All Answers 352725 Answers

\(2.5*10^5\) Standard to 1 digit. 

You are making a total fool of yourself guest.

I can see why you want to be anonymous.

Are you sure that I’m making a total fool of myself? I think I’m making only a partial-fool of myself.

If you can see why I want to be anonymous, would you please tell me?  It’s not because I’m worried about making a partial fool of myself. That should be obvious, because I had no idea I was doing that until you posted the graph that doesn’t cause partial motion-sickness.   

I may make an account. I have a partial shortlist of user names.

PartialFool

PartialIdot

PartialDumbFuck

PartialFuckFace.   

Are you partial to one of them? 

f -3   = 3 ( s -3)

f+5 = 2 (s+5)

f-3 = 3s-9    and

f+5 = 2s+10     or    -f-5 = -2s-10    add this to the first equation

-8 = s -19

s = 11                       f -3 = 3(s-3)    

                                f = 3(11-3)  + 3  = 27

11+4      +    27 + 4 = 46 years total in 4 years time

d + d-11 = 45

2d = 56

d = 28

One day, Alexis decides to write down all the numbers from 1 to 999, inclusive.
a) How many digits did Alexis write, in total?

b) Alexis chooses one of the digits written down at random. What is the probability that the chosen digit is a 7?

c) What is the sum of all the digits that Alexis wrote down?

You are given this

   Eric is twice as old as his brother Lucas       soo  E = 2L

you are given this too

  If 4 is subtracted from Eric's age and 4 is added to Lucas age, their ages will be equal.

           sooo   E-4 = 4+L

Let's put in   E = 2L into the second equation

      2L-4 = 4+L        now subtract 'L' from both sides

        L -4 = 4           Now add 4 to both sides of the equation

        L = 8      This is Lucas'  age

E = 2L   =   2(8) = 16     Eric's age

d   = amount of dodgeball time

      and the amount of volleyball time    =   d -11

              added together the two times sum to 45

                       d    +     d -11     = 45        solve for 'd'  the dodgeball time 

a) If you are counting the DIGITS of the number 1 to 999, then there are =2,889 digits between 1 and 999.

b) There are 300 "7s" between 1 and 999, including duplicates such as:77, 777......etc. Therefore, the probability that a randomly chosen number is a 7 =300 /2,889 =~ 10.38 %

c) The sum of all the digits in a) above = 13,500.

These areas satisfy A_1 = A_2/2 = A_3/3 = A_4/4.

this can be stated as   

\(A_2=2A_1\\ A_3=3A_1\\ A_4=4A_1\\ \text{So the area of the big circle is }\\ Area_{big}=A_1+2A_1+3A_1+4A_1\\ Area_{big}=10A_1\\ \text{So the ratio of the areas of the smallest to biggest circle is }1:10\\ and\\ \text{So the ratio of the radii of the smallest to biggest circles is }1:\sqrt{10}\\\)

So

\(\frac{r_4}{r_1 }=\sqrt{10}\)

You should check this answer. All answers should be checked before they are accepted.

Coding:

A_2=2A_1\\
A_3=3A_1\\
A_4=4A_1\\
\text{So the area of the big circle is }\\
Area_{big}=A_1+2A_1+3A_1+4A_1\\
Area_{big}=10A_1\\
\text{So the ratio of the areas of the smallest to biggest circle is }1:10\\
and\\
\text{So the ratio of the radii of the smallest to biggest circles is }1:\sqrt{10}\\

\frac{r_4}{r_1 }=\sqrt{10}

You are making a total fool of yourself guest.

I can see why you want to be anonymous.

As you have stated, PartialMathematician wrote

 “The parallelogram is a rhombus.”

And you responded with

"That is not the case here nor anywhere else."

He clearly meant that this Parallelogram is a rhombus and he is absolutely correct.

You seem to think that a rhombus and a square are the same thing!

A square is a special case of a rhombus, that is true enough, but a rhombus does not usually have equal diagonals.

This is the exact rhombus that meets the necessary description.

i areadly figured it out.. thanks anyways!

Melody Wrote: A Rhombus IS a special type of PARALLELOGRAM.  PartialMathematician is correct.

OK that’s true, but that is NOT what PartialMathematician wrote.

He wrote, “The parallelogram is a rhombus.” That is not the case here nor anywhere else. 

You can know the parallelogram is not a rhombus because the question states the two diagonals of a parallelogram have lengths 6 and 8. If this was a rhombus, they would be the same length. 

The diagonals bisect each other forming 4 triangles that have sides of 3 and 4. Then applying the triangle inequality z ≤ x + y that includes the degenerate triangle where z = x + y and appears as a line with zero area, then the unknown side (z) ≤ side (x) + side (y) therefore z is longer than either x or y. Then x = 3 is the longest the shortest side can be, or x < 3 is the longest the shortest side can be excluding the degenerate triangle with zero area.  

This proves PartialMathematician is wrong and he is still a dumb F u c k F a c e and he would be one even if he were right. 

I like your moving parallelogram picture.  It’s a rhombus (special case) when the points are on the y axis.  

Melody Also Wrote: I am very sorry guest (for your mother) but you must be describing yourself.

I might be a F u c k F a c e, but my mother never noticed or at least never said so. There is probably some kind of genetic code that prevents mothers from seeing these kinds of defects in their offspring.   My father didn’t have this genetic code because he sometimes referred to my brother as F u c k F a c e. I was never sure if it was a term of endearment, or if my father thought my brother wasn’t his child. We did look different, so I don’t know. I looked different from my sister too. One main difference was I had much bigger b o o b s, and this p i s s e d her off to no end. She would call me F u c k F a c e when I pointed this out.  

If we let a = 3x+4, and b = x+16 then there are two possibilities:

1.   2a + b = 180, so 6x + 8 + x + 16 = 180, or 7x + 24 = 180

and

2.   a + 2b = 180, so 3x + 4 + 2x + 32 = 180, or 5x + 36 = 180

I'll let you take it from here.

It is just an AP

s=999/2(1+999) = 999*500 = 499500

I think 35 degrees is too big either way.

It is the middle one

In your case

9^2=XB * 15

81 = XB *15

XB = 81/15 = 5.4 units

I am very sorry guest (for your mother) but you must be describing yourself.

A Rhombus IS a special type of PARALLELOGRAM

PartialMathematician is correct.

Here is a pic that I could not resist drawing.

1) In acute triangle ABC, we know AB = 7, BC = 8, and that CA is the shortest side. What is the smallest possible integer value of CA?

The smallest possible integer value of CA is  4  

3) Two sides of an acute triangle are 8 and 15. How many possible lengths are there for the third side if it is an integer?

There are only 4 possible lengths and they are:  8, 9, 10 and 11  

Adult tickets to a basketball game cost $5.
Student tickets cost $1.
A total of $2,783 was collected on the sale of 1,235 tickets.
How many of each type of ticket were sold?

\(\text{Let number of adult tickets $=a$} \\ \text{Let number of student tickets $=s$}\)

\(\begin{array}{|rcll|} \hline a+s &=& 1235 \\ \mathbf{s} &=& \mathbf{1235-a} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline 5a+s &=& 2783 \\ 5a + (1235-a) &=& 2783 \\ 5a + 1235-a &=& 2783 \\ 4a + 1235 &=& 2783 \\ 4a &=& 2783-1235 \\ 4a &=& 1548 \quad | \quad : 4 \\ \mathbf{a} &=& \mathbf{387} \\\\ \mathbf{s} &=& \mathbf{1235-a} \\ s &=& 1235-387 \\ \mathbf{s} &=& \mathbf{848} \\ \hline \end{array}\)

The number of adult tickets is 387
The number of student tickets is 848

How many two digit positive integers in the base-four representation are
twice the two digit positive integers in the base-three representation?

I assume:

\(\begin{array}{|rl|c|c|c|c|c|c|l|} \hline & & 10 & 11 & 12 & 20 & 21 & 22 & \text{base}~3 \\ & & =3 & =4 & =5 & =6 & =7 & =8 & \text{base}~10 \\ \text{base}~4 & \text{base}~10 & 6 & 8 & 10 & 12 & 14 & 16 & 2x \\ \hline 10 & = 4 & & & & & & & \\ 11 & = 5 & & & & & & & \\ 12 & = 6 &6=6\checkmark& & & & & & \\ 13 & = 7 & & & & & & & \\ 20 & = 8 & &8=8\checkmark& & & & & \\ 21 & = 9 & & & & & & & \\ 22 & = 10 & & &10=10\checkmark& & & & \\ 23 & = 11 & & & & & & & \\ 30 & = 12 & & & &12=12\checkmark& & & \\ 31 & = 13 & & & & & & & \\ 32 & = 14 & & & & &14=14\checkmark& & \\ 33 & = 15 & & & & & & & \\ \hline \end{array}\)

The answer is 5.

\(\begin{array}{|ll|} \hline 1. &12_4 = 2\times 10_3 \\ 2. &20_4 = 2\times 11_3 \\ 3. &22_4 = 2\times 12_3 \\ 4. &30_4 = 2\times 20_3 \\ 5. &32_4 = 2\times 21_3 \\ \hline \end{array}\)

(a) The ratio r is not a constant ratio, but increases by 1/4 for each term. It begins with 1/2, then it goes up to 3/4, then to 1 and 1.25.......etc.

(b) The value of r tells you that the series will diverge to infinity as r gets larger and larger.

And good catch, guest! 

I hope the above solution helps. 

Hope this helps, 

- PM

Lol I thought you were smart enough to understand... The parallelogram is a rhombus.

rhom - bus

/ˈrämbəs/

noun

a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides.

any parallelogram with equal sides, including a square.

The largest possible length of the shortest side is 5.