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1 year ago

Kurt, an artist, plans to paint and sell some miniature paintings.

Mathematics

1 answer:

Olenka [21]1 year ago

7 0

a) The amount earned by Kurt by selling the break-even units of painting at $38 each is <u>$1,064</u>.

b) The number of paintings that Kurt will be selling at the break-even point is <u>28</u>.

<h3>What is the break-even point?</h3>

The Break-even point is the sales units at which the seller's total revenue equals the total costs.

At the break-even point, there is no profit or loss.

<h3>Data and Calculations:</h3>

Fixed costs = $112

Variable cost = $34

Selling price = $38

Contribution margin = $4 ($38 - $34)

Contribution margin ratio = 10.53% ($4/$38 x 100)

Break-even point (units) = Fixed costs/Contribution margin per unit

= 28 units ($112/$4)

Break-even point (dollars) = $1,064 ($38 x 28)

Learn more about the break-even point at brainly.com/question/21137380

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Average rate of change for f(x) = x2 − 3x − 10 from x = −5 to x = 10.

11111nata11111 [884]

The average rate of change is the slope of the secant line connecting the points on f(x) from x=-5 to x=10.

In other words, it is just the slope of the straight line connecting the points
$(-5,f(-5)) \: and \: (10,f(10))$

So we were given ,

$f(x) = {x}^{2} - 3x - 10$

At
$x = - 5$
$f( - 5) = {( -5 )}^{2} - 3( - 5) - 10$
$f( - 5) = 25 + 15- 10$
$f( - 5) = 30$

Also at
$x = 10$
$f( 10) = {( 10)}^{2} - 3( 10) - 10.$
$f( 10) = 100- 30 - 10$
$f( 10) = 60$

The average rate of change
$= \frac{f(10) - f( - 5)}{10 - - 5}$
$= \frac{60- 30}{15}$
$= \frac{30}{15}$
$= 2$

3 0

3 years ago

Sarah has two similar regular pyramids with pentagon-shaped bases. The smaller has a scale factor of 2:3 when compared to the la

nordsb [41]

Answer:

(a) The volume of the pyramid 440.44 cube units

(b) No she doesn't

Step-by-step explanation:

The given parameters are;

The scale factor of the pyramids, S.F. = 2:3

The base area of the small pyramid, $A_{b1}$ = 110.11 square units

The height of the small pyramid, h₁ = 12 units

(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid

Therefore;

The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units

V₁ = 440.44 cube units

The volume of the small pyramid, V₁ = 440.44 cube units

(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid

She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid

The volume scale factor = (The linear scale factor)³

Therefore;

The volume scale factor of the pyramids = (2/3)³ = 8/27

To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁, by 27/8 as follows;

V₂ = V₁ × (27/8)

Therefore;

The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units

The volume of the larger pyramid, V₂ = 1,486.485 cube units.

5 0

3 years ago

Help see photo attached

maria [59]

The first pair of statements is the best option. h(0) based on the given equation would be the square root of -3, which is an imaginary number. Also, w(0) should be 0, since if nobody is working on making wrenches, none can be made. This is despite the graph having a value at x = 0.

The second statement in the second pair is false, since 0 is not an imaginary number.

8 0

4 years ago

Select the correct answer.

Veronika [31]

Answer:

Step-by-step explanation:

let y = 5x - 3

rearrange making x the subject

add 3 to both sides

5x = y + 3 ( divide both sides by 5 )

x = $\frac{y+3}{5}$