Answer:
45 minutes
Step-by-step explanation:
At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...
t = d/s
t = (7.5 mi)/(10 mi/h) = 0.75 h
to catch Peter.
Mitchell will catch Peter in 45 minutes.
__
Alternate Solution
Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:
3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter
_____
You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.
Question 1
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Solve the equation using the Subtraction and Addition Properties of Equality.
b + 17 = 35
be
Question Help: Video
Written Example
Submit Question
Answer:
b=18
Step-by-step explanation:
b+17=35
-17 -17
b=18
If I have a 9ft plank how many 3/4 pieces can I get
Perform the row operation 1/3R1 and replace R1 on the following matrix
[3 0 0|21]
[0 6 0|5]
[0 0 7|5]
Answer:
[tex]\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right][/tex]
Step-by-step explanation:
The given augmented matrix is
[tex]\left[\left.\begin{matrix}3 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}21\\ 5\\ 5\end{matrix}\right][/tex]
Here, we need to perform the row operation [tex]\dfrac{1}{3}R_1[/tex] and replace [tex]R_1[/tex] in the above matrix.
So, divide each element of [tex]R_1[/tex] in the given matrix and other elements remain same.
[tex]\left[\left.\begin{matrix}\dfrac{3}{3} & \dfrac{0}{3} & \dfrac{0}{3}\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}\dfrac{21}{3}\\ 5\\ 5\end{matrix}\right][/tex]
[tex]\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right][/tex]
Therefore, the required matrix is [tex]\left[\left.\begin{matrix}1 & 0 & 0\\ 0 & 6 & 0\\ 0 & 0 & 7\end{matrix}\right|\begin{matrix}7\\ 5\\ 5\end{matrix}\right][/tex].
Please help me it due today
Answer:
i think the answer is A
Step-by-step explanation:
if u select the answer C then he will not be able to collect at least 1000
each week but he can collect less.
as remaining 6 weeks and remaining signatures at least(point to be noted)
1000-520=480
so each week he will collect at least= 480/6=80 its at least but he can collect more than 80 because the limit is at least 1000.......
so the answer is including 80 or more than that....that means the answer is A.......THANK U(I think its the answer but not 100% sure)
The sum of 2 times a number and 4 is equal to 8
Answer:
2x + 4 = 8
Step-by-step explanation:
This is the answer because:
1) 2 times a number is representing 2 multiplied with an unknown number, so we can use a variable (x) to represent the number
2) "and" is representing adding. Therefore, 2x + 4 is what is representing the sentence "The sum of 2 times a number and 4"
3) Finally, "equal to 8" is representing how the expression: 2x + 4 is eual to 8
Therefore, the correct equation is 2x + 4 = 8
Hope this helps!
The local Jazz Club met 50 times last year. At each meeting there were 20 slots on the playlist, with one tune played in each slot. A careful study of the playlists for last year showed that: 40% of the slots were used for tunes that were not played at any other time that year. 45% of the slots were used for tunes that were played just twice. Half of the remaining slots were used for tunes that were played 3 times. There were only 5 other tunes played during the year, and the number of times that these were played was in the ratio 5 : 4 : 3 : 2 : 1. How many different tunes will a member who attended all meetings have heard during the year?
A655
B 705
C 880
D 930
Answer: It’s A, 655.
The total number of different tunes will a member who attended all meetings have heard during the year is 655 and this can be determined by using the given data.
Given :
The local Jazz Club met 50 times last year. At each meeting there were 20 slots on the playlist, with one tune played in each slot. A careful study of the playlists for last year showed that: 40% of the slots were used for tunes that were not played at any other time that year. 45% of the slots were used for tunes that were played just twice. Half of the remaining slots were used for tunes that were played 3 times.There were only 5 other tunes played during the year, and the number of times that these were played was in the ratio (5 : 4 : 3 : 2 : 1).The total number of slots is given by:
[tex]50\times 20 = 1000[/tex]
So, the total number of tunes in each slot is 1000.
The total number of remaining tunes is given by:
[tex]=1000-(400+450)[/tex]
= 150
According to the given data half of the remaining tunes were played thrice that is 75 tunes were played thrice and only 5 other tunes were played out of the remaining 75 tunes.
So, the total number of tunes a member will hear is given by:
[tex]=400+\dfrac{450}{2}+\dfrac{75}{3}+5[/tex]
= 655
So, the total number of different tunes will a member who attended all meetings have heard during the year is 655.
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Find the value of x using angle properties. What is the measure?
Answer: x = 7
Step-by-step explanation: 16x = 4x + 84
15) The value of x would be 20.
16) The measure of angle BFH would be 100.
17) The value of x is, 7
Used the concept of angles in a parallel line which states that,
if a transversal intersects two parallel lines, the corresponding angles will be always equal.
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Given that,
In Figure 15, both angles are corresponding angles.
And, in Figure 17, both angles are Alternate angles.
Now, by definition of Alternate and Corresponding angles we get;
17) The angles DBF and angle EFB are congruent.
So, it can be equal.
16x = 4x+ 84
Subtract 4x on both sides,
16x - 4x = 84
12x = 84
Divide 12 on both sides,
x = 84/12
Therefore, the value of x is,
x = 7
15) The angles of CBD and BFH are conguent.
So, It can be equal.
5x = 3x + 40
Subtract 3x on both sides,
5x - 3x = 40
2x = 40
Divide 2 on both sides,
x = 40/2
x = 20
16) So, the measure of angle BFH is,
∠BFH = 3x + 40
= 3 × 20 + 40
= 60 + 40
= 100
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PLEASE HELPPP!!! THANK YOU SOO MUCH ILY!!!!!!!
Answer:
1) Variables = 11a , 4a
Constants = 0
Coefficients = 11 , 4
2) Variables = 3x , 7x
Constants = 6 , -4
Coefficients = 3 , 7 , 6 , -4
3) Variables = -12m , +4m
Constants = -3 , 16
Coefficients = -12 , 4 , -3 , 16
4) Variables = 6k , k
Constants = -4 , -2
Coefficients = 6 , 1 , -4 , -2
5) Variables = -5p , -2p
Constants = 3 , 13
Coefficients = -5 , -2 , 3 , 13
6) Variables = -10r , -r , -6r
Constants = 11
Coefficients = -10 , -1 , -6 , 11
7) Variables = -5n
Constants = 19 , -8 , 14
Coefficients = -5 , 19 , -8 , 14
8) Variables = 13y , -2y
Constants = 18 , -5
Coefficients = 13 , -2 , 18 , -5
9) Variables = 8a , 3a , -7b , -2b
Constants = 1
Coefficients = 8 , 3 , -7 , -2 , 1
10) Variables = 11x , 2x , -4y
Constants = 8
Coefficients = 11 , 2 , -4 , 8
Step-by-step explanation:
Shawn is starting a woodworking project for which he needs a large number of 2x4s. He plans to buy 2x4s that are 6 feet in length and cut them into the following sizes: eight pieces that are 12.5 inches long • six pieces that are 8.75 inches long • nine pieces that are 6.25 inches long Note: A 2x4 ("two by four") is a rectangular piece of wood that is two Inches high and four inches wide, as shown in the picture. It can have varying lengths. The 2x4s that Shawn is buying have a length of 6 feet, or 72 inches. 6' or 72" 2" 4" Find the most efficient way for Shawn to cut these pieces. In other words, what is the fewest number of boards he can cut from? Describe for Shawn the most efficient way to cut his boards. You may include a diagram if you wish.
Answer:
The fewest amount number of boards Shawn can cut from is 3.... Im not very sure... Ive been stuck on this answer, too
What is the common difference and the 5 th term in the arithmetic formula for an=6n+3
Answer:
is an=6n+3 your question?
Step-by-step explanation:
Answer:
Common Difference (d) =6
5th term = 33
Step-by-step explanation:
[tex]a_n= 6n +3.... (given) \\
Plug\: n = (n +1)\\
a_{(n+1)}= 6(n+1) +3 = 6n + 6 +3 = 6n + 9\\
Common \: Difference \: (d) = a_{(n+1)} - a_n\\
= 6n + 9 - (6n+ 3)\\
= 6n + 9 - 6n - 3\\
= 9-3\\
\red{\boxed{\bold {Common \: Difference \: (d) =6}}} \\
Plug \: n = 5 \: in\: a_n= 6n +3\: we \: find:\\
a_5= 6\times 5+3= 30 + 3 = 33\\
\huge\purple {\boxed {a_5= 33}} \\[/tex]
what is the greatest common factor for x^6+y^4+x^3+y^2
Answer:
1
Step-by-step explanation:
x⁶+y⁴+x³+y² correct?
There's nothing you could factor from this that would make anything look nicer. So the GCF is just 1.
The Big Boy was a famous lovomotive built during the 1940’s. The locomotive was about 132 feet long. About how long is an s-scale model of a Big Boy locomotive?
Answer:
2.0625 feet
Step-by-step explanation:
The S-Scale ratio is 1:64, so the answer is just 132/64, or 2.0625.
If you're building a miniature locomotive, good luck man
16.2=2.7(h+1) solve for h
Step-by-step explanation:
16.2 = 2.7(h+1)
2.7(h+1) = 16.2
(h+1) = 16.2 ÷ 2.7
h+1 = 6
h = 5
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{h = 5}}}}}[/tex]
Step-by-step explanation:
[tex] \bigstar{ \sf{ \: \: 16. 2 = 2.7( \: h \: + \: 1)}}[/tex]
[tex] \tt{Step \: 1 \: }[/tex] : Swap the sides of the equation
[tex] \longmapsto{ \sf{2.7(h + 1) = 16.2}}[/tex]
[tex] \tt{Step \: 2 \: }[/tex] : Distribute 2.7 through the parentheses
[tex] \longmapsto{ \sf{2.7 \times h + 2.7 \times 1 = 16.2}}[/tex]
[tex] \longmapsto{ \sf{2.7h + 2.7 = 16.2}}[/tex]
[tex] \tt{Step \: 3 \: }[/tex] : Move 2.7 to right hand side and change it's sign
[tex] \longmapsto{ \sf{2.7h = 16.2 - 2.7}}[/tex]
[tex] \tt{Step \: 4 \: }[/tex] : Subtract 2.7 from 16.2
[tex] \longmapsto{ \sf{2.7h = 13.5}}[/tex]
[tex] \tt{Step \: 5 \: }[/tex] : Divide both sides by 2.7
[tex] \longmapsto{ \sf{ \frac{2.7h}{2.7} = \frac{13.5}{2.7}}} [/tex]
[tex] \tt{Step \: 6 \: }[/tex] : Calculate
[tex] \longmapsto{ \sf{h = 5}}[/tex]
The value of h is 5
Hope I helped!
Best regards! :D
~TheAnimeGirl
3 x² - 2x-1=0
solve using quadratic formula
Answer:
The answer to your question: x is -1/3 or 1
Describe the shape of the distribution shown in the dot plot.
The dot plot displays the golf scores from a golf tournament.
140
132
134
136
138
golf score (strokes)
A. Uniform
B. Bimodal
C. Left-Skewed
D. Right-Skewed
E. Symmetrical
F. Bell-shaped
Answer:
The answer is C. Left-Skewed
Find a2 and a3. a1=–5 an=6an–1 Write your answers as integers or fractions in simplest form. a2= a3=
The value of a2 and a3 given the formula an = 6an – 1 are -61 and -91 to respectively
Given:
an = 6an – 1
where,
a1, = first term= -5
n = number of terms
a2 = second term
a3 = third term
an = 6an – 1
a2 = (6 × -5 × 2) - 1
= (-60) - 1
= -60 - 1
a2 = - 61
an = 6an – 1
a3 = (6 × -5 × 3) - 1
= -90 - 1
a3 = -91
Therefore, the value of a2 and a3 are -61 and -91 respectively
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Two bags each contain tickets numbered 1 to 10. John draws a ticket from each bag five times, replacing the tickets after each draw. He records the number on the ticket for each draw from both the bags: Bag 1Bag 2 Draw 124 Draw 245 Draw 313 Draw 464 Draw 579 For the the first bag, the mean is 4 and the standard deviation is 2.5. For the second bag, the mean is 5 and the standard deviation is 2.3. Using the formula below or Excel, find the correlation coefficient, r, for this set of tickets John drew. Answer choices are rounded to the nearest hundredth. r equals fraction numerator 1 over denominator n minus 1 end fraction sum from blank to blank of open parentheses fraction numerator x minus x with bar on top over denominator s subscript x end fraction close parentheses open parentheses fraction numerator y minus y with bar on top over denominator s subscript y end fraction close parentheses 0.50 0.56 0.70 0.75
Answer: 0.75
Step-by-step explanation:
Given the following :
Using the formula above :
___bag 1__bag 2__(bag1-m)/sd__(bag2-m)/sd2
D 1___2____4_____-0.8________-0.4
D 2___4____5_____0_________0
D 3___1____3_____-1.2_________-0.9
D 4___6___ 4_____0.8_________-0.4
D 5___7___9_____ 1.2_________ 1.7
Bag1:
Mean = 4
Standard deviation = 2.5
Bag2:
Mean = 5
Standard deviation = 2.3
Σ-0.8*-0.4 + 0 + - 1.2*-0.8 + 0.8*-0.4 + 1.2*1.7) = 3
1/ (n-1) × 3
1/(5 - 1) × 3
(1/4) × 3
0.25 * 3 = 0.75
Answer:
0.75
Step-by-step explanation:
find the solution to K+1=3k-1
Answer: k=1
Step-by-step explanation: Isolate the variable by dividing each side by factors that do not contain the variable.
I hope this helps you out! :)
Step-by-step explanation:
the answer would be k=1
A 30-N NET FORCE ON A SKATER PRODUCES AN ACCELERATION OF 0.6 M/S SQUARED. WHAT IS THE MASS OF THE SKATER. (URGENT, HELP ASAP PLEASE!!!!!!!) WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST :)
Answer:
50 kg
Step-by-step explanation:
got deleted last time so here we go again
divide net force by the accaleration to get 50
find the integer that makes this subtraction statement true -3 - ? = -5
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{2}}}}}[/tex]
Step-by-step explanation:
Let the missing integer be x
Solve for x
[tex] \sf{ - 3 - x = - 5}[/tex]
Move 3 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x = - 5 + 3}}[/tex]
The negative and positive integers are always subtracted but posses the sign of the bigger integer
[tex] \dashrightarrow{ \sf{ - x = - 2}}[/tex]
Change the signs of both sides
[tex] \dashrightarrow{ \boxed{ \sf{x = 2}}}[/tex]
Hope I helped!
Best regards! :D
the gravitational attraction between two masses varies inversely as the square of the distance between them. if the attraction force between them is 75lbs when the bodies are eight feet apart, find the attraction when the masses are twelve feet apart
Answer:
33 1/3 lb
Step-by-step explanation:
When the distance between them goes from 8 ft to 12 ft, it is 1.5 times what it was. Then the force will be multiplied by the inverse of the square of this:
(75 lb)×1/(1.5²) = 75/2.25 lb = 33 1/3 lb
At 12 feet apart, the attraction force is 33 1/3 pounds.
I will give brainliest answer
Answer:
(-2,-1)
Step-by-step explanation:
Right now, P is at (3,-4). After the translation, it would be at
(-2,-1)
(x+5)(x-5) Multiplying special case polynomials
Answer:
x^2 - 25 ✔
Step-by-step explanation:
(x+5)(x-5)
x(x-5) +5(x-5)
x^2 - 5x + 5x - 25
x^2 - 25
The following table shows the assets and liabilities of the Smith family in 2005 and 2009.
2005
home valued at $200,000
mortgage of $30,000
car valued at $25,000
car loan of $8,000
2009
home valued at $180,000
home equity loan of $18,000
car valued at $18,000
boat valued at $20,000
personal loan of $5,000
Based on the table, which of the following is true?
a. From 2005 to 2009, both assets and liabilities decreased.
b. From 2005 to 2009, both assets and liabilities increased.
c. From 2005 to 2009, assets decreased and liabilities increased.
d. From 2005 to 2009, assets increased and liabilities decreased.
Answer:
A. From 2005 to 2009, both assets and liabilities decrease.
Step-by-step explanation:
I just took the test and it was correct
From 2005 to 2009, both Assets and Liabilities decreased.
We have - A table showing the assets and liabilities of smith family in year 2005 and 2009.
We have to estimate, whether the smith family has acquired more assets or liabilities from the year 2005 to 2009.
What do you understand by Assets and Liabilities?Assets are the items that an individual own in order to extract some economic benefit from it in the future.
Liability includes the money, services or items that you owe to other person. Example : Loan, mortgage etc.
In the question given -
Assets are : Home value, Car value, boat value.Liabilities are : Car loan, Mortgage, Equity loan, personal loan.In the year 2005 :
Assets : $2,25,000.Liabilities : $38,000.In the year 2009 :
Assets : $2,18,000.Liabilities : $23,000.Hence, it can be seen from the above figures that - From 2005 to 2009, both Assets and Liabilities decreased.
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What is 85.5 divided by 6?
Answer:
14.25
Step-by-step explanation:
How many cents is equal to $ ¼?
Answer:
25 cents
Step-by-step explanation:
Answer:
25 cents
Step-by-step explanation:
25 cents times 4 is $1
think of quarters
According to the text, the specific things that people want in life are called
Answer:
your going to have to be a little more specific than that please ;-; but if you want i can answer it this way
Reach a fabled level of success that makes you untouchable.
Create a positive work/life balance.
Feel as capable as others think you are.
Be more productive with each minute of the day.
Be recognized as talented or even brilliant.
People want dreams, goals, values and expectations in their life.
What is human life?Life is the quality which people, animals, and plants have when they are not dead, and which objects and substances do not have
Given is a statement that asks about the specific things that people want in life.
The specific things that people want in life are dreams, goals, values and expectations.
Therefore, people want dreams, goals, values and expectations in their life.
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Suppose two trains leave a station at the same time, traveling in opposite directions. Train B travels 10 mph faster than Train A. In 4.5 hours, the trains are 432 miles
apart. Find the speed of each train.
Train A's speed = x
Train B's speed = x + 10
4.5(x + x + 10) = 432
Distribute both sides by 4.5
x + x + 10 = 96
Combine like terms.
2x + 10 = 96
Subtract 10 from both sides.
2x = 86
Divide both sides by 2
x = 43
Train A = x = 43 mph
Train B = x + 10 = 43 + 10 = 53 mph
Speed is the ratio of distance and time.
Speed = Distance /Time
Distance = Speed x Time
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
Example:
The speed of a car moving 4km in 2 hours is 2km per hour.
We have,
Train A:
Speed = x
Train B:
Speed = x + 10
Speed = Distance / Time
Distance = Speed x Time
At time = 4.5 hours, the train is 432 miles apart.
This can be written as,
Distance = (Speed of train A + Speed of train B) x Time
432 = (x + x + 10) x 4.5
Divide both sides by 4.5.
432 / 4.5 = 2x + 10
96 = 2x + 10
Subtract 10 on both sides.
96 - 10 = 2x
86 = 2x
Divide both sides by 2.
2x = 96
x = 96/2
x = 48
Now,
x + 10 = 48 + 10 = 58
Thus,
If Train B travels 10 mph faster than Train A.
The speed of train A is 48 mph.
The speed of train B is 58 mph.
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The square of root of 7/8?
Answer:
[tex]\frac{\sqrt{14} }{4}[/tex]
A retail study by Deloitte revealed that 54% of adults surveyed believed that plastic, noncompostable shopping bags should be banned. Suppose 41% of adults regularly recycle aluminum cans and believe that plastic, noncompostable shopping bags should be banned. In addition, suppose that 60% of adults who do not believe that plastic, noncompostable shopping bags should be banned do recycle. If an adult is randomly selected,
a. What is the probability that the adult recycles and does not believe that plastic, noncompostable shopping bags should be banned?
b. What is the probability that the adult does recycle?
c. What is the probability that the adult does recycle or does believe that plastic, noncompostable shopping bags should be banned?
d. What is the probability that the adult does not recycle or does not believe that plastic, noncompostable shopping bags should be banned?
e. What is the probability that the adult does not believe that plastic, noncompostable shopping bags should be banned given that the adult does recycle?
Answer:
a) 27.6%
b) 68.6%
c) 81.6%
d) 59.0%
e) 40.2%
Step-by-step explanation:
Let's say R = recycles, and B = believes bags should be banned.
We're given the following probabilities:
P(B) = 0.54
P(R and B) = 0.41
P(R given NOT B) = 0.60
a. Use conditional probability:
P(R given NOT B) = P(R and NOT B) / P(NOT B)
0.60 = P(R and NOT B) / (1 − 0.54)
P(R and NOT B) = 0.276
b. P(R) = P(R and B) + P(R and NOT B)
P(R) = 0.41 + 0.276
P(R) = 0.686
c. P(R or B) = P(R) + P(B) − P(R and B)
P(R or B) = 0.686 + 0.54 − 0.41
P(R or B) = 0.816
d. P(NOT R or NOT B) = 1 − P(R and B)
P(NOT R or NOT B) = 1 − 0.41
P(NOT R or NOT B) = 0.59
e. P(NOT B given R) = P(NOT B and R) / P(R)
P(NOT B given R) = 0.276 / 0.686
P(NOT B given R) = 0.402
Using conditional probability, it is found that:
a) 0.276 = 27.6% probability that the adult recycles and does not believe that plastic, noncompostable shopping bags should be banned.
b) 0.686 = 68.6% probability that the adult does recycle.
c) 0.816 = 81.6% probability that the adult does recycle or does believe that plastic, noncompostable shopping bags should be banned.
d) 0.59 = 59% probability that the adult does not recycle or does not believe that plastic, noncompostable shopping bags should be banned.
e) 0.402 = 40.2% probability that the adult does not believe that plastic, noncompostable shopping bags should be banned given that the adult does recycle.
-----------------------------------
Conditional probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.Item a:
Event A: Bags should not be banned.
Event B: Recycle.
54% believe shopping bags should be banned, thus 46% believe that it should not be banned, and [tex]P(A) = 0.46[/tex].Of those, 60% recycle, thus [tex]P(B|A) = 0.6[/tex].We want [tex]P(A \cap B)[/tex].[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)P(B|A) = 0.46(0.6) = 0.276[/tex]
0.276 = 27.6% probability that the adult recycles and does not believe that plastic, noncompostable shopping bags should be banned.
Item b:
First, we have to find the proportion that recycle, given that they believe bags should be banned. Thus:
Event A: Believe bags should be banned.Event B: Recycle.54% of adults surveyed believed that plastic, noncompostable shopping bags should be banned.
Thus [tex]P(A) = 0.54[/tex].
41% of adults regularly recycle aluminum cans and believe that plastic, noncompostable shopping bags should be banned.
Thus P(A \cap B) = 0.41[/tex]
Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.41}{0.54} = 0.7592[/tex]
The probability that recycle is the sum of:
60% of 46%(do not believe bags should be banned)75.92% of 54%(believe bags should be banned).Then:
[tex]p = 0.6(0.46) + 0.7592(0.54) = 0.686[/tex]
0.686 = 68.6% probability that the adult does recycle.
Item c:
Sum of:
Recycle(68.6%).Do not recycle but believe bags should be banned(24.08% of 54%).Thus:
[tex]p = 0.686 + 0.2408(0.54) = 0.816[/tex]
0.816 = 81.6% probability that the adult does recycle or does believe that plastic, noncompostable shopping bags should be banned.
Item d:
Sum of:
Do not recycle(31.4%).Recycle but does not believe bags should be banned(27.6%).Thus:
[tex]p = 0.314 + 0.276 = 0.59[/tex]
0.59 = 59% probability that the adult does not recycle or does not believe that plastic, noncompostable shopping bags should be banned.
Item e:
Event A: Recycle.Event B: Believes should not be banned.68.6% recycle, thus [tex]P(A) = 0.686[/tex]27.6% recycle and believe bags should not be banned, thus [tex]P(A cap B) = 0.276[/tex]Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.276}{0.686} = 0.402[/tex]
0.402 = 40.2% probability that the adult does not believe that plastic, noncompostable shopping bags should be banned given that the adult does recycle.
A similar problem is given at https://brainly.com/question/21408404