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The maximum value of c is 8/7.

In total, we must make 10 steps, 2 up, and 8 to the right.  

In order to do this, we must choose  any 2 out of the 10 moves to go up.  

Examples are R R U R R R R U R R

The number of ways to do this is 10 choose 2, \({10 \choose 2}\), or \(\fbox{45}\) as the final answer.  

You should note that because we can never travel down, anything below C (the entire 3rd row) is irrelevant in computing the answer.  

22 green marbles.  

To solve, let x be the number of marbles added.  

\(\frac{5+x}{12+x}>\frac{79}{100}\)

 simplifying, we see that 

\(x>21\frac{1}{3}\), 

so x is at least 22.  

If we put this back into the original problem, there would be 27 green marbles and 34 marbles total.  

27/34 is about 0.79411, which is slightly above 79%.

Visualizing, you can see that for the angle to the left of the top angle to be to the right of the top angle, we have to rotate the polygon 144 degrees around A_1.  A way to think about it is to have the side to the left of A_1 be moved to the right of A_1.  In order to do this, we must rotate 144 degrees, shown in the diagram.  

Thus, the answer is 144 degrees.

n=3

calculating a few terms, we have f(2)=4/3

f(3)=9/7

f(4)=16/13

f(5)=25/21

We see that each term becomes larger than the last (easily proved and intuitive)

Thus, we know that the product will keep on increasing as n increases.  

letting n=3, we have the product equal to 12/7, or about 1.714

n=4, the product is about equal to 2.110.  

From this, we know the largest value is n=3.  

It really helps to graph on this question.  

Essentially, a function is its own inverse if it can be reflected over the line and still contain the exact same values.  

If we graph f(x) = -3x + 8 if x <= 2, we have something that passes through (2, 2), and (0, 8).

Thus, k(x) must be the reflection of the line -3x+8 over the line y=x, meaning that it must pass through (2, 2) and (8, 0)

The line that passes through these points is k(x)= -1/3x + 8/3.

If k(x) equals this, then the graph is symmetric about y=x, and thus, is its own inverse.  

Since the two equations have a +, they are commutative and can be, for example, x = 2, y = 4 and x = 4, y = 2.

\((x, \mbox{ } y) = (4, \mbox{ } 6)\), \((x, \mbox{ } y) = (6, \mbox{ } 4)\) are the only possible values of x and y.

That is correct!

Oops...

corrections:

Δ = x        O = y

3x + 2y = 21

x = (21 - 2y) / 3

3y + 2x = 19

3y + 2(21 - 2y) / 3 = 19 

y = 3       x = 5

3y = 9

https://web2.0calc.com/questions/combinations_18

Thanks melody

Sorry I think you accidentaly cut the question off. Could you try fixing it by editing?

https://web2.0calc.com/questions/stuck_16

Lemme have a go at this. 

20% of a number is 1/5 of the number

So we can do 1/5x50=10. So she has to pay $10 per delivery

   (Btw that was the example that the problem gave I think)

Now we can use that mothod for all the prices
RIght now we are looking for emilies profit.

15->12
12->9.60
20->16
18->14.40
22->17.60
(Sorry that I didnt add the dollar sign I thought it would be confusing)


Now lets add them up
We will get $69.60 excluding the tip
Now we add the tip to it.

The total tip is $21
Now we add $21+69.60
$90.60

https://web2.0calc.com/questions/geometry_42685
or
https://web2.0calc.com/questions/find-the-ratio-of-the-area-of-a-regular-hexagon-with-sides
     

https://web2.0calc.com/questions/help-me-plz_34

https://web2.0calc.com/questions/help-angle-problem

https://web2.0calc.com/questions/geometric-sequence_22

https://web2.0calc.com/questions/from-the-top-of-a-building-60-feet-high-the-angle-of-elevation-of-the-top-of-a-pole-is-14-degrees-at-the-bottom-of-the-building-the-angle

PEOPLE ALREADY ASKED THIS

Hi Melody

Second line down, let y = f(x) and you have the equation   

\(\displaystyle \frac{dy}{dx}=-y^{2}, \text{ from which } \int \frac{dy}{y^{2}}=-\int dx. \)

Solve that for y  ( = f(x) ) and substitute the result back into the original integral equation to determine the value of the constant of integration.

You should finish up with the result f(x) = 1/(x + 1).

Tiggsy

The EVEN rows are all powers of 2 as follows:

2^1 , 2^2, 2^3, 2^4 ==2nd row,  4th row,  8th row,  16th row ==4 rows < 20

r=3, 4, 5, 6

k=1, 2, 3, 4, 5, 6, 7, 8

4 x 8 ==32 possible divisions.

3/1,  3/3,  4/1,  4/2, 4/4, 5/1, 5/5, 6/1, 6/2, 6/3, 6/6 - these all give integer values. I count 11 of them.

Therefore, the probability is: 11 / 32

1, 2, 3, 4, 5 ==5 digits

5! ==120 permutations. Each permutation begins with one of the 5 digits this many times: 120 / 5 ==24 permutations. How many odd numers are there?  There are 3 such numbers: 1, 3 and 5.

Therefore, the total number of ODD permutations ==3  x  24 ==72 such permutatins.

The radius of a circle = 2√54

Δ = x        O = y

3x + 2y = 21

x = (21 - 2y) / 3

3y + 2x = 19

3y + 2(21 - 2y) / 3

y = 3       x = 5

3y = 9