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2 years ago

Which graph shows the solution to the following system of inequalities x+y>4

Mathematics

1 answer:

mylen [45]2 years ago

5 0

The solution to this system of inequalities x + y>4 , x + y <3 is Option A

The complete question is

Which graph shows the solution to this system of inequalities? x + y>4 x + y <3

The image are attached with the answer.

<h3>What are Inequality ?</h3>

When an expression is equated with another expression by an Inequality operator (< , > < etc) then the mathematical statement formed is called Inequality.

The inequalities are

x+y>4

x + y <3

After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.

Therefore the correct answer is Option A

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1) Lithium isotope rations are important to medicine, the 6Li/7Li ratio in a standard reference material was measured several ti

uysha [10]

Answer:

1) $0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

b) $ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

Step-by-step explanation:

Information given

0.082601, 0.082621, 0.082589, 0.082617, 0.082598

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

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

$\bar X=0.0826052$ represent the sample mean

$\mu$ population mean

s=0.000013424 represent the sample standard deviation

n=5 represent the sample size

Part 1

The confidence interval for the mean is given by the following formula:

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

The degrees of freedom, given by:

$df=n-1=5-1=4$

The Confidence level is 0.95 or 95%, and the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ , the critical value would be using the t distribution with 4 degrees of freedom: $t_{\alpha/2}=2.776$

Now we have everything in order to replace into formula (1):

$0.0826052-2.776\frac{0.000013424}{\sqrt{5}}=0.082588$

$0.0826052+2.776\frac{0.000013424}{\sqrt{5}}=0.0826219$

Part 2

The original margin of error is given by:

$ME= 2.776\frac{0.000013424}{\sqrt{5}}=0.0000166653$

And we want 2/3 of the margin of error so then would be: $2/3 ME = 0.00001111$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =0.00001111016 and we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (2)

Replacing we got:

$n=(\frac{2.776(0.000013424)}{0.00001111})^2 =11.25 \approx 12$

So the answer for this case would be n=12 rounded up to the nearest integer

3 0

3 years ago

A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data isa)4b)13c)17d)20Co

Degger [83]

The mode of the data of sample with 15 values is c) 17.

The mode of any sample of data can be calculated by finding the number that is present highest number of times. Based on this, we will look for the numbers that are present multiple times in the mentioned sample.

17, 18 and 5 are the three numbers that are present more than once. Now, let's see what is the frequency of each of these numbers.

Frequency of 17 - 4

Frequency of 18 - 2

Frequency of 5 - 2

Thus, the number 17 is present maximum number of times and hence is the mode of the data.

Learn more about mode -

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5 0

1 year ago

0.8% of what number is 6?

garik1379 [7]

0.8%=6
6/8=0.75(0.1%)
0.75*1000=750(100%)

Answer=750

Proof= 750*0.008=6

7 0

3 years ago

A field goal is worth 3 poins an extra point is 1 point. in 2016 adam vinaiteriof the indianapolis colts made a total of 71 fiel

Naddika [18.5K]

Answer:

field goal points: 213

extra points: 125

Step-by-step explanation:

Given that a field goal is worth 3 points, then the total points made by field goals are: number of field goals * 3. In the case of Adam, that is: 71*3 = 213 points.

An extra point is worth 1 point, then 125 extra points are equivalent to 125 points.

3 0

3 years ago

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A worker finds that it takes 9 tiles to cover one square foot of floor. Which equation represents relationship between the squar

Sedbober [7]

F= 9t . This is because each square foot is 9 tiles so however many square feet would be t. For ex. If you wanted 3 square feet then it would be f= 9(3) f=27 so you would need 27 tiles

4 0

3 years ago