The specifications for the dimensions of a new cardboard container are shown. If the volume of the container is modeled by V(h) = 2h^3 - 9h^2 + 4h and it will hold 45 cubic inches of merchandise, what are the containers dimensions?

Answers

Answer 1

Solving a cubic equation, it is found that the dimensions of the container are of 1 inch, 9 inches and 5 inches.

The volume of the cubic container is given by the following equation:

[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]

Since it holds 45 cubic inches of merchandise, we have that [tex]V(h) = 45[/tex], then:

[tex]V(h) = 2h^3 - 9h^2 + 4h[/tex]

[tex]45 = 2h^3 - 9h^2 + 4h[/tex]

[tex]2h^3 - 9h^2 + 4h - 45 = 0[/tex]

Using a cubic equation calculator, the real solution is [tex]h = 5[/tex], thus, the dimensions are:

[tex]h = 5[/tex]

[tex]h - 4 = 5 - 4 = 1[/tex]

[tex]2h - 1 = 2(5) - 1 = 10 - 1 = 9[/tex]

The dimensions of the container are of 1 inch, 9 inches and 5 inches.

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Related Questions

If AB= 4 units and DC=4 units , what is the length of BC

Answers

Answer:

4 units i think

Step-by-step explanation:

i dont know how beacuse 4 is answer

Which of the following coordinate points have a y-value of 6? Select all that apply.

A) (3, 6)
B) (6, 5)
C) (8, 6)
D) (1, 6)

Answers

Answer

A, C, and D

Step-by-step explanation:

You are trying to find the y value in (x,y) form. Therefore, it has to be A, C, and D because they all have a 6 in the y value.

Plz help I need help

Answers

Answer:

x = 6

Step-by-step explanation:

This can be written as a ratio

7 : 2

21 : x

If you times one side by 3, you have to multiply the other side by three too:

2 × 3 = 6

∴ x = 6 when y = 21

Has a slope of 4 and passes through (-2, 4)

Answers

Answer:

y = 4x + 12

Step-by-step explanation:

y = mx + b

m = slope = 4

substitute the point (-2, 4) as (x, y)

4 = 4(-2) + b

4 = -8 + b

12 = b

Hope this helps! Pls give brainliest!

The equation of line is y= 2x+ 8.

what is slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Slope= 2

and, Passes through (-2, 4)

So, using the slope- intercept form is

y= mx+ b

4 = 2(-2)+ b

4 = -4 + b

b=8

And, the equation of line is

y= mx+ b

y= 2x + 8

Hence, the equation of line is y= 2x+ 8.

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Solve pleaseee !!!..

Answers

Answer:

x=76

Step-by-step explanation:

#CarryOnLearning

Answer:x=76

Step-by-step explanation:

Distribute: -4(x-26)=-200 -4x + 104 - 104 = -200

Subtract 104 from both sides of the equation

-4x + 104-104 = -200-104

Simplify

Subtract the numbers

-4x +104-104=-200 - 104

-4x=-200 - 104

Subtract the numbers

-4x = -200 - 104

-4x = -304

Solution

x=76

Which ordered pair is a solution of the equation?
7x – 2y = -5

Answers

Answer:the answer should be (1,5)

Step-by-step explanation:

PLEASE HELP ITS MATH THANK YOUUUU

Answers

2m. 2 meters is the answer

The answer is 1cm = 2m

******Please help me help please help me ******

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

A machinist needs to drill 4 holes 6/16” in diameter. What is the hole size in eights of an inch?

Answers

Answer:

3/8"

Step-by-step explanation:

Reduce the fraction. The numerator and denominator are both divizable by 2 which leaves 3/8

The elevation of city A is 72 feet above sea level; the elevation of city C is 24 feet above sea level. The elevation of city D is of the elevation of city C. Simplify the expression and explain why the answer is negative or positive.

Answers

Answer: d=c/4

Step-by-step explanation:

1. given w(x)=4x
a. graph r(x)=4 x w(x). then complete the table of corresponding points on r (x). How do you graph this?

Answers

Answer:

Step-by-step explanation:

a). When graph w(x) is transformed to r(x) = 4 × w(x), graph of w(x) is vertically stretched by a scale factor of 4.

Table for the corresponding points will be,

x w(x) r(x)

0 0 0×4 = 0

15 60 60×4 = 240

30 120 120×4 = 480

45 180 180×4 = 720

b). As discussed in part (a), graph of w(x) will be vertically stretched by a scale factor of 4 to produce the graph of r(x).

c). Since, w(x) = 4x

and r(x) = 4[w(x)]

r(x) = 4(4x) = 16x

r(x) = 16x

HELP SOLVE PLEASEEE

Answers

Answer:

d. -6x + 2 = -15

If there are 2,000 females and 2,000 males enrolled at a college and four different students are randomly selected to receive a book scholarship, what is the probability that at least one is female?

Calculate the probability two ways: a) treat as dependent selections and b) treat as independent selections.

Answers

Answer:

500

Step-by-step explanation:

you just divide 2000 by 4 and get 500

wich one is bigger 4\5 or 0.8

Answers

Answer: They both equal the same thing.

Step-by-step explanation: 4/5=0.8

Answer: there both equal

Step-by-step explanation:

4/5 is basically 0.8 cuz 0.8 put a extra 0 in it its gonna say 0.80 and 4 x 20= 80. and that's 80/100 so yea..... 4/5 and 0.8 are equal.

this my first time answering. Sorry if I get it wrong TwT

The ratio of cups of orange juice concentrate to water in a punch recipe is 3:5. If Connor used 25 cups of water, how many cups of orange juice concentrate did he use

Answers

Answer:

15 cups of orange juice

Step-by-step explanation:

Let u be 1 unit.

5u = 25 cups

u = 25÷5

= 5

3u = 5×3

= 15

The measure of angle STV is 117°. What is the measure of angle UTV

Answers

Answer:

117 - 86 = 31°

The answe is 31

solve. −3.1=−3.5x−4.6

Answers

Answer:

x = 0.428571 repeating

Step-by-step explanation:

Answer:

-0.428571 repeating

Step-by-step explanation:

add 4.6 both sides

1.5 = -3.5x

divide -3.5 both sides

-0.428571 repeating

A truck can be rented from Company A for $70 a day plus $0.50 per mile. Company B charges $40 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answers

Answer: 300 miles, $220

Step-by-step explanation:

Identify the sampling designs that use voluntary response sampling. Check all that apply.

Mrs. O’Neill asks all her seventh-period students about their study habits.
Each customer of a fitness club is interviewed about their health as they exit.
An online poll about voter opinion of political issues is posted on social media.
A student organization interviews students in the drama club about the spring play.
A doctor’s office sends email surveys to all its patients.
A department store includes a link to an online survey on customers’ receipts.

Answers

Answer: C, E, F

Step-by-step explanation:Got it right

( sorry for the wired question )

researchers in New York city did a study on ice cream sales and murder rates in the city. this graph was included in the results

after seeing this graph as a picture with the headline "ice cream sales causes murder rates to increase" shared on social media by her best friend's second cousin, the president of a prominent HOA in the Hamptons decided to petition to ban the sale of ice cream so that people would stop being murdered .

this is the question - compare and contrast what you see on the graph.

second part to the question - was the HOA president right for doing so ? what other factors could have contributed to both the rise in ice cream sales and murders? is this an example of correlation or causation?

Answers

The presence of a correlation between statistical variables is an indication

of the existence of a relationship variables, it however, does not imply

direct causation.

Part one:

The similarities of the graphs are;

The rate of change in the sale ice cream and rate of murder are almost equal.The peak of ice cream sales and murder rate occur at the same time of the year.The rate of decrease in the sale of ice cream and murder rate are equal between the months of July and December.

The differences are;

The shape of the ice cream sale graph is more bell shapes than the graph of murder rates.The murder rates occur over a slightly more longer period than than the sale of ice cream.There is a sharp decrease in the murder rate in the month of February while the ice cream sales increases steadily from January to July.

Second part;

The HOA president's petition is in line with the social media post based on the graph.

The graph shows a strong correlation between murder rates and ice cream sales, however, selling ice cream, and murder are unrelated events.

The correlation between the sale of ice cream and murder is an indication of the existence of a common third factor.

Based on the time of the year dependence of the two variables, which corresponds to hot and cold weather, there is a correlation of both the murder rate and ice cream sales with temperature.

Therefore, the HOA president is not right for doing so

Learn more here:

https://brainly.com/question/3119351

Complete the following.Write the answers in your journal

I learned filtering of solid and liquid mixtures can be saperated with the use of____ or____ as a medium in which_______material in the medium

Sieving is a method in which ________of ________sizes are separated from a mixture on the basis of the _____

Answers

Answer:

1.FILTER WATER 2.FILTER CLOTH

3.LIQUIDS

4.INSOLUBLE

5.DIFFERENCE

help pls aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answers

The correct equation is simply just X=3 :)

Answer:

x=3

Step-by-step explanation:

y = mx + b

m = (y2 - y1)/(x2 - x1)

m = (8+4)/(3-3) = 12/0 = UD

x = 3

Georg invests $5000 for 14 years at a rate of 2% per year compound interest.
Calculate the interest he receives.

Answers

Answer:

[tex]\frac{1}{50}[/tex] or 0.02

Step-by-step explanation:

2% x 1 to give the answer

reduce it to faction like

[tex]\frac{2}{100}[/tex] = [tex]\frac{1}{50}[/tex]

Isaac wants to play miniature golf. Go Golf charges $2.50 for ball and club rental and $4.25 per game. Golf Games charges $3.25 for ball and club rental and $8.50 for two games. For how many games would the cost be the same? Write and solve an equation to determine the number of games for which the cost would be the same.

Answers

The cost would be the same for 47 Go golf and 54 golf games.

What is the Multiplication operation?

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

Given data as:

Charges for Go Golf -

Renting a ball and a club costs $2.50.

$4.25 for one game and

Charges for Golf Games -

3.25 for the rental of a ball and a club

$8.50 for two games

We have to determine the number of games would the cost be the same.

Total charges of Go golf per game = $2.50 + $4.25 = $6.75

Total charges of Golf game for 2 games = $3.25 + $8.50 = $11.75

For per game = $11.75 / 2 = $5.875

Let the game would be x for Go golf and

And let game would be y for the golf game

As per the given condition,

6.75 x = 5.875y

27/4 x = 47/8 y

Apply cross multiplication operation,

54x = 47y

x/y = 47 / 54

x = 47

So y = 54.

Hence, the cost would be the same for 47 Go golf and 54 golf games.

Learn more about Multiplication operations here:

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The cost would be the same for 47 games at Go Golf and 54 games at Golf Games.

Total charges of Go golf per game = $2.50 + $4.25 = $6.75

Total charges of Golf game for 2 games = $3.25 + $8.50 = $11.75

Cost per game at Golf Games

= Total charges for 2 games / 2

= $11.75 / 2

= $5.875

Let the number of games be x for Go Golf and y for Golf Games.

As per the given condition,

6.75x = 5.875y

To find the relation between x and y, cross-multiplication can be used:

27/4 x = 47/8 y

54x = 47y

x/y = 47/54

Comparing the value gives

x = 47 and y = 54.

Hence, the cost would be the same for 47 games at Go Golf and 54 games at Golf Games.

Learn more about Ratio here:

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What is the mean of the frequency distribution?
33
Baseball bat length
f
27
2
28
4
29
3
31
5
16
30.3
30.7
29.4
29.6

Answers

Answer:

Step-by-step explanation:

m
+ 4 = 7
Step One:
Step Two:
Step Three:
Step Four:
ma9
m/3+4+4+7+4
m/3-7
m=21
m/3+4-47-4
m/3*3+4=743
m/3-3
ma17
m/3+4-3=7-3
m/3*3=3*3
m/3+7=4
m=3
m/3+8=11
m/314-4=7
m+4=21

Answers

Answer:

Step-by-step explanation:

1. m/3+4-4=7-4

2. m/3=3

3. m/3*3 = 3*3

4. m=9

Answer:

m=9

Step-by-step explanation:

m/3+4-4=7-4

m/3=3

m/3*3=3*3

m=9

PLEASE HELP ME WITH THIS QUESTION PLEASE

and show your steps please I really need help with this question please help please

Answers

Answer:

a. 2.2 m

b. 8 m

Step-by-step explanation:

4) a. Sin 32 = x/4

= (sin 32)(4) = x

b. Cos 65 = 4.5/x

x = 4.5/Cos 65

What is the slope of the line that contains these points

Answers

Answer:

Slope = - 5

Step-by-step explanation:

Let,

x1 = 13

x2 = 14

y1 = 11

y2 = 6

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope = ( 6 - 11 ) / ( 14 - 13 )

= - 5 / 1

Slope = - 5

Answer:

[tex]\boxed{\sf slope:-5}[/tex]

Step-by-step explanation:

Slope :

[tex]\boxed{\sf m=\cfrac{rise}{run} =\cfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\sf ^*m=slope[/tex]

[tex]\sf (x_1, y_1): first \: coordinates[/tex]

[tex]\sf (x_2, y_2): second\: coordinates[/tex]

___________________

[tex]\sf \left(x_1,\:y_1\right):\left(13,\:11\right)[/tex]

[tex]\sf \left(x_2,\:y_2\right):\left(14,\:6\right)[/tex]

[tex]\sf slope\:(m)=\cfrac{6-11}{14-13}[/tex]

[tex]\sf slope\:(m)=-5[/tex]

____________________

Find the volume of the composite solid.

Answers

Answer:

The answer would be c

Step-by-step explanation:

Answer:

B, if not then it's D

Step-by-step explanation:

Using the graph of y = f(x) to the right, and given that the zero of the function is x=20, find the following.

Answers

Answer:

3.5

Step-by-step explanation:

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The specifications for the dimensions of a new cardboard container are shown. If the volume of the container is modeled by V(h) = 2h^3 - 9h^2 + 4h and it will hold 45 cubic inches of merchandise, what are the containers dimensions?​

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The specifications for the dimensions of a new cardboard container are shown. If the volume of the container is modeled by V(h) = 2h^3 - 9h^2 + 4h and it will hold 45 cubic inches of merchandise, what are the containers dimensions?