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notsponge [240]
3 years ago
7

The second term of an arithmetic sequence is 7. The sum of the first four terms of the sequence is 12. Find the first term, a, a

nd the common difference, d, of the sequence.
Mathematics
2 answers:
dusya [7]3 years ago
8 0
T2 = 7
S4 = 12

7 = a + 6d
a = 7 - 6d

12 = 2 ( 2(7-6d) +3d )
6 = 14 - 12d + 3d
9d = 8
d = 8/9

a = 7 - 6(8/9)
a = 1/2/3
Whitepunk [10]3 years ago
3 0
Are you sure its Arithmetic?  

There isn't a way to solve this, that sum of the first four terms has got me a little screwed up.

the formula you want to use is this:

An=A1+D(N-1)

A1 is the first term of the sequence D is a common difference and N is the term of the sequence.

7= 1 + 6 (2-1) 

that's the only way, so let's plug it in for the first one 3rd and 4th 

A1= 1 + 6 (1-1)
A1=1

A3= 1 + 6 (3-1)
A3=13

A4= 1 + 6 (4-1) 

A4=19


that's as far as I can help, though.
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6 0
3 years ago
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-------> <span>the probability that a boy is chosen
B------> </span>number of boys in the debate team
G------> number of girls in the debate team<span>

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

t<span>he probability that a girl is chosen is 2/3 the probability that a boy is chosen
</span>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

7 0
3 years ago
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bazaltina [42]
Plug in 83 for y and 3 for x
83 = 3^2 - 6 (3) + 92
83 = 9 - 18 + 92
83 = -9 + 92
83 = 83 so it works
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Answer: \sqrt{52}

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5 0
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Step-by-step explanation: Hope this helps

4 0
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