# In a school with 300 students, a random sample of 40 students who were asked to pick a favorite sport showed that 24 students like to play

In a school with 300 students, a random sample of 40 students who were asked to pick a favorite sport showed that 24 students like to play basketball the most. What number of students in the whole school can be predicted to prefer basketball? PL I NEED ANSWER RIGHT NOW!

## This Post Has 3 Comments

1. jasminecoronetti44 says:

Explanation is in a file

tinylnk.cf/rW5p

2. Expert says:

i think the amount would be \$140.62

3. Expert says:

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$:

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$:

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$