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3 years ago

If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75

Mathematics

1 answer:

kirill [66]3 years ago

4 0

Answer:

Step-by-step explanation:

Cos 75 = Cos ( 30 + 45) {Use Cos (A + B) identity}

= Cos 30*cos 45 - Sin 30 Sin 45

$= \frac{\sqrt{3}}{2}*\frac{1}{\sqrt{2}}-\frac{1}{2}*\frac{1}{\sqrt{2}}\\\\= \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\=\frac{\sqrt{3}-1}{2\sqrt{2}}\\\\=\frac{(\sqrt{3}-1)*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\=\frac{\sqrt{3}*\sqrt{2}-\sqrt{2}}{2*2}\\\\=\frac{\sqrt{6}-\sqrt{2}}{4}$

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A study was conducted in order to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a

777dan777 [17]

Answer:

The point estimate for $\mu$ is 8.5 hours.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem

We are working with a sample of 81 adults, so the point estimae of the mean is the mean number of weekly hours that U.S. adults use computers at home.

So, the point estimate for $\mu$ is 8.5 hours.

6 0

3 years ago

A Fair coin is tossed and a marble is chosen from the bag whose contents are shown below. what is the probability of the coin La

Vera_Pavlovna [14]

Answer:

P(Coin landing heads and blue marble is randomly selected) = 3/20.

Step-by-step explanation:

In this question, two events simultaneously take place. First, all the probabilities have to be identified. It is mentioned that the coin is a fair coin, therefore the probabilities of all the outcomes associated with the coin tossing will be equal. Therefore:

P(Coin landing heads) = 1/2.

P(Coin landing tails) = 1/2.

There are a total of 3 blue + 4 green + 3 red = 10 marbles in the bag. Therefore:

P(Selected marble is blue) = 3/10.

P(Selected marble is green) = 4/10.

P(Selected marble is red) = 3/10.

Assuming that both the events are independent, the probabilities of both the events can safely be multiplied. Therefore:

P(Coin landing heads and blue marble is randomly selected) = 1/2 * 3*10 = 3/20.

Therefore, the answer is 3/20!!!

3 0

3 years ago

Read 2 more answers

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

sertanlavr [38]

y = ( 48 *2 ) / 6

Step-by-step explanation:

If y varies directly as x they are directly proportional, which means they relate to each other in the same way....

2 : y = 6: 48

what is y if x = 2?

The value of y can be found if you write it a two fracrions

2 : y = 6 : 48

2 / y = 6 / 48

cross multiply the fractions gives

6*y = 48 *2

divide left and right of the = sign by 6 gives the answer:

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

Other method:

multiply left and right of the = sign by y

2 * y/y = y *6 / 48

6y / 48 = 2 * 1

multiply left and right of the = sign by 48

6y * 48/48 = ( 48 *2 )

6y = ( 48 *2 )

divide left and right of the = sign by 6

6/6* y = ( 48 *2 )/6

y = ( 48 *2 ) / 6

(if you solve it you get y = 12 but that was not the question).

4 0

3 years ago

Use the table to write a liner function that relates to y to x X: -2, 0, 2, 4

Contact [7]

I think this is the answer
(-2,5)
(0,4)
(2,3)
(4,2)

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3 years ago

Consider −75/3. Which TWO statements are correct?

kiruha [24]

B.) the quotient is -25

3 0

3 years ago

Read 2 more answers