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Alja [10]
3 years ago
10

Answer true or false. If​ false, explain briefly. ​a) Some of the residuals from a least squares linear model will be positive a

nd some will be negative. ​b) Least squares means that some of the squares of the residuals are minimized. ​c) We write ModifyingAbove y with caret to denote the predicted values and y to denote the observed values.
Mathematics
1 answer:
Maru [420]3 years ago
4 0
False because the squares are minimized of the least values.
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Write the terms a 1a1​, a 2a2​, a 3a3​, and a 4a4 of the following sequence. If the sequence appears to​ converge, make a conjec
Arturiano [62]

Answer:

Step-by-step explanation:

WE are given that a_n = \frac{(-1)^{n+1}}{5n-4}. Then, to now the first for terms, we must replace n by 1,2,3,4 respectively. Then

a_1 = \frac{(-1)^2}{5(1)-4} = \frac{1}{1}= 1

a_2 = \frac{(-1)^3}{5(2)-4} = \frac{-1}{6}

a_3 = \frac{(-1)^4}{5(3)-4} = \frac{1}{11}= 1

a_4 = \frac{(-1)^5}{5(4)-4} = \frac{-1}{16}= 1

Note that as n increase, a_n gets closer to 0. So, the limit of this sequence is 0.

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For every integer k from 1 to 10, inclusive the "k"th term of a certain sequence is given by (−1)(k+1)∗(12k). If T is the sum of
Katena32 [7]

Answer:

Option D. is the correct option.

Step-by-step explanation:

In this question expression that represents the kth term of a certain sequence is not written properly.

The expression is (-1)^{k+1}(\frac{1}{2^{k}}).

We have to find the sum of first 10 terms of the infinite sequence represented by the expression given as (-1)^{k+1}(\frac{1}{2^{k}}).

where k is from 1 to 10.

By the given expression sequence will be \frac{1}{2},\frac{(-1)}{4},\frac{1}{8}.......

In this sequence first term "a" = \frac{1}{2}

and common ratio in each successive term to the previous term is 'r' = \frac{\frac{(-1)}{4}}{\frac{1}{2} }

r = -\frac{1}{2}

Since the sequence is infinite and the formula to calculate the sum is represented by

S=\frac{a}{1-r} [Here r is less than 1]

S=\frac{\frac{1}{2} }{1+\frac{1}{2}}

S=\frac{\frac{1}{2}}{\frac{3}{2} }

S = \frac{1}{3}

Now we are sure that the sum of infinite terms is \frac{1}{3}.

Therefore, sum of 10 terms will not exceed \frac{1}{3}

Now sum of first two terms = \frac{1}{2}-\frac{1}{4}=\frac{1}{4}

Now we are sure that sum of first 10 terms lie between \frac{1}{4} and \frac{1}{3}

Since \frac{1}{2}>\frac{1}{3}

Therefore, Sum of first 10 terms will lie between \frac{1}{4} and \frac{1}{2}.

Option D will be the answer.

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What’s 19,975 divided by 25 show your work
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the answer to the question is 799

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