A rectangular is completety filled with dice.Each dice has volume of 2cm³.The length of the box is 5cm grater than its width and its height is 5cm.Suppose the box holds at most 150dice.What are the posibble dimensions of the box​

Answers

Answer 1

Answer:

length = 10.64 cm, width = 5.64 cm, and height = 5 cm.

Step-by-step explanation:

Total volume of dice that filled the box = (150 x 2) cm³

                                         = 300 cm³

Let the length, width and height of the box be represented by l, w and h respectively.

So that;

l = (w + 5) cm

w = w

h = 5 cm

volume of the box = length x width x height

                               = (w + 5) x w x 5

                               = (w + 5) x 5w

                               = 5[tex]w^{2}[/tex] + 25w

volume of the box = 5[tex]w^{2}[/tex] + 25w

Since the box was completely filled by 150 dice, then;

total volume of dice = volume of the box

300 = 5[tex]w^{2}[/tex] + 25w

5[tex]w^{2}[/tex] + 25w - 300 = 0

Divide through by 5 to have;

[tex]w^{2}[/tex] + 5w - 60 = 0

Applying the quadratic expression,

w = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) ÷ 2a

where: a = 1, b = 5 and c = -60

(-5 ± [tex]\sqrt{5^{2} - 4(1*-60)}[/tex] ) ÷ 2

(-5 ± [tex]\sqrt{265}[/tex]) ÷ 2

(-5 ± 16.28) ÷ 2

(-5 + 16.28) ÷ 2 OR (-5 - 16.28) ÷ 2

5.64 OR -10.64

Thus, w = 5.64 cm

So that, l = (w + 5) = 10.64 cm

The possible dimensions of the box are: length = 10.64 cm, width = 5.64 cm and height = 5 cm.


Related Questions

HELP PLS THIS IS A TEST QUESTION


Which linear inequality is represented by the graph?
y<1/2x+2
y>1/2x+2
y<1/3x+2
y>1/3x+2

Answers

Answer:

y<1/2+2

Step-by-step explanation:

Answer:

I think the answer is A because I learned about slope last year

Jim stands on a dock that is 3 3/4 feet above the lake. He dives down 12 1/2 feet below the dock. What is Jims vertical location relative to the lake surface?

Answers

Given:

Jim stands on a dock that is [tex]3\dfrac{3}{4}[/tex] feet above the lake. He dives down [tex]12\dfrac{1}{2}[/tex] feet below the dock.

To find:

The Jims vertical location relative to the lake surface.

Solution:

We have,

Vertical location of dock relative to the lake surface [tex]=3\dfrac{3}{4}[/tex] feet

He dives down [tex]12\dfrac{1}{2}[/tex] feet below the dock. So,

Vertical location relative to the lake surface [tex]=3\dfrac{3}{4}-12\dfrac{1}{2}[/tex]

[tex]=\dfrac{3\times 4+3}{4}-\dfrac{12\times 2+1}{2}[/tex]

[tex]=\dfrac{12+3}{4}-\dfrac{24+1}{2}[/tex]

[tex]=\dfrac{15}{4}-\dfrac{25}{2}[/tex]

Taking LCM, we get

[tex]=\dfrac{15-50}{4}[/tex]

[tex]=\dfrac{-35}{4}[/tex]

[tex]=-8\dfrac{3}{4}[/tex]

Here, negative sign means Jim location is below the lake surface.

Therefore, Jim is [tex]8\dfrac{3}{4}[/tex] feet below the lake surface.

Answer:-8 3/4

Step-by-step explanation:

I just took the cahoot

Draw a graph of the line that goes through the points (-4, 7) and (0, 3)
What is the y-intercept and slope of the line you've drawn?

Answers

Answer:

y = -x + 3

Step-by-step explanation:

Use this formula to get the slope [tex]\frac{y2 - y1}{x2 - x1}[/tex]

PLUG IN

[tex]\frac{3 - 7}{0 - -4} \\\\\frac{-4}{4} \\[/tex]

-4/4 = -1

The slope is -1

To find the y- intercept plug your slope and one of your points in this y=mx+b

We will use (0,3)

3 = -1(0) + b (b represents y-intercept)

3 = b

The equation would look like this

y = -x + 3

Hope this helps ya!!

Dexter is curious as to whether there is a relationship between a person’s height and thumb length. Fourteen of his classmates volunteered to be measured. He listed his data in a table.

Examine the data set and determine the relationship, if any, between height, h, and thumb length, t. Use your model to predict the thumb length of a person who is 174 cm tall.

Answers

The answer to this question is 7.404

Joe pays $25.10 for 2.5 pounds of wall-paper. What is the price, in dollars and cents, per pound of wall paper?

Answers

Answer:

10.04

Step-by-step explanation:

25.10/2.5=10.04

Answer:

10.04

Step-by-step explanation:

All you do is divide 25.10 by 2.5, the total($25.10) by the amount(2.5) then that is where

25.10 divided by 2.5 comes from, therefore your answer is 10.04

One year ago, Lindsey deposited $250 into a savings account. Her balance is now $253. Two years ago, Jenn deposited $250 into a savings account. Her balance is now $257.50. Which account has the greater simple interest rate? Explain.
This is due at 2

Answers

Jenn's account has the greater simple interest rate

Where A is the final amount after investment, P is the initial amount, r is the rate of interest and t is the time periods.

For Lindsey:

Lindsey simple interest was 1.2% annually

For Jenn:

Jenn simple interest was 1.5% annually

Therefore Jenn's account has the highest simple interest rate.

^^^^^^^^^^^^^^^^^^^^

"EamonnAdams1992"

Answer:

She has a higher interest rate

Step-by-step explanation:

Lindsay’s interest is $3 for one year. Using the formula for interest, I = prt, Lindsey’s money is earning at a rate of 1.2%. Jenn has earned $3.75 for one year. Her money is earning at a rate of 1.5%, which is a higher interest rate.

Sample answer on edge ;)

Suppose that f(x)=3x+1....

Answers

Answer:

3

Step-by-step explanation:

f(x) = 3x+1

f(x+h) = 3(x+h)+1 = 3x+3h+1

f(x+h) - f(x)= 3x+3h+1-3x-1 = 3h

3h/h=3

what would the value of X be on this one?

Answers

Answer:

i think it's 51 because if you add 106 and 23 together it's 129 then 180-129= 51

Step-by-step explanation:

Assignment
Yeshi is making Pork fing. He has only 300g of pork
So he have to adjust the ro recipe.
500g pork
150g tomatoes
100g butter
120ml water
45g green chilli
8og onion.
a How much of each of the other ingredients
should he use​ to make pork fing

Answers

Answer / Step-by-step explanation:

500g - 300g = 200  {200 ÷ 500 = 0.4}  ---- 300g pork

0.4 × 150g = 60g tomatoes

0.4 × 100g = 40g butter

0.4 × 120ml = 48ml water

0.4 × 45g = 18g green chilli

0.4 × 8og = 3.2og onion

prove algebraically that n^2 -n is never an odd number when n>1

Answers

Answer:

See Below.

Step-by-step explanation:

We want to prove that:

[tex]n^2-n[/tex]

Is never an odd number when n>1.

We will have two cases. We can prove them for each case individually.

The Even Case: n is Even:

Let n be even. Then, we can rewrite n as:

[tex]n=2k[/tex]

Where k is any positive integer.

This is because twice of any integer is even, so n must be even.

Substitute this into our expression to acquire:

[tex]=(2k)^2-(2k)[/tex]

Square:

[tex]=4k^2-2k[/tex]

4 times anything is even. 2 times anything is also even. Therefore, our expression will stay even.

The Odd Case: n is Odd:

Let n be odd. Then we can rewrite n as:

[tex]n=2k-1[/tex]

Where k is any positive integer.

This is odd because twice of any number is even, but if subtracted by 1, it yields an odd number.

We will substitute this into our expression to acquire:

[tex]=(2k-1)^2-(2k-1)[/tex]

Square:

[tex]=(4k^2-4k+1)+(-2k+1)[/tex]

Simplify:

[tex]=4k^2-6k+2[/tex]

4 times anything is even. 6 times anything is even. And anything even added to 2 will still be even.

Therefore:

[tex]n^2-n[/tex]

Will never be an odd number when n>1.

What is the measure of ∠ABD?

Answers

Answer:

m∠ABD = 114°

Step-by-step explanation:

Given measurements of interior angles are:

m∠D = 2n°

m∠C = 60°

m∠ABD = (4n+6)°

The measurement of exterior angle of a triangle is equal to the sum of two opposite interior angles.

This can be mathematically expressed as:

m∠ABD = m∠C+m∠D

Putting the respective values

[tex]4n+6 = 2n+60\\4n-2n+6 = 60\\2n+6 = 60\\2n = 60-6\\2n = 54\\\frac{2n}{2} = \frac{54}{2}\\n = 27[/tex]

Putting n=27 in (4n+6)°

[tex]=4(27) + 6\\= 108+6 = 114[/tex]

Hence,

m∠ABD = 114°

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Answers

Answer:

$52.50

Step-by-step explanation:

Set up the ratio:

[tex]\frac{24.50}{7}[/tex]

Simplify in order to find the cost per gallon.

The cost per gallon is $3.50 because 7 divided by 7 is one and 24.50 divided by seven is 3.5.

Now you have this left:

[tex]\frac{3.50}{1}[/tex]

Multiply the denominator by 15 since Robert needs 15 gallons.

Then, multiply the top by 15 because whatever you do to the denominator, you have to do to the top.

Now you have this left:

[tex]\frac{3.5}{1}[/tex] = [tex]\frac{52.50}{15}[/tex]

Therefore, Robert needs to pay $52.50 in order to recieve 15 gallons of gasoline.

CAN SOMEONE PLEASE HELP! I WILL MARK BRIANLIEST

Answers

Answer:

yes is is proportional

x=ydivided by 3.5

Step-by-step explanation:

Answer: multiplying by 3.5

Step-by-step explanation: because if you divide 7 by 2 you will 3.5

) Al repartir laminas entre mis amigos, pude darle 5 a
cada uno y me sobran 2. Pero luego llegaron 2 amigos
más, por lo que las repartí de nuevo y pude darle
láminas a cada uno. ¿cuántos amigos había al principio y
cuántas láminas tenia?​

Answers

Answer:

Había cinco amigos al principio y siete laminas en total. (Using google translate)

Step-by-step explanation:

pude darle 5 a cada = 5 amigos

5 a cada uno y me sobran 2 amigos más, por lo que las repartí de nuevo y pude darle = siete laminas

Select "Rational" or "Irrational" to classify each number

Answers

Answer:

rational

Step-by-step explanation:

I'm coochie man

What numbers? please go into further explanation

ABC and DEF are similar. Find the missing side length.

Answers

Answer:

The missing side length is 5

Step-by-step explanation:

Basically 32 to 4 and 56 to 7 is 8 to 1, so you divide 40 by 8 to get the answer, 5

(b) A solid metal cone has radius 1.65 cm and slant height 4.70 cm.
Calculate the volume of the cone.

Answers

Answer:

13.4

Step-by-step explanation:

πr2h

3

Answer:

12.5

Step-by-step explanation:

use pythag to find perpendicular height

then from that your answer should be 4.40cm

Write an equation in slope-intercept form for a line with m = 3 and includes the
point (0, 2).

Answers

Answer:

y=3x+2

Step-by-step explanation:

dont put  0 because it dont make sense

if you put 0 n the equation, you will not will get the right equation

you are playing a game you lose 4.8 points lose another 7.6 points and then win 2.5 points what is the overall change in your score?​

Answers

Answer:

9.9

Step-by-step explanation:

Fists you have to choose a number, ex. 20. Then subtract 4.8 from 20 equalling 15.2, then subtract 7.2 from 15.2, which equals 7.6, then add 2.5 and get 10.1. When you have that final number you must subtract it from the starting number to find the change, 20 - 10.2 = 9.9

What is the percent increase 41,700 and 63,00

Answers

Answer:

51.0791%

Step-by-step explanation:

Calculate percentage change

from V1 = 41700 to V2 = 63000

(V2−V1)|V1|×100

=(63000−41700)|41700|×100

=2130041700×100

=0.510791×100

=51.0791%change

=51.0791%increase

can you please help me with these two questions thank u

Answers

Answer:

the answer to question 1 is 24 and the answer to number 2 is 1

Answer:

frist one is 24. second is 1

Step-by-step explanation:

PLEASE HELP ASAP
Write the slope-intercept form of an equation of the line that passes through the
given point and is perpendicular to the graph of the equation..
(-3, -2), y = x + 2 .

Answers

Answer:

y=-x-5

Step-by-step explanation:

Please help if you can Thank you so much!

Answers

Answer:

Answers in explanations, hope they're correct!

Step-by-step explanation:

12. You will be using 0 gallons of gas when traveling 0 miles.

13. 20 gallons

14. (2,6)

15. You will package 15 dozens of cupcakes after 5 hours

Answer:

12: 0 miles uses 0 gallons of gas

13: 20 gallons

14: (1,3)

15: it takes 5 hours to make 15 dozen cupcakes

Step-by-step explanation:

13) 4 gallons for every 100 so multiple by 5 for 500

WHICH ONE DO I PICK?

Answers

AAS theorem I believe

A circular tablecloth is 6 feet in diameter. How many feet of ribbon would be required
to edge the circumference of this tablecloth? Use 3.14 as the value of pi. Round to
the nearest whole number.

Answers

Answer:

You'll need 18.85 feet of ribbon.

Step-by-step explanation:

The circumference is [tex]\pi d[/tex].

[tex]\pi * 6 = 18.85[/tex]

Solve the system of equations below.
y=3x
2x + y = 15

Answers

Answer:

x=3

Step-by-step explanation:

2x+(3x)=15

5x=15

x=3

solving for y:

3(3)=9

y=9

Answer:

(y,x) (9,3)

Step-by-step explanation

An exterior angle of a triangle is 152°. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?

a. 62°, 59°, 59°
b. 90°, 45°, 45°
c. 152°, 14°, 14°
d. 28°, 76°, 76°

Answers

9514 1404 393

Answer:

  d.  28°, 76°, 76°

Step-by-step explanation:

The sum of the "non-adjacent" interior angles of the triangle is equal to the exterior angle, so is 152°. If those angles are congruent, each is half of 152°, or 76°. The remaining angle is the supplement to 152°, so is 180-152 = 28 degrees.

The interior angles are 28°, 76°, 76°.

Determine if the figure below has rotational symmetry, line symmetry or both and
describe the transformation that mas the figure onto itself. BE SPECIFIC. You must
name the center of rotation and degree of rotation if it has rotational symmetry or
lines of reflection if it has line symmetry

Answers

Answer:

A) Given that the figure is a rectangle, it has a rotational symmetry and by rotating the figure 180° about the center of the figure, the preimage and image will coincide

The figure also has a line symmetry for the vertical line x = 5, and a line symmetry for the horizontal line y = 5

Therefore the figure has both symmetry

B) The transformation that maps the figure unto itself are therefore;

1) Rotating the figure 180° about the point (5, 5) which is the center of the figure

2) Reflection of the figure across the line x = 5 and also reflection of the figure across the line y = 5

Step-by-step explanation:

The perimeter of an isosceles triangle is 15.6 cm. Find the lengths of its sides, if: The base is 3 cm smaller than a leg.

Answers

Answer:

The sides of the isosceles triangle are 3.2 cm, 6.2 cm and 6.2 cm

Step-by-step explanation:

The sides of an isosceles triangle are equal in length

Let the base be x cm

Since it is 3 cm smaller than a leg, the legs will be (x + 3) cm

To find the perimeter of a triangle, we add up the sides

x + x + 3 + x + 3 = 15.6

3x + 6 = 15.6

3x = 15.6 - 6

3x = 9.6

x = 9.6/3

x = 3.2 cm

So the base is 3 + 3.2 =6.2 cm

please help me.
im dying

Answers

Answer:

19/37

Step-by-step explanation:

47/148 + 29/148 = 76/148 = 38/74 = 19/37

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