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
Delicious77 [7]
2 years ago
14

Find the length of side x in simplest radical form with a rational denominator.

Mathematics
1 answer:
alekssr [168]2 years ago
4 0

Answer:

x = \frac{2*\sqrt{3}}{3}

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

tan (30) = \frac{opp}{adj}

tan (30) = \frac{x}{2}

2 * tan (30) = x

2 * \frac{1}{sqrt{3}} = x (tan 30 = 1/√3)

\frac{2}{sqrt{3}} = x

Rationalize

\frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x

\frac{2*\sqrt{3}}{3} = x

You might be interested in
A manufacturer of a new medication on the market for Alzheimer's disease makes a claim that the medication is effective in 65% o
NeX [460]

Answer:

z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309  

p_v =P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

Step-by-step explanation:

Data given and notation

n=180 represent the random sample taken

X=115 represent the adults with the medication was effective

\hat p=\frac{115}{180}=0.639 estimated proportion of adults with the medication was effective

p_o=0.65 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportion is less than 0.65.:  

Null hypothesis:p \geq 0.65  

Alternative hypothesis:p < 0.65  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.639 -0.65}{\sqrt{\frac{0.65(1-0.65)}{180}}}=-0.309  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults with the medication was effective is not significantly less than 0.65

3 0
3 years ago
I need to know 2 digit times
Mekhanik [1.2K]

if you are looking how to times a 2 digit witha 2 digit number there is a video where it explains everything.

3 0
3 years ago
Justin recently drove to visit his parents who live 300 miles away. On his way there his average speed was 11 miles per hour fas
Lynna [10]

Answer:

x=1

Step-by-step explanation:

5 0
2 years ago
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP I ONLY WANT ANSWERS FROM PEOPLE WHO TRULY WANNA HELP
Sauron [17]

Answer:

I would assume $10 is the cost of the booth and 5 is how much she earns for each T-Shirt, so the equation would be 5x-10=65. Assume $65 is what she earned.

Therefore, the equation may be: (your question did not specify) 5x-10=65. so x is 15. Therefore, she sold 15 T-Shirts.

Correct Form:

_-_

_

4 0
3 years ago
The first three steps in determining the solution set of the system of equations algebraically are shown.
Ivenika [448]

(2,-1), (-4,17).

Step-by-step explanation:

Equate the equation A and equation B

Convert the quadratic equation in factored form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

Square root both sides

Find the values of y

Substitute the value of x in the equation B

3 0
3 years ago
Other questions:
  • Billy rode his bike 2/5 mile in 1/12 hour. at this rate,how far would billy ride his bike in one hour?
    15·1 answer
  • PLEASE HELP ITS A PICTURE!!!!!!!!!!!!!!!
    5·2 answers
  • Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. If f(X)=25-x^2 and
    6·2 answers
  • Evaluate the following expression when a = -3, b = 2, c = 5, and<br> d= -4.<br> 4c + d
    11·2 answers
  • What is the area of 28ft
    14·1 answer
  • if a unit price label has a unit price of 15.5 cents per ounce how much is the total price for 24 ounce package?
    11·1 answer
  • Which measurement is most accurate to describe the width of a math book?
    7·2 answers
  • If np &gt;5 and nq&gt;5 estimate P (fewer than 4) with n=13 p=0.4 by using normal distribution as an approximate to the binomial
    13·1 answer
  • If something is burning and 20 acres a minute how many acers in burning a day
    12·1 answer
  • In a bag of beads, the ratio of the number of orange to blue to white is 13:7:4. If the number of orange beads minus the number
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!