The mean of 7 numbers is 15. When an 8th number is added the mean decreases to 12. What is the 8th number?

Mathematics

1 answer:

ale4655 [162]3 years ago

3 0

Answer:

The 8th number is -9

Step-by-step explanation:

With an average, the sum of the seven numbers divided by 7 is 15.

In order to add an 8th number, we set up

$\frac{7*15+x}{8}=12\\105 + x = 96\\x = -9\\\\\frac{105-9}{8}=\frac{96}{8}=12$

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One member of the debate team is going to be chosen president. each member is equally likely to be chosen. the probability that

inessss [21]

Let
x-------> the probability that a boy is chosen
B------> number of boys in the debate team
G------> number of girls in the debate team

we know that
B+G=20-----> G=20-B-----> equation 1
probability that a boy is chosen=number of boys in the debate team/total of people
so
x=B/20-------> equation 2

the probability that a girl is chosen is 2/3 the probability that a boy is chosen
probability that a girl is chosen=(2/3)*x
probability that a girl is chosen=G/20
(2/3)*x=G/20-----> equation 3
substitute equation 1 in equation 3
(2/3)*x=[20-B]/20----> equation 4

resolve the equations system
x=B/20
(2/3)*x=[20-B]/20

using a graph tool
see the attached figure
the solution is
x=0.6
B=12
G=20-12-----> G=8

number of boys in the debate team is 12
number of girls in the debate team is 8
the probability that a boy is chosen is 0.6 ----> 60%
the probability that a girl is chosen is 0.6*(2/3)----> 0.4---> 40%

the answer is
number of girls in the debate team is 8