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: 3/14
Step-by-step explanation: P(Orange jelly bean) = 9/42 = 3/14
Answer:
Step-by-step explanation:
If they can be rounded to 70 to the nearest 10s. Then they are from 65 to 74.
Their sum is 136.
If we use 136 divided by 2 we get 68.
Since they're distinct, so one can be 67 and one can be 69
Answer:
n = -7
Step-by-step explanation:
Solve for n:
-3 n - 5 = 16
Hint: | Isolate terms with n to the left-hand side.
Add 5 to both sides:
(5 - 5) - 3 n = 5 + 16
Hint: | Look for the difference of two identical terms.
5 - 5 = 0:
-3 n = 16 + 5
Hint: | Evaluate 16 + 5.
16 + 5 = 21:
-3 n = 21
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -3 n = 21 by -3:
(-3 n)/(-3) = 21/(-3)
Hint: | Any nonzero number divided by itself is one.
(-3)/(-3) = 1:
n = 21/(-3)
Hint: | Reduce 21/(-3) to lowest terms. Start by finding the GCD of 21 and -3.
The gcd of 21 and -3 is 3, so 21/(-3) = (3×7)/(3 (-1)) = 3/3×7/(-1) = 7/(-1):
n = 7/(-1)
Hint: | Simplify the sign of 7/(-1).
Multiply numerator and denominator of 7/(-1) by -1:
Answer: n = -7
Mr. Patel used 4.5 bags of seed
<em><u>Solution:</u></em>
Given that,
Over the summer, Mr. Patel refilled a bird feeder 24 times using 6 cups of seed each time
A bag of seeds holds 32 cups
1 bag of seed = 32 cups
Given that Patel refilled 24 times using 6 cups of seed each time
<em><u>Then, the number of cups used for the 24 times is given as:</u></em>

<em><u>Now we have to find the bags of seed needed for 144 cups</u></em>
Let "x" be the number of bags of seed for 144 cups
From given,
1 bag of seed = 32 cups
"x" bags of seed = 144 cups
This forms a proportion and we can solve it by cross multiplying

Thus 4.5 bags of seed is used by Mr.patel