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Lesechka [4]
3 years ago
7

Eborah finds that the theoretical probability of flipping "heads" on a fair coin was 50%. After she flipped the fair coin 100 ti

mes, she calculated that she flipped "heads" 45 times. What is the percent difference in theoretical and experimental probability?
Mathematics
1 answer:
eimsori [14]3 years ago
3 0

Answer:

5%

Step-by-step explanation:

Given that:

Theoretical probability = 50%

The experimental probability = number of desired outcome / number of trials

Hence, experimental probability = 45 / 100 = 0.45

0.45 = 0.45 * 100% = 45%

Percentage difference in theoretical and experimental probability :

Theoretical - experimental

50% - 45% = 5%

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A study found that, in 2005, 12.5% of U.S. workers belonged to unions (The Wall Street Journal, January 21, 2006). Suppose a sam
Julli [10]

Answer:

There is not enough evidence to support the claim that union membership increased.  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 400

p = 12.5% = 0.125

Alpha, α = 0.05

Number of women belonging to union , x = 52

First, we design the null and the alternate hypothesis  

H_{0}: p = 0.125\\H_A: p > 0.125

The null hypothesis sates that 12.5% of U.S. workers belong to union and the alternate hypothesis states that there is a increase in union membership.

This is a one-tailed(right) test.  

Formula:

\hat{p} = \dfrac{x}{n} = \dfrac{52}{400} = 0.13

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

Putting the values, we get,

z = \displaystyle\frac{0.13-0.125}{\sqrt{\frac{0.125(1-0.125)}{400}}} = 0.3023

Now, we calculate the p-value from the table.

P-value = 0.3812

Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.

Conclusion:

Thus, there is not enough evidence to support the claim that union membership increased.

8 0
2 years ago
Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ<br>​
lilavasa [31]

Answer:

30°

Step-by-step explanation:

\because \:  \sin(90 \degree -  \theta) =  \cos \theta \\ \therefore \:  \sin(90 \degree - 5 \theta) =  \cos 5\theta....(1) \\  \\ \sin(90 \degree - 5 \theta) = \cos(180 \degree -  \theta)...(2) \\ from \: (1) \: and \: (2) \\ \cos 5\theta = \cos(180 \degree -  \theta) \\ 5 \theta = 180 \degree -  \theta \\  5 \theta  + \theta= 180 \degree  \\ 6\theta= 180 \degree  \\  \theta =  \frac{180 \degree}{6}  \\  \\  \huge \red{ \boxed{\theta = 30 \degree}}

8 0
3 years ago
Line GJ is tangent to point A at point G.<br><br> If AG = 9 and GJ = 12, find AJ.
kompoz [17]
GJ is a tangent
АG is a radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point   ⇒ m∠АGJ = 90°  ⇒ ΔАGJ is the right triangle.

<span>By the Pythagorean theorem:
</span>AJ² = АG² + GJ²
AJ² = 9² + 12² = 81 + 144 = 225
AJ = √225 = 15 units.
4 0
3 years ago
Read 2 more answers
If f(x)= 3x + 10x and g(x)=5x - 3 find (f+g)(x)
Illusion [34]

Answer:

18x-3

Step-by-step explanation:

f(x)= 3x + 10x

g(x)=5x - 3

f(x)+g(x) = 3x + 10x + 5x - 3

Combine like terms

             = 18x -3

6 0
3 years ago
3 3/4 + 2 1/8 = (make sure you simplify the fraction)
dusya [7]
This is 5 7/8 or 47/8
5 0
2 years ago
Read 2 more answers
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