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2 years ago

Given the arithmetic series:2+4+6....Find the sum of 41st term to 47th term

Mathematics

1 answer:

Vladimir79 [104]2 years ago

8 0

Answer:

Step-by-step explanation:

To find the 41st term to 47th term, we must find the equation of how to get those terms.

The equation for arithmetic terms is $a_{n} =a_{1} + (n-1)d$ , where d is the difference between two side-by-side terms.

By using this equation format, we get the equation $a_{n} =2+ (n-1)2 = 2n$

That means the terms are

$a_{41} =2*41 = 82\\a_{42}=2*42 = 84\\a_{43} = 2*43 = 86\\a_{44} = 2*44 = 88\\a_{45} = 2*45 = 90\\a_{46}=2*46 = 92\\a_{47} = 2*47 = 94\\$

Now to find the sum, we just add all the terms up simply

Sum = 82 + 84 +86 + 88 + 90 + 92 +94 = 616

Hope that helps!

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2 years ago

Solve the equation. |x + 5| = 9 {–4, 14} {–14, 4} {4, 14} {–14, –4}

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Answer:

{-14, 4}

Step-by-step explanation:

the absolute value function only makes sure that the result always has a positive sign.

so, (x + 5) must be either +9 or -9 to make the original equation true. the absolute value would turn both into +9.

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2 years ago

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

inn [45]

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.

Step-by-step explanation:

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.

The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.

The difference between sample means is Md=11.2.

$M_d=M_1-M_2=45.3-34.1=11.2$

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

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11.2-0}{2.066}=\dfrac{11.2}{2.066}=5.42$

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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3 years ago

Given the arithmetic series:2+4+6....Find the sum of 41st term to 47th term ​

Given the arithmetic series:2+4+6....Find the sum of 41st term to 47th term