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3 years ago

Is cos theta=cos(-theta)

Mathematics

1 answer:

saul85 [17]3 years ago

4 0

Answer:

TRUE

Step-by-step explanation:

An even function is a function that satisfies that f(x) = f(-x). Also, we know that cosine is an even function, therefore cos(theta) equals cos(-theta).

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What is Coordinate rotation

saul85 [17]

Answer:

Replace x with y and vice versa

Step-by-step explanation:

You have the same graph instead you write y in place of x. The horizontal one is y axis and vice versa. This is done mostly for reversed functions. like x^2 function and √x

4 0

3 years ago

The number of motor vehicles registered in millions in the US has grown as follows:

zysi [14]

Answer:

a) Figure attached

b) $r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.819)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=10 $\sum x = 75.819, \sum y = 43.5231, \sum xy = 330.0321, \sum x^2 =574.8598, \sum y^2 =192.8274$

$r=\frac{10(330.0321)-(75.81948)(43.5231)}{\sqrt{[10(574.8598) -(75.81948)^2][10(192.8274) -(43.5231)^2]}}=0.989$

So then the correlation coefficient would be r =0.989

4 0

3 years ago

Luke bought a jacket that was 30% off the cost. He paid sales tax of 6% after the discount had been applied. If the jacket had a

nasty-shy [4]

Answer: the actual amount that Luke paid including tax is $55.65

Step-by-step explanation:

The initial price of the jacket is $75.

Luke bought a jacket that was 30% off the cost. This means that the amount of discount on the Jacket is

30/100 × 75 = 0.3 × 75 = $22.5

The price of the jacket after the discount had been applied is

75 - 22.5 = $52.5

He paid sales tax of 6% after the discount had been applied. This means that the amount of sales tax that he paid on the jacket is

6/100 × 52.5 = 0.06 × 52.5 = 3.15

Therefore, the actual amount that Luke paid including tax is

52.5 + 3.15 = $55.65

5 0

3 years ago

You wash dishes for a chemistry laboratory to make extra money for laundry. You earn 12 dollars/ hour, and each shift lasts 75 m

melomori [17]

It would pay with 3 loads

8 0

3 years ago

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The lengths of two sides of a triangle are 14 inches and 4 inches. Which of the following dimensions is the third side of this t

Varvara68 [4.7K]

The correct answer is A) 10 inches...Brainliest?...

3 0

3 years ago

Read 2 more answers