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How do you know Hectictar?

You are right, it is Hectictar's birthday today.

Hectictar, I know you are still about.  How about logging on and saying hello :))

Anyway, I hope you are having a fantastic day !     

What is the average of all positive integers that have four digits when written in base 3, but three digits when written in base 6? Write your answer in base 10.

\(3^3\le x \le3^4-1\qquad \cup \qquad 6^2\le x\le6^3-1\\~\\ 27\le x \le 80 \qquad \cup \qquad 36 \le x\le 215\\~\\ 36\le x \le 80\)

\((36+37+ ....+80)  /  (80-36+1)\\~\\ =(36+37+ ....+80)  /  45\\~\\ =\frac{45}{2}(36+80) / 45\\~\\ =\frac{1}{2}(116) \\~\\ =58\)

Or I could have just said  36+  (80-36) / 2 = 36+22 = 58

All jars of cookies sold = x

Amanda sold 1/3   or  5/15x

Maybelline sold          3/15x

Owen sold                  7/15x

"Owen sold 32 more jars of cookies than Amanda".

7/15x - 32 = 5/15x             x = 240

240 * 12 = 2880

Try this:       x² + (3x)² = 5  

AC = sqrt(41 - 25) + sqrt(34 - 25)

If a is 4 percent of b and b is 25 percent of c, what percent of a is c??

c = 100

b = 25% of c = 25

a = 4% of b = 1

c = 10,000% of a

0.08

HE = 4.95

Same guy here. I got 48. Sorry. I just did 3+1) x 3 x 4. 

To find the inverse, interchange the variables and solve for y.

h^-1(x)=x+1/8-3x

Add -8, 16, -32, 64, -128, 256, and -512

(-8)+16+(-32)+64+(-128)+256+(-512)=-344

Let Amanda sold x cookies 

      1/3^th is x cookies

     the whole is 3x cookies

  =>  Maybelline sold = 3/10 x 2x = 8x/10 = 3x/5

         Owen sold = 7/10 x 2x = 7x/5

  given Owen sold 32 more jars than Amanda

  => 7x/5 = 32 + x

  => 2x/5 = 32      => x = 80

  Total number of cookies = 3x

                                         = 3(80)

                                         = 240.

 
Total amount collected     = 240 x 12

                                         = $2880

Find the smallest value of x such that  x^2 + 10x + 25 = 49.    

                                                 x² + 10x + 25  =  49 

Subtract 49 from both sides      x² + 10x – 24  =  0  

Factor left side                          (x + 12)(x – 2)  =  0  

Set each factor to zero                        (x + 12)  =  0   

                                                            (x – 2)  =  0   

So    x = –12  and  x = +2    The smaller of these is x = –12  

_.

First minus 49 both sides

\(x^2 + 10x - 24 = 0\)

Using the Quadratic cross method ( https://www.youtube.com/watch?v=at7MIBm-it8&ab_channel=MisterBrash )

\((x-2)(x+12) = 0\)

So \(x\) have to be either 2 or -12. And we are finding the smallest value so it's -12

We know that shortleg^2 + longleg^2 = \(\sqrt{5}^2\) or 5

If the shorter leg is x then the longer leg would be 3x

Therefore we have:

\(x^2 + 9x^2 = 5\)

simplify it to

\(10x^2 = 5\)

divide 4 each side

\(x^2 = \frac{5}{10}\)

square root both side

\(x = \sqrt{\frac{5}{10}}\)

So the shorter leg is \(\sqrt{\frac{5}{10}}\) and the longer leg is \(3 \sqrt{\frac{5}{10}}\)

Now we need to find the area

Multiply them:

\(3\sqrt{\frac{5}{10}}\cdot \sqrt{\frac{5}{10}} = 3 \cdot \frac{5}{10} = \frac{15}{10} = \frac{3}{2}\)

And don't forget we also have to divide by 2

\(\frac{3}{2} \div 2 = \frac{3}{4}\)

thank you for showing us your anwers.  

The wording in the question is not completely clear.     (spelling edit, it was 'working' and maybe that was confusing)

It is hard to make the wording exact for questions like this.

But yes a and b are correct.  

c) there are 6 different  2 coloured squares.  But lots of each.

So he has 6 to choose from for his first and 6 to choose from for his second = 36 if he can choose 2 the same.

If they both have to be different then he has   6*5 = 30 possible choices

x+9=43+9

      =52

2.8(x+9)=2.8⋅52

             =145.6

Therefore he collects $145.6 from chips sale.
 

A card is drawn at random from a standard pack of playing cards. 
Then a fair coin is flipped. 
What is the probability of selecting a spade and the coin landing on heads?

[10  *  21 ]  -  21  -  10==179 - The largest number.

HOW DO YOU GET 145.60 ???

Same question on https://web2.0calc.com/questions/help_23722. Please do not post a new thread with the same problem as a previous one.

By the way, I am DottedCaculator.

Orz me now.

Gopal sells a hot dog bun at $3.30 each and a packet of potato chips at $2.80

each. After selling for a day, he collected $3.70 more from the sale of potato

chips than the sale of hot dog buns. He sold 9 more packets of potato chips than

hot dog buns.

a)   How many hot dog buns did he sell?

b)   How much did he collect from the sale of potato chips?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hot dog buns sold => x         Potatoe chips sold => x + 9

2.8(x + 9) - 3.3x = 3.7

x = 43

a/    He sold 43 hot dog buns

b/   $145.60

the '...' shows that its an infinite list

The domain is [3,4]

There are only three integers: $\sqrt{4096}$, $\sqrt[3]{4096}$, and $\sqrt[4]{4096}$.