Answer:
A)P(A ∩ B) cannot be equal to 0.5.
B)P(A ⋃ B) = 0.7
C)P[(A ∪ B)'] = 0.3
D)P(A ∩ B') = 0.3
E)probability that the selected student has exactly one of these two types of cards = 0.4
Step-by-step explanation:
A) We want to find out if P(A ∩ B) = 0.5
Now, this value is not possible because the probability of intersection of two events can not be greater than the probability of each individual event.
We are told that P(A) = 0.6 and P(B) = 0.4.
Due to the fact that the probability of B is less than 0.4 which is less than 0.5, It means that the intersection of A and B can't be greater than 0.4.
Thus, P(A ∩ B) cannot be equal to 0.5.
B) Now, P(A ∩ B) = 0.3
The probability that the selected student has at least one of these two types of cards would be P(A ⋃ B)
Now, this is expressed as;
P(A ⋃ B) = P(A) + P(B) − P(A ∩ B)
Thus,
P(A ⋃ B) = 0.6 + 0.4 - 0.3
P(A ⋃ B) = 0.7
C) Probability that the selected student has neither type of card would be expressed as; P[(A ∪ B) ' ]
Thus is further expressed as;
P[(A ∪ B) ' ] = 1 − P(A ∪ B)
P[(A ∪ B)'] = 1 - 0.7
P[(A ∪ B)'] = 0.3
D) We want to describe in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.
This is simply an intersection of event A and compliment of event B. Thus, it implies that we we will remove the events when student has both types of cards from the events of A. This probability is expressed as P(A ∩ B')
Thus gives;
P(A ∩ B') = P(A) - P(A ∩ B)
P(A ∩ B') = 0.6 - 0.3
P(A ∩ B') = 0.3
E) Now, we want to find the probability that the selected student has exactly one of these two types of cards.
This is simply the addition of intersection of event A with compliment of event B and intersection of event B with compliment of event A . The probability is given by:
P(A ∩ B') + P(A' ∩ B)
Expanding this gives;
P(A ∩ B') + P(B) - P(A ∩ B)
Plugging in the relevant values gives;
0.3 + 0.4 - 0.3 = 0.4
Determine the value of the variables a, b, and when simplifying and evaluating the expression. 3/^8 3/^4 =a^b= c
a=
b=
c=
Answer:
A=3
B=4
C=81
Step-by-step explanation:
Just did it
Answer:
a =
✔ 3
b =
✔ 4
c =
✔ 81
Lavender grew from 38 inches to 52 inches in one month; what was
the % increase in growth ?
Please answer this ASAP please!!!
Amelia rolls two fair number cubes numbered from 1 to 6. She first defines the sample space as shown below: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) Based on the sample space, what is the probability of getting a total of 4? Just say a simple answer, please.
Answer:
1/12
Step-by-step explanation:
There are 36 possible outcomes
Out of the 36 there are only 3 where the sum is 4 that is (1,3),(2,2),(3,1)
Hence probability= 3/36 which equals to 1/12
Answer:
you just add them together
Classify each sample as random, systematic, stratified, or cluster
1. In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years.
2. Every seventh customer entering a shopping mall is asked to select his or her favorite store.
3. Nursing supervisors are selected using random numbers in order to determine annual salaries.
4. Every hundredth hamburger manufactured is checked to determine its fat content.
5. Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year.
Answer:
(1) Cluster sample
(2) Systematic sample
(3) Random sample
(4) Systematic sample
(5) Stratified sample
Step-by-step explanation:
A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.
Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.
Stratified sampling is a kind of sampling in which whole-population is distributed into homogeneous subgroups before one takes a sample. These subgroups are called strata which is mutually exclusive or related.
In this process the population members cannot be excluded.
Cluster Sampling is a method to randomly select samples from a population that is too enormous for simple random sampling.
Using cluster sampling, the experimenter distributes the entire-population into distinct groups, called clusters. Then, a simple random sample of clusters is chosen from the population. Then the experimenter performs the analysis on data from the sampled clusters.
Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and a static, periodic interval.
Consider all the definitions of different types of samples.
(1) Cluster sample
(2) Systematic sample
(3) Random sample
(4) Systematic sample
(5) Stratified sample
Using sampling concepts, it is found that the classifications are:
1. Cluster
2. Systematic
3. Random
4. Systematic
5. Stratified
Samples are classified as:
Random: All the options into a hat and drawn some of them. Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed. Stratified: Also divides the population into groups. However, only some elements of each group are surveyed.Item 1:
Teachers divided into groups according to their school, and all teachers are interview, hence Cluster sampling is used.
Item 2:
Every 7th customer, that is, every kth customer, hence Systematic sampling is used.
Item 3:
Random numbers, hence, Random sampling is used.
Item 4:
Every 100th customer, that is, every kth customer, hence Systematic sampling is used.
Item 5:
Four groups, then 10 for each group are selected, that is, a few members, hence Stratified sampling it used.
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Korey is planning to open a comic book store. His store will cost $12,500 to open and will come with a $8,000 total annual operational cost. If his store makes $12,000 in profit during the first year, and profits increase by 6% each year from then, how long will it take for Korey to see an overall profit in his business (where total profits exceed total expenses)? a. Korey will see an overall profit in his first year of business. b. Korey will see an overall profit in his second year of business. c. Korey will see an overall profit in his third year of business. d. Korey will see an overall profit in his fourth year of business.
Answer:
c. Korey will see an overall profit in his third year of business
Step-by-step explanation:
His cost for first year
= 12500+8000
=$ 20500
Profit first year= $12000
Net Profit first year= -$8500
Second year cost= $8000
Profit second year
= 12000+12000(0.06)
= 12000+720
=$ 12720
Net profit second year = -8500+12720-8000
= -3780
Third year
Cost = $8000
Profit= 12720+12720(0.06)
Profit=$13483.2
Net profit= 13483.2-8000-3780
Net profit= $1703.2
Korey will see an overall profit in his third year of business.
What is profit?The amount of money earned by any seller on the cost price is called the yield.
His cost for the first year
= 12500 + 8000
=$ 20500
Profit first year= $12000
Net Profit first year= -$8500
Second year cost= $8000
Profit second year
= 12000+12000(0.06)
= 12000+720
=$ 12720
Net profit second year = -8500+12720-8000
= -3780
Profit for Third-year
Cost = $8000
Profit= 12720+12720(0.06)
Profit=$13483.2
Net profit= 13483.2-8000-3780
Net profit= $1703.2
Therefore Korey will see an overall profit in his third year of business.
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The answer to the problem rhenbehejrjrjrhjfjf
Through my trials and tribulations I have decided that the answer is.
Y E S
The U.S. Department of Agriculture reported that out of every milk drinkers drink skim milk. If a storeowner orders gallons of milk, how many should be skim? Round the answer to the nearest gallon. To supply all of the skim milk drinkers, out of the gallons of milk ordered, gallons were skim milk.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The value is [tex]s = 12 \ gallons[/tex]
Step-by-step explanation:
From the question we are told that
The number of milk drinkers considered is [tex]m = 100[/tex]
The number of skim milk drinkers [tex]n = 50[/tex]
The gallons of milk supplied is q = 23 gallons
Generally the proportion of skim milk drinkers is mathematically represented as
[tex]p = \frac{n}{m}[/tex]
[tex]p = 0.5[/tex]
Generally the gallons of milk order that is skim milk is mathematically represented as
[tex]s = 0.5 * 23[/tex]
=> [tex]s = 12 \ gallons[/tex]
Which is a factor of 5x2 − 15x − 20?
Answer:
x= -1, x=4
Step-by-step explanation:
5x²-15x-20
5x²-20x+5x-20=0
5x(x-4) +5(x-4)
(5x+5) (x-4) =0
5x=-5 or x=4
x= -5/5. or x=4
x= -1 or x=4
An airplane cruises 1 kilometer in 1 12 of a minute. What is its cruising speed?
Answer:
Step-by-step explanation: 12 ur welcome
Speed is Distance traveled/time, then 12 kilometer per min is the cruising speed of airplane when airplane cruises 1 kilometer in 1 12 of a minute.
What is speed?Speed=Distance traveled/time
An airplane cruises 1 kilometer in 1 12 of a minute. We need to find the speed.
Given distance=1 km
time=1/12 min
We need to find speed.
Speed=Distance traveled/time
=1/(1/12)
=1*12/1
=12kilometerperminute
Therefore 12 kilometer per meter is the speed required.
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3^3-5(6) simplify this equation
Answer:
-3
Step-by-step explanation:
27-30
Answer:
-3
Step-by-step explanation:
3³-5(6)
3*3*3-30
27-30
-3
Solve for (4x+6)+(-x+2) please i need help
Answer:
3x - 8
Step-by-step explanation:
Step 1:
( 4x + 6 ) + ( - x + 2 )
Step 2:
4x - 6 + - x - 2
Step 3:
3x - 6 - 2
Answer:
3x - 8
Hope This Helps :)
Answer:
(3x+8)
Step-by-step explanation:
(4x+6)+(-x+2)
combine like terms
(4x+-x)+(6+2)
you would end up with
(3x+8)
Skkskskswks
................
Answer:
Skkskskswks....................
Step-by-step explanation:
???
Answer:
sksksksksksksksk.
Step-by-step explanation:
equals visco girl.
How many times as large 12 is than 2
Answer:
12 is 6 times larger than 2
Step-by-step explanation:
2*6=12
Answer:
12 is 6 times larger than 2.
Step-by-step explanation:
12, 6, and 2 are all common. Let's say we multiply 2 by 6, we get 12. We divide 12 by 2, we get 6.
Given that 4x - 2y < 8, solve for y. Put them in order from steps . plz help
Answer:
y > 2x - 4
Step-by-step explanation:
Step 1: Write out inequality
4x - 2y < 8
Step 2: Subtract 4x on both sides
-2y < -4x + 8
Step 3: Divide both sides by -2
y > 2x - 4
How to express a vector as a product of its length and direction?
Answer:
So the way to express a vector( [tex]v = 2i - 2j - 2k[/tex]) as a product of its length and direction is
[tex]v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]
Step-by-step explanation:
Generally a vector is expressed as a product of its length and direction using the formula below
[tex]v = |v|\cdot u[/tex]
Here v is the vector
|v| is its magnitude (length)
u is its unit vector (direction)
Now let take an example
Let
[tex]v = 2i - 2j - 2k[/tex]
The magnitude is mathematically evaluated as
[tex]|v| = \sqrt{ 2^2 + (-2)^2 + (-2)^2 }[/tex]
[tex]|v| = \sqrt{12}[/tex]
The unit vector is mathematically represented as
[tex]u = \frac{v}{|v|}[/tex]
[tex]u = \frac{ <2 , -2 , -2>}{\sqrt{12} }[/tex]
[tex]u = \frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} }[/tex]
So
[tex]v = |v| u = \sqrt{12} (\frac{2}{ \sqrt{12} } , -\frac{2}{ \sqrt{12} }, - \frac{2}{ \sqrt{12} })[/tex]
About half of the world’s population of 7.8 billion people live in urban areas. How many
people live in urban areas?
PLEASE HELP ASAP!!!!!!!!!!!!
Answer: D
Step-by-step explanation: becasue i did it
Simplify (X2/3) ^4/5
The answer to your questions is x8/15. Hope this helps!
15. After 20 minutes at work, Ellen was able to finish 3 tasks. If she works an 8 hour day, how
many tasks should she expect to finish?
Answer:
72
Step-by-step explanation:
An hour is 60 minutes.
Multiply the amount of tasks to the amount of times 20 goes into 60 (60/20).
3×3= 9
Once you have the amount of tasks finished in an hour (9 tasks), you will multiply 8 hours by 9 tasks.
8×9= 72
find the exponential nation of 3125
Step-by-step explanation:
I hope this would be the right answer....A _ is a constant, variable, or the product of a constant and variables.
Answer:
term
Step-by-step explanation:
term is a constant, variable, or the product of a constant and variables.
Term
An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.
An algebraic expression that is a number, a variable, or a product or quotient of numbers and variables is known as a term.
So,
A term is a constant, variable, or the product of a constant and variables.
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Simplify the given expression.
6•9^3=
Answer:
4,374
Step-by-step explanation: solve the exponent first then do the multiplication
Solve for x. Show steps.
7x - 17 = 4x + 1
-x + 5 = x - 11
5x + 8 = 7x + 2
Combine the same numbers and do the opposite of either subtraction or addition.
Then, multiply or divide with the coefficient.
Answer:
see below
Step-by-step explanation:
⇒ 7x - 17 = 4x + 1
combine like terms
7x - 4x = 1 + 17
3x = 18
x = 18/3
x = 6
⇒ -x + 5 = x - 11
combine like terms
- x - x = - 11 - 5
-2x = -16
x = 16 / 2
x = 8
⇒ 5x + 8 = 7x + 2
combine like terms
5x - 7x = 2 - 8
- 2x = - 6
x = 6 / 2
x = 3
Find the length of an arc of a circle with radius 18 cm if the arc subtends a central angle of 30°.
Answer: 9.42 cm.
Step-by-step explanation:
Length of arc is given by :-
[tex]l= \dfrac{x}{360}\times2\pi r[/tex] , where r= radius and x= central angle subtended by arc.
As per given , we have
[tex]x=30^{\circ}\\\\ r=18\ cm[/tex]
Then, the length of arc will be :
[tex]l=\dfrac{30}{360}\times2(3.14)(18)\\\\=\dfrac{1}{12}\times113.04\\\\=9.42\ cm[/tex]
Hence, the length of arc is 9.42 cm.
The length of an arc of a circle with radius 18cm is; L = 9.426cm
Length of an arcThe length of an arc can be evaluated using the formula;
L = (∆/360) × 2πrHence, the length of the given arc is;
L = (30/360) × 2 × 3.142 × 18cmL = 9.426cmRead more on length of an arc;
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all real numbers at least -5 and at most 9
What are 3 careers where similarity is used
Answer:
Management Farming Construction
Step-by-step explanation:
[tex]-2(3 - 2x) = -6x + 8(x + 2)[/tex]
solve step by step
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 2(3 - 2x) = - 6x + 8(x + 2)}[/tex]
Distribute -2 through the parentheses
Similarly, Distribute 8 through the parentheses
[tex] \dashrightarrow{ \sf{ - 6 + 4x = - 6x + 8x + 16}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ - 6 + 4x = 2x + 16}}[/tex]
Move 2x to left hand side and change it's sign
Similarly, move 6 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{4x - 2x = 16 + 6}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{2x = 16 + 6}}[/tex]
Add the numbers : 16 and 6
[tex] \dashrightarrow{ \sf{2x = 22}}[/tex]
Divide both sides by 2
[tex] \dashrightarrow{ \sf{ \frac{2x}{2} = \frac{22}{2} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = 11}}[/tex]
Hope I helped!
Best regards! :D
The following are molecular formulas. Which formula represents an alkene? Decane (C10H22) Butane (C4H10) Ethane (C2H6) Propene (C3H)
Answer: Propene (C3H6)
Step-by-step explanation: Using the formula CnH2n to solve for Alkenes, propane is the only molecule that has an alkene, with twice as many hydrogen and carbon Atoms
The Alkene is the propene having Molecular formula [tex]C_3H_6[/tex].
What is Alkene?Alkenes are acyclic (branched or unbranched) hydrocarbons having one carbon-to-carbon double bond (C=C) and the general molecular formula CnH2n
Given:
For First, Carbon have 10 molecules then alkene have 2(10) = 20 Hydrogen.
So, (C10H22) is an Alkane.
Second, Carbon have 4 molecules then alkene have 2(4) = 8 Hydrogen.
So, (C4H10) is an Alkane.
Third, Carbon have 2 molecules then alkene have 2(2) = 4 Hydrogen.
So, (C2H6) is an Alkane.
Fourth, Carbon have 3 molecules then alkene have 2(3) = 6 Hydrogen.
So, (C3H6) is an Alkene.
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The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. (Due to budgeting constraints, only one new picture can be undertaken at this time.) She feels that script 1 has a 70 percent chance of earning about $10,000,000 over the long run, but a 30 percent chance of losing $2,000,000. If this movie is successful, then a sequel will be produced, with an 80 percent chance of earning $5,000,000, but a 20 percent chance of losing $1,000,000. On the other hand, she feels that script 2 has a 60 percent chance of earning $12,000,000, but a 40 percent chance of losing $3,000,000. If successful, its sequel would have a 50 percent chance of earning $8,000,000, but a 50 percent chance of losing $4,000,000. Of course, in either case, if the original movie were a flop, then no sequel would be produced. What is the probability that script 1 will be a success, but its sequel will not?
Answer: $9,000,000
Step-by-step explanation:
Probability is simply defined as the chance or likelihood that an event is going to happen or occur.
The probability that script 1 will be a success, but its sequel will not is the success of script 1 added to the failure of its sequel.
The total payoff will simply be the sum of the individual layoffs of both the success and the failure. This will be:
= $10,000,000 + (- $1,000,000)
= $10,000,000 - $1,000,000
= $9,000,000
Using conditional probability, it is found that there is a 0.14 = 14% probability that script 1 will be a success, but its sequel will not.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
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.In this question:
Event A: Script 1 is a sequel.Event B: It's sequel is not.Sequel 1 has a 70% probability of being a success, hence [tex]P(A) = 0.7[/tex].If it is a success, the sequel has a 80% probability of being a success, hence a 20% probability of being a failure, thus [tex]P(B|A) = 0.2[/tex]Then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)P(B|A)[/tex]
[tex]P(A \cap B) = 0.7(0.2)[/tex]
[tex]P(A \cap B) = 0.14[/tex]
0.14 = 14% probability that script 1 will be a success, but its sequel will not.
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The area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the wall of the barn.
Answer: 258
Step-by-step explanation: 270-12=w
The width of the wall is 9 feet and length is 30 feet.
What is perimeter of a rectangle ?The perimeter of a rectangle is the sum of all the sides.
According to the given question the area of a rectangular wall of a barn is 270 square feet. It’s length is 12 feet longer than twice it’s width.
Assuming the width of the rectangular wall to be x feet.
∴ From the given data length is 2x + 12 feet.
We know area of a rectangle is product of it's length and width.
So, { x × ( 2x + 12 ) } = 270.
2x² + 12x = 270.
2x² + 12x - 270 = 0
x² + 6x - 135 = 0
x² + 15x - 9x - 135 = 0
x(x + 15) - 9(x + 15) = 0
( x + 15 ) = 0 OR ( x+ 9 ) = 0
∴ x = -15 OR x = 9. ( we know length can note be negative )
So, Width of the rectangle is 9 feet and length is 30 feet.
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