Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Kerri got a score of 80.8; this version has a mean of 62.1 and a standard deviation of 11. Cade got a score of 286.4; this version has a mean of 271 and a standard deviation of 22. Vincent got a score of 7.9; this version has a mean of 7.2 and a standard deviation of 0.7. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job

Answer:

a) Yes

b) Yes

c) Yes

d) 0.6

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A large population has skewed data with a mean of 70 and a standard deviation of 6.

This means that [tex]\mu = 70, \sigma = 6[/tex]

Samples of size 100

This means that [tex]n = 100[/tex]

a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?

According to the Central Limit Theorem, yes.

b) Will the mean of the means of the samples remain close to 70?

According to the Central Limit Theorem, yes.

c) Will the distribution of the means have a smaller standard deviation?

According to the Central Limit Theorem, the standard deviation of the population is divided by the sample size, so yes.

d) What is that standard deviation?

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{100}} = \frac{6}{10} = 0.6[/tex]

So 0.6.

Answer:

2, 3, 4, 7, 8, 10 I hope

Answers

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Explanations:

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Acronyms

SSS = side side side

SAS = side angle side

ASA = angle side angle

AAS = angle angle side

Answer:

6

Step-by-step explanation:

The product of three consecutive numbers is divisible by ​6

Let us say the numbers are x, x+1 , x+2

if x = 1,

Product of the three consecutive numbers,

(1)(2)(3)

=> 6, which is divisible by 6

if x = 2,

Product of the three consecutive numbers,

(2)(3)(4)

=> 24, which is divisible by 6

Similarly if we take any 3 consecutive numbers their product will be divisible by 6.

Answer:

The probability mass function is:

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Step-by-step explanation:

The people are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability mass of the hypergeometric probability distribution is given by:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

22 + 25 = 47 jurors, so [tex]N = 47[/tex]

22 are women, which means that [tex]k = 22[/tex]

Jury of 12, which means that [tex]n = 12[/tex].

Thus

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = x) = h(x,47,12,22) = \frac{C_{22,x}*C_{25,12-x}}{C_{47,12}}[/tex]

Which is the probability mass function.

Answer:

Ask your Teacher if you are missing any work and if you are do it and do some things for extra credit

Step-by-step explanation:

Answer: yes,it depends on the points

if you have 65% and you score a 80 on a 45 point assingment it can go up to a c

+ep explanation:

Answer:

a) correct

b) 70 degrees

Step-by-step explanation:

since in the triangle BXC the sides BX and XC have the same length, they must also have the same angles with the baseline BC.

so, we know, XBC = 55 degrees.

and therefore BCX = 55 degrees.

the sum of all angles in a triangle is always 180 degrees.

so,

BXC = 180 - 55 - 55 = 70 degrees

The formula for perimeter is 2(Length) + 2(width)

Fill in the known information:

22 = 2(6.5)+ 2(width)

Simplify:

22 = 13 + 2(width)

Subtract 13 from both sides:

9 = 2(width)

Divide both sides by 2:

Width = 4.5m

Answer:

[tex]R = \frac{x(x+1)}{2x+1}[/tex] --- total resistance

Step-by-step explanation:

Given

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Required

Find R when

[tex]R_1 = x[/tex]

[tex]R_2 = x+1[/tex]

So, we have:

[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2}[/tex]

Substitute values for both R's

[tex]\frac{1}{R} = \frac{1}{x} + \frac{1}{x+1}[/tex]

Take LCM

[tex]\frac{1}{R} = \frac{x+1+x}{x(x+1)}[/tex]

Collect like terms

[tex]\frac{1}{R} = \frac{x+x+1}{x(x+1)}[/tex]

[tex]\frac{1}{R} = \frac{2x+1}{x(x+1)}[/tex]

Inverse both sides

[tex]R = \frac{x(x+1)}{2x+1}[/tex]

9514 1404 393

Answer:

 C.  45

Step-by-step explanation:

Apparently, your recursive definition is ...

  [tex]a_1=5\\a_n=a_{n-1}\cdot3[/tex]

Each term is 3 times the previous one, so the sequence starts ...

  5, 15, 45, 135, 405, ...

The 3rd term is 45.

Answer:

the answer is (4)

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Answer:

x = 1/2

hope it helps

have a nice day

Answer:

maybe  x=3.5

Step-by-step explanation:

6x= 1/2 (2x+5)

we take the 1/2 and distribute it into (2x+5) so we end up with

6x= 1x (or just x) + 2.5

We subtract 2.5 from both sides of the equation and we end up with

3.5x= 1x

we then need to isolate the x, so we divide both sides of the equation by x

and then we end up with

3.5= x/x, which ends up just being

3.5=x

Answer:

0.4069 ; 1.843

Step-by-step explanation:

Given:

Base of parallelogram, b = (2x - 1)

Height = (4x - 7)

Area = 1

Area of parallelogram = Base * height

Area of parallelogram = (2x - 1) * (4x - 7)

(2x - 1) * (4x - 7) = 1

8x² - 14x - 4x + 7 = 1

8x² - 18x + 7 - 1 = 0

8x² - 18x + 6 = 0

Divide through by 2

4x² - 9x + 3 = 0

Solving the quadratic equation :

Using the formula

-b ± √(b² - 4ac) / 2a

a = 4 ; b = - 9 ; c = 3

Plugging in the values :

-(-9) ± √((-9)² - 4(4)(3)) / 2(4)

9 ± √(81 - 48) / 8

9 ± √33 / 8

(9 ± 5.7445626) / 8

(9 - 5.7445626) / 8) = 0.4069

(9 + 5.7445626) / 8 = 1.843

Answer:

x = 12 , y = 7

Step-by-step explanation:

Let the numbers be x and y

Sum of the numbers,         x + y = 19 -------- ( 1 )

Difference of the number , x - y = 5 -------- ( 2)

( 1 ) + ( 2 ) => 2x = 24  

                    x = 12

Substitute : x in ( 2 ) => 12 - y = 5

                               => 12 - 5 = y

                              => 7 = y

Answer:

0.016

Step-by-step explanation:

Answer:

0.016

Step-by-step explanation:

Answer: 180 degrees rotation, center (1.5, -0.5)

=====================================================

Explanation:

Notice how point (1,-1) on triangle A moves to (-2,0) and then that rotates to (2,0)

Form a line segment from (1,-1) to (2,0) to show the beginning and end states. The equation of the line through these two points is y = x-2

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Similarly, the point (1,-4) moves to (-2,-3) after applying the translation vector, then it rotates to (2,3). Draw a line through (1,-4) and (2,3). The equation of this line is y = 7x-11

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We have this system of equations

[tex]\begin{cases}y = x-2\\y = 7x-11\\\end{cases}[/tex]

Equate the right hand sides and solve for x

7x-11 = x-2

7x-x = -2+11

6x = 9

x = 9/6

x = 3/2

x = 1.5

which leads to

y = x-2 = 1.5-2 = -0.5

or

y = 7x-11 = 7(1.5)-11 = 10.5-11 = -0.5

Either way, x = 1.5 leads to y = -0.5

We get the ordered pair (x,y) = (1.5, -0.5)

This is the center of rotation when rotating figure A to have it match up with triangle C (the triangle in the upper right quadrant)

Notice in the diagram below point D is that center of rotation. Also, notice that if we use the distance formula, you should find that

AD = A''D

BD = B''D

CD = C''D

Answer:

C. (4, -6)

Hope it helps :)

Answer:

[tex]y> 3x + 2[/tex]

Step-by-step explanation:

Hope it is helpful....

The linear inequality that represents the given graph is y > 3x + 2.

The solutions to the graph of the inequalities is given as;

(x, y) = (0, 2)

(x, y) = (-3, -7)

To determine the inequality represented in the graph;

Thus, the linear inequality that represents the given graph is y > 3x + 2.

Learn more about graphs of linear inequality here: https://brainly.com/question/371134

Answer:

Rectangle

Step-by-step explanation:

Given the points :

(0, 8), (5,2), (0, 2), and (5, 8).

Based on the vertices given :

If we mark the points on a graph and then join the points, we'll Obtain a rectangle ; this is because the length and with are not equal, with a length of 6 unit and width of 5 unit

Attached below is a rough sketch if the plot created in a notebook.

Answer:

2025 is not a perfect cube

Answer:

7 hours

Step-by-step explanation:

9 : 30 to 17:00 = 7 hours 30 minutes

Minus 30 minutes = 7 hours

Answer:

ok so this is what we have to do

250*0.95*0.95*0.95

ok so

214.34375

so about 214.3

Hope This Helps!!!

9514 1404 393

Answer:

  x = -7, 5

Step-by-step explanation:

The equation is written as a product equal to zero. The "zero product rule" tells us that a product is zero if and only if one or more factors are zero. Each factor will be zero when x takes on a value equal to the opposite of the constant in that factor.

  x -5 = 0   ⇒   x = 5

  x +7 = 0   ⇒   x = -7

The solutions to the equation are x = -7, 5.

Answer:

2

Step-by-step explanation:

The mean is calculated as

mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

x = 20

Step-by-step explanation:

We can use a ratio to solve

10         14

------ = ----------

x          28

Using cross products

10 * 28 = 14*x

280 = 14x

Divide by 14

280/14 = 14x/14

20 =x

Answer:

20 cm

Step-by-step explanation:

It says that both of these shapes are similar. If we divide 28/14=2.

Then we can also multiply 10 cm by 2 cm to get 20 cm .

x= 20 cm

Hope this helps!

Answer:

$1

max rev = 80(4) = $320

Step-by-step explanation:

let us do this in pennies  

R = (100 - x/5)(300 + x)

d/dr = -2x - 200

               5

(-2x-200)/5 = 0  

-2x = 200

x = 100

An amount of $320 is the admission price that should be charged in order to maximize revenue.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, Let x represent the revenue function.

Hence, We can formulate;

x = (3 + 0.1(x))(100 - 2x)

x = 300 - 6x + 10x - 0.2x²

x = 300 + 4x- 0.2x²

x' = 4 - 0.4x

Generally, a maximum revenue occurs when x' = 0:

x' = 4 - 0.4x = 0

4 = 0.4x

x = 4 / 0.4

x = 10

Hence, The admission price,

= 3 + 0.1x

= 3 + 0.1 x 10

= 3 + 1

= $4

Thus, The Maximum revenue is,

= $4 (100 - (10 x 2)

= $4 (100 - 20)

= $4 x 80

= $320

In conclusion, the amount of $320 is the admission price that should be charged in order to maximize revenue.

Learn more about maximize revenue visit:

brainly.com/question/13799721

#SPJ2

Answer:

12. if 3/5 of them like chocolate ice cream 2/5 don't and 2/5 of 20 is 8.

A=8

13. 296 divided by 8 is 37

A=37

14. 123 divided by 7 is 17.5714285714 so each child will get 17 sweets and there will be 4 left over.

A=17 remainder of 4

15. umm i don't know just multiple 4.50 by the amount of soccer balls

A=?

16. srry i don't realy know there not enough of the pattern

Brainlest please

Your Welcome

BIFFY OUT!!!

Answer:

x=-1

Step-by-step explanation:

the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1