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goldfiish [28.3K]
3 years ago
15

Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n

Mathematics
1 answer:
kogti [31]3 years ago
4 0

Answer:

(2n + 1)[(2n + 1) � 1]

(2n + 1)(2n + 1 � 1)

(2n + 1)(2n), or 2n(2n + 1)

2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number

Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER

Step-by-step explanation:

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Answer:

87.9

Step-by-step explanation:

Use a calculator or table to find the z-score that corresponds to 25%.

P(Z < z) = 0.25

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Now find the value that corresponds to that z score.

z = (x − μ) / σ

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Step-by-step explanation:

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Sam the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. How fa
Liula [17]

Answer:

24.59 feet

Step-by-step explanation:

Let x represent the distance between Sam and the bird.

We have been given that am the owl is looking down at a 24° angle from the top of a tree that is 10 ft tall, when he spots a bird on the ground. We are asked to find the distance between Sam and the bird.

We can see from our attachment that Sam, the bird and angle of depression forms a right triangle with respect to ground. We can see that side 10 ft is opposite side and and side x is hypotenuse for the 24 degree angle.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

\text{sin}(24^{\circ})=\frac{10}{x}

x=\frac{10}{\text{sin}(24^{\circ})}

x=\frac{10}{0.406736643076}

x=24.5859333557

x\approx 24.59

Therefore, the bird is approximately 24.59 feet away from Sam.

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Hope you could understand.

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