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Lady_Fox [76]
3 years ago
6

Does anyone know the answer?

Mathematics
1 answer:
Lorico [155]3 years ago
3 0

Answer:

n = 59

Step-by-step explanation:

Since the difference between consecutive terms is constant, then the sequence is arithmetic.

The n th term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

Given

a_{10} = 40, then

a₁ + 9d = 40 → (1)

Given

a_{20} = 20, then

a₁ + 19d = 20 → (2)

Subtract (1) from (2) term by term

10d = - 20 ( divide both sides by 10 )

d = - 2

Substitute d = - 2 in (1)

a₁ - 18 = 40 ( add 18 to both sides )

a₁ = 58

The sum to n terms of an arithmetic sequence is

S_{n} = \frac{n}{2}[2a₁ + (n - 1)d ]

Here a₁ = 58, d = - 2 and S_{n} = 0, thus

\frac{n}{2}[ ( 2 × 58) - 2(n - 1)] = 0

\frac{n}{2}( 116 - 2n + 2) = 0

Multiply through by 2

n(118 - 2n) = 0

Equate each factor to zero and solve for n

n = 0

118 - 2n = 0 ⇒ - 2n = - 118 ⇒ n = 59

However, n > 0 ⇒ n = 59

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What is the solution to 6x^2 + 2x + 4 = 0?
Angelina_Jolie [31]

Step 1) Divide 6 and 4 (the last 2 numbers) and bring everything else down

<em>6x^24x+2x+4</em>

Step 2) Place in parentheses

<em>(6x^24x)+(2x+4)</em>

Step 3) Figure out what you can take out of each parentheses.

**In the first one, you can take out 6x because both numbers have x and 6 is the largest number 6 and 24 can go into.**

**In the second one, you can only take out 2 because 2 is the largest number that goes into 2 and 4.**

Step 4) You will know you did it correctly when the parentheses match up

<em>6x(x+4) + 2(x+4)</em> <<< this is how it should look

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The average annual premium for automobile insurance in the United States is $1411. A representative sample of annual premiums fo
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Using confidence interval concepts, it is found that:

a) The point estimate is the sample mean.

b) The confidence interval is: \overline{x} \pm T\frac{s}{n}

c) If $1411 is between the bounds of the interval yes, otherwise no.

--------------

  • At item a, it asks to provide a point estimate for the population mean, which is the sample mean \overline{x}

--------------

Item b:

  • In the spreadsheet, it is possible to find the <em>standard deviation for the sample</em>, thus, the t-distribution is used.
  • The confidence interval will be given by:

\overline{x} \pm T\frac{s}{n}

In which:

  • \overline{x} is the sample mean.
  • T is the critical value, from the t-distribution, with a two-tailed area of \frac{1 - 0.95}{2} = 0.025 and n-1 degrees of freedom.
  • s is the standard deviation for the sample.
  • n is the sample size.

--------------

Item c:

We have to check if 1411 is between \overline{x} - T\frac{s}{n} and \overline{x} +T\frac{s}{n}.

  • If it is, the interval includes the National Average, otherwise, it does not.

A similar problem is given at brainly.com/question/24232455

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