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3 years ago

A parking lot has 27 empty spaces. If the ratio of empty spaces to taken spaces is 3:5, how many spaces are there total?

Mathematics

2 answers:

zlopas [31]3 years ago

7 0

Answer:

72 spaces in total

Step-by-step explanation:

If there are 27 empty spaces in a 3:5 ratio, that means that for every 3 spaces that are empty, there are 5 that are taken. We notice that there are 9 times of 3 spaces that are empty, so we must multiply 9 by 5 to get 45 spaces that are taken. We then add these up to get the total amount of spaces 27 + 45 = 72 spaces

Wittaler [7]3 years ago

3 0

Answer:

There are 72 spaces

Step-by-step explanation:

You would first have to do 27/3, which shows what 1/5 is. This would get you 9, then multiply that by 5 to find the amount of taken spaces. Add 27 and 45 to get 72 spaces.

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2 years ago

How many cubes with side lengths of 1/3 cm does it take to fill the prism?

user100 [1]

Answer:

The number of cubes that fill the prism is 24

Step-by-step explanation:

Given as :

The length of cube (l) = $\frac{1}{3}$ cm

The length of prism (L) = 1 cm

The width of prism (w) = 2 $\frac{2}{3}$ = $\frac{8}{3}$ cm

The height of prism (h) = $\frac{2}{3}$ cm

Let the number of cubes that fill the prism = x

Now, Volume of cube with length (l) = l³ cm³

Or, Volume of cube with length (l) = $(\frac{1}{3})^{3}$ cm³

Or, Volume of cube with length (l) = $(\frac{1}{27})$ cm³

Again , Volume of prism = $\frac{1}{2}\times Length \times width \times height$

Or, Volume of prism = $\frac{1}{2}\times 1 \times \frac{8}{3} \times \frac{2}{3}$

Or, Volume of prism = $(\frac{8}{9})$ cm³

<u>So , The number of cubes to fill prism </u>

The number of cubes × Volume of cube = Volume of prism

Or, x × $(\frac{1}{27})$ cm³ = $(\frac{8}{9})$ cm³

or x = $\frac{8\times 27}{9}$ = 24

Hence The number of cubes which fill the prism is 24 Answer

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3 years ago

The dashed line shows how you cut the bottom of a rectangular door so it opens more easily.

Anastaziya [24]

See the picture attached to better understand the problem

we know that
m ∠ACD=91.5°
m ∠ACD+m ∠ACB=180°-------> by supplementary angles
so
m ∠ACB=180-91.5-----> m ∠ACB=88.5°

m∠CAB+m ∠ACB=90°-----> by complementary angles
so
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m∠ CAB is <span>the new angle at the bottom left side of the door

the answer is
1.5</span>°

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