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Simplify the following expression.

AlekseyPX

Answer:

The answer is cosx cot²x ⇒ the first answer

Step-by-step explanation:

∵ cot²x = cos²x/sin²x

∵ secx = 1/cosx

∴ cot²x secx - cosx = (cos²x/sin²x)(1/cosx) - cosx

= (cosx/sin²x) - cosx

Take cosx as a common factor

∴ cosx[(1/sin²x) - 1] ⇒ use L.C.M

∴ cosx[1-sin²x/sin²x]

∵ 1 - sin²x = cos²x

∴ cosx(cos²x/sin²x) = cosx cot²x

6 0

2 years ago

How to simplyfy 2x+2x

VladimirAG [237]

Answer:

Your answer is 4x.

Step-by-step explanation:

Add 2+2

Combine your x's (like terms)

then you got 4 from 2+2

Add the leftover x so it makes 4+x then add it will give you 4x.

4 0

2 years ago

A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the

Novay_Z [31]

The horizontal distance between light house and boat is 1588.78 feet approximately.

The figure is given by,

Here, AB = height of the lighthouse bacon light above the water = 139 feet

Now angle ACB = 5 degree

Let the horizontal distance of light house from the boat = BC = x feet

So by trigonometric function we get,

tan 5 = AB/BC

tan 5 = 139/x

x = 139/tan 5 = 1588.78 (approximately)

Hence the horizontal distance between light house and boat is 1588.78 feet approximately.

To know more about Trigonometric Function refer to:

brainly.com/question/1143565

#SPJ9

5 0

9 months ago

How does the Counting Principle help when determining the sample space for a probability distribution?

andreyandreev [35.5K]

Answer:

This is also known as the Counting rule.

The Fundamental Counting Principle is used in determining all the possible outcomes and the total possible ways different events can be combined with each other. It is usually done by multiplying all the events together to get the total possible outcome. Doing this also helps in determining the sample space of a probability.

For example there are events a, b and c. The total sample space or possible outcome will be a*b*c.

7 0

2 years ago

Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that

Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is $\\ P(x>76) = 0.99865$ .

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two parameters, the population mean $\\ \mu$ and the population standard deviation $\\ \sigma$ .

To determine probabilities for the normal distribution, we can use the standard normal distribution, whose parameters' values are $\\ \mu = 0$ and $\\ \sigma = 1$ . However, we need to "transform" the raw score, in this case x = 76, to a z-score. To achieve this we use the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

And for the latter, we have all the required information to obtain z. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

$\\ \mu = 85$

$\\ \sigma = 3$

$\\ x = 76$

From equation [1], we have:

$\\ z = \frac{76 - 85}{3}$

Then

$\\ z = \frac{-9}{3}$

$\\ z = -3$

Second: Interpretation of the previous result.

In this case, the value is three (3) standard deviations below the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of $\\ z = -3$ , we can obtain this probability consulting the cumulative standard normal distribution, available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the cumulative standard normal distribution are for positive values of z. Fortunately, since the normal distributions are symmetrical, we can find the probability of a negative z having into account that (for this case):

$\\ P(z>-3) = 1 - P(z>3) = P(z$

Then

Consulting a cumulative standard normal table, we have that the cumulative probability for a value below than three (3) standard deviations is:

$\\ P(z$

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, $\\ \mu = 85$ and $\\ \sigma = 3$ ) is $\\ P(x>76) = P(z>-3) = P(z$ .

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

We can see below a graph showing this probability.

As a complement note, we can also say that:

$\\ P(z3)$

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

5 0

2 years ago