Ask question

Ask question

All categories

3 years ago

11

There are 750 toothpicks in a regular sized box. If a jumbo box is made by doubling all the dimensions of the regular sized box,

how many toothpicks will the jumbo box hold? (With work pls)

2 answers:

Serga [27]3 years ago

7 0

To answer this, let the 3 sides of the regular sized rectangular box be x, y, and z.

When we double all the sides, the new sides have lengths 2x, 2y, and 2z, respectively.

Since the regular box (with dimensions x,y, and z) have 750 toothpicks, we can write

$xyz=750$

Similarly we can write for the jumbo box as,

$(2x)(2y)(2z)$

which is equal to $8(xyz)$

So this is 8 times the original of $xyz$ . Hence the jumbo box will have 8 times 750 number of toothpicks.

ANSWER: $8*750=6000$ toothpicks

stellarik [79]3 years ago

4 0

Answer:

6000

Step-by-step explanation:

You might be interested in

Maria placed a rain gauge in her yard to measure the amount of rain that fell during the

julsineya [31]

.5 that your answer, just .5 your welcome

5 0

2 years ago

Marcos purchased a sail boat for $56,900. He anticipates each year the boat will decrease in value by 8.1% from the previous yea

Varvara68 [4.7K]

Answer: $56,900\left( 0.919\right)^x$

Step-by-step explanation:

Given

Marcos purchased a sailboat for $\$56,900$

Each year the boat will decrease in value by $8.1\%$

After 1 year it is

$\Rightarrow 56,900-56,900\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\\$

after another year it becomes

$\Rightarrow 56,900\left( 1-0.081\right)-56,900\left( 1-0.081\right)\times 0.081\\\Rightarrow 56,900\left( 1-0.081\right)\cdot \left( 1-0.081\right)\\\Rightarrow 56,900\left( 1-0.081\right)^2$

After $x$ years it is

$\Rightarrow 56,900\left( 1-0.081\right)^x$

$\Rightarrow 56,900\left( 0.919\right)^x$

5 0

2 years ago

If you are receiving $57.94 in change, what is the lowest combination of bills and coins that will still give you the correct ch

mestny [16]

1 50 dollar bill

1 5 dollar bill

2 1 dollar bills

3 quarters

1 dime

1 nickel

4 pennies

7 0

3 years ago

What's the nearest hundred thousand to 491,852

kirza4 [7]

500,000 round up from 491,852 to 500,000

3 0

3 years ago

Read 2 more answers

2 Construct a rational function that will help solve the problem. Then, use a calculator to answer the question.

vaieri [72.5K]

Answer:

<u><em>Dimension of box:-</em></u>

Side of square base = 10 in

Height of box = 5 in

Minimum Surface area, S = 300 in²

Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

$500=x^2y$

Therefore, $y=\dfrac{500}{x^2}$

It is open box. The surface area of box, S .

$S=x^2+4xy$

Put $y=\dfrac{500}{x^2}$

$S(x)=x^2+\dfrac{2000}{x}$

This would be rational function of surface area.

For maximum/minimum to differentiate S(x)

$S'(x)=2x-\dfrac{2000}{x^2}$

For critical point, S'(x)=0

$2x-\dfrac{2000}{x^2}=0$

$x^3=1000$

$x=10$

Put x = 10 into $y=\dfrac{500}{x^2}$

y = 5

Double derivative of S(x)

$S''(x)=2+\dfrac{4000}{x^3}$ at x = 10

$S''(10) > 0$

Therefore, Surface is minimum at x = 10 inches

Minimum Surface area, S = 300 in²

7 0

3 years ago