What is the value of the correlation coefficient r of the data set?

If someone could help me answer this and possibly give me a step-by-step for future reference that'd be great thanks.

andreyandreev [35.5K]

Answer:

Let's look at the Venn diagram and the data we have:

There are 12 pupils

9 have a brother

7 have a sister

2 have neither.

Now let's look at the diagram.

We know that the circle B represents the pupils who have a brother

Circle S represents the students that have a sister.

Then the intersection of the circles, represents the number of students that have both.

And the space outside the circles represents the pupils that do not have a brother nor a sister.

Then the first thing we can complete is a 2 in the bottom left corner, because we already know that there are 2 pupils that do not have brothers nor sisters.

Now let's find the number of students that have both, brothers and sisters:

There are 12 pupils.

9 have a brother

7 have a sister

2 have neither

if we add that, we get:

9 + 7 + 2 = 18

This is larger than 12, this means that we are counting some of the students more than once.

If X is the number of students that we are counting twice, we should have:

18 - X = 12

18 -12 = X = 6

There are 6 students who we are counting twice, and this happens because these 6 students have a brother and a sister.

Then in the intersection of both circles we should put a 6.

At the left of that (in the part that we have only circle B) we need to write the number of students that only have a brother, this is the number of students that have a brother minus the number of pupils that have a brother and a sister, this is:

9 - 6 = 3

We need to write a 3 in that square.

And in the last square (the one that is only one circle S) we need to write the number of pupils that only have a sister, this is calculated in the same way than before, this is:

7 - 6 = 1

We need to write a 1 in the rightmost square.

6 0

2 years ago

Find the mean of 7, 9, 6, 15, 22, 25, 31. Round to the nearest whole number.

nexus9112 [7]

Add all the numbers and divide it by the number of numbers --> (7+9+6+15+22+25+31) = 115
115/7 = 16.4 --> conventional rounding would mean the answer would be 16

4 0

3 years ago

A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood. The devi

Xelga [282]

Answer: 1)The drivers with low alcohol in take from the breathlyser, being above the limit, A = 5/100;

2)The drivers above the alcohol limit, give reading below that level, B = 15/100;

3) The drivers above the alcohol limit that are arrested at radom by police, C = 12/100

Step-by-step explanation: a) A + B + C = 5/100 + 15/100 + 12/100 = 32/100

b) 1 - ( A + B + C) = 1 - 32/100 = 68/100

c) A = 5/100

d) 1 - 5/100 = 95/100

3 0

3 years ago

Mauricio scored a total of 34.42 points in five gymnastic

Olegator [25]

Answer:

Mauricio's score for each event is 7.

Step-by-step explanation:

Mauricio scored a total of 34.42 points in five gymnastic events.

We can round off his score as 35.

To find Mauricio's score for each event, divide total score and no of events as follows :

$n=\dfrac{35}{5}\\\\=7$

Hence, Mauricio's score for each event is 7.

3 0

3 years ago

Find the area of the shaded region

kogti [31]

Answer:

7. 183 in^2

8. 192.42 m^2

9. 239.4 ft^2

Step-by-step explanation:

7. The figure seems most easily seen as a trapezoid with a triangle removed. The trapezoid has bases of 26 and 14, and a height of 15. So, its area is ...

A = (1/2)(b1 +b2)(h) = (1/2)(26+14)(15) = 300 . . . . . . square inches

The triangle has a base of 26 and a height of 9, so an area of ...

A = (1/2)bh = (1/2)(26)(9) = 117 . . . . . . square inches

Then the shaded area is ...

300 in^2 -117 in^2 = 183 in^2

__

8. The area of the donut can be found different ways. One way is to multiply the width of the shaded area (3.5 m) by the circumference of its centerline.

The centerline diameter is 21 m - 3.5 m = 17.5 m, so the circumference of that circle is ...

C = πd = π(17.5 m) = 17.5π m

Then the area of the shaded part is ...

(3.5 m)(17.5π m) = 61.25π m^2 ≈ 192.42 m^2

__

9. As in problem 7, this can be treated as a parallelogram less a triangle. Here, we need to do a little work to find the area of the triangle.

The triangle of interest is a right triangle with hypotenuse 23.8 ft and one leg 21 ft. The Pythagorean theorem can be used to find the other leg:

h = √(23.8^2 -21^2) = √125.44 = 11.2

Then the area of the triangle is ...

A = (1/2)bh = (1/2)(21)(11.2) = 117.6 . . . ft^2

The area of the parallelogram (including the triangle) is ...

A = bh = (23.8 ft)(15 ft) = 357 ft^2

So, the shaded area is the difference ...

357 ft^2 -117.6 ft^2 = 239.4 ft^2

_____

<em>Comment on significant digits</em>

The area in problem 8 may be considered to be 192.325 m^2 if you are required to use 3.14 as the value for pi. Since that value is only good to 3 significant digits, it is quite pointless to report the answer to 6 significant digits when using that value. It is quite reasonable to use 192 m^2 for the answer, especially if you're required to round to whole numbers.

8 0

3 years ago