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3 years ago

Solve: e/3+ 2 < 5 Please show working out.

Mathematics

1 answer:

Scilla [17]3 years ago

5 0

Answer:

e < 9

Step-by-step explanation:

e/3 + 2 < 5

-2 -2

e/3 < 3

Multiply both sides by 3 to get e by itself

e < 3 × 3

e < 9

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Use the figure below to identify angles and segment lengths

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So Angle GEN and FED are vertical angles, which means that their angles are congruent. Therefore, Angle FED is 60°

Angle GEN and DEN are a linear pair, which means that they are supplementary angles (add up to 180). To find Angle DEN, we have to form the equation: 60 + DEN = 180

For this, all you have to do is subtract 60 on both sides, and your answer will be: DEN = 120°

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3 years ago

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The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together a

alexandr402 [8]

$100\%-25\%=75\%=\frac{75}{100}=0.75\\\\100\%+20\%=120\%=\frac{120}{100}=1.2\\\\1.2\cdot0.75=0.9=0.9\cdot100\%=90\%\\\\100\%-90\%=10\%\\\\Answer:Single\ reduction\ is\ 10\%.$

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3 years ago

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.

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How are determinants used to find areas of polygons?

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For example, consider the vertices of a triangle: (1,1), (2,3), (3,-1). Its area can be computed as
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