All Answers 358514 Answers

Ex. Calgary is 3000km from Montreal. How far apart are they on a map with a scale of 1:25 000 000?

1mm represents 25 000 000mm

1mm represents 25 000 m

1mm represents 25km

$${\frac{{\mathtt{1}}}{{\mathtt{25}}}} = {\frac{{\mathtt{x}}}{{\mathtt{3\,000}}}} \Rightarrow {\mathtt{x}} = {\mathtt{120}}$$

that's 120mm = 12cm

does that make sense?

See what happens when you turn over a new leaf!

google it.

I think this one is better than some of the nonsense number posts. 

Plus I like your answer.

The number of 5 digit combinations (order doesn't matter) from 40 is

40C5

$${\left({\frac{{\mathtt{40}}{!}}{{\mathtt{5}}{!}{\mathtt{\,\times\,}}({\mathtt{40}}{\mathtt{\,-\,}}{\mathtt{5}}){!}}}\right)} = {\mathtt{658\,008}}$$

only one of those wins so the chance is     $$\frac{1}{658008}$$

Just like FoxTears said!

Thanks Foxtears.

Foxtears, I don't think that yours was assuming that the numbers could be reused.

It was just assuming that the order they were chosen in was of no consequence.

GoldenLeaf I believe yours would have been correct if the numbers had to be chosen in a specific order.

cos15=cos(45-30) and

cos(a-b)=cosa cosb + sina sinb

that should help.

0.8 i think

Do you mean

$${\sqrt[{{\mathtt{{\mathtt{8}}}}}]{{\mathtt{1.316\: \!8}}}} = {\mathtt{1.034\: \!999\: \!112\: \!125\: \!890\: \!8}}$$

This is an approximation.

hi again GoldenLeaf,

Your logic and your answer are botf good.

however I don not like this line

15a(-54+54) = (9+54)

this implies 15a * (-54+54) = 15a * 0 = 0

and that is definitely not what you meant.

just write it like this - brackets usually help but in this case that make the working wrong.

15a-54+54 = 9+54

You may both teach and learn a lot here GoldenLeaf.  This is how I have always wanted the forum to be used.  

Mine was assuming the numbers can be reused

Though I don't necessarily believe that your life depends on this, I am still glad to help, and since this is a graph, I'll just post a graph with 10 units on each side.

The red line is y = 2/3x - 3

The blue line is y = -2x + 5

The solution is (3,-1)

Calculate the numerator: There is only one winning combination. So the numerator of the desired probability is 1. Calculate the denominator: There are "40 numbers, choose 5", or 40C5 possible combinations. So the denominator of the desired probability is 40C5. So the probability is 1/40C5=1/658008

Answer: 1/658008

For this kind of probability problem, assuming the number is removed from play once chosen, the probability increases by one each time.

$$\left({\frac{{\mathtt{1}}}{{\mathtt{40}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{39}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{38}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{37}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{36}}}}\right)$$

The bottom five numbers multiply to 78960960, which means that the odds are 1/78960960

@Melody Ah, I haven't done scientific notation in a while, so that's what I thought it was  Thanks Anon for the correct answer, and thanks Melody for the refresher.

This problem is a Pythagorean Theorem problem, I assume?

• The rope is the hypotenuse (h = 26 yards)
• Length of the ground from the pole is side 'a' (a = 22 yards)

Thus, the set-up for this problem is:

$${{\mathtt{22}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{26}}}^{{\mathtt{2}}}$$

Taking these values, the next step is to square 22 and 26.

22^2 = 484

26^2 = 676

The equation after simplifying the numbers is:

$${\mathtt{484}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {\mathtt{676}}$$

Now, it is necessary to isolate the 'b^2'.

$$\left({\mathtt{484}}{\mathtt{\,-\,}}{\mathtt{484}}\right){\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = \left({\mathtt{676}}{\mathtt{\,-\,}}{\mathtt{484}}\right)$$

$${{\mathtt{b}}}^{{\mathtt{2}}} = {\mathtt{192}}$$

Now, in order to completely isolate the 'b^2', we must take the square root of it, and in turn, 192.

$${\sqrt{{{\mathtt{b}}}^{{\mathtt{2}}}}} = {\sqrt{{\mathtt{192}}}}$$

$${\mathtt{b}} = {\sqrt{{\mathtt{192}}}}$$

The square root of 192 is 13.8564064605510183, which, when rounded to the nearest tenth, is about 13.9

@Anon: You rounded to the nearest hundredth, but you summed it up pretty well. I do have a habit of extracting it to the barebones 

Sorry! :) 

No hard feelings.

If you draw a model of the pole and the rope touching the ground, a right triangle is formed. The rope would be the hypotenuse, which is 26yards long. The distance between the pole and rope forms one side, 22 yards long. The length of the pole would form the third side. A^2+B^2=C^2

A^2+22^2=26^2     

A^2+484=676             Subtract 486 from both sides.

A^2=192                     Take the square root of 192.

A= 13.86

The length of the pole would be approximately 13.86 yards.

First, ratios are in the form of:

n:n (where 'n' equals any number)

While proportions are:

n(1)/n(2) = n(1`)/n(2`) (where n(1) is able to be multiplied/divided by a number to reach n(1`) (and vice versa for n(2) and n(2`)))

Now, on to the problem!

First, to be proportional means that the numbers are the same, just in different forms. This means that 3/1 and 24/8 must be the name number to be a proportion.

A simple way of doing that is to take the fraction's numerator and divide it by its denominator, and do it for all the listed fractions.

3/1 = 3

24/8 = 3

If all of the fractions simplify to the same number, then they are proportional.

3 = 3

Thus, 3/1 is proportional to 24/8

Yes, because 24/8 reduces to 3/1.

Also, if you set them up as a proportion and solve, they will equal each other.

Good answer GoldenLeaf!

$${\sqrt{{\mathtt{2.8}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{-{\mathtt{13}}}}} = {\mathtt{0.000\: \!000\: \!529\: \!150\: \!26}}$$

I did this straight on the site calc using the "Math input=result" tab

Note this is an aprroximation.  It is an irrational number and cannot be written exactly in digits. 

I hope you don't mind me checking some of your answers..  I will do it less as your ability, and my confidence in it, grows.

First, get like terms on the same side.

START: 7x + 4 = 5x + 5

Do one term at a time: I will start with the variable.

(7x - 5x) + 4 = (5x - 5x) + 5

2x + 4 = 5

Then, do the integers.

2x + (4 - 4) = (5 - 4)

2x = 1

Then, isolate the 'x'.

2x/2 = 1/2

x = 1/2

And that is your answer.

This sequence can go two ways: Are you doing an arithmetic sequence or a geometric sequence?

I will do both just in case.

For a geometric sequence, the rate 'r' is -1/2: Thus, the sequence would be:

{6, -3, 1.5, -0.75}

And that would be the answer.

HOWEVER, it is also possible to have an arithmetic sequence. The rate 'r' for that would be -9: Thus, the sequence would be:

{6, -3, -12, -21}

And thus, that is your other answer.