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solniwko [45]
3 years ago
8

Use​ Gauss's approach to find the following sums​ (do not use​ formulas). 1+3+5+7+...+1001

Mathematics
1 answer:
kramer3 years ago
5 0
Hello,

s=1+2+3+...+1000+1001=\sum_{i=1}^{1001}\  i \ (1) \\ 

s=1001+1000+...+3+2+1=\sum_{j=1}^{1001}\ 1002-j \ (2)\\

(1)+(2)==\textgreater \ 2*s=(1+1001)+(2+1000)+...+(1000+2)+(1001+1)\\

=1002*1001=(\sum_{i=1}^{1001}\  i )\ +(\sum_{i=1}^{1001}\ 1002-i )\ \\

=\sum_{i=1}^{1001}\ ( i+1002-i)\ = \sum_{i=1}^{1001}\  1002=1001*1002\\

So\ s= \dfrac{1001*1002}{2} =501501\\
 





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Answer:

Step-by-step explanation:

8:60 is the rate

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Divide by 2 again.

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7 0
3 years ago
g Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether event
vagabundo [1.1K]

Answer:

There is not sufficient evidence to support the claim.

Step-by-step explanation:

The claim to be tested is:

The mean respiration rate (in breaths per minute) of students in a large statistics class is less than 32.

To test this claim the hypothesis can be defined as follows:

<em>H₀</em>: The mean respiration rate of students is 32, i.e. <em>μ</em> = 32.

<em>Hₐ</em>: The mean respiration rate of students is less than 32, i.e. <em>μ</em> < 32.

The sample mean  respiration rate of students is 31.3.

According to the claim the sample mean is less than 32.

The sample mean value is not unusual if the claim is true, and the sample mean value is also not unusual if the claim is false.

Thus, there is not sufficient evidence to support the claim.

7 0
3 years ago
Which of the following properties is always true for a parallelogram and why ?
posledela
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5 0
3 years ago
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Help find the answer for problem number 4
Olin [163]
Adult ticket (a) = $5
Child ticket (c) = $2

785 tickets = $3280

a + c = 785 tickets
5a + 2c = $3280

c = 215 child tickets
a = 570 adult tickets

570 + 215 = 785 tickets
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There were 215 child tickets sold on Saturday



3 0
4 years ago
Solve the Equation |x-8|=16
choli [55]
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⇒ x= 24 or x= -8

Final answer: x= 24 or x= -8~
4 0
3 years ago
Read 2 more answers
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