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3 years ago

In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an. Then write the first three terms of the sequence.

1 answer:

7 0

$a_4=ra_3$
$a_5=ra_4=r^2a_3$
$a_6=ra_5=r^3a_3$

$40=-5r^3\implies r^3=-8\implies r=-2$

$a_3=ra_2=r^2a_1$

$-5=(-2)^2a_1\implies a_1=-\dfrac54$

You know the first and third terms, $a_1$ and $a_3$ , so you just need to find the second term $a_2$ :

$a_2=ra_1\implies a_2=-2\left(-\dfrac54\right)=\dfrac52$

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Assuming that the population is normally distributed, construct a 9090% confidence interval for the population mean for each o

jasenka [17]

Given:

Set A: 1 4 4 4 5 5 5 8

Mean: 4.5

Standard dev: 1.9

Set B:

Mean: 4.5

Standard dev: 2.45

% = 90

Set A:

Standard Error, SE = s/ √n = 1.9/√8 = 0.67

Degrees of freedom = n - 1 = 8 -1 = 7

t- score = 1.89457861

Width of the confidence interval = t * SE = 1.89457861* 0.67 = 1.272685913

Lower Limit of the confidence interval = x-bar - width = 4.5 - 1.272685913 = 3.23

Upper Limit of the confidence interval = x-bar + width = 4.5 + 1.272685913 = 5.77

The 90% confidence interval is [3.23, 5.77]

Set B:

Standard Error, SE = s/ √n = 2.45/√8 = 0.87

Degrees of freedom = n - 1 = 8 -1 = 7

t- Score = 1.89457861

Width of the confidence interval = t * SE = 1.89457861* 0.87 = 1.641094994

Lower Limit of the confidence interval = x-bar - width = 4.5 - 1.641094994 = 2.86

Upper Limit of the confidence interval = x-bar + width = 4.5 + 1.641094994 = 6.14

The 90% confidence interval is [2.86, 6.14]

We can obviously see that sample B has more variation in the scores than sample A. The fact that the standard deviation is 2.45 for B and 1.9 for A). Therefore, they yield dissimilar confidence intervals even though they have the same mean and range.

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3 years ago

Is f(x)=3/4 a function?

Marat540 [252]

Answer:

Yes, f(x) = $\frac{3}{4}$ is a constant function.

Step-by-step explanation:

A function is defined to be a relation from 1 set of numbers to another set of numbers.

The main condition for a relation to be a function is that for every number in the domain there should be a unique image

Here the given function is f(x) = $\frac{3}{4}$

This function is a constant function and gives the value 0.75 for all values of x.

Hence the graph would be a straight line parallel to the x-axis passing through y = 0.75.

Hence the f(x) = 0.75 is a function.

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3 years ago

aliya0001 [1]

C is correct
(im taking quiz)

6 0

3 years ago

Read 2 more answers

What is the value of StartFraction 1.6 times 10 Superscript 14 Baseline Over 3.2 times 10 Superscript 7 Baseline EndFraction in

Helga [31]

Answer:

5.0 times 10 Superscript 6

Step-by-step explanation:

What is the value of StartFraction 1.6 times 10 Superscript 14 Baseline Over 3.2 times 10 Superscript 7 Baseline?

This is represented mathematically as:

1.6 × 10¹⁴/ 3.2 × 10⁷

Solving for this

1.6 × 10¹⁴/ 3.2 × 10⁷

= [1.6/3.2] × 10¹⁴-⁷

= 5 × 10⁶

= 5.0 times 10 Superscript 6

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3 years ago

A dog weighs two pounds less than three times the weight of a cat. The dog also weights twenty-two more pounds than the cat. Wri

Solnce55 [7]

Answer:

the cat weighs 21 pounds.

the dog weighs 43 pounds

Step-by-step explanation:

dog = 3x-20 = x + 22

cat = x

3x-20 = x+22

3x = x+42 (add 20 to both sides)

2x = 42 (subtract x from both sides)

x = 21

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3 years ago