Answer:
The 8th term of the sequence is 896/2187.
Step-by-step explanation:
We want to find the 8th term of a geometric sequence whose common ratio is 2/3 and whose first term is 7.
We can write a direct formula. Recall that the direct formula of a geometric sequence is given by:
Where <em>a</em> is the initial term and <em>r</em> is the common ratio.
Substitute:
To find the 8th term, let <em>n</em> = 8. Substitute and evaluate:
In conclusion, the 8th term of the sequence is 896/2187.
Answer:
not rational
Step-by-step explanation:
Answer:
As an improper fraction: 27 
As a mixed fraction: 
Step-by-step explanation:
Any number could be expressed as a fraction 27 is 
and since 0.43 is forty-three hundredths we can express it as .
To find the answer as a mixed fraction we have to put the whole number in the beginning and the fraction in the end. 27
As an improper fraction we have to add 27 / 1 + 43/100 =
Answer: 60 gallons of the 20% solution and 120 gallons of the 50% solution should be mixed.
Step-by-step explanation:
Let x represent the number of gallons of 20% solution that should be mixed.
Let y represent the number of gallons of 50% solution that should be mixed.
A 20% solution of fertilizer is to be mixed with a 50% solution of fertilizer in order to get 180 gallons of a 40% solution. This means that
0.2x + 0.5y = 0.4×180
0.2x + 0.5y = 72- - - - - - - - - - - -1
Since the total number of gallons is 180, it means that
x + y = 180
Substituting x = 180 - y into equation 1, it becomes
0.2(180 - y) + 0.5y = 72
36 - 0.2y + 0.5y = 72
- 0.2y + 0.5y = 72 - 36
0.3y = 36
y = 36/0.3
y = 120
x = 180 - y = 180 - 120
x = 60
