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emmainna [20.7K]
2 years ago
5

Develop an explicit formula in terms of n for the nth term of the following sequence:

Mathematics
1 answer:
nalin [4]2 years ago
4 0
<h2>Answer with explanation:</h2>

The given sequence :  0,4,18,48,100,180,......

We can write the terms of the sequence as :

\text{Ist term }:a_1=1(1^2-1)=0\\\\\text{IInd term }: a_2=2^2(2-1)=4(2-1)=4\\\\\text{IIIrd term }:a_3=3^2(3-1)=9(2)=18\\\\\text{IVth term }:a_4=4^2(4-1)=(16)(3)=48\\\\\text{Vth term }:a_5=5^2(5-1)=25(4)=100\\\\\text{VIth term }:a_6=6^2(6-1)=36(5)=180

From the above presentation of the terms, the explicit formula in terms of n for the nth term will be :-

a_n=n^2(n-1)

Put n= 7 , we get

a_7=7^2(7-1)=49(6)=294

Therefore, the seventh term of the given sequence = 294

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Answer:

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Step-by-step explanation

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Here a right angled triangle given. one angle with measure 45^o given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle 45^o is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}, where x is the angle given.

To get x, we will use tan. So we will get,

tan(45^o) = \frac{4}{x}

We know the value of tan(45^o) = 1. By substituting the value we will get,

1 =\frac{4}{x}

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

(1)(x) = (\frac{4}{x}) (x)

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So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

sin(45^o) =\frac{4}{y}

we know the value of sin(45^o) =\frac{\sqrt{2}}{2}

By substituting the value we will get,

\frac{\sqrt{2}}{2}  = \frac{4}{y}

By cross multiplying we will get,

(\sqrt{2}) (y) = (4)(2)

\sqrt{2}y = 8

We will get y by dividing both sides by \sqrt{2}, we will get,

\frac{\sqrt{2}y}{\sqrt{2}}   =\frac{8}{\sqrt{2} }

y =\frac{8}{\sqrt{2}  }

Now we will rationalize the denominator by multiplying \sqrt{2} to the top and bottom.

y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}

y =\frac{8\sqrt{2}}{2}

y = 4\sqrt{2}

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Answer:

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Step-by-step explanation:

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A type I error is the rejection of a true null hypothesis, this means that we would get a "false positive" with this error.

A type II error is the non rejection of a not true null hypothesis, this error would give us a "false negative".

In this problem, we are told that the mean match score to identify a suspect is 80. However, the test shows that the mean match score is more than 80 when the person doesn't have a fingerprint match (and therefore the person would not be a suspect). Therefore, this person would appear as a suspect when he/she really isn't one. This means that the test is giving a "false positive". Thus, this is a type I error.

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