There are 500 toothpicks in a small box. if a jumbo box is made by doubling all the dimensions of the small box, how many toothpicks will the jumbo box hold?
a. 2,000 tooth picks
b. 8,000 tooth picks
c. 1,000 tooth picks
d. 4,000 tooth picks

Option: D is the correct answer.

D. 4000 Tooth picks.

Step-by-step explanation:

It is given that:

There are 500 toothpicks in a small box.

so, let the dimensions of small box be:

x units×y units×z units.

This means that the volume of the small box is:

Volume(V)=xyz cubic units.

Now a jumbo box is made by doubling all the dimensions of the small box.

This means that the dimensions of the jumbo box are:

2x units×2y units×2z units.

Hence, the volume of jumbo box is:

Volume(V')=8xyz cubic units.

As the number of toothpicks hold by a box of volume xyz cubic units are:500.

So, the number of toothpicks hold by a box of volume 8xyz cubic units will be:8×(500)=4000

Hence, the number of toothpicks that jumbo box can hold are:

D. 4,000 Tooth Picks

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation:

simplifying

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

reorder the terms:

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

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

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .