A manager is assessing the correlation between the number of employees in a plant and the number of products produced yearly. The table shows the data: Number of employees (x) 0 50 100 150 200 250 300 350 400 Number of products (y) 100 1,100 2,100 3,100 4,100 5,100 6,100 7,100 8,100 Part A: Is there any correlation between the number of employees in the plant and the number of products produced yearly? Justify your answer. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points).

Answers

Answer 1

The correlation coefficient of the number of employees and the number of products is 0.1.

What is the correlation coefficient?

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

1 indicates a strong positive relationship.-1 indicates a strong negative relationship.

A result of zero indicates no relationship at all, therefore, independent variable.

A.) In order to find the correlation between the two quantities we need to know the mean of the two values, therefore, the mean of the number of employees can be written as,

The mean of the  number of employees

[tex]\text{Mean of the number of employees} = \dfrac{0+50+100+150+200+250+300+350+400}{9}[/tex]

[tex]\text{Mean of the number of employees} = 200[/tex]

The mean of the  number of products

Mean of the number of Products [tex]= \dfrac{100+1100+2100 +3100+ 4100 +5100+ 6100+ 7100+ 8100}{9}\\\\\\=4100[/tex]

Now, the table can be written in the following manner as shown below, using the formula of the correlation,

[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

[tex]r =\dfrac{(30 \times 10^4)}{\sqrt{(15 \times 10^4)\times (60 \times 10^6)}}\\\\r = 0.1[/tex]

B.) The given data follows the linear relationship, therefore, the function of the given data will follow the general equation of a line.

y = mx + C

If we look at the value of y when the value of x was 0,

[tex]y = mx +C \\\\100 = m(0) + C\\\\C = 100[/tex]

Substitute the value of C in any other data point we will get,

[tex]y = mx+C\\\\1100 = m(50) +100\\\\m = 20[/tex]

Hence, the function that best fits the data is y=20x+100.

C.)  The slope and y-intercept of the plot indicate that as the number of employees in the organization increases the number of products increases as well. The y-intercept shows us that if there are no employees in the company at that point the company will be able to produce 100 products on its own.

Learn more about Correlation Coefficients:

https://brainly.com/question/15353989

A Manager Is Assessing The Correlation Between The Number Of Employees In A Plant And The Number Of Products

Related Questions

What is the range for this set of data?
7, 15, 12
O 3
O 5
O 8
O 12

Answers

Answer:

C/8

Step-by-step explanation:

Because the range is the biggest number subtracted by the lowest number and in our data sat 7,15,and 12 15 is the biggest number and 7 is the smallest so what's 15-7?

8 so C

Have a great day.

“Order the following workers in order from highest hourly pay (on top) to lowest hourly pay (on bottom) : Molly worked 15 hours and earned $277.50
Paul worked 3 hours and earned $51
Jake worked 40 hours and earned $770
Jackie worked 6.5 hours and earned $126.75


I just need someone to put them in order pls it’s on a test and I got it wrong the first time,and when I asked no one answered on this app

Answers

I’m pretty sure you have to divide money by hours
Paul- $17.00
Jake- $19.25
Jackie- $19.50

A city has cone shaped buildings for storing salt and sand for icy roads. Each building has a radius of 50 feet and a height of 30 feet find the volume of the building use 3.14 for π.

Answers

Answer:

Radius=50 ftπ=3.14Height=30 ftVolume=?

We know that,

[tex]\star \: \: \purple{Volume_{(cone)} =\pi {r}^{2} \frac{h}{3} }[/tex]

[tex]\star \: \: \purple{Volume_{(cone)} =3.14 \times {(50)}^{2} \times \: \cancel\frac{30}{3} \: }[/tex]

[tex]\star \: \: \purple{Volume_{(cone)} = 3.14 \times (50 \times 50) \times 10} [/tex]

[tex]\star \: \: \purple{Volume_{(cone)} =3.14 \times 2500 \times 10 }[/tex]

[tex]\star \: \: \purple{Volume_{(cone)} =78500 }[/tex]

Thus,the third option is correct.

[tex]\star \: \: {\blue{DisneyPrincess29}}[/tex]

Find the equation of a line, in slope intercept form, that has a slope of 3 and passes through the point (-4, 2)

Answers

Answer:

y= 3x+14

Step-by-step explanation:

3x because the slope is 3

14; solve for B by plugging in x=-4, y=-2 into y=3x+B

A candy company claims that 31% of the candies are orange. We randomly sample 100 candies. We wish to know the probability our sample is 29% orange candies or less. Round answers to 4 decimal places and answer numerically (0.31, not 31%)

Find the probability our sample is 29% orange candies or less P(x<0.29)

Answers

Using the normal distribution and the central limit theorem, it is found that:

P(x < 0.29) = 0.2981.

Normal Probability Distribution

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].

In this problem:

31% of the candies are orange, hence p = 0.31.We randomly sample 100 candies, hence n = 100.

Then, the mean and the standard error are given by:

[tex]\mu = p = 0.31[/tex]

[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.31(0.69)}{100}} = 0.04625[/tex]

The probability our sample is 29% orange candies or less is the p-value of Z when X = 0.29, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.29 - 0.31}{0.04625}[/tex]

[tex]Z = -0.43[/tex]

[tex]Z = -0.43[/tex] has a p-value of 0.2981.

Hence:
P(x < 0.29) = 0.2981.

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

Error Analysis Allie says JKL ~ XYZ
What is Allie's error?

Answers

Similar triangles may or may not have equal measures

Allie's error is that Allie did not state the similarity theorem

How to determine Allie's error

The statement JKL ~ XYZ means that:

Triangles JKL and XYZ are similar triangles

From the complete question, we have the following highlights:

Angles J and X have equal measures of 55 degreesThe side lengths of triangle XYZ are 3 multiplied by the corresponding side lengths of triangle JKL

The above means that, both triangles are similar by SAS or SSS

In Allie's statement, the similarity theorem is not stated

Hence, Allie's error is that Allie did not state the similarity theorem

Read more about similar triangles at:

https://brainly.com/question/14285697

What is the equation of the line that passes through the point (4,-7)(4,−7) and has a slope of 1/2?

Answers

Answer:

Add 22 Then eat caca

Step-by-step explanation:

Thats it

1. Which three lengths could be the lengths
of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm

Answers

Answer:

B. 10cm, 15cm, 24cm

Step-by-step explanation:

The 2 shortest sides of a triangle added together must be longer than the longest side of the triangle.

10cm + 15cm > 24cm, so the answer is B.

Solve for x. Explain.
Show your work in the space provided

Answers

Answer:

X=7

Step-by-step explanation:

Both are equal angles( the little 2 arrows prove that) so we set up the equation like this

75=11x-2

We need to isolate x to solve for it so we add 2 to both side since it's the opposite of subtraction.

our equation will then look like this

77=11x

last but not least, we divide 11 to both sides since it's the opposite of multiplication which 11 and X are doing

the answer is 7

WILL GIVE BRAINLIEST

CAN SOMEONE GIVE A EXPLAINATION ABOUT CLOSURE PROPERTY WITH A SIMPLE EXAMPLE THAT IS EASY TO UNDERSTAND

Answers

Explanation:

A set is "closed" for a particular operation if performing that operation on members of the set always gives a member of the set.

closed example

For example, the set {0, 1} is closed for multiplication:

  0 × 0 = 0

  0 × 1 = 0

  1 × 1 = 1 . . . all result values are members of the set

Performing multiplication on any two members of the set gives a member of the set.

__

not closed example

The same set {0, 1} is not closed for addition:

  0 +0 = 0

  0 +1 = 1

  1 +1 = 2 . . . not a member of the set

Performing addition on any two members of the set does not always give a member of the set.

_____

Additional comment

Sometimes you are asked to demonstrate closure of a particular set using a particular example. As we see with addition, above, some examples may seem to demonstrate closure, while another example may prove the set is not closed. In short, you can demonstrate that the set is closed for a particular operation on a particular example, but that does not demonstrate closure in general.

Find the average rate of
change, from 20 to 60 in
the table below.
Х
20
40
60
80
100
у
15
35
65
105
155

Answers

Answer:

20

20, 30, 40, 50

I think this might be the answer

Find tan B. WILL MARK BRAINLIEST

Answers

Tan of B is opposite over adjacent aka 12/9 simplify to 4/3

I NEED HELP ASAP PLEASE!!!

Answers

Answer:

He can buy up to 2 outfits.

Step-by-step explanation:

440.12 + 2(12.86) + 19.26 + 53.96o ≤ 620

53.96o + 485.10 ≤ 620

53.96o ≤ 134.9

o ≤ 2.5

He can buy up to 2 outfits.

How many ones does it take to make a ten?

Answers

Answer:

it takes 10 ones to make a ten.

what are the length and width of a rectangular traffic sign if the length exceeds the width by 22 inches and the perimeter is 136 inches?

Answers

Answer: L=46in

Step-by-step explanation:

Using the formulaP=2(l+w)Solving forll=P2﹣w=1362﹣22=46in

4x-4=4x+-4x


I NEED HELP!!!

Answers

Answer:

x= 1

if thats not what u trien find lmk and ill fix it n give correct answer

Step-by-step explanation:

what is equivalent to (3x - 4)^4

a. (3x - 4)(3x - 4)(3x - 4)(3x - 4)
b. (3x + 4)(3x + 4)(3x - 4)(3x - 4)
c. x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4
d. 9x^2 - 24x + 16

Answers

The correct Answer should be D. 9x^2 - 24x + 16 hope this helps

What is the range for this set of data? 7, 15, 12 3 5 8 12.

Answers

The range of the data set is 12.

Answer:

its D

Step-by-step explanation:

The cost of a truck is $42,500 but the dealership wants to mark up the price by 40. What is the selling price of the truck?

I NEED THIS WITHIN HE NEXT HOUR PLS GUYS

Answers

Answer:

$59,500

Step-by-step explanation:

Assuming you mean 40%:

Two ways:

$42,500 + ($42,500 x 0.4)

OR

$42,500 x 1.4

= $59,500

Label the vertex, axis of symmetry, max or min,
range and domain.
f(x) = 2 (x - 2) + 5
=

Answers

Answer:

X=3

Step-by-step explanation:

The measure of Angle 1 is (3x - 75)°. Find the value of x.​

Answers

Answer:

∠1=90°-->(3x-75)°=90°-->3x=90+75-->3x=165-->x=165/3=55Answer.

If you bought a stock last year for a price of $120, and it has gone down 10% since
then, how much is the stock worth now, to the nearest cent?

Answers

Answer:

it is now at 108

Step-by-step explanation:

10% of 120 is 12 120-12=108

guys pls helpp me!!!!

Answers

Answer:

26

Step-by-step explanation:

Rectangle J and Rectangle K are similar

You can divide 13 by 3.25


13/3.25=4

If Rectangle J is 4 times bigger than K all you have to do is devide 104 by 4 and you get 26


Rationalize the denominator!
Question in the picture

Answers

Answer:

A

Step-by-step explanation:

[tex]\frac{10}{9+\sqrt{7} }[/tex]

To rationalise the denominator multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 9 + [tex]\sqrt{7}[/tex] is 9 - [tex]\sqrt{7}[/tex]

= [tex]\frac{10(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{90-10\sqrt{7} }{81-7}[/tex]

= [tex]\frac{90-10\sqrt{7} }{74}[/tex] ( divide terms on numerator/ denominator by 2 )

= [tex]\frac{45-5\sqrt{7} }{37}[/tex] → A

Answer:

A[tex]\frac{45-5\sqrt7}{37}[/tex]

Step-by-step explanation:

Easy. First let's multiply numerator and denominator by [tex]9-\sqrt7[/tex] since we will create a difference of squares to get rid of the root, then start doing the calculations

[tex]\frac{10(9-\sqrt7)}{(9+sqrt7)(9-\sqrt7)}=\frac{10(9-\sqrt7)}{81-7} = \frac{10(9-\sqrt7)}{74} =\\\frac{5(9-\sqrt7)}{37}=\frac{45-5\sqrt7}{37}[/tex]

ulsi and Gary are competing in a basketball free throw competition. Tulsi’s ratio of free throws made to free throws missed is 3 to 5. Gary’s ratio of free throws made to free throws missed is 10 to 15. Who has the better ratio for making free throws?

Answers

Answer:

Gary because 10 to 15 rounds down to 2/3 which is greater than 3 to 5

Step-by-step explanation:

Answer:

Garyyy!! super late but yea

Step-by-step explanation:

:)

Are the triangles shown congruent? If so, how do you know?

Please help

Answers

Answer:

6. yes they are congruent, they are exactly the same shape and size

7. no they are not congruent, they are different sizes

8. they are congruent, they have the same shape and size

Step-by-step explanation:

     

What is the correct justification for the first step in solving this
equation? 3(x - 4) + 1 = 12x *
-
O Addition Property
O Division Property
O Commutative Property
O Distributitive Property

Answers

Answer:

x=11/9

Step-by-step explanation:

Determine the sum of the measures of the indicated angles.

Answers

Answer: 720 deg

Step-by-step explanation:

The given angles are just all the interior angles in 2 quadrilaterals

So since the sum of the int. angles in 1 quadrilateral is 360 deg, the sum in 2 is 720 deg

What is the y-intercept of the line

Answers

Answer:

1

Step-by-step explanation:

rewrite 2 11/12 as a fraction greater than 1

Answers

[tex] \tt 2 \dfrac{11}{12} [/tex]

[tex] \\ \\ [/tex]

[tex] \to\tt \dfrac{35}{12} [/tex]

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