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2 years ago

A bookstore costs $120 a day to keep open, and it spends $14 for each book that it sells. 11

Mathematics

1 answer:

frozen [14]2 years ago

8 0

<u>Answer:</u>

The break-even point for this bookstore is 20 units

<u>Explanation:</u>

We know that break even point is given by the following formula,

$\frac{\text { Fixed costs }}{\text { (Price per unit - Variable costs) }}$

Here, we are given that bookstore costs $120 per day to keep open so fixed cost = 120$

Price per unit = price of each book =20$ and

variable cost = $14

Substituting these in the formula, we get

$\frac{120}{(20-14)}$

= $\frac{120}{6}$ = 20

20 units which is the The break-even point for this bookstore.

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Missing number in the series 9, ____, 6561, 43046721 is: 81 25 62 31 18 9. one number is 2 more than 3 times another. their sum

Nadusha1986 [10]

Alright, lets get started.

Missing number fom the series : 9, ..... , 6561, 43046721

43046721 is square of its previous number 6561, means

$6561^2 = 43046721$

It means the missing number will be square of its previous number

Means $9^2 = 81$ , so missing number is 81. : Answer

Next : one number is 2 more than 3 times another. their sum is 22. find the numbers.

Suppose one number is x and second number is y

As per given equation, $x = 3y + 2$ ......equation (1)

Their sum is 22 means, $x+y = 22$ .......equation (2)

Putting the value of x from equation1 into equation 2

$3y + 2 + y = 22$

$4y + 2 = 22$

Subtracting 2 in both sides

$4y + 2 - 2 = 22 - 2$

$4y = 20$

$y = 5$

$x = 22 - y = 22 - 5 = 17$

Means numbers are 17 and 5. : Answer

Next : the missing number in the series 1, 4, 27,____, 3125 is

1 could be written as 1

4 could be written as $2^2$

27 could be written as $3^3$

So , next number would be $4^4$

$4^4 = 256$

Next one is $5^5 = 3125$

So, the missing number is 256 : Answer

Next : the next number in the series 3, 4, 6, 7, 9, 10 is

After 3,4 (5) is mising, 6, 7 (8) is missing, 9, 10 (11) will be missing

So, next number will be 12. : Answer

Next : a farmer is planting a straight row of crops with 3 feet between each plant. if 23 are planted, what is the distance between the first and last plant?

Between 2 plants, the distance is = $3 * (2-1) = 3$

Between 3 plants, the distance is = $3 * (3-1) = 6$

So, between 23 plants, the distance is = $3 * (23-1) = 3 * 22 = 66$

hene the distance between first and last plant woule be 66 feet. : Answer

7 0

2 years ago

Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th

ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

pool in his area

- He plotted the data and determined that the average community

pool membership cost consists of a one-time registration fee and

a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

4 0

2 years ago

Find the equivalent ratio of 15/5 and 45/15?

mixer [17]

1. 3 0/5

2. 3 0/15

These are your answers

4 0

3 years ago

On Monday Headley paid $1.70 for two of coffee and one doughnut, including the tip. On Tuesday he paid $1.65 for two doughnuts a

stich3 [128]

Answer:

i dont wanna say

Step-by-step explanation:

3 0

3 years ago

Help if you can do this please

olga nikolaevna [1]

Answer:

Step-by-step explanation:

a. Since the parabola is compressed by a factor of 1/3 we can state:

a parabola is written this way : y=(x-h)²+k
h stands for the translation to the left ⇒ 2*3=6
k for the units down ⇒4*3=12

So the equation is : y=(x-6)²+12

b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2

We khow that a parabola is written this way : y=(x-h)²+k
(h,k) are the coordinates of the vertex
the maximum value is 7*0.5=3.5
we khow tha the derivative of a quadratic function is null in the maximum value
so let's derivate (x-h)²+k= x²+h²-2xh+k
f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
Now we khow that 1 is the point where the derivative is null
f(1)=3.5
3.5=(x-1)²+k
3.5= (1-1)²+k⇒ k=3.5

So the equation is : y=(x-1)²+3.5

the maximum height is where the derivative equals 0

h= -5.25(t-4)²+86
h= -5.25(t²-8t+16)+86
h=-5.25t²+42t-84+86
h=-5.25t²+42t+2

Let's derivate it :

f(x)= -10.5t+42
-10.5t+42=0
42=10.5t
t= 42/10.5=4

When the height was at max t=4s

h(max)= -5.25(4-4)²+86 = 86 m

h was 86m

8 0

2 years ago