Thread: [SOLVED] I have a lot of math problems/questions

1. [SOLVED] I have a lot of math problems/questions

1.
If f(y) = [(the absolute value of y)+16], what is the value of f(-4)?
I don't understand what exactly to do on this one, can anyone help explain?

2.
How many numbers from 1 to 100 inclusive are equal to some integer to the fourth power?
Same as above, what to do and what are they asking exactly?

3.
Minoo had a dinner party and was serving cups of earl grey tea and cups of chamomile tea at a ratio of 5 to 1. Then one of the guests arrived late and started drinking chamomile tea to soothe her nerves after a bad day she had 3 cups, which changed the ratio of earl grey cups and chamomile cups to 5 to 2. How many cups of tea did Minoo serve in all?
I can try to guess and insert random numbers to figure out this one but what's the faster way(some sort of equation?).

4.
3^n = 3^2(n). What is the value of n?
Again, not sure what to do.

5.
If b is positive, what part of 4b is 8?

a. 4%
b. b/100%
c. b/4%
d. 4/b%
e. 200/b%
Same as above.

2. Hello Forum_User

welcome to the forum. next time, don't post questions between quote tags, because they don't show up when other users quote you message
Originally Posted by Forum_User
1. I don't understand what exactly to do on this one, can anyone help explain?

If f(y) = [(the absolute value of y)+16], what is the value of f(-4)?
as with any other function. whatever goes into the brackets, you replace the variable with it in the function definition

$f(y) = |y| + 16$

$\Rightarrow f({\color{red}-4}) = |{\color{red}-4}| + 16$

can you continue?

3. Originally Posted by Forum_User
1. I don't understand what exactly to do on this one, can anyone help explain?

2. Same as above, what to do and what are they asking exactly?

3. I can try to guess and insert random numbers to figure out this one but what's the faster way(some sort of equation?).

4. Again, not sure what to do.

5.
Same as above.
I have time for a couple:

1. Do you understand the mod function .....? |-4| + 16 = 4 + 16 = 20.

2. 1^4 = 1, 2^4 = 16, 3^4 = 81, 4^4 = 256, ..... So how many do you think there are?

4. You need n = 2n (why?). Therefore ...

5. (8/4b) times 100 = ...... (You times by 100 to convert to a percentage)

4. Originally Posted by Forum_User
2. How many numbers from 1 to 100 inclusive are equal to some integer to the fourth power?
well, you want numbers that you get from raising some integer to the fourth power.

for example, 16 would be one of the numbers you would select. why? because $16 = 2^4$, that is, an integer (namely, 2) raised to the fourth power.

just start counting them of.

leave out zero...

$1^4 = 4$

$2^4 = 16$

$3^4 = 81$

$4^4 = 256$

and so on and so fourth. these are the first few integers. do we need to find anymore? which ones would you choose?

EDIT: Whoah, Bessie! Mr F came out of nowhere and answered all the questions. well, he left out number 3... don't know if he's gonna do it... are you, Mr F?

5. Hmmm, seems Mr F left...
Originally Posted by Forum_User
3. Minoo had a dinner party and was serving cups of earl grey tea and cups of chamomile tea at a ratio of 5 to 1. Then one of the guests arrived late and started drinking chamomile tea to soothe her nerves after a bad day she had 3 cups, which changed the ratio of earl grey cups and chamomile cups to 5 to 2. How many cups of tea did Minoo serve in all?
ok, let $g$ be the number of cups of Earl Grey tea served before the late guest got there, and $c$ be the number of cups of Charmomile tea served before the late guest got there

we have 5 times as many g as we do c, since the ratio is 5:1. now, ratios can be written as fractions, so lets do that to develop our equation.

$g:c$ is $5:1$

$\Rightarrow \frac gc = \frac 51$

$\Rightarrow g = 5c$ ..........5 times as many g as c, our equation makes sense

now, when 3 more cups of c are served, the ratio goes from 5:1 to 5:2

that is, $g:c + 3$ is $5:2$

or in other words:

$\frac g{c + 3} = \frac 52$

but $g = 5c$, thus we have:

$\frac {5c}{c + 3} = \frac 52$

now you can solve for c. once you have c, it is easy to find g. once you have c and g, you can find out how many cups were served in all

good luck

6. Thanks for the help everyone. I understand the questions now, though I haven't tried out answering the questions again yet. I'll try out the solutions later, I am literally having kind of a headache trying to figure out all this math.

Thing is, I haven't done math in a looooong time and I vaguely remember what to do with some of the math problems which is why I need a math break for maybe an hour or so before I try out answering all the questions again.

Thanks again everyone.

7. Originally Posted by Jhevon
[snip]
EDIT: Whoah, Bessie! Mr F came out of nowhere and answered all the questions. well, he left out number 3... don't know if he's gonna do it... are you, Mr F?
I nearly said that I'd come back and do it when I had more time.

8. Originally Posted by mr fantastic
I nearly said that I'd come back and do it when I had more time.

inside joke