Find the equation that shows the relationship between the number of pens, p, and the

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

chubhunter [2.5K]

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3 $\sqrt$ 3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3 $\sqrt$ 3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48 $\sqrt$ 3]

Divide both sides by 0.04

275 = 24l + 48 $\sqrt$ 3

Subtract 48 $\sqrt$ 3 from both sides

24l = 275 - 48 $\sqrt$ 3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

brainly.com/question/6613758

6 0

2 years ago

A jacket that originally sold for $60.00 was on sale for 10% off. When it didn't sell after several weeks, the sale price was di

sammy [17]

The final price of the jacket was $32.40 after both the 10% and 40% discount. The total discount is NOT equal to a 50% discount. When 10% off, the price was $54, bringing the next 40% off to a whole different number, not necessarily off the original price.

I don't know if that makes sense to you, sorry xD

7 0

3 years ago

A bee beats its wings 250 times each second what is the average time for a single beat of a bee's wing

eduard

No. Of times bee beats in 1 sec=250
Average time =?
Frst find how many times bee beats in 1 min.
No. Of times bee beats in 1 min= 250*60=15000
Average time= 15000/ 250
Average time=60 times

3 0

3 years ago

Read 2 more answers

Which of the following conditions must be met in order to make a statistical inference about a population based on a sample

klasskru [66]

Answer:

For this case if we want to conclude that the sample does not come from a normally distributed population we need to satisfy the condition that the sample size would be large enough in order to use the central limit theoream and approximate the sample mean with the following distribution:

$\bar X \sim (\mu, \frac{\sigma}{\sqrt{n}})$

For this case the condition required in order to consider a sample size large is that n>30, then the best solution would be:

n>= 30

Step-by-step explanation:

For this case if we want to conclude that the sample does not come from a normally distributed population we need to satisfy the condition that the sample size would be large enough in order to use the central limit theoream and approximate the sample mean with the following distribution:

$\bar X \sim (\mu, \frac{\sigma}{\sqrt{n}})$

For this case the condition required in order to consider a sample size large is that n>30, then the best solution would be:

n>= 30

7 0

3 years ago

The engine torque y (in foot-pounds) of one model of car is given by y=−3.75x2+23.2x+38.8, where x is the speed (in thousands of

Stels [109]

Answer:

Step-by-step explanation:

If the engine torque y (in foot-pounds) of one model of car is given by y=−3.75x^2+23.2x+38.8

The engine speed is at maximum if dy/dx = 0

dy/dx = -2(3.75)x+23.2

dy/dx = -7.5x + 23.2

since dy/dx = 0

0 = -7.5x + 23.2

7.5x = 23.2

x = 23.2/7.5

x = 3.093

Hence the maximum torque is 3.09 rev/min

8 0

3 years ago