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pshichka [43]
3 years ago
11

There are 40 boys in a computer club. The ratio of girls to boys is 2 to 5. How many girls are in the club?

Mathematics
2 answers:
Serggg [28]3 years ago
7 0

Answer:

50x2 =100

So the final box is 50x2 = 100

Step-by-step explanation:

There is a pattern in this table.  5, 2, and 2.  Ex. 2x5=10, 10x2 =20 on top

The pattern is the same on the bottom: 5x5 =25, 25x2=50, and 50x2 =100

So the final box is 50x2 = 100

Mandarinka [93]3 years ago
4 0
Set up a proportion. 2/5 = x/40
to solve the equation first cross multiply.
x*5=40*2
x*5=80
now divide both sides by 5, 80 divided by 5 is equal to 16.
so the number of girls in the computer lab is 16. 
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Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66
Ipatiy [6.2K]

Answer:

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

If you prefer it a little more simplified:

\sum_{n=1}^{16}(5x-14)

Step-by-step explanation:

First my favorite part, finding a pattern between the consecutive terms.

This is an arithmetic series because the terms are going up by 5 each time.

So arithmetic sequence, think linear equations:

x     |      y

1            -9

2           -4

3             1

4             6

..................

n             66

We are going to have to find that n but will will eventually...

The equation for a line in point slope form is y-y_1=m(x_x_1) where (x_1,y_1) is a point on the line and m is the slope.

We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).

I'm going to use the first point (1,-9).

So the equation in point slope form is y-(-9)=5(x-1)

Subtract 9 on both sides:

y=5(x-1)-9

Now we need to know how many terms we are adding so what is x if y=66.

66=5(x-1)-9

Add 9 on both sides:

75=5(x-1)

Divide both sides by 5:

15=x-1

Add 1 on both sides:

16=x

We have 16 terms in this sequence where the 16th term is 66.

Summation notation is:

\sum_{n=1}^{16}[5(x-1)-9]

You could simplify the 5(x-1)-9.

Distribute:  5x-5-9

Add like terms:  5x-14

3 0
2 years ago
Read 2 more answers
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