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dem82 [27]
2 years ago
5

A large rectangular room needs to be carpeted and has dimensions 18.75 ft by 28 ft.

Mathematics
1 answer:
vichka [17]2 years ago
3 0

Answer:

$13912.50

Step-by-step explanation:

First you find how much carpet you need by finding the area of the room.

18.75*28= 525ft^2

Then multiply the amount of carpet needed by 26.50 to find the total cost.

525*26.50= 13912.50

Hope this helps!

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8.1

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30 points!!<br> What is the sum of the first six terms of the series?<br> 48 - 12 + 3 - 0.75 +...
Lunna [17]

Answer:

The sum of the first six terms is 38.39

Step-by-step explanation:

This is a geometric sequence since the common difference between each term is -\frac{1}{4}

Thus, r=-\frac{1}{4}

To find the sum of first six terms, we need to find the fifth and sixth term of the sequence.

To find the fifth term:

The general form of geometric sequence is a_{n}=a_{1} \cdot r^{n-1}

To find the fifth term, substitute n=5 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{5} &=(48) \cdot\left(-\frac{1}{4}\right)^{5-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{4} \\&=(48)\left(\frac{1}{256}\right) \\a_{5} &=0.1875\end{aligned}

To find the sixth term, substitute n=6 in a_{n}=a_{1} \cdot r^{n-1}

\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}

To find the sum of the first six terms:

The general formula to find Sn for |r| is S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}

\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}

Thus, the sum of first six terms is 38.39

5 0
2 years ago
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