Mathematics College

Question 1 – Probability [Total: 13 marks]
A prominent plastic recycling centre in Adelaide have made some recent frustrating observations
regarding the behaviour associated with disposal of plastic bottles. Some people are failing to remove
lids, caps and rings from plastic bottles prior to disposal, although this is clearly stated as a requirement
prior to disposal on their website. So they conducted a survey, noting the bottle’s “resin identification
code” and whether the lid/cap/ring had been correctly removed. The 2 plastic bottle types recorded
were: CODE 1 Polyethylene Terephthalate (PET) and CODE 2 High-Density Polyethylene (HDPE). Of 2036
PET and HDPE bottles, 936 of these bottles had their lid/cap/ring correctly removed prior to disposal,
with 70% of the 890 HDPE bottles having their lid/cap/ring correctly removed.
What is the probability of the following events?
Show all working. No marks awarded for the correct answer without working out.
Hint: A cross tabulation or contingency table can help.
I. What is the probability that a randomly selected bottle has a lid/cap/ring still attached?
[2 marks]
II. What is the probability that a randomly selected bottle is a PET bottle or has the lid/cap/ring still
attached?
[2 marks]
III. What is the probability that a randomly selected bottle is a HDPE bottle and has the lid/cap/ring
removed?
[2 marks]
IV. What is the probability that a randomly selected bottle is a PET bottle given that the lid/cap/ring
is removed?
[2 marks]
V. Are the events “lid/cap/ring removed” and “HDPE plastic bottle type” independent?
Demonstrate this appropriately. Then provide a brief description of what independence refers to
in this specific case.
[5 marks]
Marking Criteria for Question 1:
You need to demonstrate understanding of the probability concepts involved in each part of this
question and how to make appropriate interpretations of each numerical answer. Thus, for full marks
you need to show all workings (including the equation used with correct notation) AND provide a very
brief relevant written statement interpreting the answer to the question (so place the numerical answer
into a correct full statement showing you understand what it means).

Answers

Answer 1

9514 1404 393

Answer:

  I. 0.540; II. 0.694; III. 0.306; IV. 0.334; V. 0.177 ≠ 0.306 (not independent)

Step-by-step explanation:

I. P(ring) = 1100/2036 = 275/509 ≈ 0.540

The probability that a randomly selected bottle will have its ring attached is the ratio of such bottles to the total number of bottles: 1100/2036 ≈ 0.540.

__

II. P(PET∨ring) = 1 -P(HDPE∧no ring) = 1 -623/2036 = 1413/2036 ≈ 0.694

The probability that a random bottle is PET or has the ring attached is the ratio of such bottles to the total: 1413/2036 ≈ 0.694.

__

III. P(HDPE∧no ring) = 623/2036 ≈ 0.306

The probability that a random bottle is HDPE and has the ring removed is the ratio of such bottles to the total number of bottles: 623/2036 ≈ 0.306.

__

IV. P(PET | no ring) = P(PET∧no ring)/P(no ring) = 313/936 ≈ 0.334

The probability that a random bottle is PET given that it has no ring is the ratio of ringless PET bottles to the total number of ringless bottles: 313/936 ≈ 0.334.

__

V. P(ringless) = 936/2036 ≈ 0.460

  P(HDPE) = 890/2036 ≈ 0.386

  P(ringless)×P(HDPE) = 0.460×0.386 ≈ 0.177 ≠ P(HDPE∧no ring) = 0.306

If events A and B are independent, the probability of the joint event A∧B is the product of the probabilities of the individual events. Here the probability of an HDPE bottle having no ring is about 0.306, while the product of probabilities that a bottle is HDPE and that a bottle has no ring is about 0.177. "Ring removed" and "HDPE bottle type" are not independent.

_____

Attached is the recommended cross tabulation table. The numbers in blue are given in the problem statement (623 = 70%×890). The numbers in black are the numbers required in order to achieve the given totals.

Question 1 Probability [Total: 13 Marks]A Prominent Plastic Recycling Centre In Adelaide Have Made Some

Related Questions

Queens help me solve this
-0.125(0.25x - 0.5)

Answers

Answer:

−0.03125x + 0.0625

Step-by-step explanation:

Answer:

0.03125x−0.0625

Step-by-step explanation:

PLS HELP EN UNDERSTAND THIS

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Answer:

-5.5x+5.8

Step-by-step explanation:

To do this you need to remove the parenthesis and subtract like terms only (-3.6x - 1.9x) and the same thing for the other like terms.

How do you solve 14x14x14?

Answers

Answer:  2744

Step-by-step explanation: 14x14= 196 x14 =2744

Answer:

The answer is 2744.

Step-by-step explanation:

First solve for 14 x 14, which is 196.

Then solve for 196 x 14, which is 2744.

Hence, the answer is 2744.

PLEASE MARK AS BRAINLIEST!!!!!

HELP ME ON THIS QUESTION PLZ!!!

Answers

x + 10 + x + 10 = 2x + 20

= 2 (x + 10)

So, option (d) is correct

A bacteria can double every 4 hours. If you start with 22, how many will you have in 18 hours?

Answers

Answer:

ii cud givee uu an explanation for understandment for help if still don't understand im sowwyy thenn.

Step-by-step explanation:

It is given that the number of bacteria doubles every hour.

Therefore, the number of bacteria after every hour will form a G.P.

with first term (a=30) and common ratio (r=2)

∴a

3

​

=ar

2

=(30)(2)

2

=120

Therefore, the number of bacteria at the end of 2nd hour will be 480.

a

5

​

=ar

4

=(30)(2)

4

=480

and a

n+1

​

=ar

n

=(30)(2)

n

 

Thus the number of bacteria at the end of nth hour will be (30)(2)

n

Geometric sequence can model the considered situation. The number of bacteria in 18 hours for the considered situation will be 264

What is  a geometric sequence and how to find its nth terms?

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.The second parameter is the quantity by which we multiply previous term to get the next term.The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]  

Then the sequence would look like

[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)

Thus, the nth term of such sequence would be

[tex]T_n = ad^{n-1}[/tex]

We can model the given situation with the geometric sequence since each previous count is being doubled(multiplied by 2) per 4 hours.

We're given initial number of bacteria = a = 22

Each new element will be denoting number of bacteria after 4 hours from previous count.

So, from 0 to 16 hours, there are four set of 4 hours. Thus, n = 4

Since number of bacteria are doubling, thus, d= 2

We get fourth term  = number of bacteria after 16 hours

[tex]T_n = a(d)^{n-1} = 22 \times (2)^3 = 176[/tex]

Now, in the last 2 hours, assuming that if x -> 2x in 4 hours(which is increment of x), then in 2 hours, only x/2 must be incremented.(assuming linear growth in each 4 hour group).

Thus, after 18 hours, 176 + 176/2 will be the number of bacteria.

Thus, Number of bacteria after 18 hour for the given case = 176 + 88 = 264

Learn more about geometric sequence here:

https://brainly.com/question/2735005

anyone have the answer to this one?

Answers

Area of the rectangle is 60

Area of the semi circle 14.13 ir 14.1

60 plus 14.1 is 74.1

I hope its right

the area of it is 60!

WILL GIVE BRAINILEST TO CORRECT ANSWER! TYSM IF U ANSWER :D


Compare each pair of fractions. Use <, =, or >.

2/3____5/8


Answers:

A. >
B. <
C. =

Answers

Answer:

>

2/3 is bigger than 5/8 because 5/8 is split into smaller portions

Step-by-step explanation:

hope this helps

Q9) When working on a problem recently, Mya saw the polynomial expression 4 - 3x”. She decided to
re - write it as - 3x + 4. Which property of real numbers justifies (allows) Mya's action? Explain your
answer.

Answers

Answer:

Commutative Property of Addition

a + b = b + a

which says

"commute = to get up and move to a new location : switch places"

4-3x = -3x +4

Find the solution of the system of equations. 6x -y= 21. -5x + y= -18​

Answers

First one is -6 and the second one is -3

I need help in statistics
​

Answers

Answer:

What help you neep? Please ask with out no fear

A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is
located at (15,2) and the Bus Station is located at (5,-10).
The Train Station is located at point?

Answers

Answer:

A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is

located at (15,2) and the Bus Station is located at (5,-10).

The Train Station is located at point?

15. Tom is deciding whether or not he should become a gym member to use their basketball courts. The membership cost is $135. Members pay $3 to rent out the basketball courts. Non-members can rent the courts also, but they have to pay $11 each time. How many times would Tom need to rent the court in order for it to be cheaper to be a member than a non-member?​

Answers

Answer:

Tom need to rent the court in order for it to be cheaper more than 15 times.

Step-by-step explanation:

Answer:

Tom needs to rent it atleast 17 times.

Step-by-step explanation:

1) First, write your equations. x in this case equals the # of times you rent the court.

For members: y = 135 + 3x (members)

Non-members: y = 11x (non-members)

From here, there can me many methods that can work. Right now I can only think of one though :/.

So what you can do is plug in numbers and see what happens. I suggest you work with easy numbers when you plug stuff in. Once you find that non-members is greater than the amnt for members have, that's your answer!

a) x = 10

For members: 135 + 3(10) = 165

Non-members: 11(10) = 110

Didn't work. :(

b) x = 20

For members: 135 + 3(20) = 195

Non-members: 11(20) = 220

Aha! We have a valid answer. However, we need to find the minimum number of times Tom needs to rent it.

c) x = 15

For members: 135 + 3(15) = 180

Non-members: 11(15) = 165.

So our answer is between 15 and 20.

If you keep doing this, you'll find that 18 is the minimum number of times tom will have to rent the court. So your answer is anything greater than equal to 17.

x = 17

For members: 135 + 3(17) = 186

Non-members: 11(17) = 187

Sorry I made this tedious, but this is one method. Though I helped you find the answer, I hope someone else can help you find the best method!

Hello need help on this question (:

Answers

Answer:

the answer is B. the 2 in the hundredths place is 1/10 the 2 in the tenths place

Simplify 3xy²-2a²b-4xy²+8a²b​

Answers

Answer: 6a^2b - xy^2

Step-by-step explanation:

Answer:

If you EVALUATE it is [tex]6ba^{2}[/tex] - [tex]xy^{2}[/tex]

Differentiate w.r.t. x means the answer is

[tex]-y^{2}[/tex]

Step-by-step explanation:

HELP!!!!!!!!!!!!!!!! I WILL GIVE BRAINILEST.

Answers

Answer:

B. 2/5

Step-by-step explanation:

dividing by 2 both numerator and denominator we get

2/5

hope it helps u

mark me brainliest pls

A is the point (8, 5) and B is the point(- 4, 1).Calculate the length of AB. *

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Answer:

..............................

Put x + 2y=4 into slope-intercept form? y=mx+b format

Answers

Answer:

[tex]y=-\frac{1}{2} x+2[/tex]

Step-by-step explanation:

1.  First we want to get the y all by itself

So we would subtract x from both sides and get [tex]2y=-x+4[/tex]

2. Then we would divide 2 from both sides

Answer: [tex]y=-\frac{1}{2} x+2[/tex]

Which expression uses the associative property to make it easier to evaluate 14(1/7 2/5)?
A. 14(2/5.1/7)
B. 7(1/14.2/5)
C. (14.5/2)1/7
D. (14.1/7)2/5

Answers

Answer:

B

Step-by-step explanation:

Answer:

A. 14(2/5.1/7)

Step-by-step explanation:

Please answer this problem worth 59 pts

Answers

Answer:

35.2

Step-by-step explanation:

Find the missing angle:

m∠L = 180° - 60° - 45° = 75°

Use the law of sines to determine the lengths of the sides:

LM / sin ∠K = KM / sin 75°12 / sin 60° = KM / sin 75KM = 12 sin 75° /sin 60° = 13.4 (rounded)KL / sin ∠M = LM / sin ∠KKL / sin 45° = 12 / sin 60°KL = 12 sin 45° / sin 60° = 9.8 (rounded)

Find perimeter:

P = 12 + 13.4 + 9.8 = 35.2

Write each fraction as a decimal and as a percent.​

Answers

Answer:

0.35 and 35%

Step-by-step explanation:

7/20=35/100

35/100=0.35=35%

An employee earns $10.75 per hour. Write an equation that represents the total earnings in a week, y, as it relates to time in hours? Use your equation to find the total earnings for a 40 hour week.

Answers

Answer:

40 X 10.75= 430  

10.75/2= 5.375 round up 5.38  

10.75 + 5.38 = 16.13  

16.13 X 10 = 161.30  

430+161.30= 591.3

the qustion is to make 5 dinner rolls 1/3 cup of flour is used how much flour is needed to make 1 dinner roll​

Answers

Answer:

[tex]\frac{1}{15}[/tex] cup of flour

Step-by-step explanation:

5 rolls = [tex]\frac{1}{3}[/tex] cup

? × 5 = [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex] ÷ 5 = ?

[tex]\frac{1}{3}[/tex] ÷ [tex]\frac{5}{1}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{15}[/tex]

4 is the _____ of 4n

Answers

Answer:

4 is the coefficient of 4n

Step-by-step explanation:



Luke owns a 1200 ft2 apartment. If
Luke is planning on tiling of his
apartment's total square footage and
Home Depot charges $6.75 for 1 ft of
tile. How much money will Luke
spend on tiling his apartment?

Answers

Answer:

$8100

Step-by-step explanation:

= 1200 *6.75=$8100

Help please thanksss

Answers

Yes because of AAA. They have the same angles, so their sides must also be proportionate, making them congruent

Please help fast !!!!!!!!!

Answers

Answer:

x >= -2

Closed circle and going to the right, so it is greater than or equal to -2.

Which expression shows the result of applying the distributive property to 3(1/5x−1/7)?


3/5x+3/7

−3/5x+3/7

−3/5x−3/7

3/5x−3/7

Answers

Answer:

d. 3/5x−3/7

Step-by-step explanation:

Use distributive property.

3(1/5x−1/7)(3×1/5x) - (3×1/7)3/5x - 3/7

∴ choice d. 3/5x−3/7 is correct.

Help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

2.02

Step-by-step explanation:


If you need to find the value of a variable in an equation, you need to
equation, which means to find the set of values that makes the equation true.
A.isolate
B.simplify
C.check
D.solve

Answers

A isolate the variable

Hi, need help on this simple division question (:

Answers

Answer:

775

Step-by-step explanation:

186÷0.24=775

your welcome

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