Answer:
hi
Step-by-step explanation:
1. Circle the two boats you picked for your trip.
the yacht and the tall ship (aka the pirate ship)
2. Make sense of the problem.
what do you know?
The tall ship makes the trip in 10 hours. The yacht makes the trip in 2.5 hours. The tall ship is 30 knots slower than the yacht.
what do you want to find out?
How fast is each boat traveling in knots (nautical miles per hour)?
what kind of answer do you expect?
probably just some numbers like 10 miles per hour or 40 miles per hour
Writing some expressions
3. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time. (2 points)
the expression would be D = 10(x-30), d is the distance. it could also be simplified to 10x - 300
4. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island. (2 points)
so the yacht's speed would be S = x knots, s is for speed.
5. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time. (2 points)
the distance returning from the island would be D = 2.5x.
6. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island. (1 point)
10x - 300 = 2.5x
7. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)
10x - 300 = 2.5x
10x - 300 + 300 = 2.5x + 300
10x -2.5x = 300
7.5x = 300
x = 40
x is the speed of the yacht. (40 nautical miles per hour)
8. How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)
the yacht travels at 40 nautical miles per hour and the tall ship travels at 100 (10x - 300) nautical miles per hour.
9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.
Find the speed for the kayak. Use one of these facts to help.
The steamboat's speed is 4 less than 8 times the speed of the kayak.
The tall ship's speed is 1 more than 3 times the speed of the kayak.
The yacht's speed is 5 less than 15 times the speed of the kayak.
Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)
the equation for the speed of the kayak is 40 = 15x - 5, which in this case, x is the speed of the kayak
40 = 15x - 5
40 + 5 = 15x -5 + 5
45 = 15x
x = 3
therefore, the speed of the kayak is 3 nautical miles per hour.
10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.
It's 2:00 p.m. now, and your boat leaves the island at 7:30 p.m. Will you be able to kayak to the reef and back by then?
If so, how long will you have to spend at the reef?
If not, how late will you be for the return trip?
Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)
the distance to the island is 100 nautical miles, so the expression would be 100 = 20x -40, with x being the distance to the reef.
we can solve for x by doing:
100 = 20x -40
100 + 40 = 20x - 40 + 40
140 = 20x
140 / 20 = x
x = 7
so the distance from my starting point to the reef will be 7 nautical miles, and the distance from the island to the reef would be 93 nautical miles.in that case, I would be like a day and a half late, but if you are trying to say that the ship is waiting for me at the starting point of my "adventure", then I would not be late if I kayak from my starting point to the reef, in fact, I could stay at the reef for like 50 min, because:
7 / 3 = 2 1/3 hours.
2 1/3 x 2 = 4 2/3 hours or 280 min. (to the reef and back)
7:30 p.m. - 2:00 p.m. = 5 1/2 hours or 330 min. (how much time I have till the ship leaves)
330 - 280 = 50 min. (how many min I can spend at the reef)
This is for the people that want to find out how to find the distance to the island.
jamescodwell answered all the questions correctly btw.
Step-by-step explanation:
Distance travelled divided by trip time = speed
trip time multiplied by speed = distance travelled
So the steamboat makes the trip in 5 hours travelling at a speed of 20 knots.
5 * 20 = 100 The trip to the island is 100 nautical miles.
Which is the correct interpretation of the x-intercepts of the function? Their difference is the number of the most promo codes in a single day. Their sum is the total number of days the number of codes increased. Their sum is the total number of promo codes the publicist is releasing before the new record. Their difference is the number of days the first promo codes were released before the new record.
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
provide brainliest plz I need that bread
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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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
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 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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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)
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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Write a system of inequalities to match the graph and prove that the coordinate point (-10, -14) is in the solution set
Answer:
y < x - 2
y ≥ 2x + 5
Step-by-step explanation:
For the equation of the dotted line,
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since the dotted lines passes through the points (-7, -9) and (2, 0)
Slope = [tex]\frac{-9-0}{-7-2}[/tex]
[tex]m_1[/tex] = 1
Therefore, equation of the line passing through (2, 0) and slope = 1 will be,
y - y' = m₁(x - x')
y - 0 = 1(x - 2)
y = x - 2
Since, shaded area is below the dotted line,
y < x - 2 will be the inequality.
Slope of the solid line passing through (-7, -9) and (0, 5) is,
[tex]m_2=\frac{-9-5}{-7-0}[/tex]
= 2
Therefore, equation of the line passing through (0, 5) and slope = 2 will be,
y - 5 = 2(x - 0)
y = 2x + 5
Since, the given line is a solid line and shaded area is above the line,
y ≥ 2x + 5 will be the inequality.
Since, (-10, -14) is lying in the common shaded area of both the inequalities, it will be the solution set of the graphed inequalities.
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
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
3 x² - 2x-1=0
solve using quadratic formula
Answer:
The answer to your question: x is -1/3 or 1
The square of root of 7/8?
Answer:
[tex]\frac{\sqrt{14} }{4}[/tex]
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.
If I have a 9ft plank how many 3/4 pieces can I get
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
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:
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)
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].
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
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:
(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
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
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.
What is 85.5 divided by 6?
Answer:
14.25
Step-by-step explanation:
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]
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
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.
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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
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!