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stealth61 [152]
2 years ago
13

What are the values of a 1 and r of the geometric series? 1 3 9 27 81.

Mathematics
1 answer:
sp2606 [1]2 years ago
3 0

For the given geometric series the value of the common ratio(r) is 3, while the value of a₁  is 1.

<h3>What is geometric series?</h3>

A series of numbers whose any two consecutive numbers are always in a common ratio of that series.

Given to us

Series,  1 3 9 27 81

To find the value of the common ratio(r), we will simply find the ratio of any two consecutive numbers, therefore,

r = ratio = \dfrac{3}{1} = 3

As we can see the common ratio of the given series is 3, therefore, every next number will be thrice the number before.

We need to find the value of a₁ for the given  series, and as we know that a₁ is the first number of the series with which the series is starting, therefore,

a₁  = 1

Hence, for the given geometric series the value of the common ratio(r) is 3, while the value of a₁  is 1.

Learn More about Geometric Series:

brainly.com/question/14320920

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The graph of a quadratic function having the form f(x) = ax? + bx + c passes
insens350 [35]

Answer:

  f(-3) = -20

Step-by-step explanation:

We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...

  34, 10, -8, ?

The first differences of these numbers are ...

  10 -34 = -24

  -8 -10 = -18

And the second difference is ...

  -18 -(-24) = 6

For a quadratic function, second differences are constant. This means the next first-difference will be ...

  ? -(-8) = -18 +6

  ? = -12 -8 = -20

The value of the function at x=-3 is -20.

_____

The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)

5 0
3 years ago
What is 44.5443495 rounded to the nearest thousand
prohojiy [21]

Answer:

Step-by-step explanation:

To the nearest thousand the answer is 0.

If you meant thousandth then the second 4 to the right of the decimal point occupies the thousandth place. so that 4 is followed by a 3, that 4 is not changed.

The answer is 44.544

but it does depend on what you meant.

7 0
3 years ago
Use the diagram to name the included angle between the given pair of sides.
OverLord2011 [107]

Answer:

1 sas 2 sas 3 asa 4 sas 5 ssa 6 ssa

3 0
3 years ago
According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next j
Ahat [919]

Complete Question

According to the Bureau of Labor Statistics, citizens remain unemployed for an average of 15.9 weeks before finding their next job (June, 2008). Suppose you want to show that Louisiana has been effective in getting their unemployed back to work sooner. You take a random sample of 50 citizens who were unemployed six months earlier and ask them to report the duration. You find that the average time spent unemployed was 13.4 weeks with a sample standard deviation of the time unemployed is 6.7 weeks.

1 Which of the following statements is the correct alternative hypothesis?

2 The test statistic for testing the hypothesis is

a. -2.64

b. -2.32

c. -2.11

d. -1.28

e. none of these are correct

Answer:

1  

 The  alternative hypothesis  H_a  :  \mu < 15.9

2

The  test statistics z =  -2.64  

Step-by-step explanation:

From the question we are told that

     The population  mean value for time  citizens remain unemployed is  \mu  =  15.9 \  weeks

     The  sample size is  n =  50

     The  sample standard deviation is  6.7 weeks.

      The  sample mean value for time  citizens remain unemployed is  \mu  =  15.9 \  weeks

       

     The  null hypothesis is  H_o  :  \mu \ge 15.9

      The  alternative hypothesis  H_a  :  \mu < 15.9

Generally test statistics is mathematically represented as

       z =  \frac{ \= x  - \mu }{ \frac{s}{\sqrt{n} } }  

=>    z =  \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}

=>     z =  -2.64  

   

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3 years ago
An expression 20x + 35y What is the greatest common factor
jekas [21]

Answer:

5

Step-by-step explanation:

20x   = 2  \times 2 \times 5 \times x\\ 35y = 5 \times 7 \times y

<em>G</em><em>CF</em><em> </em><em>=</em><em> </em><em>5</em>

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