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2 years ago

Write the sum using summation notation, assuming the suggested pattern continues. 2 - 8 + 32 - 128 + ...

1 answer:

4 0

This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
an = a1*r^(n-1)

The sum is the sum of such terms.
$sum=\sum\limits_{n=1}^{\infty}{2(-4)^{(n-1)}}$

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How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winner

Liula [17]

Answer:

The 95% confidence interval would be given by (14444.04;33657.30)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: $26,650 $6,060 $52,820 $8,490 $13,660$25,840 $49,840 $23,790 $51,480 $18,960$990 $11,450 $41,810 $21,060 $7,860

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=24050.67$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=17386.13 represent the sample standard deviation

n=15 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

Now we have everything in order to replace into formula (1):

$24050.67-2.14\frac{17386.13}{\sqrt{15}}=14444.04$

$24050.67+2.14\frac{17386.13}{\sqrt{15}}=33657.30$

So on this case the 95% confidence interval would be given by (14444.04;33657.30)

6 0

2 years ago

Paul makes a base monthly salary of $1500.As a vendor,he must sell %19000 worth of items per month.He also makes a 6% commission

Orlov [11]

Answer:

$3000

Step-by-step explanation:

3 0

2 years ago

Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately_______ .

Julli [10]

In this question , we have a graph given, and we have to find the x coordinate of the intersection point .

From the graph , the input value is approximately 3.3 .

In the graph,

$f(x) =3$

And for g(x), we need the slope and y intercept .

Slope is the ratio of rise and run .

Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .

So the equation of g(x) is

$g(x) = \frac{3}{2}x -2$

We need to do

$f(x)= g(x)$

Substituting the values of the two functions, we will get

$3 = \frac{3}{2}x -2$

Adding 2 to both sides

$5 = \frac{3}{2}x$

Cross multiplication

$10 =3x
\\
x = \frac{10}{3}$

$x = 3.3$

So the input value is 3.3 approx

6 0

2 years ago

Read 2 more answers

Write the perimeter of the floor plan shown as an algebraic expression in x.

Nimfa-mama [501]

The perimeter is the sum of the enclosing side.

From the figure, the perimeter is
P = 11 + (x-2) + (11-3) + [(x-2) - (x-11)] + (x-11)
= 11 + x - 2 + 8 + 9 + x - 11
= 2x + 15

Answer: 2x + 15

5 0

2 years ago

What is the best estimate for 7.8 x 37.86?<br> A. 46<br> B. 50<br> C. 300<br> D. 400

lana66690 [7]

I think it’s C since it’s 295.308

8 0

2 years ago

Read 2 more answers