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faust18 [17]
3 years ago
5

Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, wh

ere a0 = 4.
Mathematics
1 answer:
WINSTONCH [101]3 years ago
7 0
The closed formula for  <span>an = an-1 – n will be found using the formula for arithmetic sequence given by:
an=a+d(n-1)
where
a=first term
d=common difference
n=number of terms
From the formula given:
a=4
d=n
thus the formula will be:
an=a+n(n-1)
an=4+n(n-1)

</span>
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3 years ago
Quit smoking: In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking.
Flauer [41]

Answer:

The p-value of the test is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.

Step-by-step explanation:

Test if less than half of HIV-positive smokers have used a nicotine patch:

At the null hypothesis, we test if the proportion is of at least half, that is:

H_0: p \geq 0.5

At the alternative hypothesis, we test if the proportion is below 0.5, that is:

H_1: p < 0.5

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that \mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5

In a survey of 444 HIV-positive smokers, 202 reported that they had used a nicotine patch to try to quit smoking.

This means that n = 444, X = \frac{202}{444} = 0.455

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.455 - 0.5}{\frac{0.5}{\sqrt{444}}}

z = -1.9

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.455, which is the p-value of z = -1.9.

Looking at the z-table, z = -1.9 has a p-value of 0.0287.

The p-value is of 0.0287 < 0.05(standard significance level), which means that it can be concluded that less than half of HIV-positive smokers have used a nicotine patch.

5 0
3 years ago
I really don’t get this one please i’ve been stuck forvever
expeople1 [14]

Answer:

ASA

Step-by-step explanation:

The Angle Side Angle Postulate (ASA) says that "triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles."

Hope this helps! :)

7 0
1 year ago
Read 2 more answers
Use linear combination. To solve system <br> -2x+7y=10<br> X-3y=-3
Tamiku [17]
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Viefleur [7K]

STEP 1

Equation at the end of step

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Equation at the end of step 2

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STEP 3

STEP 4

Pulling out like terms

4.1     Pull out like factors :

  14x2 - 7xy - 147y2  =   7 • (2x2 - xy - 21y2)

Trying to factor a multi variable polynomial :

4.2    Factoring    2x2 - xy - 21y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization  :  (2x - 7y)•(x + 3y)

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