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3 years ago

Write your own explicit formula. List the first 4 terms and solve for the 10th term using the formula. (show your work)

Mathematics

1 answer:

Shalnov [3]3 years ago

4 0

Answer:

See below.

Step-by-step explanation:

Formula:

$a_n = 3(n + 4)$

First term: n = 1

$a_1 = 3(1 + 4) = 15$

Second term: n = 2

$a_2 = 3(2 + 4) = 18$

Third term: n = 3

$a_3 = 3(3 + 4) = 21$

Fourth term: n = 4

$a_4 = 3(4 + 4) = 24$

Tenth term: n = 10

$a_{10} = 3(10 + 4) = 42$

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Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one s

r-ruslan [8.4K]

Answer:

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 185, \pi = \frac{100}{185} = 0.5405$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123$

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

3 0

3 years ago

Identify each function that has a remainder of -3 when divided x+6

Sergeu [11.5K]

Answer:

Step-by-step explanation:

According to remainder theorem, you can know the remainder of these polynomials if you plug in x = -6 into them.

So we will plug in -6 into x of all the polynomials ( A through D) and see which one equals -3.

For A:

$x^5 + 2x^2 - 30x + 30\\=(-6)^5 + 2(-6)^2 - 30(-6) + 30\\=-7494$

For B:

$x^4 + 4x^3 - 21x^2 - 53x + 12\\=(-6)^4 + 4(-6)^3 - 21(-6)^2 - 53(-6) + 12\\=6$

For C:

$x^3 - 10x^2 - 7\\=(-6)^3 - 10(-6)^2 - 7\\=-583$

For D:

$x^4 + 6x^3 - 10x - 63\\=(-6)^4 + 6(-6)^3 - 10(-6) - 63\\=-3$

The only function that has a remainder of -3 when divided by x + 6 is the fourth one, answer choice D.

5 0

3 years ago

A random sample of 169 observations is to be drawn from a population with a mean of 80 and a standard deviation of 39. find the

Drupady [299]

Mu=80, sigma=39, X=85
Z=(X-mu)/sigma = 5/39=0.128=0.13
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so, P(X>85)=1-0.5517=0.4483 approx. thats 44.8% probability.

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3 years ago

Diego wants to have $1,000,000 in 5 years. He plans to invest $250,000 to start and make yearly payments of $125,000 to the acco

julia-pushkina [17]

Answer:

Yes

Step-by-step explanation:

With the $875,000 from his input alone he is really close to $1,000,000 and doing simple intrest on the $250,000 is $105,000 a year is he earns 3.5% intrest a month.

So in 5 years he'll have about $1,662,500 using simple intrest but with compound it'd be more like 2mil

Hope this helps!

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2 years ago

Please help asap…………

sineoko [7]

Answer: linear

Step-by-step explanation:

4 0

2 years ago