All categories

3 years ago

Plz help with this word problem

Mathematics

1 answer:

egoroff_w [7]3 years ago

4 0

The contribution made by each sale is
.. $135 -75 = $60

To make $3300, the store must sell
.. $3300/($60/bicycle) = 55 bicycles

The store must sell 55 bicycles each month to break even.

You might be interested in

Write a function rule for "the output is six times the input".

Romashka [77]

Answer:

y=6x

Step-by-step explanation:

In this function, the input is the variable x. The problem says that the output is six times the input, so we will need to multiply the input by 6. To write this as a function, set the output (y) equal to 6 times the input (x):

3 0

3 years ago

Can someone help me with this? And ty

klemol [59]

Answer:

Step-by-step explanation:

4 0

3 years ago

Addison's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 70 espressos in all

Valentin [98]

Answer:

The number of single-shot espressos sold by the cafe was 49.

Step-by-step explanation:

It is provided that Addison's Cafe offers two kinds of espresso: single-shot and double-shot.

Total number of espressos sold by the cafe yesterday afternoon was,

N = 70

The proportion of single-shot espresso sold was, p = 0.70.

Let X = number of single-shot espressos sold.

Compute the number of single-shot espressos sold by the cafe as follows:

$E(X)=N\times p$

$=70\times 0.70\\=49$

Thus, the number of single-shot espressos sold by the cafe was 49.

6 0

3 years ago

A house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Com

Mariulka [41]

We know that
scale------------> 1 in/4 ft
[blueprint]=scale*[actual]

Part 1) Living room
lenght (20 ft) -------------> [blueprint]=(1/4)*20=5 in
width (8 ft) ----------------> [blueprint]=(1/4)*8=2 in

Part 2) Kitchen
length (16 ft) -------------> [blueprint]=(1/4)*16=4 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 3) Office
length (8 ft) -------------> [blueprint]=(1/4)*8=2 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 4) Bedroom 1
length (8 ft) -------------> [blueprint]=(1/4)*8=2 in
width (16 ft) ----------------> [blueprint]=(1/4)*16=4 in

Part 5) Bedroom 2
length (20 ft) -------------> [blueprint]=(1/4)*20=5 in
width (20 ft) ----------------> [blueprint]=(1/4)*20=5 in

Part 6) Bathroom
length (6 ft) -------------> [blueprint]=(1/4)*6=1.5 in
width (8 ft) ----------------> [blueprint]=(1/4)*8=2 in

see the attached figure to view the table

3 0

4 years ago

Read 2 more answers

show that the curve has 3 points of inflection and they all lie on 1 straight line:\[y=\frac{1+x}{1+x^{2}}\]

ohaa [14]

Y = (1 + x) / (1 + x^2)

y'
= [(1 + x^2)(1) - (1 + x)(2x)] / (1 + x^2)^2
= [1 + x^2 - 2x - 2x^2] / (1 + x^2)^2
= [-x^2 - 2x + 1] / (1 + x^2)^2

y''
= [(1 + x^2)^2 * (-2x - 2) - (-x^2 - 2x + 1)(2)(1 + x^2)(2x)] / (1 + x^2)^4
= [(1 + x^2)(-2x - 2) - (4x)(-x^2 - 2x + 1)] / (1 + x^2)^3
= [(-2x - 2x^3 - 2 - 2x^2) - (-4x^3 - 8x^2 + 4x)] / (1 + x^2)^3
= [-2x - 2x^3 - 2 - 2x^2 + 4x^3 + 8x^2 - 4x] / (1 + x^2)^3
= [2x^3 + 6x^2 - 6x - 2] / (1 + x^2)^3

Setting y'' to zero, we have:
y'' = 0
[2x^3 + 6x^2 - 6x - 2] / (1 + x^2)^3 = 0
(2x^3 + 6x^2 - 6x - 2) = 0

Using trial and error, you will realise that x = 1 is a root.
This means (x - 1) is a factor.
Dividing 2x^3 + 6x^2 - 6x - 2 by x - 1 using long division, you will have 2x^2 + 8x + 2.

2x^2 + 8x + 2
= 2(x^2 + 4x) + 2
= 2(x + 2)^2 - 2(2^2) + 2
= 2(x + 2)^2 - 8 + 2
= 2(x + 2)^2 - 6

Setting 2x^2 + 8x + 2 to zero, we have:
2(x + 2)^2 - 6 = 0
2(x + 2)^2 = 6
(x + 2)^2 = 3
x + 2 = sqrt(3) or = -sqrt(3)
x = -2 + sqrt(3) or x = -2 - sqrt(3)

Note that -2 - sqrt(3) < -2 + sqrt(3) < 1
We will choose random values belonging to each interval and test them out.

-5 < -2 - sqrt(3) < -2 < -2 + sqrt(3)
f''(-5) = [2(-5)^3 + 6(-5)^2 - 6(-5) - 2] / (1 + (-5)^2)^3 = -9/2197 < 0
f''(-2) = [2(-2)^3 + 6(-2)^2 - 6(-2) - 2] / (1 + (-2)^2)^3 = 18/125 > 0
Note that one value is positive and the other is negative.
Thus, x = -2 - sqrt(3) is an inflection point.

-2 - sqrt(3) < -2 < -2 + sqrt(3) < 0 < 1
f''(-2) = [2(-2)^3 + 6(-2)^2 - 6(-2) - 2] / (1 + (-2)^2)^3 = 18/125 > 0
f''(0) = [2(0)^3 + 6(0)^2 - 6(0) - 2] / (1 + (0)^2)^3 = -2 < 0
Note that one value is positive and the other is negative.
Thus, x = -2 + sqrt(3) is also an inflection point.

-2 + sqrt(3) < 0 < 1 < 2
f''(0) = [2(0)^3 + 6(0)^2 - 6(0) - 2] / (1 + (0)^2)^3 = -2 < 0
f''(2) = [2(2)^3 + 6(2)^2 - 6(2) - 2] / (1 + (2)^2)^3 = 26/125 > 0
Note that one value is positive and the other is negative.
Thus, x = 1 is an inflection point.

Hence, we have three inflection points in total.

When x = -2 - sqrt(3), we have:
y
= (1 - 2 - sqrt(3)) / (1 + (-2 - sqrt(3))^2)
= (-1 - sqrt(3)) / (1 + 4 + 4sqrt(3) + 3)
= (-1 - sqrt(3)) / (8 + 4sqrt(3))

When x = -2 + sqrt(3), we have:
y
= (1 - 2 + sqrt(3)) / (1 + (-2 + sqrt(3))^2)
= (-1 + sqrt(3)) / (1 + 4 - 4sqrt(3) + 3)
= (-1 + sqrt(3)) / (8 - 4sqrt(3))

When x = 1, we have:
y
= (1 + 1) / (1 + 1^2)
= 2 / 2
= 1

Using the slope formula, we have:
(y - 1) / (x - 1) = [[(-1 + sqrt(3)) / (8 - 4sqrt(3))] - 1] / ( -2 + sqrt(3) - 1)
(y - 1) / (x - 1) = 1/4, which is the equation of the line which the inflection points at x = 1 and x = -2 + sqrt(3) lies on.

Note that I am skipping the intermediate steps for simplifying here, but the trick is to rationalise the denominator by multiplying a conjugate on both numerator and denominator.

Now, we just need to check that the inflection point at x = -2 - sqrt(3) lies on the same line as well.
L.H.S.
= [[(-1 - sqrt(3)) / (8 + 4sqrt(3))] - 1] / (-2 - sqrt(3) - 1)
= 1/4
= R.H.S.

Once again, I am skipping simplifying steps here.

Anyway, this proves all three points of inflection lies on the same straight line.

4 0

3 years ago