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3 years ago

6 1⁄3 + 7 1⁄4 – 2 1⁄2 =

Mathematics

1 answer:

Korvikt [17]3 years ago

6 0

Answer:

11 1/12

Step-by-step explanation:

6 1/3 = 19/3

7 1/4 = 29/4

2 1/2 = 5/2

19/3 + 29/4 - 5/2

We must find the LCM of 3, 4, and 2. This happens to be 12

3*4 = 12

4*3 = 12

2*6 = 12

Multiply each fraction by the factor that'll get it to 12.

19/3 * 4/4 = 76/12

29/4 * 3/3 = 87/12

5/2 * 6/6 = 30/12

Now go through the problem

76/12 + 87/12 - 30/12

76 + 87 = 163

163/12 - 30/12

163 - 30 = 133

133/12

Simplify

133/12 = 11.0833... or 11 1/12

Hope this helps.

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The dot plot above identifies the number of pets living with each of 20 families in an apartment building. What fraction of the

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Step-by-step explanation:

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2 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 = probability of obtaining head.

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

Ashley had a doll collection consisting of 43 dolls. As she got older she ended up selling some. She only kept her

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Answer:

27.9 i think in in a fraction 12 / 43

Step-by-step explanation:

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3 years ago

What are the solutions to the system of equations?

bogdanovich [222]

Answer:

(0, - 3 ) and (- 1, - 5 )

Step-by-step explanation:

Given the 2 equations

y = 4x² + 6x - 3 → (1)

y = 2x - 3 → (2)

Substitute y = 4x² + 6x - 3 into (2)

4x² + 6x - 3 = 2x - 3 ( subtract 2x - 3 from both sides )

4x² + 4x = 0 ← factor out 4x from each term

4x(x + 1) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

x + 1 = 0 ⇒ x = - 1

Substitute these values into (2) for corresponding values of y

x = 0 : y = 2(0) - 3 = 0 - 3 = - 3 ⇒ (0, - 3 )

x = - 1 : y = 2(- 1) - 3 = - 2 - 3 = - 5 ⇒ (- 1, - 5 )

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2 years ago

The reciprocal of 7 is 7/1 true or false

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Answer:

False

Step-by-step explanation:

A reciprocal is when a whole number fraction is flipped

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3 years ago

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