A block of wood is in the shape of a rectangular prism with dimensions (n+5) cm, (n+8) cm, and (n+14) cm. All faces of the block are painted, and then the block is cut into 1 cm cubes using parallel cuts to each face. If exactly half of the cubes have no paint on them, find the total number of cubes.

Answers

Answer 1

Answer:

The total number of cubes in the rectangular prism are 1,120 cubes

Step-by-step explanation:

The given parameters are;

The dimensions of the rectangular prism block of wood = (n + 5), (n + 8), and (n + 14)

The volume of the block of wood = (n + 5)×(n + 8)×(n + 14) = n³ + 27·n² + 222·n + 560

The quantity of the 1  cm cubes that have no paint = 1/2 of the total quantity = 1/2 the volume of the original cube

The cubes that have paint on them are the surface cubes, we have;

One layer of cube is removed from each of the eight sides, therefore, we have the dimensions of the cube rectangular prism that have no paint on them given as (n + 5 - 2), (n + 8 - 2), and (n + 14 - 2), which gives the dimensions as (n + 3), (n + 6), and (n + 12);

Therefore, we have

2 × (n + 3)×(n + 6)×(n + 12) = (n + 5)×(n + 8)×(n + 14)

2 × (n + 3)×(n + 6)×(n + 12) - (n + 5)×(n + 8)×(n + 14) = 0  

Which gives;

n³ + 15·n² + 30·n - 128 = 0

n = 2

n = -17/2 - √(33)/2 = -5.6277

n = √(33)/2 - 17/2 = -11.3722

Therefore, given that the smallest dimension of the painted prism = (n + 5), the possible value for n = 2

The volume of the rectangular prism = (n + 5) × (n + 8) × (n + 14) = (2 + 5) × (2 + 8) × (2 + 14) = 1120 cm³

Given that the cuts are 1 cm³ each, the total number of cubes in 1,120 cm³ = 1,120 cubes.


Related Questions

Please answer fast. Three hens can lay 3 eggs in 3 days. How many hens would lay 12 eggs in 12 days.

Answers

Answer:

They lay 3 eggs over 3 days. Well, make this easier on yourself. 1 egg=1 day. So, the answer would definitely be 12 days from 3 hens=12 eggs.

Step-by-step explanation: put me as brainliest please !

There are 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 bacteria cells after 3 hours. Write the repeated multiplication as a power and then evaluate.

Answers

Answer:

2 over the power of 3

Step-by-step explanation:

Answer:

bocock

Step-by-step explanation:

When finding the common denominator between fractions, which value can be helpful, GCF, or LCM? How?

Answers

Answer:

The answer would be GCF because when you finding the common denominator GCF is how you do it. at least thats what I do and I got it right! :p

hope this helps! :) I don't really know how to explain lol

Please help me get 100% I have so much more to do

Answers

Fraction = 23/100

Decimal = .23

Percent = 23%

Hope this helps!

Fraction: 23/100
Decimal: 0.23
Percent: 23%

GIVING BRAINIEST for the correct answer

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Last one is 6.3 pounds and the other one is 8.5 dollars

Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?

Answers

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

because I said so :)

One cantaloupe costs $2. How many
cantaloupes can you buy for $6?

Answers

Answer:

3

Step-by-step explanation:

ignore this i need more letters lol have a good day

Answer:

You could buy 3 cantaloupes.

Step-by-step explanation:

So, you have $6. Now, what we would do is (O is 1 cantaloupe):

If O cost $2, do the following:

O O O O O

2  2  2  2 2

Now, lets count up til we get 6:

2 + 2 = 4; 4 + 2 = 6;

After you have done that step, count how many 2's you see in that equation. I see 3.

Therefore, you could buy 3 cantaloupes.

What is the correct ratio?
Sin 40=w/28
Tan 40=w/28
Cos 40 = w/28
Sin 40 = 28/w

Answers

Answer:

As we know that

tanФ = opposite ÷ adjacent

Therefore,  the correct ratio is:

tanФ = opposite ÷ adjacent

        = w ÷ 28

       = w/28

i.e.

tanФ = w/28

Step-by-step explanation:

As we know that

tanФ = opposite ÷ adjacent

Given the triangle with an angle of 40°.

As the opposite of an angle 40° is the length 'w', and adjacent to the angle

40° is the length '28'.

As we know that

tanФ = opposite ÷ adjacent

Therefore,  the correct ratio is:

tanФ = opposite ÷ adjacent

        = w ÷ 28

       = w/28

i.e.

tanФ = w/28

Answer:As we know that tanФ = opposite ÷ adjacentTherefore,  the correct ratio is:tanФ = opposite ÷ adjacent        = w ÷ 28       = w/28i.e.tanФ = w/28Step-by-step explanation:As we know that tanФ = opposite ÷ adjacentGiven the triangle with an angle of 40°.As the opposite of an angle 40° is the length 'w', and adjacent to the angle 40° is the length '28'.As we know that tanФ = opposite ÷ adjacentTherefore,  the correct ratio is:tanФ = opposite ÷ adjacent        = w ÷ 28       = w/28i.e.tanФ = w/28

I really need your help guys.

Answers

Answer:

The average rate of change from 0 to 20 years old is -2.

Step-by-step explanation:

Average rate of change means slope.

slope = y2 - y1 / x2 - x1

Pick any points between 0-20. They have given on the graph already (0, 112) and (20, 72) so plug it into slope equation.

112 - 72/ 0 - 20

40/-20

= -2

The average rate of change from 0 to 20 years old is -2.

Bart budgeted $285.75 each month for utilities. His utility bills this month were $130.50 for electric, and $240 for gas. How much over budget is he? *
!!

Answers

Answer:

$84.75 over budget

Step-by-step explanation:

Barts' budget is 285.75

Bills: 240 + 130.50 = $370.50

(subract by his budget)

370.5 - 285.75 = $84.74

:)

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hahaha help me
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hahaha help me
hahaha help me
hahaha help me
hahaha help me
hahaha help me

Answers

Answer:

B. could be the answer for me

Answer:

3

Step-by-step explanation:

A pair of shoes cost $12 for Nike to make. If Nike marks up the price 430%, what is the price of the mark-up?

Answers

Answer:

The price of the mark-up is $51.60

Step-by-step explanation:

ZzzzZZZZZzzzzzZZZZZZzzzzZZZZZZZzzzzzzZZZZzzzzZZZZZzzzZZZZzzzzZzzzz.....................................*wakes* *looks at hw* OMG IM NOT DONE YET!!!!!! HELP ME

Answers

Answer:

12

Step-by-step explanation:

simplify the expression and THEN evaluate it if f=3 and g=-2

(4f-3+2g)-(-4g+2)

Answers

4f-3+2g +4g-2

4f +6g -5

4(-3)+6(-2)-5

-12-12-5

-29

Will mark as brainliest ❤️

Answers

Answer:

is just a "place-holder" or "variable.

If

f

x

=

x

+

7

then (using a different variable)

f

(

t

)

=

t

+

5

or

using a constant

f

(

x

)

=

5

+

7

Since

5

+

7

=

12

for the given example

f

(

5

)

=

12

I need help with this!

Will give brainliest, thank you :)

Answers

Answer:

y=x-3

Step-by-step explanation:

The slope is just x, and the y intercept will be one over from (1,-2) which is (0,-3), so -3 is the starting point.

Please help me
Which one do I choose for each one

Answers

For the first one i would choose the second answer, Not both.

A nurse has an annual income of $52, 175. The income tax that she must pay is 9%. How much does she have to pay in taxes in dollars and cents?

Answers

ответ на картинке !!!!

I need help on number 5 plz

Answers

Answer:

x5-8x+3y i don't sure for my answer hihihi understand my answer heheh sorry if I don't help you

3 1/3÷1/6
I Mark brainlies ​

Answers

Answer:

20

Step-by-step explanation:

A garden with dimensions 50 feet by 70 feet is surrounded by a walkway of
uniform width. The total area of the walkway is greater than 350 square feet but is less than 500 square feet. Find the possible widths of the walkway.

Answers

bulok man ko og math guys. wakoy ika tabang nimo

bro i didnt even go on brainly for the past week and a half and they do this?
omg brainly PLEASE fix these bots Imao

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Yeah sameee, they remove my brainliests too☹️

Answer:

thats tough

Step-by-step explanation:

tough a f

n 8y7h7y

I need to find the p(9) ,p(3),when p(x) =3x-5​

Answers

P(9) = 22, p(3) = 4 hth

Callie has 11 dollars and 33 cents. The cookies she plans on is $2.25. She has about 5 friends she plans on buying cookies. Will she be able to buy each friend a cookie?

Answers

Yes, she will be able to buy a total of 5 cookies
yes she will (seeing there are no taxes and things like that AND she is not buying one for herself)

2.25 x 5 = 11.25
so she will have 8 cents left

If she is buying one for herself, she will not have enough to buy everyone a cookie

Kelsey jogs 60 feet in 6 seconds. What is this rate in miles per hour? Round to the nearest tenth.

Answers

Answer:

10 miles per hour

Step-by-step explanation:

60 / 6 = 10

Therefore, she is jogging 10 miles per hour.

Pretty sure this is running, not jogging.

The rate of jogging is 10 miles per hour

The calculation can be done as follows

Kelsey jogs a total of 60 feet in 6 seconds

The rate is = 60/6

= 10 miles/hour

Hence the rate in miles per hour to the nearest tenth is 10 miles per hour

Please see the link below for more information

https://brainly.com/question/19856531?referrer=searchResults

Write in exponential form​

Answers

Answer and explanation in screenshot:

m a t h w a y solution: (2/5)^3 = 8/125

Symbolab explanation in image

Liz spent $170 in 5 days on food and groceries. What integer best represents the average amount her checking account changed per day?

Answers

Answer:It is 34:1

brainliest please

A banner company sells 5-foot banners to retailers for x dollars. The St. James Sign Shop marks them up 90%. Express the retail price at the St. James store algebraically.

Answers

Answer:

$1.9x

Step-by-step explanation:

Given that :

Cost of banner = x dollars

Markup percentage at st. James store = 90%

Retail price at st. James store :

Initial cost + markup

Cost of banner + 90% of cost

x + 0.9x

= 1.9x

Hence, retail.price at st. James store is $1.9x

Please help meeee

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

Answers

Answer:

<1=33, <2=90, <3=57

Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

Consider the table that includes the input and output values of a function. Which answer classifies the function using finite differences? The function is quadratic with a constant second difference of –96. The function is quadratic with a constant second difference of 96. The function is cubic with a constant third difference of –96. The function is cubic with a constant third difference of 96.

Answers

Answer:

b, quadratic with constant second difference of 96

Step-by-step explanation:

The function is cubic with a constant third difference of 96.

What is Function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Using differences:

X            f(x)             first difference          second difference             third

3            39                        -                                    -                                -

5            187             (187-39)/2= 74                       -                                -

7            551            (551-187)/7-5 = 182     182 - 74/2 = 54                   -

9           1227          (1227-551)/(9-7)=338   338-182/2=78          78-54/2 = 12

11           2311           (2311-1227)/2=542      542-338/2=102       102-78/2 = 12

According to table,

The function is cubic, because the third average change rate is constant of 12.

12>0, so the third difference is >0 then -96 is false.

Thus, the function is cubic with a constant third difference of 96.

Learn more about function from:

https://brainly.com/question/12431044

#SPJ2

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