Answer:
-4.57142857143 rounded to -4.57 or -4.6
Step-by-step explanation:
calculator
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).
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.
Four bank account balances are $11, -$16. $2, and $15. Write the balances in order from least to greatest.
Answer:
-$16, $2, $11, and hope this helps
Answer:
-$16, $2, $15, and $11.
Question 8 (1 point)
A company laid off 80% of its work force. The number of employees after the layoff is 400. How many employees were
there before the layoff?
15,000
Oь
O
Od
2000
3600
2200
Next Page
Once you click Next Page you will not be able to change your answer
Step-by-step explanation:
The number of employees before the layoff = 2000
What is percentage?"It is a number can be expressed as a fraction of 100."
For given question,
Let 'n' be the the number of employees before layoff.
A company laid off 80% of its work force.
The number of employees after the layoff is 400.
The number of employees after the layoff would be,
⇒ n - (80 percent of n) = 400
[tex]\Rightarrow n-(n\times \frac{80}{100} )=400\\\\\Rightarrow n[1-0.8]=400\\\\\Rightarrow n\times 0.2=400\\\\\Rightarrow n=2000[/tex]
Therefore, the number of employees before the layoff = 2000
Learn more about percentage here:
https://brainly.com/question/22111589
#SPJ3
PLEASE HELP I'll give brainliest
Answer:
First equation is already in slope-intercept form
The y-intercept of the first equation is (0,4)
The slope of the first equation is -2
Second equation is y= -1/2x-2 in slope-intercept form
The y-intercept of the second equation is (0,-2)
The slope of the second equation is -1/2
Find an equivalent ratio for the ratio 4 : 5.
In the figure shown, r || s. If the measure of ∠ 2 = 146°, what is the measure of ∠ 7
Answer:
34°
Step-by-step explanation:
1. First, let's find the measure of ∠1 because since r || s, that means ∠1 = ∠7 because they're both alternate exterior angles. Alternate exterior angles are congruent.
2. (Solving for ∠1)
[tex]146 + x = 180[/tex] [tex]146 + x - 146 = 180 - 146[/tex] [tex]x = 34[/tex]3. Now, since we know ∠1 = ∠7, ∠7 = 34°.
2x - 6y = 6
6x - 4y = 2
Answer:
x = - 3/7
y = - 8/7
Step-by-step explanation:
(2x - 6y = 6)/2 =
x - 3y = 3
x = 3y + 3
Substitution:
6 (3y +3) - 4y = 2
18y + 18 - 4y = 2
14y = -18+2
y = -16/14
y = - 8/7
Substitution:
x = 3(-8/7)+3
x = -24/7 + 3
x = -3/7
9514 1404 393
Answer:
(x, y) = (-3/7, -1 1/7)
Step-by-step explanation:
We can divide each equation by 2 and subtract the constant to put them in general form.
x -3y -3 = 0
3x -2y -1 = 0
This form facilitates use of the "cross multiplication method" of solution. That method tells us ...
1/d1 = x/d2 = y/d3
where the differences d1, d2, d3 are the differences of cross-products:
d1 = 1(-2) -(3(-3)) = 7
d2 = -3(-1) -(-2(-3)) = -3
d3 = -3(3) -(-1(1)) = -8
Then the solutions are ...
x = d2/d1 = -3/7
y = d3/d1 = -8/7
(x, y) = (-3/7, -8/7)
_____
Additional comment
When the general form equations ax+by+c=0 and dx+ey+g=0 have their coefficients written in two rows: (note the repeated first coefficient)
a, b, c, ad, e, g, dThe pattern in the cross-differences is relatively easy to see:
d1 = ae -dbd2 = bg -ecd3 = cd -gaThe expressions for the solution values, (x, y) = (d2/d1, d3/d1), are substantially identical to those of Cramer's method.
142% as a fraction or mixed number
What is 3.125 as a
Fraction!
Chris donated half of his t-shirts to charity then he went to the store and bought 4 new T-shirts he now has 17 T-shirts how many T-shirts did he have before the donation
Math Practices and Problem Solving Solve th * 10. © MP.4 Model Gemma fills 2 baskets with 9 berries each. She gives both baskets to Alan. Does Alan have an odd or even number of berries? Draw a picture to solve. Then write an equation.
Answer:
Even
Step-by-step explanation:
One basket has 9 berries. Since there are two baskets, the equayion is 9x2=18. 18 is an eben number.
h(x)=(x+1)^2 find functions f(x) and g(x) so that h(x)=f(g)(x))
9514 1404 393
Answer:
f(x) = x²g(x) = x+1Step-by-step explanation:
There are numerous possible solutions. Perhaps the simplest is to look at what happens to x in the expression for h(x).
x has 1 addedthe sum is squaredThis suggests that f(x) will square the result of g(x), and that g(x) will add 1 to x:
g(x) = x +1
f(x) = x²
__
Check
h(x) = f(g(x)) = f(x+1) = (x+1)² . . . . as required
_____
Additional comment
For some (almost) arbitrary function g(x), the function f(x) can include its inverse (to get the value of x+1), then perform the square. If g(x) involves powers of x, then f(x) only needs to do enough of an inverse to find (x+1)². Here's a relatively simple example.
g(x) = 2x+3
f(x) = (x -1)²/4
Then h(x) = f(g(x)) = f(2x +3) = ((2x +3) -1)²/4 = (2(x+1))²/4 = (x+1)²
Please answer! No links!!!
Picture is included
Answer:
10x+276
Step-by-step explanation:
multiply length times width to get the area
12(5/6x +23)
simplify
10x +276
i hope your test is going well <3
can you do 1 2 and 3
Answer: can you do 1 2 and 3
Step-by-step explanation:
Solve and check the equation.[tex]\frac{x}{10}=\frac{5x}{7} -43[/tex]
Answer:
x = 70
Step-by-step explanation:
Step 1: Simplify both sides of the equations.
[tex]\frac{x}{10} = \frac{5x}{7}-43[/tex] [tex]\frac{1}{10}x=\frac{5}{7}x-43[/tex]Step 2: Subtract 5/7x from both sides.
[tex]\frac{1}{10}x- \frac{5}{7}x = \frac{5}{7}x - 43 - \frac{5}{7}x[/tex] [tex]\frac{-43}{70}x = -43[/tex]Step 3: Multiply both sides by 70/(-43).
[tex]\frac{-43}{70}x * \frac{70}{-43} = -43*\frac{70}{-43}[/tex] [tex]x = 70[/tex]Step 4: Check if solution is correct.
[tex]\frac{(70)}{10}=\frac{5(70)}{7} -43[/tex] [tex]7 = \frac{350}{7} - 43[/tex] [tex]7 = 50 - 43[/tex] [tex]7 = 7[/tex]Therefore, x = 70.
Describe the type of transformation from figure A to figure B.
nahhhh man ain't answering that lololollozz
Suppose you write 10 consecutive natural numbers on a board. When one of the numbers is erased, the sum of the remaining numbers is 2015. What number was erased?
*NOTE: If any troll/false responses are added, I won't hesitate to report.*
y = 1/2x^2 – 2x + 1
Does anyone know how to turn this into vertex form?
Answer:
i do just simplyfy it that the easeasttttttt way am always. here to help i will be your persenol assitent
Step-by-step explanation:
likeeee eomg simplify to it yea i will always helpppppp youuu i likeee helppppppppppppppinggg
A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 45 pounds each, and the small boxes weigh 20 pounds each. There are 135 boxes in all. If the truck is carrying a total of 4450 pounds in boxes, how many of each type of box is it carrying?
Answer:
45 - big boxes, 200 - small boxes
Step-by-step explanation:
45 x 10 = 450
200 x 20 = 4000
Total = 4,450
Hope it's correct
The sales tax rate for the state of Washington was 9.4%. what is the state sales tax on a $3900 car in Washington? What is the final cost of the car, including tax?
Answer:
3900 x.094 = 366.60
366.6+3900=4266.60
A chemist is using 353 milliliters of a solution of acid and water. If 16.6% of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
If c = 5, what is the value of 9 + c?
Answer:
The value of 9 + c= 14 because 9 + 5=14
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe people's habits as
they sneeze. Complete parts (a) through (c)
(a) What is the probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing?
Using the binomial distribution, the probability is
(Round to four decimal places as needed.)
(b) What is the probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing?
Using the binomial distribution, the probability is 1
(Round to four decimal places as needed.)
(c) Would you be surprised if, after observing 12 individuals, fewer than half covered their mouth when sneezing? Why?
No, I would not be surprising, because using the binomial distribution, the probability is . which is v0.05
(Round to four decimal places as needed.)
Using the binomial distribution, it is found that:
a) There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
b) There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
c) The probability is higher than 5%, so it would not be unusual.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, with p probability.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
Sample of 12, thus [tex]n = 12[/tex]0.267 probability that a person covers their mouth, thus [tex]p = 0.27[/tex].Item a:
This probability is P(X = 7), so:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{12,7}.(0.267)^{7}.(0.733)^{5} = 0.0162[/tex]
There is a 0.0162 = 1.62% probability that among 12 randomly observed individuals, exactly 7 do not cover their mouth when sneezing.
Item b:
The probability is P(X < 4), which is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.267)^{0}.(0.733)^{12} = 0.0241[/tex]
[tex]P(X = 1) = C_{12,1}.(0.267)^{1}.(0.733)^{11} = 0.1052[/tex]
[tex]P(X = 2) = C_{12,2}.(0.267)^{2}.(0.733)^{10} = 0.2107[/tex]
[tex]P(X = 3) = C_{12,3}.(0.267)^{3}.(0.733)^{9} = 0.2558[/tex]
Then
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0241 + 0.1052 + 0.2107 + 0.2558 = 0.5958[/tex]
There is a 0.5958 = 59.58% probability that among 12 randomly observed individuals, fewer than 5 do not cover their mouth when sneezing.
Item c:
This probability is:
[tex]P(X < 6) = P(X < 4) + P(X = 5) = 0.5958 + P(X = 5)[/tex]
Negative probabilities do no exist, thus, this probability is guaranteed to be above 0.05, which means that it would not be unusual if fewer than half covered their mouth when sneezing.
A similar problem is given at https://brainly.com/question/24923631
Solve the equation below for y:
12y+2x=24
Answer:y =12/7
Step-by-step explanation:
Answer:
y= 2-x/6
Step-by-step explanation:
-7.532 devided by (-2.69)
Kevin's earnings vary directly with the number of hours he works. Suppose that he worked 7 hours yesterday and earned $112. How much will he earn today if he works 10 hours?
Answer:
$160 in 10 hours
Step-by-step explanation:
We know that Kevin earns $112 for working 7 hours. To find the answer for 10 hours, we need to find the unit rate.
Divide 112÷7= $16 for every 1 hour he works.
Now, we can use the unit rate to find the amount earned for 10 hours.
16×10= $160
Solve for f(x)
f(x)=a[x-(-5)][x-(-5)][x-(5-5i)][x-(2-5i)]
Step-by-step explanation:
I caught it bad yesterday
You hit me with a call to your place
Ain't been out in a while anyway
Was hoping I could catch you throwing smiles in my face
the sum of the outer angles is half the sum of inner angles. how many sides does it have?
.............................
plzz help me .....
Answer:
The sum of the outer angles of polygon is twice the sum of the inner angles. (i) How many sides does it have? (ii) What if the sum of outer angles
Quinn sold 3 of her old softball mitts at Mickey's Secondhand Thrift Mart and received the
same amount of cash for each. Before she left, she spent $23 of her earnings on a used
batting helmet. She had $7 remaining. What was the value of each softball mitt?
Answer:
$10
Step-by-step explanation:
Each mitt was sold for $10 each.
First, add the total of the money she made off of all three mittens (23+7=30) this equation gives you the amount of money that Quinn got for all three mitts.
Then, to find the value of each mitt, take the total of all the mitts and divide it by the number of mitts (30÷3=10)
This gives you the answer that each mitt was $10
The cost of each softball mitt is $10.
We have Quinn sold 3 of her old softball mitts at Mickey's Secondhand Thrift Mart. Before she left, she spent $23 of her earnings on a used batting helmet. Now, She has $7 remaining with her.
We have the cost of each softball mitt.
If the cost price of the object is equal to its selling price, then the profit percentage is?The cost price (C.P.) is equal to selling price (S.P.). Therefore -
Profit = SP - CP = 0
Hence, the profit percentage is zero.
According to the question -
Assume that the cost of 3 softballs is $x.
Cost of batting helmet = $23
Money remaining = $7
Therefore, the following equation can be used to represent the situation-
x - 23 = 7
x = 30
Now -
cost of 3 soft balls = 30
cost of 1 soft ball will be = 30/3 = 10
Hence, the cost of each softball mitt is $10.
To solve more questions on Expression modelling, visit the link below-
brainly.com/question/20876878
#SPJ2
An orchard has 352 apple trees. The number of rows exceeds the number of trees per row by 6. How many trees are there in each row?
Answer:
16 trees
Step-by-step explanation:
1. First, let's find the positive factors of 352.
1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 3522. Now, let's find the two factors that have one number 6 more than the other.
1, 3522, 1764, 888, 4411, 3216, 223. Okay, 16 and 22 have one number that's 6 more than the other. Since the number of rows exceeds the number of trees per row by 6, 22 is the number of rows, and there are 16 trees in each row.