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2 years ago

The height of a right triangle is √6 units and the base is √9 units. Find the area of the triangle

Mathematics

1 answer:

In-s [12.5K]2 years ago

3 0

Answer:

Step-by-step explanation:

h = √6 units

b = √9 units

A = b*h/2 = √6·√9 /2 = √(6·9)/2 = √(2·3·3·3)/2 = 3√3 /2 units ²≈ 2.6 units²

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The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years

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Answer:

b. The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

c. Student's t distribution, as it is a two-sample test for the difference between means.

d. Test statistic t = 5.42.

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e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.

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This is a hypothesis test for the difference between populations means.

The claim is that the mean life spans in the county is significantly different for whites and nonwhites.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.

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The difference between sample means is Md=11.2.

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The estimated standard error of the difference between means is computed using the formula:

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The degrees of freedom for this test are:

df=n_1+n_2-2=124+82-2=204

This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>5.42)=0.0000002$

As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.

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