Communicate and Justify
A store made $650 on Monday. It made $233 on Tuesday
morning and $378 on Tuesday afternoon.
Leah says the store made more money on Tuesday.
Her work is shown at the right.
1. What is Leah's argument? How does she support it?
2. Tell how you can analyze Leah's reasoning.
3. Does Leah's reasoning make sense?
Answers
Leah's argument is that the rounded up figures for Tuesday sales are greater than the sales for Monday. She supports it by summing up the sales figures.
Leah's reasoning is wrong because she rounded up $ 233 to $ 300 instead of to $ 200.
Leah's reasoning therefore does not make sense.
What should Leah have done ?Leah attempts to round the Tuesday sales figures to the nearest 100. In doing so, she rounded $ 233 to $ 300 instead of $ 200 which was the closest.
If she had done so, the result would be :
= 200 + 400
= $ 600
This would then show that Monday's figures were higher than Tuesday.
Find out more on stores at https://brainly.com/question/1885513
#SPJ1
Related Questions
In order to reduce your end-of-season inventory of gloves, you create grab bags that each contain 2 pairs of gloves. You have 20 pairs of lined gloves that cost $25 and 100 pairs of knit gloves that cost $12. Your assistant made 60 grab bags wheres 2 bags have two pairs of lined gloves 16 bags have one pair of lined gloves and one pair of knit gloves and 42 bags have two pairs of knit gloves.
Compute the expected value of each grab bag the assistant made, rounded to the nearest 50.01_________
If you sell these for $29.99 and sell all 60 grab bags, how much total profit will you make? Give your answer to the nearest 50.01
Answers
The expected value of each grab bag is $1.67 for two pairs of lined gloves, $9.87 for one pair of lined gloves and one pair of knit gloves, and $16.80 for two pairs of knit gloves. the total profit made from selling all 60 grab bags is $149.40.
For the 2 bags that have two pairs of lined gloves, the total cost is:
2 pairs * $25/pair = $50
Total gloves = 4
For the 16 bags that have one pair of lined gloves and one pair of knit gloves, the total cost is:
1 pair lined gloves * $25/pair + 1 pair knit gloves * $12/pair = $37
Total gloves = 4
For the 42 bags that have two pairs of knit gloves, the total cost is:
2 pairs * $12/pair = $24
Total gloves = 4
The probability of selecting a bag with two pairs of lined gloves is:
2/60 = 1/30
The probability of selecting a bag with one pair of lined gloves and one pair of knit gloves is:
16/60 = 4/15
The probability of selecting a bag with two pairs of knit gloves is:
42/60 = 7/10
The expected value of a bag with two pairs of lined gloves is:
(1/30) * $50 + (0) * $37 + (0) * $24 = $1.67
The expected value of a bag with one pair of lined gloves and one pair of knit gloves is:
(4/15) * $37 + (0) * $50 + (0) * $24 = $9.87
The expected value of a bag with two pairs of knit gloves is:
(7/10) * $24 + (0) * $50 + (0) * $37 = $16.80
The total cost of the gloves used to make the grab bags is:
2 bags * $50/bag + 16 bags * $37/bag + 42 bags * $24/bag = $1,650
The total revenue from selling all 60 grab bags is:
60 bags * $29.99/bag = $1,799.40
Therefore, the total profit is:
$1,799.40 - $1,650 = $149.40
Learn more about expected value here:
https://brainly.com/question/10675141
#SPJ4
What will be the
surface area of the
ramp
50 in.
60 in.
O 3672 inches squared
O 5760 inches squared
O 7392 inches squared
O 2880 inches squared
Answers
The surface area of the ramp is 3672 in².
Option A is the correct answer.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The ramp consists of three rectangular surfaces and two triangles.
Now,
Triangle.
Base = 48 in
Height = 14 in
Area of a triangle.
= 1/2 x base x height
= 1/2 x 48 x 14
= 48 x 7
= 336 in²
Rectangle.
Since the back and the bottom rectangle are not included.
Front rectangle.
Length = 50 in
Width = 60 in
Area = 50 x 60
Area = 3000 in²
Now,
The surface area of the ramp.
= 300 + 2 (336)
= 3000 + 672
= 3672 in²
Thus,
The surface area of the ramp is 3672 in².
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answers
Answer:
[tex]x=-3,x=-3,x=7[/tex]
Step-by-step explanation:
[tex]We\ know\ that\ the\ roots\ of\ an\ equation\ are\ its\ intercepts\ cut\ on\ the\ x-axis.\\We\ can\ observe\ that\ the\ graph\ of\ y=f(x)\ cuts\ the\ x\ axis\ at\ the\ point (7,0)\\ and\ touches\ the\ x-axis\ at\ (-3,0).\\[/tex]
[tex]Hence,\\The\ curve\ represents\ a\ cubic\ polynomial\ with\ double\ roots\ (-3,0),(-3,0)\\ as\ well\ as\ a\ distinct\ root:\ (7,0)[/tex]
Hunter is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Hunter's test score (out of 100) if he got 5 questions wrong? What would be his score if he got � x questions wrong?
Answers
For answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be f(x)=100-5*x.
What is a function?A function is defined as the relationship between input and output, where each input has exactly one output. The inputs are the elements in the domain and the outputs are elements in the co-domain.
Hunter is taking a multiple choice test with a total of 100 points available.
Each question is worth exactly 5 points,
From that the number of questions in the test is ,[tex]\frac{100}{5}=20[/tex]questions
Hunter's test score (out of 100) if he got 5 questions wrong,
20-5=15 questions correct.
Each question carries 5 marks, then 15*5= 75 marks.
Hunter score will be 75 marks.
And again each question carries 5 marks, If hunter answers x questions wrong his score will be f(x)=100-5*x.
It is a linear equation.
Hence, for answering 5 questions wrong Hunter's score is 75 and for for answering x question wrong his score will be f(x)=100-5*x.
Learn more about functions here:
https://brainly.com/question/29631554
#SPJ9
Question 5.4° A school with 20 professors forms 10 committees, each containing 6 profes- sors, such that every professor is on exactly 3 committees. Prove that it is possible to select a distinct representative from each committee.
Answers
Since there are 20 professors and each professor is on exactly 3 committees, there must be a total of 60 committee positions.
Let's assume that it is not possible to select a distinct representative from each committee. This means that there must be some committee that does not have a distinct representative.
Let's consider the professors on this committee. Since each professor is on exactly 3 committees, each of the professors on this committee must also be on 2 other committees.
Let's consider the 2 other committees for each of the professors on this committee. Since there are 6 professors on the committee, there are a total of 12 other committees to consider.
Each of these 12 committees must have a representative chosen from the remaining 14 professors, since we have assumed that it is not possible to select a distinct representative from the original 10 committees.
However, since there are only 14 professors remaining, and each professor can only be on 3 committees, it is not possible to choose a representative from all 12 of these committees without choosing at least one professor to be on 4 committees. This is a contradiction, since we have assumed that each professor is on exactly 3 committees.
Therefore, our assumption that it is not possible to select a distinct representative from each committee must be false, and it is indeed possible to do so.
You can read more about probability at https://brainly.com/question/24756209
#SPJ4
61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94 WHAT IS THE RANGE
Answers
The value of the range is 33
How to determine the rangeFrom the question, we have the following parameters that can be used in our computation:
61, 61, 63, 64, 65, 66, 66, 66, 67, 68, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 94
To find the range of a set of numbers, we need to subtract the smallest number from the largest number.
In this set of numbers:
The smallest number is 61 and the largest number is 94.
Therefore, the range of this set of numbers is:
94 - 61 = 33
Hence, the range of the given set of numbers is 33.
Read more about range at
https://brainly.com/question/11341692
#SPJ1
I am having a very hard time figuring this out can someone help me with #5 please
Answers
What is the equation of the line that passes through the point (-8, 6) and has a slope
of -1/4?
Answers
Answer:
= 4y + x - 16 = 0.
Step-by-step explanation:
Point are (-8,6)
where
x1 = -8 and y1 = 6
the equation o the line is given by the formula
[tex] = \frac{y - y1}{x - x1} = m[/tex]
where (m) is the gradient
the gradient (m) = -1/4
therefore the equation of the line
[tex] \frac{y - y1}{x - x1} = m \\ = \frac{y - 6}{x - ( - 8)} = \frac{ - 1}{4} \\ = \frac{y - 6}{x + 8} = \frac{ - 1}{4} \\ = 4(y - 6) = - 1(x + 8) \\ = 4y - 24 = - x - 8 \\ = 4y = - x - 8 + 24 \\ = 4y = - x + 16 \\ = 4y + x - 16 = 0.[/tex]
therefore the equation of the line is = 4y + x - 16 = 0.
note// y and x where not given any value.
Assume there are 11 homes in the Quail Creek area and 8 of them have a security system. Three homes are selected at random:
What is the probability all three of the selected homes have a security system? (Round your answer to 4 decimal places.)
What is the probability none of the three selected homes has a security system? (Round your answer to 4 decimal places.)
What is the probability at least one of the selected homes has a security system? (Round your answer to 4 decimal places.)
Are the events dependent or independent?
Dependent
Independent
Joint
Answers
The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.
The probability of all three of the selected homes having a security system is 0.3277, which can be calculated using the formula P(A and B and C) = P(A) x P(B) x P(C). In this case, P(A) is the probability of the first home having a security system, which is 8/11 (since 8 out of 11 homes have a security system). P(B) is the probability of the second home having a security system, which is 7/10 (since 7 out of 10 remaining homes have a security system). P(C) is the probability of the third home having a security system, which is 6/9 (since 6 out of 9 remaining homes have a security system). Therefore, P(A and B and C) = (8/11) x (7/10) x (6/9) = 0.3277.
The probability of none of the three selected homes having a security system is 0.0414, which can be calculated using the formula P(A and B and C) = P(A') x P(B') x P(C'). In this case, P(A') is the probability of the first home not having a security system, which is 3/11 (since 3 out of 11 homes do not have a security system). P(B') is the probability of the second home not having a security system, which is 3/10 (since 3 out of 10 remaining homes do not have a security system). P(C') is the probability of the third home not having a security system, which is 3/9 (since 3 out of 9 remaining homes do not have a security system). Therefore, P(A and B and C) = [tex](3/11) x (3/10) x (3/9) = 0.0414[/tex].
The probability of at least one of the selected homes having a security system is 0.9709, which can be calculated using the formula P(A or B or C) = 1 - P(A' and B' and C'). In this case, P(A' and B' and C') is the probability of none of the three selected homes having a security system, which is 0.0414 (as calculated above). Therefore, P(A or B or C) = 1 - 0.0414 = 0.9709.
The events are dependent because each selection is affected by the previous selections. For example, the probability of the second home having a security system is affected by whether or not the first home had a security system. If the first home had a security system, then there are 7 out of 10 remaining homes with a security system; if the first home did not have a security system, then there are 8 out of 10 remaining homes with a security system.
The probability of all three of the selected homes having a security system is 0.3277, the probability of none of the three selected homes having a security system is 0.0414, and the probability of at least one of the selected homes having a security system is 0.9709. The events are dependent.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Cricket is a sport played with a ball and a rectangular bat. Players protect themselves with batting gloves and other equipment. The table shows the weights, in pounds, of several pieces of cricket equipment. CRICKET EQUIPMENT Equipment Ball Glove Bat Weight (pounds) 0.35 0.77 2.63 A cricket bag holds 4 balls, 2 gloves, and 2 bats. What is the total weight, in pounds, of the balls, gloves, and bats in the cricket bag? Show your work.
Answers
The total weight in the bag is given as follows:
8.2 pounds.
How to obtain the total weight?The total weight is obtained applying the proportions in the context of the problem.
From the table, the weight of each equipment is given as follows:
Ball: 0.35 pounds.Glove: 0.77 pounds.Bat: 2.63 pounds.Hence the total weight of a bag with 4 balls, 2 gloves, and 2 bats is given as follows:
4 x 0.35 + 2 x 0.77 + 2 x 2.63 = 8.2 pounds.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
A cliff diver plunges from a height of 100 ft above the water surface. The distance the diver falls in seconds is given by the function d(t)=16t^2.a.) after how many seconds will the diver hit the water?b.) with what velocity does the diver hit the water?
Answers
(a) The diver hit the water after 2.5 seconds
(b) The diver hit the water with a velocity of 80 ft/s
How to find the diver's velocity?
Since the cliff diver plunges from a height of 100 ft above the water surface and the distance the diver falls in seconds is given by the function d(t) = 16t². We can say d(t) = 100ft. So we have:
d(t) = 16t² = 100
t² = 100/16
t² = √(100/16)
t = 10/4
t = 2.5 seconds
The derivative of the distance will give us the velocity. That is:
v(t) = d'(t) = 32t
Substitute t =2.5 into v(t):
v(2.5) = 32(2.5)
v(2.5) = 80 ft/s
Learn more about velocity on:
https://brainly.com/question/25749514
#SPJ1
Answer question on the picture attached
Answers
The average rate of change over the interval (-2,0) is -2.
What is the average rate of change?The average rate of change describes how quickly one quantity changes in comparison to another. It indicates how much the function changed per unit during the specified interval.
Given that the interval is (-2,0). The coordinate of the point from the interval -2,0 is ( -2 , 4 ).
The average rate of change will be calculated as:-
Rate of change = ΔY / ΔX
Rate of change = ( 4 - 0 ) ( -2 - 0 )
Rate of change = -2
Therefore, the average rate of change will be -2.
To know more about the average rate of change follow
https://brainly.com/question/8728504
#SPJ1
Subtract the polynomials (35 + 83) − (72 − 63). Show all work
Answers
Answer:
35 + 83) − (72 − 63) = 109
Step-by-step explanation:
To subtract the polynomials (35 + 83) − (72 − 63), we'll simplify each term in the polynomials first and then subtract the corresponding terms:
(35 + 83) = 118
(72 - 63) = 9
Now we can subtract the corresponding terms:
118 - 9 = 109
So the result of (35 + 83) − (72 − 63) is 109.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Answer:
Okay first do what is in the parenthesis:
35 + 83 = 118
72 - 63 = 9
Now subtract:
118 - 9 = 109
The answer is: 109
Step-by-step explanation:
Hope it helps!
I need help on confused I don’t get it once so ever
Answers
The value of x is given as follows:
x = 34.
The angle measures are given as follows:
<B = 102º. <C = 78º.How to obtain the angle measures?In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.
Angles A and B are consecutive, hence the value of x is obtained as follows:
2x + 10 + 3x = 180
5x = 170
x = 34.
Then the angle measures are given as follows:
<B = 3(34) = 102º. <C = 78º. (consecutive with B, 180 - 102 = 78).More can be learned about angle measures at https://brainly.com/question/2046046
#SPJ1
8. At a home supply store, bags of concrete mix are on sale. Every third bag that you buy is discounted by 75%. A bag of concrete mix sells for $3.88. How much will you spend if you buy 14 bags of concrete mix? 75
Answers
The total amount spend is 391.88
What is discount?The noun discount refers to an amount or percentage deducted from the normal selling price of something.
If 14 bag of mix cement are bought and and every third bag is discounted
no of bag on discount = 14/3 = 4 remainder 2
therefore 4 bags will be on discount
discount on a bag = 3.88× 75/100
= 291/100 = 2.91
therefore each bag on discount will cost = 3.88 - 2.91
= 0.97
for 4 bags = 0.97 ×4 = 3.88
for remaining 10 bags = 3.88 × 10
= 388
therefore the total amount = 388+3.88
= $391.88
learn more about discount from
https://brainly.com/question/7459025
#SPJ1
Referring to the figure, evaluate the expression shown
when a = 3, b = 7, c = 2
Answers
Answer:-17
Step-by-step explanation:
b=7,then
b^2=49
square root of 49-4*3*2=-17
Which pair of values are equivalent? choose two correct answers
Answers
Answer:
first 2 pairs
Step-by-step explanation:
[tex]\frac{6}{100}[/tex] = 6 ÷ 100 = 0.06 ← equivalent
[tex]\frac{7}{10}[/tex] = 7 ÷ 10 = 0.7 ← equivalent
[tex]\frac{5}{10}[/tex] = 5 ÷ 10 = 0.5 ≠ 0.05
[tex]\frac{32}{100}[/tex] = 32 ÷ 100 = 0.32 ≠ 3.2
I don't know what answer please help quickly
Answers
The inequality changes if both sides of the expressions are switched or multiplied by a negative sign
Changing the signs of an inequality.Inequalities are expressions not separated by an equal sign.
From the given inequalities
For -10.5 < 3e
3e > -10.5
e > -10.5/3
This shows that the sign changes
For b/6≤ 7
b ≤ 6(7)
b≤ 42
The inequality sign does not change.
For the inequality -4.5c > 9
4.5c < -9
c < -9/4.5
c < -2
The inequality sign changes.
For the inequality -21/5 ≤ -5/2 d
21/5 ≥ 5/2d
5/2d≤ 21/5
d ≤42/25
The inequality sign does not change
Learn more on inequality here: https://brainly.com/question/24372553
#SPJ1
If ABCD is a parallelogram,
find the value of x.
7x + 2
9x-28
Answers
Solve
Solution
X=15
I need help it’s 9th grade algebra 1
Answers
The system of equations has one solution, which is (2, 3).
What is the Solution to the Graphed System of Equations?To find the solution to a graphed system of equations, you need to find the points where the graphs of the two equations intersect. These points represent the coordinates of the solution, which are the values of x and y that make both equations true simultaneously.
The system of equations as shown in the graph has one solution, which is: (2, 3). This is because the liens intersect at the point (2, 3).
Learn more about solution to system of equations on:
https://brainly.com/question/2948266
#SPJ1
Calculate (8.42 x 109) − (2.35 x 108).
A. 8.185 x 108
B. 8.185 x 109
C. 6.07 x 101
D. 6.07 x 109
Answers
Answer:
it could be D but D gives us 661.63 C gives us 613.07 B gives us 892.165 and A gives us 883.98 so your closes answer is D
Step-by-step explanation:
8.42x109=917.78-253.8=663.98
which of the following are true statements? (check all that apply)
Answers
The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
Given that line passes through (0,0) and (2,1)
(Note that any two points are sufficient to determine the equation of the line)
The slope = change in y/change in x
= (1-0)/(2-0)
= 1/2
Hence answers are:
Variable y varies directly with x. (if x increases y also increases and vice versa)
The constant of variation = slope of line = 1/2
The constant of variation is 2 is wrong since slope = 1/2
The variable y does not vary directly with x is wrong since when x increases by 1 unit y increases by 1/2 unit for all real x.
To learn more on slope click:
brainly.com/question/3605446
#SPJ1
I need help with this question 632/572(127+276)
Answers
Hi! The answer would be 445.272727273
Glad I can help :)
Complete the sentence that describes the slope from the graph below.
Average Minutes to Clean up a Car Accident
200
190
180 y=0.7794x-1435.5
170
160
150
140
130
120
110
100
90
80
70
60
50
Every
1970
1975
1980
1985
1990
1995
minutes.
2000 2005
after 1970, the average number of
to clean up an accident has
2010
2015
by
2020
Answers
The Average Minute to Clean up a Car is 0.7794.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The equation of the graph is y=0.7794x-1435.5.
When we compare the equation with the standard form of equation y=mx+b.
The m will be 0.7794 which means slope is 0.7794.
Hence, 0.7794 is the Average Minute to Clean up a Car.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ1
Find the interest rate (with annual compounding) that makes the statement true. Round to the nearest tenth when necessary. $4081 grows to $8404.54 in 21 years 3.5% o 3% o 6.5% 6%
Answers
The interest rate that can explain how $4081 grew to $8404.54 in 21 years with annual compounding is option (a) 3.5%, rounded to the nearest tenth.
The interest rate and the compounding frequency determine the growth of the initial amount over time. In this problem, we need to find the interest rate that can explain how an initial amount grew to a specific amount over a certain number of years.
The problem asks us to find the interest rate that can explain how an initial amount of $4081 grew to $8404.54 in 21 years with annual compounding. We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^{nt}[/tex]
where A is the future value of the investment, P is the initial amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we know that P = $4081, A = $8404.54, n = 1 (annual compounding), and t = 21. We need to find the value of r that makes the equation true.
We can rearrange the formula to solve for r:
[tex]r = n[(A/P)^{1/nt} - 1][/tex]
Substituting the known values, we get:
[tex]r = 1[(8404.54/4081)^{1/(1*21)} - 1][/tex]
r = 0.0353 or 3.53%
This means that if the initial amount was invested with an annual interest rate of 3.5%, it would have grown to the given future value after 21 years.
To know more about compound interest here.
https://brainly.com/question/29335425
#SPJ4
-8c + 13 ≥ 47 solve the inequality
Answers
Answer: c[tex]\leq[/tex]-17/4
Step-by-step explanation:
-8c+13[tex]\geq[/tex]47
-8c[tex]\geq[/tex]47-13
-8c[tex]\geq[/tex]34
c[tex]\leq[/tex] -17/4 or -4 1/4
Write the ratio as a fraction: $42 for 81 juice boxes. Simplify your answer.
Answers
Answer: The ratio $42/81$ can be simplified by dividing both the numerator and denominator by the greatest common factor of 42 and 81, which is 9.
$42/81 = (42 \div 9) / (81 \div 9) = 4/9$
So, the ratio $42/81$ can be expressed as the simplified fraction $\frac{4}{9}$.
Step-by-step explanation:
Ayden is buying bagels for a family gathering. Each bagel costs $2.00. Answer the
questions below regarding the relationship between the total cost and the number of
bagels purchased.
Answers
The total cost of the bagels will depend on the number of bagels purchased. If Ayden buys one bagel, the total cost will be $2.00. If Ayden buys two bagels, the total cost will be $4.00. The total cost increases by $2.00 for each additional bagel purchased. So, if Ayden buys three bagels, the total cost will be $6.00. If Ayden buys four bagels, the total cost will be $8.00. In general, the total cost of the bagels will be equal to the number of bagels purchased multiplied by $2.00.
I need help with these questions. Excuse my failed attempts.
Answers
The measure of the angle B is found to be 184 degrees.
Explain about the co interior angles?When a transversal intersects two parallel lines, co-interior angles result between the lines. On the very same face of the transversal, the two angles always sum to 180 degrees.The angles given in question:
line AB || DC
∠B = 9x + 2
∠C = 5x - 4
So,
∠B + ∠C = 180 ( co interior angles )
9x + 2 + 5x - 4 = 180
9x - 2 = 180
9x = 180 + 2
x = 182/9
Then,
∠B = 9x + 2
∠B = 9*182/9 + 2
∠B = 182 + 2
∠B = 184
Thus, the measure of the angle B is found to be 184 degrees.
To know more about the co interior angles, here
https://brainly.com/question/26981078
#SPJ1
The diagram of the correct question is attached.
Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.7 and P(B) = 0.4.
A. Could it be the case that P(A ∩ B) = 0.5? Pick one:
i. Yes, this is possible. Since B is contained in the event A ∩ B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
ii. Yes, this is possible. Since A ∩ B is contained in the event B, it must be the case that P(B) ≤ P(A ∩ B) and 0.5 > 0.4 does not violate this requirement.
iii. No, this is not possible. Since B is equal to A ∩ B, it must be the case that P(A ∩ B) = P(B). However 0.5 > 0.4 violates this requirement.
iiii. No, this is not possible. Since B is contained in the event A ∩ B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
v. No, this is not possible. Since A ∩ B is contained in the event B, it must be the case that P(A ∩ B) ≤ P(B). However 0.5 > 0.4 violates this requirement.
B. From now on, suppose that P(A ∩ B) = 0.3. What is the probability that the selected student has at least one of these two types of cards?
C. What is the probability that the selected student has neither type of card?
D. In terms of A and B, the event that the selected student has a Visa card but not a MasterCard is A ∩ B' . Calculate the probability of this event.
E. Calculate the probability that the selected student has exactly one of the two types of cards.
Answers
Option A. No, this is not possible. Since A and B are not mutually exclusive events, we have P(A ∩ B) = P(A) + P(B) - P(A ∪ B), where P(A ∪ B) is the probability that the selected student has either a Visa or a MasterCard.
Since 0.5 > 1 - P(A ∪ B) = P(A') ∩ P(B'), we must have P(A') ∩ P(B') < 0, which is impossible.
B. The probability that the selected student has at least one of these two types of cards is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.4 - 0.3 = 0.8.
C. The probability that the selected student has neither type of card is given by P(A' ∩ B') = 1 - P(A ∪ B) = 1 - 0.8 = 0.2.
D. The probability of the event A ∩ B' is given by P(A ∩ B') = P(A) - P(A ∩ B) = 0.7 - 0.3 = 0.4.
E. The probability that the selected student has exactly one of the two types of cards is given by P((A ∩ B') ∪ (A' ∩ B)) = P(A ∩ B') + P(A' ∩ B) = 0.4 + 0.1 = 0.5.
You can read more about probability at https://brainly.com/question/13604758
#SPJ4