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2 years ago

What is the location of the point on the number line that is 3/7 of the way from A=6 to B=20?

Mathematics

1 answer:

-Dominant- [34]2 years ago

7 0

Answer:

Step-by-step explanation:

20-6=14 (Distance between points) then 14*3/7=6.

3/7 of the distance from A=6 to B=20 is 6. Thus, we find the point that is

3/7 of the distance from A=6 to B=20 by adding 6 to 6.

6+6= 12

Therefore, the point that is

3/7 from A=6 to B=20 is 12.

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Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

Rashid [163]

Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

$\sum_{i=1}^n \frac{x_i}{n}$

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $\bar X=62.6$

In order to find the sample deviation we can use this formula

$s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}$

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is $s=5.713$

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case $df=n-1=6-1=5$

The formula for the confidence interval would be given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is $\alpha=1-0.95=0.05$ , and $\alpha/2=0.025$ , and $1-\frac{\alpha}{2}=0.975$ so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got $t_{\alpha/2}= 2.571$

And we can replace into equation (1) and we got:

$62.6 \pm 2.571\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is $\alpha=1-0.99=0.01$ , and $\alpha/2=0.005$ , and $1-\frac{\alpha}{2}=0.995$ so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got $t_{\alpha/2}= 4.032$

And we can replace into equation (1) and we got:

$62.6 \pm 4.032\frac{5.713}{\sqrt{6}}$

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

8 0

3 years ago

Ella and Iris are planning trips to nine countries this year. There are 12 countries they would like to visit. They are deciding

NISA [10]

Using the combination formula, it is found that there are 220 ways to decide which countries to skip.

The order in which the countries are skipped is not important, hence the <em>combination formula </em>is used to solve this question.

<h3>What is the combination formula?</h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, 3 countries are skipped from a set of 12, hence the number of ways is given by:

$C_{12,3} = \frac{12!}{3!9!} = 220$

More can be learned about the combination formula at brainly.com/question/25821700

#SPJ1

5 0

2 years ago

7. Rosa Collects data on what students at her school like to eat at the movie

Margaret [11]

Answer:

Her data are partially shown in the table. Of the students she asks, 60% of those

who like to eat popcorn also like to eat candy. Complete the table to show the

number of student in each category.

Step-by-st

Rosa Collects data on what students at her school like to eat at the movie

theater. She asks a random sample of 120 students two questions. Do you liko

eat popcorn at the movie theatre? Do you like to eat candy at the movie theatre?

Her data are partially shown in the table. Of the students she asks, 60% of those

who like to eat popcorn also like to eat candy. Complete the table to show the

number of student in each category.

7 0

3 years ago

Tell wether x and y show a proportional relationship.<br><br> x 1 2 3 4<br> y 4 8 12 16

Delicious77 [7]

Answer:

They do because y is always 4 times of x.

Step-by-step explanation:

7 0

3 years ago

What is the solution to the following system of linear equations?

Lostsunrise [7]

<span> x − 2y = −1 => x = 2y -1

2x + y = −12
2(2y - 1) + y = -12
4y - 2 + y = -12
5y = -10
y = -2
x = 2</span>·(-2) - 1
x = -4 - 1
x = -5

Answer <span>D (-5,-2)</span>

8 0

3 years ago