All Answers 358201 Answers

I understand that it's not (−3,1) or (4,∞), but I don't know if the rest are ALL the correct answers :'-(

This is a tough one, because there are so many exceptions:

Here is my attempt:

There are 18 numbers between 5 and 99
There are 16 numbers each, between 100 and 999, with the exception of 500, in which there are only 8 such numbers. So:
16 x 8 + 8 + 18 =154 numbers.
1025, 1035, 1045, 1065, 1075, 1085, 1095.................7 such numbers.
1230, 1240, 1250, 1260, 1270, 1280, 1290.................7........................
1205, 1235, 1245, 1265, 1275, 1285, 1295.................7........................ 
5120, 5130, 5140, 5160, 5170, 5180, 5190.................7 such numbers x 7
So, the total should be=154 + (112 x 8) + (7 x 7) =1,099 such numbers.

It isnt b because its asking a reason for everything you work out to find angle x

Let the number of children = C, then:

The number of adults =215 - C

3C + 5[215 - C] = 925

3C + 1,075 - 5C = 925

-2C =925 - 1075

-2C = -150

C = -150 / -2

C =75 - Number of children, or number of tickets purchased by children.

215 - 75 = 140 adults, or adult tickets purchased.

1 inch: 0.51 mile {Scale}, then:

7 inches x 0.51 mile =3.57 miles - distance between hills.

its b

So, what is the question??.

@Cphill

Thanks so much for your answers Heureka!  I think I'm having an issue with the website though.  I see on the side of my screen that there were 5 answers posted to the thread in the little (+5) notification bubble, and I had 5 questions posted here which makes sense, but on the actual post itself I only see your answers to 3, 4, and 1, in that order.  I think this might be a problem with the website but does anyone know how I can view the other answers?  I have tried reloading the site.

Thanks

Can someone help me with this , I don`t  understand how   is equal  step by step pleas.

It isn't k that is 14.  k is 392.

Thank you so much.

nCr(10,8)*0.5^10 = 0.0439453125

1:  A line with slope 6 bisects the area of a unit square with vertices (0,0), (1,0), (1,1), and (0,1).
What is the y-intercept of this line?

\(\begin{array}{|lrcll|} \hline & y &=& mx + b \quad & | \quad m = 6 \\ & y &=& 6x + b \\\\ P_1 = (a,0): & 0 &=& 6a+b \\ & -6a &=& b \\\\ P_2 = (1-a,1): & 1 &=& 6(1-a)+b \\ & 1 &=& 6-6a + b \quad & | \quad -6a = b \\ & 1 &=& 6 +b + b \\ & 1 &=& 6 +2b \\ & -5 &=& 2b \\ & 2b &=& -5 \\\\ & b &=& -\dfrac{5}{2} \\ & b &=& -2.5 \\ \hline \end{array}\)

The y-intercept of this line is -2.5

4:  The lines

\(y = \frac{5}{12} x \)

and 

\(y = \frac{4}{3} x \)

are drawn in the coordinate plane.

Find the slope of the line that bisects the angle between these lines.

\(\text{Let $\tan(\varphi_1) = \frac{5}{12}$ } \\ \text{Let $\tan(\varphi_2) = \frac{4}{3}$ }\)

\(\begin{array}{|rcll|} \hline \text{slope}_{bisect} &=&\tan \left( \dfrac{\arctan(\varphi_1)+\arctan(\varphi_2) } {2} \right) \\\\ &=&\tan \left( \dfrac{22.6198649480^{\circ}+53.1301023542^{\circ} } {2} \right) \\\\ &=&\tan \left( \dfrac{75.7499673022^{\circ} } {2} \right) \\\\ &=&\tan (37.8749836511^{\circ} ) \\\\ &=& 0.77777777778 \\\\ &=& \dfrac{7}{9} \\ \hline \end{array}\)

3:  Find the largest real number x for which there exists a real number y such that x^2 + y^2 = 2x + 2y.
 

\(\begin{array}{|rcll|} \hline x^2+y^2 &=& 2x+2y \\ x^2-2x + y^2-2y &=& 0 \\ (x-1)^2 -1 + (y-1)^2 -1 &=& 0 \\ (x-1)^2 + (y-1)^2 &=& 2 \\\\ \text{circle}_{\text{center}} &=& (1,1) \\ \text{circle}_{\text{radius}} &=& \sqrt{2} \\ x_{\text{max}} &=& x_{\text{center}} + \text{ radius} \\ x_{\text{max}} &=& 1 + \sqrt{2} \\ x_{\text{max}} &=& 2.41421356237 \\ \hline \end{array}\)

cos^-1(0.573)=55.04^o

To enter inverse cosine on the web2.0calc calculator, hit shift as you press cos, or enter acos(value)

Rate of work problems use the formula:
\(\frac{1}{x}+\frac{1}{y}=\frac{1}{T}\); where x = time to complete work for 1st thing, y = time to complete work for 2nd thing, T = time to complete work for the 1st and 2nd thing working together. Also, 1/x = rate of work for thing 1, 1/y = rate of work for thing 2, 1/T = rate of work of thing 1 and 2 together.

Since all of the people work at the same rate and we have the time it takes all of them working together, we can just write:
\(\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=\frac{1}{\frac{10}{3}}\\ \frac{3}{x}=\frac{3}{10}\\ x=10\)

In this case, x=10 means it takes each of them 10 days individually to complete the work (T). It also means, they complete 3/10 of the work in one day (1/T).

To find the rate of only Robert and Joseph, we use the formula I mentioned in the beginning.
\(\frac{1}{x}+\frac{1}{y}=\frac{1}{T}\)

Since, they work at the same rate, it can be rewritten as:
\(\frac{1}{x}+\frac{1}{x}=\frac{1}{T}\)

We know that it takes each of them 10 days individually to complete the work, so x = 10

\(\frac{1}{10}+\frac{1}{10}=\frac{1}{T}\\ \frac{2}{10}=\frac{1}{T}\\ 2T=10\\ T=5\)

It takes them both 5 days to complete the work.
1/T gives how much they can do in one day, which is
\(\frac{1}{5}\)

You can multiply 98 by a fraction such as 8/49 and you get: 98 x 8 / 49 = 16^1/4 =2.

But your question says "positive integer", or "whole number", so I can't see a smaller number than 392.

Well then let’s see YOU solve this Mr. Genius, everyone has different experience with math.