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2 years ago

BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...

Mathematics

2 answers:

arsen [322]2 years ago

6 0

Answer:

-21

Step-by-step explanation:

1-2+4-8+16-32

=-21

Thepotemich [5.8K]2 years ago

3 0

Answer:

The sum of the first 6 terms of the infinite series will be - 21.

Step-by-step explanation:

In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,

$\sum _{{k=0}}^{{n}}(-2)^{k}$

Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,

1 - 2 + 4 - 8 + 16 - 32

= - 1 + 4 - 8 + 16 - 32

= 3 - 8 + 16 - 32 = - 5 + 16 - 32

= 11 - 32 = Solution : - 21

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In a reliability test there is a 42% probability that a computer chip survives more than 500 temperature cycles. If a computer c

Strike441 [17]

Answer:

The probability is $P(B' n A ' ) =$ 16%

Step-by-step explanation:

From the question we are told that

A is the event that the chip was "made by company A"

B is the event that a chip "survives 500 temperature cycles"

The probability that a computer chip survives more than 500 temperature cycles is

$P(B) = 42$ % $= 0.42$

The probability that does not survive more than 500 temperature cycles and it was manufactured by company A is $P(A | B' ) = 0.73$

The probability that the computer chip is not manufactured by company A and does not survive more than 500 temperature cycles is mathematically evaluated as

$P(B' n A ' ) = P (B' | A' ) P(B ')$

Where $B' \ and \ A'$ are a A and B complements and | represented AND operator

$P(B' n A ' ) = [1 - P (B' | A )] [1 - P(B )]$

substituting values

$P(B' n A ' ) = [1 - 0.73] [1 - 0.42 ]$

$P(B' n A ' ) = (0.27 )(0.58)$

$P(B' n A ' ) =0.16$

$P(B' n A ' ) =$ 16%

7 0

2 years ago

Solve the systems of equations 6x+3y=9 2x+3y=1

patriot [66]

Solve by elimination.
The goal is to cancel out one of the variables in order to easily solve for the other variable.

Do this by changing the equations so that the coefficients of either x or y add up to 0.

Notice the coefficients of y are 3 and 3, if we make one of them negative then they add up to 0. 3+ (-3) = 0

Multiply 2nd equation by -1.

6x +3y = 9
-2x -3y = -1
__________
4x +0y = 8

Solve for x
4x = 8
x = 8/4 = 2

Plug x=2 back into one of original equations to find y.
---> 2(2) + 3y = 1
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Therefore solution is (2,-1)

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2 years ago

Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?

juin [17]

Answer:

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of $r=\frac{36}{12}=\frac{12}{4}=3$

When we add the terms of a geometric sequence we get a geometric series.

4+12+36+ ... is a geometric series, it has a common ratio of $r=\frac{36}{12}=\frac{12}{4}=3$

4 + 12 + 20 + ... is not a geometric series because it has no common ratio

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The second choice is correct

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2 years ago

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Over [174]

Answer:

sepalacola

Step-by-step explanation:

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2 years ago

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aivan3 [116]

Answer:

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Step-by-step explanation:

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Use double angle formula.

2 sin x cos x − cos x

Factor.

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2 years ago