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3 years ago

A cube of aluminum measures 3 cm on each side and weighs 81 g. What is its density? (hint: find the volume of the block first).

SAT

1 answer:

irakobra [83]3 years ago

5 0

Answer:

3 grams per cubic centimeter.

Explanation:

density = mass ÷ volume.

d = m ÷ v.

m=81 g.

volume = length × width × height.

volume = 3 cm × 3 cm × 3 cm = 27 cubic centimeters.

v = 27 cubic centimeters.

d = 81 ÷ 27

density = 3 grams per cubic centimeter.

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A box contains 40 number tiles numbered 1 to 40. If a tile is drawn at random, what is the probability that the number drawn is

BlackZzzverrR [31]

Explanation 1 P (3 or 4):

There are 40 number tiles numbered 1 to 40.

Multiple of 3 in 1 to 40 are:

There are 10 multiples till 30 (since $3 \times 10 = 30$ ) and then 33, 36, and 39 are other three multiples till 40. So there are 13 multiples of 3 from 1 to 40.

Multiples of 4 in 1 to 40 are:

There are 10 multiples till 40 (since $4 \times 10 = 40$ ) . So there are 10 multiples of 4 from 1 to 40.

Common Multiples of 3 and 4 in 1 to 40 is,

12, 28, 36, only 3

So, the probability of 3 or 4 is,

$P(\text {mult of 3})+P(\text {mult of 4}) -P(\text {mult of 3 and 4})$

$=\frac{13}{40} +\frac{10}{40} -\frac{3}{40}$

$=\frac{23}{40} -\frac{3}{40}$

$=\frac{20}{40}$

$=\frac{1}{2}$

So the probability of 3 or 4 is $\frac{1}{2}$ .

Explanation 2 P(4 or 5):

Multiples of 4 in 1 to 40 are:

There are 10 multiples till 40 (since $4 \times 10 = 40$ ) . So there are 10 multiples of 4 from 1 to 40.

Multiple of 5 in 1 to 40 are:

There are 8 multiples in 40 (since $5 \times 8 = 40$ ). So there are 8 multiples of 5 from 1 to 40.

Common Multiples of 4 and 5 in 1 to 40 is,

20 and 40 only 2

So, the probability of 4 or 5 is,

$P(\text {mult of 4})+P(\text {mult of 5}) -P(\text {mult of 4 and 5})$

$=\frac{10}{40} +\frac{8}{40} -\frac{2}{40}$

$=\frac{18}{40} -\frac{2}{40}$

$=\frac{16}{40}$

$=\frac{2}{5}$

So the probability of 4 or 5 is $\frac{2}{5}$ .

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