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ANTONII [103]
2 years ago
14

Lucy is working with a series whose first term is 12 and that is generated by the equation t(n) = −9 + 21n. The sum of her serie

s is 3429. How many terms are in her series? *hint: the last term can be written as -9 + 21n if we say there are n terms. You will need to solve a quadratic equation to solve for n.
Mathematics
1 answer:
mafiozo [28]2 years ago
7 0

There are 18 terms are in her series

<h3>What is Arithmetic progression series?</h3>

Arithmetic Progression (AP) is a sequence of numbers in order in which the difference of any two consecutive numbers is a constant value.

Given that: t(n) = −9 + 21n=l

a= 12, Sum = 3429

As, Sum of series =3429

     n/2 (a+l) =3429

     n/2 (12 +21n-9)= 3429

     n/2 (3+21n)=3429

     21n² + 3n= 6858

     21n² + 3n- 6858=0

    7n² + n- 2286=0

For solving for n, get

    n= 18 or n= -127/7

Thus, there 18 terms in the series.

Learn more about series here:

brainly.com/question/12146981

#SPJ1

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The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation
Lostsunrise [7]

Answer:

ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

The confidence level is 0.98 and the significance is \alpha=1-0.98 =0.02 and \alpha/2 =0.01 and the critical value using the table is:

z_{\alpha/2}= 2.326

And replacing we got:

ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76

Step-by-step explanation:

For this case we have the following info given:

\sigma = 425 represent the population deviation

n =22 the sample size

\bar X =1520 represent the sample mean

We want to find the margin of error for the confidence interval for the population mean and we know that is given by:

ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

The confidence level is 0.98 and the significance is \alpha=1-0.98 =0.02 and \alpha/2 =0.01 and the critical value using the table is:

z_{\alpha/2}= 2.326

And replacing we got:

ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76

3 0
3 years ago
A rectangular pitcher is 3 inches wide, 9 inches long and 16 inches tall. If water is filled up to 5 inches, how much more water
iris [78.8K]

Answer:

397 inches

Step-by-step explanation:

5 0
3 years ago
How is. X^2=36 rational?
elena55 [62]

Answer:

{x}^{2}  = 36 \\ x =  \sqrt{36 } \\ x = 6 \\ it \: is \: rational \: number \: because \: we \: can \: write \: 6as \: 6 \1 \: it \: is \: in \: the \: form \: of \: p  \q \: where \:  \: q \: i \: not \: equals \: to \: 0

hope this will help you.

6 0
3 years ago
Pls help with explanation. Will give brainliest
muminat

Answer:

E - 40°

Step-by-step explanation:

Angle O = 2 × y

{Angle at center is equal to twice the angle at circumference formed by the same arc}

O = 2 × 70°

O = 140°

x + 90° + 90° + O = 360°

{Sum of angles in a quadrilateral is equal to 360°}

x + 90° + 90° + 140° = 360°

x + 320° = 360°

x = 40°

7 0
3 years ago
The product of the page numbers on two facing pages of a book is 156. Find the page numbers
Gnoma [55]

Let x be the page number then x+1 would be the other page number (because the pages are two facing pages which means they follow on consecutively)

Then

(x)(x+1) = 156

x^2 + x - 156 = 0

x = 12 or x = -13( but x can't be a negative number)

so x = 12

and the next page is 13

3 0
3 years ago
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