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3 years ago

Write the following two sequences using summation notation:

Mathematics

1 answer:

o-na [289]3 years ago

7 0

Answer:

Step-by-step explanation:

Sequence 1:

This is a finite sequence ending with 40

5-10+15-20+...40

= 5(1-2+3-4+5-6+7-8) (by taking 5 as common factor)

This is an alternating series with even numbers in the series having negative sign

Hence can be written as

$\Sigma _{1} ^{8} 5[(-1)^{n-1} (n)$

This gives the I sequence in the summation notation. Since there are only 8 terms n can take values as 1 to 8, with odd terms positive.

---------------------------------

Sequence 2:

This is the same as the previous sequence but with end point as infinite

This is an infinite series. Hence n can vary from 1 to infinity.

Thus sum would be

$\Sigma _{1} ^{\infty } 5[(-1)^{n-1} (n)$

(Note that only the ending number is difference for both.)

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A husband and wife ted and suzanne share a digital music player that has a feature that randomly selects which song to play. A t

seraphim [82]

Answer:

$z=\frac{0.733 -0.5}{\sqrt{\frac{0.5(1-0.5)}{30}}}=2.552$

$p_v =2*P(z>2.552)=0.0107$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of songs selectd at random differs from 0.5 .

There is strong evidence that the proportion of songs downloaded by Ted and Suzanne differs from 0.5.

Step-by-step explanation:

Data given and notation

n=30 represent the random sample taken

X=22 represent the number of songs selectd at random

$\hat p=\frac{22}{30}=0.733$ estimated proportion of songs selectd at random

$p_o=0.5$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of random songs selected is 0.5 (random) or no.:

Null hypothesis: $p=0.5$

Alternative hypothesis: $p \neq 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.733 -0.5}{\sqrt{\frac{0.5(1-0.5)}{30}}}=2.552$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level assumed for this case is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>2.552)=0.0107$

There is strong evidence that the proportion of songs downloaded by Ted and Suzanne differs from 0.5.

7 0

4 years ago

What is the slope of the line passing through the points (-9,-3) and (7,-7)

Gnoma [55]

Answer:

The slope is $\frac{1}{4}$

Step-by-step explanation:

$\frac{Y_{2} -Y_{1} }{X_{2}-X_{1} }$

-7-(-3)= -7+3= 4

4/?

7-(-9)= 7+9 = 16

4/16=1/4

I hope this helps :-)

3 0

3 years ago

The ages of a group of 135 randomly selected adult females have a standard deviation of 18.3 years. Assume that the ages of fema

NeTakaya

Answer:

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student is 3625 female statistics student

Step-by-step explanation:

Here, we have

$n = \left (\frac{(z_{\alpha/2}) (\sigma) }{E} \right )^{2}$

Where:

n = Required sample size

σ = Standard deviation = 18.3

E = Margin of error = 1/2 year

$z_{\alpha /2}$ = Critical score from the confidence level = 1.645

Therefore,

$n = \left (\frac{(1.645) (18.3) }{\frac{1}{2} } \right )^{2} = 3624.88$

Therefore, the number of female statistics student ages that must be obtained in order to estimate the mean age of all female statistics student = 3625 female statistics student.

3 0

3 years ago

Will mark brainlist to whoever answers first<br> (3).

puteri [66]

Answer:

Step-by-step explanation:

in parallelograms, the measure of reciprocal angles is equal to 180 because they are supplementary,

m<D = 110 so the measure of m<A which is reciprocal to m<D is equal to 70

4 0

2 years ago

D=domain and the domain is 0

Temka [501]

What specifically do you need help with? range is the y-values and domain is the x-values. so if you write down each point you’ll have domain and range.... comment what else i can help with?

4 0

3 years ago