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san4es73 [151]
3 years ago
7

If |x| + 3 =9, then x =?

Mathematics
1 answer:
sasho [114]3 years ago
3 0
|x| = 6

{ x= 6
{ x= -6

X= { 6,-6}
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A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that
mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, H_0 : p = 0.5

Alternate Hypothesis, H_A : p \neq 0.5

(a) The significance level of the test which is represented by \alpha is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

            P(Type I error) = \alpha

         P(X = 0/H_0 is true) + P(X = 10/H_0 is true) = \alpha

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/H_0 is true) + P(X = 10/H_0 is true) = \alpha

\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0}  +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}  = \alpha

(1\times 1\times 0.5^{10})  +(1 \times 0.5^{10} \times 0.5^{0}) = \alpha

\alpha = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - \beta).

So, here, X ~ Binom(n = 10, p = 0.1)

1-\beta = P(X = 0/H_0 is true) + P(X = 10/H_0 is true)

1-\beta = \binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0}  +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}  

1-\beta = (1\times 1\times 0.9^{10})  +(1 \times 0.1^{10} \times 0.9^{0})

1-\beta = 0.3487

Hence, the power of the test is 0.3487.

3 0
3 years ago
Help?!<br> ???????????LK
Katarina [22]

Answer:

Equation: 65+1.50m=78.50

Solution to the equation= 9 minutes

Step-by-step explanation:

The parents have to give 65 dollars for their children to be under care till 6 o'clock. AFter 6 o'clock, they had to pay 1.50 dollars for one minute. This parent gives a total of 78.50 dollar for that day. So, the equation is :

65+1.50m=78.50

(btw, m stands for minutes)

So to solve the equation:

1.50m=13.50

m= 9

3 0
3 years ago
What is the value if the expression 6+18÷3×4
Liula [17]
In the order of PEMDAS
the first thing you would do is divide 18/3 = 6
then multiply 6 x 4 = 24
then add 24 + 6 = 30
8 0
3 years ago
Read 2 more answers
Which choice is the solution to the inequality below?<br> 2x &lt; 20
sergey [27]
X less than 10 is the answer I think
7 0
3 years ago
Will give brainliest:)<br><br>-2x-¼(12x-8)​
katrin2010 [14]

answer

Answer:

here you go

Step-by-step explanation:

-5x+2

8 0
3 years ago
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