A watering can contained 512 quarts water. After all the plants were watered, only 4 cups remained. How many cups of water were
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The chairs in the auditorium illustrates an arithmetic sequence
- The recursive rule is: an = an-1 + 8; a1 = 26
- The explicit rule is: an = 18 + 8n
- There are 74 seats in the 7th row
- 840 chairs can fit the auditorium
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at:
Answer:
a. Let the variable be for the fundraising activities and
as the revenue for foundation.
b.
c. $43.2
d. $1416.67
Step-by-step explanation:
Given that:
The World Issues club donates 60% of the total of their fundraising activities.
Answer a.
Let us choose the variable to represent the money earned during fundraising activities and
for the revenue generated for foundation.
Answer b.
Foundation will receive 60% of the total of the fundraising activities.
Equation to determine the money that will be received by foundation:
Answer c.
Given that x = $72, M = ?
Putting the value of x in the equation above:
Answer d.
Given that M = $850, x = ?
Putting the value of M in the equation above to find x:
So, the answers are:
a. Let the variable be for the fundraising activities and
as the revenue for foundation.
b.
c. $43.2
d. $1416.67
Answer:
The division will be represented as:
Step-by-step explanation:
1) Let's find a number with a variable that multiplied by 6x gives as 18x². It will be 3x, because (6x+5)3x=18x²+15x.
Now, let's subtstract:
2) Let's find a number with a variable that multiplied by 6x gives as -18x. It will be -3, because (6x+5)(-3)=-18x-15.
Now, let's subtstract:
Therefore, the division will be represented as:
I hope it helps you!