Mathematics
OpenStudy (anonymous):

What is the probability of rolling a sum of 8 on at least one of two rolls of a pair of number cubes?

OpenStudy (shubhamsrg):

from 1 to 6 ..what pairs add up to 6 ? i'll start with it,,you continue.. (2,6), (3,5) ... ??

OpenStudy (anonymous):

idk omggggg imma fail -______-

OpenStudy (shubhamsrg):

comeon,,you cant be dumber than me! ;) just tell me a pair of 2 nos between 1 and 6 that add up to 8..whats the big deal?

OpenStudy (anonymous):

i'm not getting what you are saying. i'm seriously getting frustrated haha..

OpenStudy (anonymous):

guys, could you help me on this one? get the common ratio if the 4th and 7th term of a geometric sequence is -4 and 108, respectively. I badly seek for the answer.. please show the formula. :)

OpenStudy (shubhamsrg):

hmmn,,i think you should take some rest and try all this later @katelynx3 ..it'll be of no use if i/or anyone else simply tells you the ans..hmmn..

OpenStudy (anonymous):

yeah it will be! but ugh k.

OpenStudy (anonymous):

btw, 2 pairs of nos. that can sum up to8.. (1,7) (2,6) (3,5) (4,4) :)

OpenStudy (shubhamsrg):

@lovelyDee the nth term of a GP is ar^(n-1) a=1st term,,r is common ratio..and n is term no.. hope this helps and by the way,,altough the listed the pairs right,,but mind you,,7 doesnt come on a dice,,unless you use some out of this world dice,, l)

OpenStudy (anonymous):

@shubhamsrg ohh. :)) i didn't get to read that "dice" part.. :) so i was hoping to type all those possible nos. :)

OpenStudy (anonymous):

@katelynx3 yes I'm still here.. :)

OpenStudy (anonymous):

Parth (parthkohli):

There are 36 possibilities. Probability of rolling a sum of 8 here is in these cases: {6,2}{5,3}{4,4}{3,5}{2,6}

OpenStudy (anonymous):

.. what is the 13th term in an arithmetic sequence whose 1st term is is 10, and whose 4th term is 1?? please.. i just need the answer and the formula to get it. ty!! :)

Parth (parthkohli):

Common difference is -3. The formula for nth term in an arithmetic sequence is: $$a_n = a_1 + (n - 1)d$$ So, $$\Large \color{Black}{\Rightarrow a_{13} = 10 + -3(13 - 1)}$$ $$\Large \color{Black}{\Rightarrow a_{13} = 10 + -3(12) }$$ $$\Large \color{Black}{\Rightarrow a_{13} = 10 - 36 }$$ $$\Large \color{Black}{\Rightarrow a_{13} = -26 }$$

OpenStudy (anonymous):

ohh! thank you!! well I am just curious.. how did you get the common difference?.. represented by "d"? :)

Parth (parthkohli):

Because you're adding -3 every time :)

OpenStudy (anonymous):

ohh.. so you used a little of common sense to get it. right?? ;)

Parth (parthkohli):

Lol yeah

OpenStudy (anonymous):

okaaay. thanks so much. :)

OpenStudy (anonymous):

@ParthKohli uhm how abt this one.. how many integers between 65/9 and 2024/9 are exactly divisible by 7?? :))

Parth (parthkohli):

$$\Huge \color{Black}{\mathfrak{<tips hat>} }$$

Parth (parthkohli):

65/9 is approximately 7.something 2024/9 is approximately 224.something You can count now..

Parth (parthkohli):

It'll start at 14 and end at 224.

OpenStudy (anonymous):

i think its 31.. am i right??

Parth (parthkohli):

7 * 2 = 14 7 * 32 = 224 31 numbers. Correcto!

OpenStudy (anonymous):

yey!! :)

OpenStudy (anonymous):

how about this one??... if the first 2 terms of a geometric progression are $4x ^{2}$ and 3/y, then the third term is...??

Parth (parthkohli):

Hmm.. see the common ratio

Parth (parthkohli):

$$\Large \color{Black}{\Rightarrow {4x^2 \over 3\div y } }$$ is the common ratio. Multiply this to 3/y to get the next one.

OpenStudy (anonymous):

then i get...9/$4x ^{2}y ^{2}$.... ??? right?

OpenStudy (anonymous):

ok... ty for this!!! :)

Parth (parthkohli):

Lol $$\Huge \color{orange}{<tipshat - again>}$$