If a whole circle equals 360° ,what does a line equal?

Find all solutions in the interval [0, 2π). tan x + sec x = 1

svp [43]

Use the identity
sec^2x = 1 + tan^2 x
- so sec x = sqrt(1 + tan^2 x) then:-
tan x + sqrt( 1 + tan^2 x) = 1
sqrt ( 1 + tan^2 x) = 1 - tan x
1 + tan^2 x = 1 + tan^2x - 2 tan x
0 = -2 tanx

tan x = 0

x = 0, π
π is an extraneous root because sec 180 = -1
So the answer is 0 degrees

6 0

3 years ago

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probabili

svlad2 [7]

Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.

<h3>What is the critical probability?</h3>

Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.

As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and it is given by the formula

$\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}$

where the value of the α is expressed as,

$\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}$

Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,

$\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42$

Further, the critical probability, assuming a confidence level of 58% is,

$\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79$

Hence, the critical probability is 0.79.

Learn more about Critical Probability:

brainly.com/question/5625386

6 0

1 year ago

Express 56.4% as a fraction in simplest form.

laiz [17]

56.4/100 you always put your beginning number over 100

3 0

3 years ago

A group of 100 students took a quiz. Their average score was 76 points. If the average score for the boys was 80 points and the

sveta [45]

Answer:

The number of girls participated in quiz is 40 .

Step-by-step explanation:

Given as :

Total number of students took quiz = 100

Average score of 100 students = 76 points

The Average score of boys = 80 points

The Average score of girls = 70 points

Let The number of boys participated in quiz = b

Let The number of girls participate in quiz = g

Now, According to question'

Total number of students took quiz = number of boys participated in quiz + number of girls participated in quiz

Or, b + g = 100 ........A

<u>Again</u>

∵ Average score of 100 students = 76 points

∴ Total score of 100 students = 76 × 100 = 7600

So, Average score of boys × number of boys participated + Average score of girls × number of girls participated = Total score of 100 students

Or, b × 80 + g × 70 = 7600

Or, 80 b + 70 g = 7600 .........B

Now, Solving equation A and B

(80 b + 70 g ) - 70 ×( b + g ) = 7600 - 70 × 100

I.e (80 b - 70 b) + (70 g - 70 g) = 7600 - 7000

Or, 10 b + 0 = 600

∴ b = $\dfrac{600}{10}$

i.e b = 60

So, The number of boys participated in quiz = b = 60

Put the value of b into eq A

∵ b + g = 100

So, g = 100 - b

Or, g = 100 - 60

i.e g = 40

So, The number of girls participated in quiz = g = 40

Hence, The number of girls participated in quiz is 40 . Answer

6 0

2 years ago

What is the value of x in the figure below?

zhenek [66]

Again, nice problem. These are not super easy. You need to imagine the triangles in the figure and relate sides.

For instance: ADC, its hypotenuse is 15

For ABC, it is 20,

so 20/15 is the ratio between both triangles. Now let's choose the side with 'x'

x is one side of ADC, the corresponding side in ABC is 15 (the second longest sides). You need to rotate the triangles, etc ... That's the tricky part :)

So:

20/15 =15/x ----> x = 15*15/20 = 225/20 = 45/4

Which is C

Not sure whether it's too late to help you though!!!!

Also notice that it's kind of a product rule:

x * 20 = 15 * 15

I am sure the book explains a short way of getting to this equation, like sides opposite, blah blah, but what i told you is the reason. You asked for understanding it! Best luck!

7 0

2 years ago