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EastWind [94]
3 years ago
15

Find the greatest rational number r such that the ratios 8/15 ÷r and 18/35 ÷r are whole numbers.

Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

  2/105

Step-by-step explanation:

"r" is the greatest common divisor (GCD) of the two fractions. It can be found using Euclid's algorithm in the usual way.

  (8/15) - (18/35) = 56/105 - 54/105 = 2/105 . . . . . this is (8/15) mod (18/35)

We can see that the next step, division of 54/105 by 2/105, will produce a remainder of 0, so the GCD is 2/105.

The greatest rational number r is 2/105.

_____

<em>Check</em>

The ratios are (8/15)/(2/105) = 28; (18/35)/(2/105) = 27. These whole numbers are relatively prime, so there is no larger r than the one we found.

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6 0
3 years ago
What is the slope line of m (0,6),(3,0)<br><br>​
mezya [45]

Answer:

slope= <u>y²-y¹</u>

x²-x¹

<u>0</u><u>-</u><u>6</u>

3-0

<u>-</u><u>6</u>

3

= -2

3 0
2 years ago
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat,
Paraphin [41]

Answer:

3/7.

Step-by-step explanation:

The total number of ways to pick 4 out of 8 = 8C4

= 8!/ 4!4!

= 70 ways.

The number of ways when  2 are women =  5C2 * 3

= 10 * 3

= 30.

So the required probability = 30/70

= 3/7.

6 0
3 years ago
A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. The central angle formed by the peach co
Vsevolod [243]

Answer:

D. 5 inches

Step-by-step explanation:

Given:

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.

That means complete angle having 360° is divided into 3 section.

The central angle formed by the peach cobbler is 105 degrees.

The central angle formed by the pasta is 203 degrees.

<u>Question asked:</u>

What is the approximate length of the arc of the section containing the peas?

<u>Solution:</u>

The central angle formed by the peas = 360° - 105° - 203°

                                                                = 52°

Ridius,r=\frac{Dameter}{2} =\frac{12}{2} =6\ inches

As we know:

Length\ of\ arc=2\pi r\times\frac{\Theta }{360}

                        =2\times\frac{22}{7} \times6\times\frac{52}{360} \\ \\ =\frac{13728}{2520} \\ \\ =5.44\ inches

Therefore, the approximate length of the arc of the section containing the peas are 5 inches.

6 0
3 years ago
How do write 2 3/4 as an improper fraction
kolezko [41]
11/4 is the mixed fraction of that
8 0
2 years ago
Read 2 more answers
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