A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Grace needs to ship a package that is 3x-5 centimeters long, 2x centimeters wide, and x + 20 centimeters tall. A.Write a polynomial expression to represent the situation if Grace plan as to spend a maximum of $7.50
B. Write and solve a system of equations
C. What should the dimensions of the package be to have the maximum volume?

Answers

Answer 1

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

What is an inequality?

An inequality is an expression that shows the non equal comparison between two or more numbers and variables.

A shipping company will ship a package for $7.50 when the volume is no more than 15,000 cubic centimeters. Hence, if Grace plan as to spend a maximum of $7.50:

Volume (V) = (3x - 5)(2x)(x + 20) = 6x³ + 110x² - 200x

The inequality is:

6x³ + 110x² - 200x ≤ 15000

6x³ + 110x² - 200x - 15000 ≤ 0

x = 10

The maximum volume is at:

V' = 0

V' = 18x² + 220x - 200 = 0

x = 0.85 cm

The maximum volume is at x = 0.85 cm. The inequality is 6x³ + 110x² - 200x ≤ 15000

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Related Questions

sin^2(theta)(1+cot^2(theta))-1=0

Answers

Hope it helpssss….best of luck

PLEASE EXPLAIN’

Which set of numbers correctly
shows a number, its opposite, and
its absolute value, in that order?
A 98.4
-98.4 98.4
B -74.3 -74.3
-74.3 74.3
C 46.2 46.2 -46.2
D 28.9 -28.9 -28.9

Answers

Answer:

A

Step-by-step explanation:

because -98.4 is the opposite of 98.4 and 98.4 is it's absolute value

express in the form 1 : n give n as a simplifeid fraction 8 : 6​

Answers

Answer:

So, Simplified fraction of 8:6 is 4:3.

Express 100,000 as a power of 10

Answers

Answer:

10^5

Step-by-step explanation:
10 multiplied by itself five times (10*10*10*10*10) is 100,000.

Find the value of cos
V
V rounded to the nearest hundredth, if necessary.

Answers

Answer:

image

Step-by-step explanation:

image

3+8+(87÷4)=(12345676×3825829){=dheg

Answers

Answer:

Read the explanation

Step-by-step explanation:

look at the photo

I REALLY NEED HELP MY GRADES GO IN TONIGHT AND I CANT SOLVE THIS I NEED A REAL ANSWER I WILL CHECK BEFORE GIVING POINTS!!!!!!!!!!!!!!!!!

Answers

Answer:

K. 8

N. 12

A. 29

H. 5

I. -297

G. 89

T. 50

S. -7

W. 165

WHAT'S SHAKING

Answer:

K: 8

N: 12

A: 29

H: 5

I: -297

G: 89

T: 50

S: -7

W: 165

WHATS SHAKING [Answer]

Step-by-step explanation:

Please rate!!

The length is :____meters and the width is____meters.

Answers

Answer:

Length = 42, Width = 14

Step-by-step explanation:

Say width = x

3x + x = 56

4x = 56

x = 14

14 x 3 = 42.

Answer:

width = 7

length = 21

Step-by-step explanation:

x + 3x = 56/2

4x = 28

x = 7

Give me a real life example of when you would use area. * (your own wording please!!!!)

Answers

A real word example where area would be useful is if you were building a house or if you designed clothes

Answer:

Area is very commonly used in our world we just may not immediately recognize it. Most if not all construction workers use area to figure out how much Sq feet they have to work with. When decorating your home you need to know how much space is in each room. When installing carpet or hardwood you'll need to figure out the area of your room.

Hopefully this helps!  

What is the value of x in the equation 1/3x-2/3=-18
?
O -56
O -52
O 52
O 56

Answers

Answer:

x = -52

Step-by-step explanation:

Multiply both sides of the original equasion by 3 to get:

x - 2 = -54

Slide over the - 2 across the equal sign to get a +

x = -54 + 2

-54+2 = -52

Soo

x = -52

what is the relationship between the sine and cosine of the complementary angles in this diagram? drag and drop the answers into the boxes to correctly complete the statements.
Both sin(41) and cos(x) can be represented by the ratio ____. the angles measuring 41 and x are complementary angles. this means x+41=____. therefore x=____. since sin(41) = cos(x), this also shows that sin(41)=cos(_____).

Answers

Answer:

Step-by-step explanation:

Both sin(41) and cos(x) can be represented by the ratio b/c

What is complementary angles?

If the sum of two angles is equal to 90 degrees, then such angles are called complementary angles. The total of the two angles' measurements determines their complement and supplement. The pair of angles is said to be complimentary if the product of the two angles equals the measurement of a right angle. Example:

   40° is the complement of 50°.

   50° is the complement of 40°.

sin (41) = b/c

cos (x) = b/c

∴both sin(41) and cos(x) can be represented by the ratio b/c

x + 41 = 90 (∵ complementary angles)

x = 90-41 = 49

∵ sin 41 = cos x

∴ sin 41 = cos (90-41)

To know more about complementary angles please visit:

https://brainly.com/question/5708372

#SPJ2

An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure.

Which of the following is the angle formed by the sun's rays and the ground?

A.30
B.40
C.50
D.60

Answers

Answer:

The answer should be C=50

Step-by-step explanation:

For context, question 6 is:
What inverse operation will be used to undo the volume of Julie's jewelry box to find its edge lengths?

Volume formula for a cube is: volume = edge^3

//I have already answered This, I need help with #7, which is:
"If V = 216, what is the edge length of Julie's jewelry box?"

Answers

Answer:

6

Step-by-step explanation:

The inverse of cubed is cubed root. The cubed root of 216 is 6.

how many times should you expect to see heads if a fair coin is tossed 3500 times?​

Answers

Answer:

1750

Step-by-step explanation:

If you flip a coin, you should theoretically get heads 50% of the time and tails 50% of the time. So in this case you would get heads 1,750 times.

25 am
15 cm
15 om
E9 cm
-
9 cm
What is the area of the trapezold?
O
354 cm
o
408 cm2
0 510 cm2
0 O
595
cm2

Answers

The answer is 408 cm2 after applying the formula of right angled triangle,adding 25 and both 9 and applying the formula 1/2(p1+p2)h

Please give me brainliest

based on sample 2, how many students from the entire student population would prefer not to start at 7:45 am

Answers

Answer:

270

Step-by-step explanation:

from web

solve the system by substitution​

Answers

1) Solve one of the equations for either variable.

2) Substitute the expression from Step 1 into the other equation.

3) Solve the resulting equation.

4) Substitute the solution in Step 3 into one of the original equations to find the other variable.

5) Write the solution as an ordered pair.

Hooray! Poplin Elementary collected 1,224 Box Tops! The 8 volunteer moms will have to tape them to the turn-in sheet. If they share the work equally, how many will each mom need to do?

Answers

They will each need to do 153!


Use the Pythagorean Theorem to find the missing length and then round the
result to the nearest tenth.

Answers

Answer:2 squared +3 squared and the square root of that number

Step-by-step explanation:

Which of the following is a perfect square trinomial?

A. 4x^2 + 20xy - 25y^2

B. 4x^2 - 14xy + 25y^2

C. 4x^2 + 14xy - 25y^2

D. 4x^2 - 20xy + 25y^2

Answers

Answer:

[tex]D.~4x^2-20xy+25y^2[/tex]

Step-by-step explanation:

[tex]4x^2-20xy+25y^2\\\\=(2x)^2-2\cdot 2x \cdot 5y+(5y)^2\\\\=(2x-5y)^2[/tex]

Jenna's pool is 22 feet long, 12 feet across and 6 feet deep.How many square feet of plaster will it take to cover it? (Be careful:Think about which parts will or won't be covered in plaster)

Answers

Answer:

264sq feet

Step-by-step explanation:

because you only need to cover the top you multiply 22 x 12 to get 264 sq feet

The circumference of a circle is 18.84 yards. What is the circle's diameter?

Answers

Circumference = 18.84 yards
Diameter = 6 yards

What is the range of this data set? 64°, 72°, 74°, 68°, 70°, 68°, 68°, 75°, and 44°

Answers

Answer:

31

Step-by-step explanation:

First put your numbers in order

44 , 64 , 68 , 68 , 68 , 70 , 72 , 74  ,

Then subtract the Highest and Lowest numbers by each other

75 - 44 = 31

A private club grew by 7 members each week for 63 weeks. What was the total change in the club's size? members​

Answers

Answer:

The answer is 441

Step-by-step explanation:

7 x 63 = 441

¿ Cuanto es 3 por 5 centésimas ?

Answers

Answer:

0.15 or 3.05

Step-by-step explanation:

3*(5/100) = 15/100 = 3/20 = 0.15

or

3 5/100 = 305/100 = 61/20 = 3.05

dependiendo de lo que esté tratando de encontrar

lo siento si mi español es malo

espero que esto ayude

The expression below is the factorization of what trinomial?

(5x + 6)(3x - 2)

A. 15x^2 + 4x + 12

B. 15x^2 + 4x - 12

C. 15x^2 + 8x + 12

D. 15x^2 + 8x - 12

Answers

Answer:

Choice D is the correct answer

Step-by-step explanation:

Use the foil method and expand

.325 equals what fraction

Answers

Answer:

according to desmos scientific calculator, the answer is 13/40

13/40 is the correct answer

Answer the question 3523+4353

Answers

Answer:

7,876

Step-by-step explanation:

brainliest please

PLEASE HELP! 50 POINTS! Consider the following set of sample data: (34, 32, 34, 32, 40, 37, 31, 31, 29, 27). Which of the following will give a 95% t confidence interval for the mean of the population from which the sample was drawn?

Answers

Answer:

(15.23,41.016)

Step-by-step explanation:

WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.
[tex]= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125[/tex]
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:
[tex]= ((21 - 28.125)^{2} + (24 - 28.125)^{2} +(25 - 28.125)^{2} + (32 - 28.125)^{2} + (35 - 28.125)^{2} + (31 - 28.125)^{2} + (29 - 28.125)^{2} (28 - 28.125)^{2}[/tex]
[tex]= 148.877/8 = 18.6[/tex]
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:
[tex]= 28.125 + (1.96 *18.6)/(\sqrt{8} )[/tex]
[tex]= 41.016[/tex]
[tex]= 28.125 - (1.96 * 18.6)/(\sqrt{8}) = 15.23[/tex]
The confidence interval for this data set is (15.23,41.016)

Answer:

32.7 ± 2.262(1.19)

Step-by-step explanation:

See attached pictures

PLSS ANSWER

Round each fraction to help you estimate the solution for the equation.

three sixths plus three sixths

A. 0
B. one half
C. 1
D. one and one half

Answers

[tex] \frac{3}{6} = three \: sixths[/tex]

[tex] \frac{3}{6} + \frac{3}{6} = \frac{3 + 3}{6} = \frac{6}{6} = 1[/tex]

Letter C
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