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3 years ago

Cscθ - sinθ = _____

1 answer:

galina1969 [7]3 years ago

4 0

So you maybe know that $\csc x = \frac{1}{\sin x}$ . Now let us try to simplify the expression

$\csc x - \sin x = \frac{1}{\sin x} - \sin x = \frac{1}{\sin x} - \frac{\sin^2 x }{\sin x}=\frac{1-\sin^2 x}{\sin x} =$

$= \frac{\cos^2 x}{\sin x} = \cot x \cdot \cos x$

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Which shows a way to take apart 7?

sashaice [31]

Add 7 and 7 which is 14 and then take it apart because it is an even number

3 0

2 years ago

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A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator.

AVprozaik [17]

Answer:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

8 0

2 years ago

Jim went to the playground. He played on the swings for 45 minutes and went on the slide for 55 minutes. It was 4:35 P.M. when J

aleksklad [387]

Answer:

2:55 P.M.

Step-by-step explanation:

First, add the amount of time Jim played outside; 45+55=100

100 minutes is equal to 1 hour 40 minutes.

If he left the playground at 4:35 P.M., then you have to subtract in order to find out when he arrived there.

Subtract 1 hour 40 minutes from 4:35 P.M. to then get 2:55 P.M.

To confirm your answer, you can add back the 1 hour and 40 minutes to 2:55 P.M. and you'll get 4:35 P.M.; back with what you started with.

Hope this helped !!!

4 0

2 years ago

Find the value of x and the length of both chords if BW=2x+10, WD=4, CW=7x+5, and WE=2.

daser333 [38]

Answer:

The value of x is 5

The lengths of the chords are 24 units and 42 units

Step-by-step explanation:

In a circle if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal

∵ BD and CE are two chords in a circle intersected at W

∴ The two segments of chord BD are BW and WD

∴ The two segments of chord CE are CW and WE

- By using the rule above

∴ BW × WD = CW × WE

∵ BW = 2x + 10 and WD = 4

∵ CW = 7x + 5 and WE = 2

- Substitute them in the rule above

∴ (2x + 10) × 4 = (7x + 5) × 2

∴ 4(2x) + 4(10) = 2(7x) + 2(5)

∴ 8x + 40 = 14x + 10

- Subtract 14x from both sides

∴ - 6x + 40 = 10

- Subtract 40 from both sides

∴ - 6x = - 30

- Divide both sides by - 6

∴ x = 5

∵ Chord BD = 2x + 10 + 4

∴ Chord BD = 2x + 14

- Substitute the value of x to find its length

∴ Chord BD = 2(5) + 14 = 10 + 14

∴ Chord BD = 24 units

∵ Chord CE = 7x + 5 + 2

∴ Chord CE = 7x + 7

- Substitute the value of x to find its length

∴ Chord CE = 7(5) + 7 = 35 + 7

∴ Chord CE = 42 units

5 0

2 years ago

A student scored a 98, 86, 93 and 75 in math for the quarter. What is the student's math average for the quarter?

NNADVOKAT [17]

98+86+93+75=352

352/4=88

The math average is 88.

3 0

2 years ago

Read 2 more answers