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4 years ago

3/8d+3/4 factor out coefficient

Mathematics

1 answer:

Orlov [11]4 years ago

5 0

Coefficient is a number next to the variable so the coefficient of this expression is 3/8

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A 1980 study was conducted whose purpose was to compare the indoor air quality in offices where smoking was permitted with that

kotegsom [21]

Answer:

The null hypothesis is not rejected.

There is no enough evidence to support the claim that the CO level is lower in non-smoking working areas compared to smoking work areas.

P-value = 0.07.

Step-by-step explanation:

We have to perform a test on the difference of means.

The claim that we want to test is that CO is less present in no-smoking work areas.

Then, the null and alternative hypothesis are:

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

being μ1: mean CO level in smoking work areas, and μ2: mean CO level in no-smoking work areas.

The significance level is assumed to be 0.05.

Smoking areas sample

Sample size n1=40.

Sample mean M1=11.6

Sample standard deviation s1=7.3

No-smoking areas sample

Sample size n2=40

Sample mean M2=6.9

Sample standard deviation s2=2.7

First, we calculate the difference between means:

$M_d=M_1-M_2=11.6-7.3=4.3$

Second, we calculate the standard error for the difference between means:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{7.3^2}{40}+\dfrac{2.7^2}{40}}=\sqrt{\dfrac{53.29+7.29}{40}}=\sqrt{\dfrac{60.58}{40}}\\\\\\s_{M_d}=\sqrt{1.5145}=1.23$

Now, we can calculate the t-statistic:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{4.3-0}{1.23}=3.5$

The degrees of freedom are calculated with the Welch–Satterthwaite equation:

$df=\dfrac{(\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2})^2}{\dfrac{s_1^4}{n_1(n_1-1)}+\dfrac{s_2^4}{n_2(n_2-1)}} \\\\\\\\df=\dfrac{(\dfrac{7.3^2}{40}+\dfrac{2.7^2}{40})^2}{\dfrac{7.3^4}{40(39)}+\dfrac{2.7^4}{40(39)}} =\dfrac{(\dfrac{53.29}{40}+\dfrac{7.29}{40})^2}{\dfrac{2839.82}{1560}+\dfrac{53.14}{1560}} \\\\\\\\df=\dfrac{1.5145^2}{1.8545}=\dfrac{2.2937}{1.8545}=1.237$

The P-value for this right tail test, with 1.237 degrees of freedom and t=3.5 is:

$P-value=P(t>3.5)=0.07$

The P-value is bigger than the significance level, so the effect is not significant. The null hypothesis is not rejected.

There is no enough evidence to support the claim that the CO level is lower in non-smoking working areas compared to smoking work areas.

8 0

4 years ago

Identify the recursive formula for the following sequence: 8, 26, 80, 242, . . .

AVprozaik [17]

Answer:

Recursive formula is $a_n = (a_{n-1} *3) + 2$

Step-by-step explanation:

8, 26, 80, 242, . . .

8 is the first term

To get 26 we multiply 8 by 3 and then add 2

8*3 = 24 + 2= 26

26 * 3= 78+2 = 80

80*3 = 240 + 2 = 242

So to get next term we multiply the previous term by 3 and then we add 2

$a_n = (a_{n-1} *3) + 2$

7 0

3 years ago

Read 2 more answers

Three people own all of the stock in a company.one person owns 1/3 of the stock.which of the following could be the fractional p

DIA [1.3K]

1/3 since its divided into three.

7 0

3 years ago

Write an equation of a line in slope-intercept form with the given slope and y-intercept.

Nostrana [21]

Answer:

y = -6x - 2

y = x - 12

Step-by-step explanation:

Slope-intercept equation for line of slope m and y-intercept b:

y = mx + b

A. m = -6, b = -2

y = -6x - 2

B. m = 1, b = -12

y = x - 12

6 0

3 years ago

A pair of running shoes costs five dollars more than a pair of regular tennis shoes .. the total cost for both is one 115 $ What

Mashcka [7]

115-5=110/2=55

$55 for the pair of Regular

4 0

3 years ago