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3 years ago

14

a middle school band has 45 sixth and seventh graders. The ratio of sixth graders to seventh graders is 2 to 3. How many sixth g

raders are in the band

1 answer:

stepan [7]3 years ago

8 0

There are 18 sixth graders in the band

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A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

7 0

3 years ago

Which expression is equivalent to 19x − 6x + 2 and why?

Sonbull [250]

<span>2 + 13x, because (19x − 6x) + 2 = 13x + 2 = 2 + 13x</span>

7 0

2 years ago

Read 2 more answers

Jill and Sam are racing go-karts. Jill's completed 16 laps in 12 minutes. If Sammy raced at the same rate, how many minutes did

Umnica [9.8K]

It would take 2.25 minutes to complete 3 laps because each lap takes .75 minutes.

4 0

3 years ago

Please help with #12

ExtremeBDS [4]

Answer:

a. 1 1/8 b. 8/9

Step-by-step explanation:

You can set this up as a proportion to solve. For part a. we know that 2/3 of the road is 3/4 mile long. 2/3 + 1/3 = the whole road, so we need how many miles of the road is 1/3 its length. Set up the proportion like this:

$\frac{\frac{2}{3} }{\frac{3}{4} } =\frac{\frac{1}{3} }{x}$

Cross multiplying gives you:

$\frac{2}{3}x=\frac{1}{3}*\frac{3}{4}$

The 3's on the right cancel out nicely, leaving you with

$\frac{2}{3}x=\frac{1}{4}$

To solve for x, multiply both sides by 3/2:

$\frac{3}{2}*\frac{2}{3}x=\frac{1}{4}*\frac{3}{2}$ gives you

$x=\frac{3}{8}$

That means that the road is still missing 3/8 of a mile til it's finished. The length of the road is found by adding the 3/4 to the 3/8:

$\frac{3}{4}+\frac{3}{8}=\frac{6}{8}+\frac{3}{8}=\frac{9}{8}$

So the road is a total of 1 1/8 miles long.

For b. we need to find out how much of 1 1/8 is 1 mile:

1 mile = x * 9/8 and

x = 8/9. When 1 mile of the road is completed, that is 8/9 of the total length of the road completed.

8 0

3 years ago

Mr.Smith waters one of his plants every 10 days and another plant every 14 days. If he waters both plants today, when is the nex

Allushta [10]

Answer:

After 140 days

Step-by-step explanation:

The next time both plants will be watered together is simply the LCM of 10 and 14.

10 has multiples: 10, 20, 30, 40 , 50 ....

14 has multiples: 14, 28, 42, 56 ....

When will they next be equal?? That's the LCM.

We first do prime factorization of the numbers and then multiply each factor the greatest number of times it occurs in either number.

<u>Prime Factorization</u>

10 = 2 * 5

14 = 2 * 7

So,

LCM = 2^2 * 5 * 7 = 140

After 140 days

6 0

2 years ago