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!

Explanation is in a file

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i think the amount would be $140.62

[tex]2^{2x+11}=3^{x-31}[/tex]

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

[tex]\ln2^{2x+11}=\ln3^{x-31}[/tex]

apply the exponent property - this says that [tex]\ln a^b=b\ln a[/tex]:

[tex](2x+11)\ln2=(x-31)\ln3[/tex]

distribute the log terms on both sides:

[tex](2\ln2)x+11\ln2=(\ln3)x-31\ln3[/tex]

group like terms together:

[tex](2\ln2-\ln3)x=-11\ln2-31\ln3[/tex]

divide through both sides by the coefficient on [tex]x[/tex]:

[tex]x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}[/tex]

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

[tex]x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}[/tex]

[tex]x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}[/tex]

[tex]x=-\log_{4/3}2^{11}3^{31}[/tex]