1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
STatiana [176]
3 years ago
15

The point (5/13, y) in the fourth quadrant corresponds to angle theta on the unit circle. Find sec theta and cot theta

Mathematics
1 answer:
VikaD [51]3 years ago
8 0
Cos (theta) =\frac{5}{13} sec (theta) = \frac{1}{cos(theta)} =  \frac{1}{ \frac{5}{13} }= \frac{13}{5} sin(theta)=\sqrt{1- cos^{2}(theta) } =  \sqrt{1 -  \frac{25}{169} } = \sqrt{ \frac{144}{169} }=- \frac{12}{13} cot(theta)=\frac{cos(theta)}{sin(theta}= \frac{ \frac{5}{13} }{ \frac{-12}{13} }= \frac{-5}{12}
You might be interested in
SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as
vovangra [49]

Answer:

a) P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

P(Z>1.25)=1-P(Z

b) P(400

P(-1

P(-1

c) z=-0.842

And if we solve for a we got

a=500 -0.842*100=415.8

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.  

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".  

Part a

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

X \sim N(500,100)  

Where \mu=500 and \sigma=100

We are interested on this probability

P(X>625)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>1.25)=1-P(Z

Part b

We are interested on this probability

P(400

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(400

And we can find this probability with this difference:

P(-1

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-1

Part c

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.8   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.842

And if we solve for a we got

a=500 -0.842*100=415.8

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.  

8 0
2 years ago
9] A bike is being sold for 78% of its original
mestny [16]

Answer:

The new and discounted price is now $66.69

Step-by-step explanation:

Hope this helps :)

7 0
3 years ago
If y=-8 when x=-2, find x when y=32
masya89 [10]
Tryfind the relationships between x and y.
I am sure that it is y=4x because when you multiply 4 to the -2 it becomes -8...
and then you plug in the 32 into the y:
32=4x
 then divide 4 from the both sides for the value of x.
  <u>x=8</u>
6 0
3 years ago
Read 2 more answers
How do you solve the problem
atroni [7]
Since the two labelled angles are corresponding angles, they are equal.
10x = 9x + 10
Subtract both sides by 9x 
x = 10
Also, if you need to know, the angle length is 100 degrees.

Have an awesome day! :)
8 0
2 years ago
Find the value of x so that the function has the given value.<br> t(x) = -3x -5; t(x) = 4
seraphim [82]
-17 i think//////////
6 0
3 years ago
Other questions:
  • An art gallery has 8 new paintings, all the same size, but enough room on the wall for only 6 of them. How many ways can the dir
    9·1 answer
  • Can you finish this for me please? My calculator isn’t making sense and I’m sure I typed the equation in right. I will mark Brai
    11·2 answers
  • Which graph/graphs are proportional? Please hurry!
    8·1 answer
  • 637 x 3 find the products. Show your thinking. The first row gives some ideas for showing your thinking
    15·1 answer
  • Simplify.<br> 32<br> 478<br> 016<br> 0 16V2<br> 4v2
    15·1 answer
  • Graph a line with a slope of.....
    9·2 answers
  • I need help now please ​
    10·1 answer
  • F(x)=x^2. what is g(x)?
    10·1 answer
  • Giving brainlyest<br> 5/8 +1/n = 7/8
    5·1 answer
  • Margret is inviting 3 friends to a party. If each friend will get 8 cookies and each box has 6 cookies, how many boxes does Marg
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!