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zavuch27 [327]
3 years ago
12

Evaluate the infinite sum

Mathematics
2 answers:
mote1985 [20]3 years ago
8 0

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Effectus [21]3 years ago
6 0

The sum does not converge because \dfrac76>1.

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Answer:

The answer to your question is  20x + 21y + 14        

Step-by-step explanation:

Data

Expression             1/5 (150x - 80y + 50 - 50x - 25y + 20)

Process

1.- Multiply 1/5 by each term

                                     150/5x - 80/5y + 50/5 - 50/5x - 25/5y + 20/5

2.- Simplify

                                      30x - 16y + 10 - 10x - 5y + 4

3.- Simplify like terms

                                      (30x - 10x) + (-16y - 5y) + (10 + 4)

4.- Result

                                        20x + 21y + 14                                        

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Answer:

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Step-by-step explanation:

After the third step, take the square root of both sides.

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Thus, the fourth step is:

\sqrt{(x+\frac{b}{2a})^2}=\sqrt{ \frac{b^2-4ac}{4a^2}} }

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(x+\frac{b}{2a})=\pm\sqrt{ \frac{b^2-4ac}{4a^2}} }

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A recent study found that 51 children who watched a commercial for Walker Crisps (potato chips) featuring a long-standing sports
hichkok12 [17]

Answer:

1

The claim is that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

2

The kind of test to use is a t -test because a t -test is used to check if there is a difference between means of a population

3

t  =  3.054

4

The p-value  is   p-value  =  P(Z >  3.054) = 0.0011291

5

The conclusion is  

There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

The test statistics is  

Step-by-step explanation:

From the question we are told that

   The first sample size is  n_1  =  51

    The first sample  mean is \mu_1  =  36

    The second sample size is  n_2  =  41

    The second sample  size is  \mu_2  =  25

     The first standard deviation is  \sigma _1  =  21.4 \  g

    The second standard deviation is  \sigma _2  =  12.8 \  g

  The  level of significance is  \alpha =  0.05

The  null hypothesis is  H_o  :  \mu_1 = \mu_ 2

The  alternative hypothesis is  H_a :  \mu_1 > \mu_2

Generally the test statistics is mathematically represented as

    t  =  \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2}{n_1}  + \frac{s_2^2}{n_2}  } }

=>   t  =  \frac{ 36 - 25}{ \sqrt{ \frac{ 21.4^2}{51}  + \frac{ 12.8^2}{41}  } }

=> t  =  3.054

The  p-value is mathematically represented as

     p-value  =  P(Z >  3.054)

Generally from the z table  

             P(Z >  3.054) =  0.0011291

=>   p-value  =  P(Z >  3.054) = 0.0011291

From the values obtained  we see that p-value  < \alpha so  the null hypothesis is rejected

Thus the conclusion is  

  There is sufficient evidence to conclude that the mean amount of Walker Crisps eaten was significantly higher for the children who watched the sports celebrity- endorsed Walker Crisps commercial

5 0
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