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AfilCa [17]
3 years ago
15

The answer is 48 I just don’t know how to get there. Please solve using proportions and show me

Mathematics
1 answer:
OleMash [197]3 years ago
3 0

Answer:

x=48

Step-by-step explanation:

What number out of 75 gives you 64%

What number out of 75 gives you 64 out of 100

x                    64

------------ = -----------

75                 100

Using cross product

100x = 64*75

100x =4800

Divide each side by 100

100x/100 = 4800/100

x=48

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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
Translate the phrase "in 3 years" into algebraic terms
Semenov [28]

Answer:

In three years can be into algebraic terms as:  3 + x. Where 'x' comes to be today's age.

For example, my age in three years will be:

If I'm 24 years right now, My age in three years = 3 + x ⇒ My age in three years = 3 + 24 = 27.

3 0
3 years ago
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nydimaria [60]

Answer:

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Step-by-step explanation:

3 times 4 times 2

3 times 4 is 12

12 times 2 is 24

Hope this helps you

4 0
3 years ago
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Answer:

Based on the situation above and the choices provided the he coordinates of S should be (2,4) while the coordinates of R is (-1, 1), and for the T it should be (–3, 3). I hope the answer will help.

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3 years ago
the outdoor temperature was 8 degrees at midnight the. temperature declined 5 degrees during each. of the next 3 hours what was
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-7 degrees would be the answer
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