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andrey2020 [161]
3 years ago
12

The common ratio of a geometric series is \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction and the sum of the first

444 terms is 170170170.
Mathematics
1 answer:
myrzilka [38]3 years ago
8 0

Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

r =  \frac{1}{4}

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

s_n=\frac{a_1(1-r^n)}{1-r}

common ratio, n=4 and equate to 170.

\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170

\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4}  \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2}  \\\\\frac{1}{256} a_1 = \frac{1}{2}  \\\\ a_1 = \frac{1}{2}   \times 256\\\\a_1 = \frac{1}{2}   \times 256 \\\\= 128

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Which statements about square roots are true? Check all that apply.
USPshnik [31]

Answer:

The only correct answer is:

All positive numbers have two square roots

Step-by-step explanation:

This is true because in any situation all positive numbers have two square roots. For example, the square root of 25 is +/- 5 which means that 5 is a square root (because 5x5=25) and -5 is a square root (because -5x-5=25).

The others such as 18 = 9, 149 = 7, and 25 = 5 are all false statements.

5 0
3 years ago
A coffee seller makes a salary of 3,500 dollars per month plus $12 commission for every $100 of coffee he sells. a case of coffe
QveST [7]

Th coffee seller must have sold 130 coffee case but for him to make at least $3650, he must've sold 131 cups of coffee

Data;

  • monthly salary = $3500
  • commission = $12
  • amount due for commission = $100
  • cost of coffee = $25
  • total amount = $3650

<h3>Word Problem</h3>

These are verbal expressions used to represent mathematical problems and if we want to solve them, we must translate them into equations.

If his total pay is $3650 and he earns a commission of $12 for every $100 coffee sold.

How many coffee case are inside $100

100/25=4

This shows that for every 4 coffee case sold, she made ($100 + $12) as profit.

If 4 coffee = $112

how many coffee will give us $3650

4coffee=$112\\x coffee = $3650\\x = \frac{4*3650}{112} \\x = 130.35

From the calculations above, he must've sold at least 131 cups of coffee to make $3650.

Learn more on word problems here;

brainly.com/question/21405634

3 0
2 years ago
Read 2 more answers
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!
swat32
The answer will be 14^12
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3 years ago
A container is leaking 0.42 liters of solution each hour. What is the overall change after 5 hours?
OLga [1]

Answer:

2.3 liters leaked

Step-by-step explanation:

0.42 * 5

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3 years ago
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The file contains the solution to the question

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