A roller coaster is being designed that starts at (0,22) and ends at (19,2),

Along the ride there is a relative minimum at (5,6) and a relative

maximum at (10,18). The roller coaster is almost finished but one

section is missing. Find the correct function that completes the roller

coaster so that the ride is smooth and continuous.

Answer:

a) S = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}

b) p(x) = 0.3 if x = 0

          = 0.6 if x = 1

          = 0.1 if x = 2

          = 0 otherwise

Step-by-step explanation:

Given - Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair  (1, 2) represents the selection of boards 1 and 2 for inspection.

To find - (a) List the ten different possible outcomes.

              (b) Suppose that boards 1 and 2 are the only detective boards in a lot of five. Two boards are to be chosen at random. Define X to be the # of defective boards observed among those inspected. Find the pmf.

Proof -

(a)

Given that there are 5 computer boards

Let,

The Boards are 1, 2, 3, ,4 and 5.

Now,

Total Number of possible ways of selecting 2 boards out of 5 by inspection = ⁵C₂ = [tex]\frac{51}{2! (5-2)!}[/tex] = [tex]\frac{5!}{2! 3!}[/tex] = [tex]\frac{5.4.3!}{2! 3!}[/tex] = [tex]\frac{5.4}{2.1}[/tex] = 10  

And the choices be

Choice I -

Boards 1 and Board 2

Choice II -

Board 1 and Board 3

Choice III -

Board 1 and Board 4

Choice IV -

Board 1 and Board 5

Choice V -

Board 2 and Board 3

Choice VI -

Board 2 and Board 4

Choice VII -

Board 2 and Board 5

Choice VIII -

Board 3 and Board 4

Choice IX -

Board 3 and Board 5

Choice X -

Board 4 and Board 5

And

These outcomes becomes

S = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}

(b)

Given that,  X be the number of defective boards

And there are only two defective boards (Board 1 and Board 2) in the lot

Therefore,

X can be 0, 1, and 2.

Now,

If X = 0

⇒ There is no defective boards

⇒ Possible outcomes be - { (3,4), (3,5), (4,5) }

So,

P(X=0) = [tex]\frac{3}{10}[/tex] = 0.3

Now,

If X = 1

⇒ There is one defective board

⇒ Possible outcomes be - { (1,3), (1,4), (1,5), (2,3), (2,4), (2,5) }

So,

P(X=1) = [tex]\frac{6}{10}[/tex] = 0.6

Now,

If X = 2

⇒ There is two defective boards

⇒ Possible outcomes be - { (1,2) }

So,

P(X=2) = [tex]\frac{1}{10}[/tex] = 0.1

And

P(x) = 0 if x ≠ 0, 1, 2

SO, The pmf be

p(x) = 0.3 if x = 0

      = 0.6 if x = 1

      = 0.1 if x = 2

      = 0 otherwise

Answer:

width equals 16

length = 20

Step-by-step explanation:

Hello there!

we know that the perimeter is 72 m

and the width is 4 m less then the length

perimeter is 2w+2l

w=width and l = length

72 + (2x-4) = 72+8 = 80

80 / 4 (because there are 4 values, w, w, l, l ) = 20

so now...

20 - 4 = w

16 = w

and 20 = l

16+16 = 32

20+20 = 40

32+40 = 72

Answer:

[tex] \frac{3}{4} [/tex]

Step-by-step explanation:

Slope is equal to the change in y over the change in x.

[tex]m = \frac{change \: in \: y}{change \: in \: x} [/tex]

The change in x is equal to the difference in x-coordinates, and the change in y is equal to the difference in y-coordinates .

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Substitute in the values of x and y into the equation to find the slope.

[tex]m = \frac{5 - (2)}{7 - (3)} [/tex]

Simplify.

[tex]m = \frac{3}{4} [/tex]

Hence, the slope is 3/4.

Answer:

27

Step-by-step explanation:

111÷4=27.75

Hope this helps!

Answer:

27

Step-by-step explanation:

111/4 = 27

Answer:

CI = ( 0,1433  ;  0,4067 )

Step-by-step explanation:

College of Engineering

sample size  n₁  =  200

sample proportion ( with laptop )    p₁ = 91/ 200   p₁ = 0,455  q₁ = 1 - p₁

q₁ = 0,545

College of Arts

sample size  n₂  =  100

sample proportion ( with laptop )    p₂ = 73/ 100   p₂ = 0,73  q₂ = 1 - p₂

q₂ = 0,27

CI = 98 %      significance level   α = 2 %  α = 0,02    α/2 = 0,01

From z-table we find z(c) for 0,01

z(c) = 2,328

CI = [  ( p₂ - p₁ ) ± z(c) * √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂ ]

CI

[ ( 0,73 - 0,455 ) ±  2,328 * √ (0,455*0,545)/ 200  + ( 0,73*0,27)/100

CI = ( 0,275 ) ±  2,328 *√0,00123 + 0,001971

CI = ( 0,275 ± 2,328* 0,0566)

CI = ( 0,275 - 0,1317  ;  0,275 + 0,1317 )

CI = ( 0,1433  ;  0,4067 )

The values of the CI  for  the difference are always positive meaning that the proportion of students of Arts is greater than the proportion of students of Engineering

Answer:

a. m = -1, y-int = 0

b. m = 2/3, y-int = -5/3

c. m = -1/2, y-int = 2

Step-by-step explanation:

-Expand equations on both sides.

-Make 'y' the subject by collecting like terms and moving everything to the right, e.g. y = ...

-Slope is the number in front of x.

-Find y-intercept by letting x = 0 and solve the equation.

95141 1404 393

Answer:

  3 liters

Step-by-step explanation:

There's a simple and effective "visual" way to solve mixture problems that makes short work of this.

In the attached, the concentrations of the contributors are listed on the left. It can work well to put the largest contributor on top (though that is not strictly necessary). The target concentration is put in the middle between them, and the differences along the diagonals are computed.

The diagonal differences are reduced to lowest terms as a ratio in the right-hand column. These numbers can be compared to the problem statement to see how they relate.

In this case, the total is 4 L of juice, and the total of the ratio units is 4. Then the ratio units are the number of liters of the corresponding contributor:

Answer:

m=16

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :  3/4*m-3-(9)=0

Step 1: Simplify 3/4

Equation at the end of step 1: ((3/4 x m) - 3) - 9 = 0

Step2: Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

        3     3 • 4

   3 =  —  =  —————

        1       4  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3m - (3 • 4)                               3m - 12

—————4———————  =  ———4————

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 3•(m-16)

 ———————— • 4 = 0 • 4

    4    

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  3  •  (m-16)  = 0

6.2      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solve  :    m-16 = 0

Add  16  to both sides of the equation :

                     m = 16

Answer:

400 mL

Step-by-step explanation:

0.50x + 0.20(600-x) = 0.40*600

50x + 20*600 - 20x = 40*600

30x = 20*600

x = 20*20

x = 400 mL

Answer:

12 dollars per chair

Step-by-step explanation:

294 - 198 = 96

96 divided by 8 = 12

Answer:

Kaitlin's answer is wrong because she is supposed to by dividing. When trying to get rid of a number from a variable you have to divide the number by itself and whatever you do to one side you have to do to the other side

so you would do 5/5 - cancels out

15/5=3

y=3

Step-by-step explanation:

have a great day :D

Answer:

Explanation (Part A):

Solution (Part B):

The correct answer must be 'y = 3'.

Answer:

I RLY HOPE THIS IS CORRECT WISH THE BEST OF LUCK

Answer:

12.08

Step-by-step explanation:

If you order these numbers from least to greatest, you would get...

12.08, 12.087, 12.7, 12.78, 12.807

The least second it took to complete the race is 12.08

hope you have a wonderful day too! <3

9514 1404 393

Answer:

  direct variation

Step-by-step explanation:

The given equation can be written in the direct variation form ...

  y = kx

  y = -8x . . . . rewrite of the given equation (multiply by -4)

This is an example of direct variation.

Answer:

29

Step-by-step explanation:

P=a+b+c=11+5+13=29

Answer:

D. It interferes with motor responses

Step-by-step explanation:

Don't ask why I know this

Answer:

y=8

Step-by-step explanation:

the angle that is equal to 10x-3 and the angle that is equal to 7x+45 are equal to each other because they are corresponding angles so we setup an equation which would be

10x-3=7x+45

step 1

add 3 to each side

-3+3 = they cancel out

45+3=48

now we have

10x=7x+48

step 2

subtract each side by 7x

7x-7x cancels out

10x-7x=3x

3x=48

step 3

divide each side by 3

3/3 cancels out

48/3=16

so x =16

now we plug it into to 10x+3

10x16=160 160-3= 157

so the angle that is equal to 157 and the one that is equal to 3-y are supplementary angles so they will add up to equal 180 so to solve y we setup the equation which would be

180=157+3y-1

step 1 combine like terms

157-1=156

180=156+3y

step 2 subtract each side by 156

156-156 cancels out

180-156=24

so now we have

24=3y

next we divide each side by 3

3/3 cancels out

24/3=8

y=8

hope this makes sense :D

Answer:

swdfghjkl;'[

Step-by-step explanation:

asdfghjkl;'iy7u6j54hy3feqdwsrtfyuiop;lkjhgf

Answer:

nbmmmmmmmmmmmmmmmmmm

Step-by-step explanation:

Answer:

x+(6x-15) = 90 degrees

for the whole angle measure is 90 degree and making smaller angles out of it , their sum should be 90 degrees

Answer:

Answer:

The number on top of sigma is the number of terms.

The answer is C. 8 terms.

Answer:

Expression of the statement = 18 - 2x

Answer:

18 - 2x

Step-by-step explanation:

Answer:

12.5%

Step-by-step explanation:

Answer:

Step-by-step explanation:

simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form:

6√35

Decimal Form:

35.49647869

Answer:

2x(30+8-6)-20

Step-by-step explanation:

Answer:

It is already in simplest form.

Step-by-step explanation:

Answer:

Already in simplest form

Step-by-step explanation:

I mean you could do 6(x+2) but its already in its simplest form.

Answer:

You must survey 784 air passengers.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Assume that nothing is known about the percentage of passengers who prefer aisle seats.

This means that [tex]\pi = 0.5[/tex], which is when the largest sample size will be needed.

Within 3.5 percentage points of the true population percentage.

We have to find n for which M = 0.035. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.035 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.035\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.035}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.035})^2[/tex]

[tex]n = 784[/tex]

You must survey 784 air passengers.

Answer:

h = 1296 feet

Step-by-step explanation:

Given that,

The vertical position of the object is :

[tex]h(t)=-16t^2+160t+896[/tex] .....(1)

We need to find the highest height reached by the object. For highest height,

Put dh/dt = 0

[tex]\dfrac{d}{dt}(-16t^2+160t+896)=0\\\\-32t+160\\\\t=\dfrac{160}{32}\\\\t=5\ s[/tex]

Put t = 5 in equation (1).

[tex]h(5)=-16(5)^2+160(5)+896\\\\=1296\ ft[/tex]

So, the height reached by the object is 1296 feet.