + 22x - h²+ 22h - 2xh)

f(x+h)- f(x) = (-x² + 22x - h²+ 22h - 2xh) - (22x - x²)

f(x+h)- f(x) = -x² + 22x - h²+ 22h - 2xh - 22x + x²

f(x+h)- f(x) = -x² + x² + 22x - 22x  - h²+ 22h - 2xh

f(x+h)- f(x) = - h²+ 22h - 2xh

c) f(x+h)- f(x) = - h²+ 22h - 2xh

[tex]\frac{f(x+h)-f(x)}{h}=\frac{- h^2+ 22h - 2xh}{h}\\ \\\frac{f(x+h)-f(x)}{h}=\frac{- h^2}{h}+\frac{22h}{h}-\frac{2xh}{h}\\\\\frac{f(x+h)-f(x)}{h}=-h+22-2x[/tex]

[tex]\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}= \lim_{h \to 0} (-h+22-2x )=22-2x[/tex]

Answer:

300 feet an hour

Step-by-step explanation:

in three hours they went down 1200 feet so that means in 1 hour they will go down 300 feet if they take no break

Answer:

Second answer:

"The product of two irrational numbers can be rational or irrational"

Step-by-step explanation:

notice from the first product

[tex]\sqrt{2} \,* \,\sqrt{2} = \sqrt{4} = 2[/tex]

that the product of two irrational numbers can give us a rational one.

from the other three examples, the answer for the products always contains a square root that cannot be reduced, so they all result in an irrational number.

Then, depending on the type of irrationals used, the product can be either rational or irrational.

Answer: y=2

Step-by-step explanation:

y/6 = 3/9        multiply both sides by 6/1 (since 6/1 times y/6 equals 1y or just y)

y = 18/9          now that y is isolated, just simplify 18/9

y=2                 18 divided by 9 is 2

1/8 since 4*2=8 and there is one spot you can land on with 6.

Answer:

2/8

Step-by-step explanation:

If you are spinning it twice and there is 4 places that is where you get the 8        The 2 comes from how many times you are spinning

Answer:

[tex]a=4[/tex]

Step-by-step explanation:

So we have the equation:

[tex]a+2a-1=11[/tex]

First, combine like terms:"

[tex]3a-1=11[/tex]

Now, add 1 to both sides:

[tex]3a=12[/tex]

Divide both sides by 3:

[tex]a=4[/tex]

And we're done!

Answer:

670

Step-by-step explanation:

32 hours at 17  plus 14 hours at 9

32 *17 + 14 *9

544+126

670

Answer:

job 1 = 544 dollars he made job 2 = 126$

Step-by-step explanation:

You multiply the amount he made for 1 hour by the total hours same thing with job 2.

Answer:

Find AC+CB

Step-by-step explanation:

Answer:

Find [tex]AC + CB[/tex]; 10

Find AB; 10

Step-By-Step Explanation:

[tex]AC (3) + CB (7) = 10[/tex]

Find AB is the same thing, just phrased differently.

Step-by-step explanation:

she is showing how many wheels are on each bike and skateboard,on each bike there are 2 wheels,on each skateboard there are 4 wheels. sarahs is different because she shows how many wheels are on each of those bikes

Answer:

a= -858

Step-by-step explanation:

46 times -18 equals -846

-846-12 equals -858

Answer:

a=-858

Step-by-step explanation:

12+a=846

a=-846-12

a=-858

Answer:

Here are the basic steps to follow to simplify an algebraic expression:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Step-by-step explanation:

Answer:

The first consecutive integer is 17 while the second is 19

Step-by-step explanation:

Let us say that the first odd integer is x

At this point, the second odd integer will be x+2.

This is because to obtain the next consecutive odd integer, 2 will have to be added to the original number.

From the question, we can set up an equation as shown below:

[tex]6x= 7+5(x+2)[/tex]

from this, we can simply evaluate and find out the value of x

[tex]6x=7 +5x +10\\x=17[/tex]

therefore, the first consecutive integer is 17 while the second is 19

Answer:

first person payed$4, second person payed$12 and the third person payed $24

Step-by-step explanation:

find the sum of the ratio

find

1 divided by the total ratio time $40 to get first person

follow in that order to get the amount each person payed.

Answer:

The 10-yard line on a football field

Step-by-step explanation:

A geometric line segment is a straight path of points(that is a line) that has two end points (that is a beginning and an end). A 10 yard line on a football field is a line segment because it has two endpoints which is at the beginning of the 10 yard and at the end of the 10 yard.

A scientist's line of vision as he looks into space with a telescope is not a line segment because it extends forever (has no end).

A line of 15 dancers on stage is not a line segment, A light shone into the darkness is not a line segment because it continues forever and also, the hands of a clock is also not a line segment.

Answer:

Step-by-step explanation:

5. (6.5 - 2)/(7 - 4) = 4.5/3 = 1.5

6. (8 - 8)/(-5 - 10)= 0/-15= 0

7. (-3 + .75)/(4 - 1) = -2.25/3 = -.75= -3/4

8. (2 + 7)/(18 - 18)= 9/0 = undefined

Answer:

Option C

Step-by-step explanation:

It will be graphed as function:

Since is has a very small slope of 0.019 it will be shown almost parallel to x axis.

Some points on the graph:

Correct graph is option C

Answer:

Step-by-step explanation:

This number is not only larger, but also longer in digits than 8.5.

Answer:

Coordinates of the point B will be (14, 3.5).

Step-by-step explanation:

From the graph attached,

Distance between the Quarterback and Receiver = x-coordinate of the point B = 14 yards

Similarly, height of the football from the ground at point B = y-coordinate of the point B = 9 + [tex]\frac{12-9}{2}[/tex]

                   = 9 + 1.5

                   = 10.5 feet

Since, 1 feet = [tex]\frac{1}{3}[/tex] yards

10.5 feet = [tex]\frac{10.5}{3}[/tex]

               = 3.5 yards

Therefore, coordinates of the point B will be (14, 3.5).

Answer:

30

Step-by-step explanation:

For every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable and one or more independent variables.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for typically two variables for a collection of data. It uses Cartesian coordinates. When the points are coded, a further variable can be seen.

Given that store recorded the number of sweatshirts sold on several days throughout the year. The scatterplot shows the relationship between the average daily temperature and the number of sweatshirts sold.

Here is the scatter plot, it is observed that by increasing the temperature the number of sweatshirts sold is decreasing. For every 10-degree depression of temperature, the number of the sells is decreased by 50.

Therefore, for every 10-degree increase in temperature, the store sells around 50 fewer sweatshirts. The correct option is D.

To know more about regression analysis follow

https://brainly.com/question/26755306

#SPJ2

Answer:

i'm not sure so i'm sorry if it is not the right answer

Step-by-step explanation:

Let's assume AC is a straight line and B is on the line between A and C

AC=AB+BC

AC=4x+7+5x-8

AC=9x-1

Answer:

1) 19.0km

2) 23.9mi

3) 53.9yd

4) 30.0mi

(all answers rounded off to the nearest tenth)

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

A

X, 5x

Step-by-step explanation:

A

X, 5x   yes, both variables are x

B

3x, 2xy   no, the first variable is x  the second is x times y

C

2x, 2y  no the first variable is x and the second is y

D

-4, -4y  no, the first is a constant and the second has a variable

Answer:

Pair A

Step-by-step explanation:

Pair A (x, 5x) are like terms.

Like terms are terms in a expression or equations with the same variables.

'x' and '5x' have the same variable (you can think of 'x' as '1x'), so they are like terms. All other pairs have different variables.

Hope this helps.

15 is divisible by 75 true or false

Answer:

True