Find the probability that a randomly selected car from this sample had 222 doors or 444 doors.
Answers
A car is selected from random sample of 100 cars,
a) The events for which the selected car has 2 doors and 4 doors are mutually exclusive event ;
i.e P(A ∩ B) = 0.
b) The probability that a randomly selected car from this sample had 2 doors or 4 doors is 0.77..
Mutually exclusive event :
A and B are mutually exclusive if they cannot occur at the same time. This means that A and B have no common result and P(A and B) = 0.
We have given a Venn diagram which consists the cars have sunroof , 2 doors and 4 doors.
Firstly we need to understand the Venn diagram properly for determining the required probability values.
From Venn diagram ,
Total number of cars in sample = 100
Cars with sunroof only = 13
Number of cars with 2 doors only = 14
Number of cars with 4 doors only = 25
Number of cars with sunroof and 2 doors = 18
Number of cars with sunroof and 4 doors = 20
a) let us consider two events A and B
A : car with two doors
B : car with four doors
As we see in Venn diagram,
the number of cars with 4 doors and 2 door, n(A∩B) = 0 => P(A and B) = 0
so, by definition of mutually exclusive event
A and B are are mutually exclusive events.
b) Probability that car with 2 doors, P(A)
= favourable outcomes for A / total outcomes
= 14+18/100 = 32/100
Probability that car with 4 doors, P(B)
= favourable cases for B/ total outcomes
= 25+20/100 = 45/100
Probability that randomly selected car from this sample had 2 doors or 4 doors = P( A or B)
= P(A) + P(B) = 77/100 = 0.77
Hence, the required probability is 0.77..
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Complete question:
Two-way tables, Venn diagrams, and probability Sunroof 13 10 18 20 14 25 2 doors 4 doors In this sample, are the events "2 doors" and "4 doors" mutually exclusive? Choose 1 answer A Yes O No Find the probability that a randomly selected car from this sample had 2 doors or 4 doors. O of 4
Related Questions
What are the 3 forms of an equation?
Answers
Answer:
There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
Which tatement are true? Select all that apply. A) The equation |-x - 4| = 8 will have two olution. B) The equation 3. 4|0. 5x - 42. 1| = -20. 6 will have one olution. C) The equation |1/2x - 3/4| = 0 will have no olution. D) The equation |2x - 10| = -20 will have two olution. E) The equation |0. 5x - 0. 75| 4. 6 = 0. 25 will have no olution. F) The equation |1/8x - 1| = 5 will have infinitely many olution
Answers
The true statement is option (A) The equation |-x - 4| = 8 will have two solution
Consider each statement
All the statements are absolute value equation
Part A
|-x-4| = 8
We can write it in two way
-x - 4 = 8
- x = 12
x = -12
Then,
-(-x-4) = 8
x+4 = 8
x = 4
It has two solution
Part B
3. 4|0. 5x - 42. 1| = -20. 6
Divide both side by 3.4
|0.5x - 42.1| = -103/17
Absolute value cannot be negative
The equation has no solution
Part C
|1/2x - 3/4| = 0
1/2x - 3/4 = 0
1/2x = 3/4
x = 3/4 ÷ 1/2
x = 3/2
The equation has one solution
Part D
|2x - 10| = -20
Absolute value cannot be negative
This equation has no solution
Part E
|0. 5x - 0. 75| 4. 6 = 0. 25
Divide both side by 4.6
|0.5x - 0.75| = 5/92
The equation divided into two
0.5x - 0.75 = 5/92
x = 37/23
0.5x - 0.75 = -5/92
x = 32/23
The equation has two solution
Part F
|1/8x - 1| = 5
1/8x - 1 = 5
x = 48
1/8x - 1 = -5
x = -32
The equation has two solution
Therefore, the equation |-x - 4| = 8 will have two solution is true
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What is surface area of any figure?
Answers
Surface area of any figure is the area that the outer surface of any figure covers.
If we look at the different figures we find that these figures if placed somewhere or if we need to cover the figures with some kind of material then in order to find the the dimensions of the material we will need to find out the area that the overall surface of the figure will cover. This will reduce the time and complication of the calculations of every part of the shape. For example, If there is a need to find the surface area of the cylinder then we use the formula for its curved surface area as
S = 2πrh where r is the radius and h is the height of cylinder
Also, the total surface area will be expressed as
T = 2πr(r + h) where r is the radius and h is the height.
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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Answers
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is that we can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Define meteorologists.A person with specific training in meteorology applies scientific principles to describe, comprehend, observe, or forecast atmospheric occurrences on earth and/or how the atmosphere impacts the planet's surface and life are meteorologists.
Given,
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is,
e. We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
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-4x² + x - 7 = y
2x + 8 = -y ( solve by elimination )
Answers
A technique for solving an equation system is elimination.
What is elimination method ?Elimination is a method of solving a system of equations. In elimination, the goal is to eliminate one of the variables by adding and subtracting equations in order to create an equation with a single variable. This equation can then be solved for the single variable. For example, given the system of equations 2x + 8 = -y and 4x² + x - 7 = y, we can use elimination to solve for the variables x and y. To do this, we first need to multiply the first equation by -4, giving us -8x - 32 = 4y. We then add the two equations together, which gives us 4x² + 9x - 39 = 0. This equation can be solved using the quadratic formula, which gives us x = -3. To solve for y, we can plug x = -3 into either of the original equations. Plugging this value into the first equation gives us 2(-3) + 8 = -y, which simplifies to -6 + 8 = -y, and therefore y = 2. This method of using elimination to solve a system of equations can be used to solve any system of equations with two variables.2x + 8 = -y
-4x² + x - 7 = -y
Subtracting 2x + 8 from both sides:
-4x² - x + 15 = 0
(4x - 5)(x + 3) = 0
4x - 5 = 0
x = 5/4
x + 3 = 0
x = -3
Solutions:
x = 5/4 and x = -3
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Write an inequality for the statement:
negative three eighths is at most the product of a number and negative five sevenths
A negative 3 over 8 ≤ negative 5 over 7w
B negative 5 over 7 ≤ negative 3 over 8w
C negative 5 over 7 ≥ negative 3 over 8w
D negative 3 over 8 ≥ negative 5 over 7w
Answers
The inequality for the statement negative three eighths is at most the product of a number and negative five sevenths is negative 3 over 8 ≤ negative 5 over 7w which is option A.
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
negative three eighths = -3/8
negative five sevenths = -5/7
At most for inequality symbol = [tex]\leq[/tex]
mathematically
-3/8 [tex]\leq[/tex] -5/7w
which is negative 3 over 8 ≤ negative 5 over 7w
In conclusion the inequality for the statement is negative 3 over 8 ≤ negative 5 over 7w
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Which of the following is the equation of the ellipse with a vertical major axis, center at (1, –3), a = 7, and b = 5?
(Don't mind the answer that is already selected.)
Answers
The required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1. which is the correct answer would be an option (A).
What is the equation of the ellipse?The equation of an ellipse with a vertical major axis and center at (h, k) is given by the formula (x - h)² / a² + (y - k)² / b² = 1, where a is the length of the major axis and b is the length of the minor axis.
As per the question, the ellipse has a vertical major axis and center at (1, -3), a = 7, and b = 5.
Substituting these values into the formula, we get:
(x - 1)² / 7² + (y + 3)² / 5² = 1
Simplifying this expression, we get:
(x - 1)² / 49 + (y + 3)² / 25 = 1
Thus, the required equation of the ellipse is (x - 1)² / 49 + (y + 3)² / 25 = 1.
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The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mm3, find the lengths of the sides a and b of the triangle.
Answers
A prism having a triangular base is a right triangle of sides a and b = 2a.
The lengths of side "a" is 3.464 mm.
The length of side "b" is 6.928 mm.
Volume of the Triangular Prism:
A triangular prism is an object in three dimensional space with a triangular base and three other triangles connected to it. A triangular prism has four corners, and the distance from the base to the diagonal vertex is called the height of the triangular prism.
It is given by the multiplication of the area of the base to the height of the prism.
V = (Area × height of prism)/3
=> V = Ah/3
we have given that,
Base of prism is right angle triangle with sides "a" and "b" such that b = 2a ---(1)
Height of prism (h) = 10mm
Volume (V) = 40mm³
the Area of triangluar base = 1/2 × base× height of triangular base
A = (1/2)a ×b
=> A = (1/2)a × 2a = a²
Volume of prism (V) = a²×h/3 = 40
=> a²×10/3 = 40
=> a² = 120/10 = 12
=> a = √12 = 2√3
=> a = 2(1.732) = 3.464
from equation (1) , b = 2a = 2(3.464)
=> b = 6.928
So, the lengths of sides of triangle are
a= 3.464 and b = 6.928
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PLEASE HELP ME WITH MY MATH HOMEWORK
ill give you brainliest
Answers
Answer: [tex]H = -16s(s-6)[/tex]
Work Shown:
[tex]H = -16s^2+96s\\\\H = -16s*s+16s*6\\\\H = -16s(s-6)\\\\[/tex]
The answer can be confirmed by using the distributive rule to multiply -16s by each term inside the parenthesis. You should get [tex]-16s^2+96s[/tex] after distributing.
Which of the following is the correct classification of AMNP if m/M = 37° and m/P = 106° ?
A Right
B Isosceles
C Acute
D Scalene
Answers
Answer:
B Isosceles
Step-by-step explanation:
You want to know the classification of ∆MNP when ∠M = 37° and ∠P = 106°.
Third angleThe third angle of the triangle can be found using the fact that the sum of angles is 180°.
∠N = 180° -37° -106° = 37°
This tells us angles M and N have the same measure (37°), so ...
the triangle is isosceles.
please help me!!!.....
Answers
Answer: 52 degrees
Step-by-step explanation:
angles stay the same even when the size is decreased. they are similar so the angle is the same. while line ab might be 2 units, and line de might be 1, the angle would stay the same.
HELPPPPPP PLEASEEE I NEED HELP
Answers
The volume of pyramid with square base is 15466.67 cm³.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given, the pyramid has square base.
And the side of square is 40 cm
And the height is 29cm.
The volume of the pyramid with square base
V = base area x height/3
V = (40 x40) x 29/3
V = 15466.67 cm³
Therefore, the volume of pyramid with square base is 15466.67 cm³.
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students who study for 7 hours over the course of a week will perform better than students who cram for 7 hours the night before the exam. the dependent variable in this hypothesis is:
Answers
The dependent variable in this hypothesis is test performance.
What is a dependent variable?
In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).
The outcome of this hypothesis is the dependent variable.
Hence, the dependent variable in this hypothesis is test performance.
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Rightround is a firm that manufactures record players. Suppose rightround sells its record players to online retailers for $342 each and requires those online retailers to charge at least $362 to shoppers for each record player.
Answers
False. All economists do not believe that predatory pricing is a profitable business strategy.
What does "predatory pricing" mean?
A dominant company will often use predatory pricing as a deliberate strategy to drive out rivals by setting exceptionally cheap prices or supplying products for less than the company would otherwise have to spend on manufacturing (often equated for practical purposes with average variable costs).
Predatory pricing, sometimes referred to as undercutting, is a pricing strategy in which a good or service is offered at an extremely low cost with the goal of driving out rivals or establishing barriers to entry for potential new competitors.
If a competitor was selling a TV for $100 and you were offering the same TV for $80, you would be using predatory pricing.
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Last year, Elsa opened an investment account with$5400 . At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year? Increase in amount and Year-end amount
Answers
Answer:
Here you go
Step-by-step explanation:
The increase in amount is $351.00 ($5400 x 0.065 = $351). The amount in the account at the end of the year was $5751.00 ($5400 + $351 = $5751).
bert and ernie each have a well-shuffled standard deck of 52 cards. they each draw one card from their own deck. compute the probability that: bert and ernie both draw a heart.
Answers
The probability that Bert and Ernie both draw a heart = (1/4)²
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Bert:
Probability of drawing a heart = 1/4
Ernie:
Probability of drawing a heart = 1/4
The probability that Bert and Ernie both draw a heart = 1/4 * 1/4 = (1/4)²
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Two dice are rolled. What is the probability that the sum of the numbers rolled is either 2 or 5? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer: first lowest: 1/3 second lowest:2/6
Step-by-step explanation:
What are the 5 infinitives?
Answers
The five types of infinitives are full infinitives, bare infinitives, split infinitives, continuous infinitives , and perfect continuous infinitive.
Explanation:
Types of infinitives:
Five types of infinitives are as follow:
Full infinitives : Add 'to' Infront of the verb to complete the the situation.Bare infinitives: here " to" get omitted from the sentence.Split infinitives : Here adjectives slides between infinitives marker.To hear : full infinitives changes to split infinitives : to slowly hear.
Continuous infinitives: Action going for certain period of required time.Example : to be missing
Perfect continuous infinitives: prior to a time :Example : to have seen
Therefore, there are are five types of infinitives .
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there are about 10,000 taste buds on a human tongue. write this number in scientific notation
Answers
Answer:
I guess 1*10^4 is the answer. Not sure.
Answer:
1 * 10⁴
Step-by-step explanation:
10,000 = 10 * 10 * 10 * 10 = 1 * 10⁴
2x-7y=12 slope intercept form please help
Answers
Answer:
[tex]y=\frac{2}{7} x -\frac{12}{7}[/tex]
edges 1. at the world tic-tac-toe championship, each player must play against 7 other players. new games start every hour. how many hours will the tournament take?
Answers
Each game starts every hour then 28 games will be occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Given, there are total 8 players playing the tournament of world tic-tac-toe championship.
Also, new game start each hour.
We have to find the number of hours the tournament will take to complete.
Total games occurred be,
we will use the concept of A.P. to find the total number of games
First player will play with 7 players, second player will play with 6 players and so on.
Total games = 8/2[14 + 7×(-1)]
Total games = 4×7
Total games = 28
Now, if each game start every hour then 28 games will occurred in 28 hours and therefore the tournament will take 28 hours for completion.
Hence, the tournament will take 28 hours for completion.
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29. The school that Lilly goes to is selling tickets to a drama performance. On the first day of ticket sales the
school sold 3 adult tickets and 1 child ticket for a total of $38. The school took in $104 on the second
day by selling 6 adult tickets and 4 child tickets. Find the price of an adult ticket and the price of a child
ticket.
Answers
Answer:
the price of an adult ticket is $8, and the price of a child ticket is $14.
Step-by-step explanation:
To find the price of an adult ticket and the price of a child ticket, we need to set up a system of equations. Let "A" represent the price of an adult ticket and "C" represent the price of a child ticket.
On the first day, the school sold 3 adult tickets and 1 child ticket for a total of $38, so we can set up the following equation to represent this information:
3A + C = 38
On the second day, the school took in $104 by selling 6 adult tickets and 4 child tickets, so we can set up the following equation to represent this information:
6A + 4C = 104
Now that we have our two equations, we can solve for the values of A and C. We can use the elimination method to solve this system of equations. To do this, we need to multiply one of the equations by a constant so that one of the variables has the same coefficient in both equations. We'll multiply the first equation by 2:
6A + 2C = 76
We can then subtract this equation from the second equation to eliminate the C term:
6A + 4C - 6A - 2C = 104 - 76
This simplifies to:
0A + 2C = 28
Dividing both sides by 2, we get:
C = 14
We can now substitute this value for C in one of our original equations and solve for A. We'll use the first equation:
3A + 14 = 38
Subtracting 14 from both sides, we get:
3A = 24
Dividing both sides by 3, we get:
A = 8
Therefore, the price of an adult ticket is $8, and the price of a child ticket is $14.
Help please, it’s hard and I’m having a difficult time!
Answers
Answer:
1) Median
2) Mode
3) Mean
(Hope this is correct :D )
Step-by-step explanation:
Mode is the number that is most repeated in the data set, and it would best describe the center of the data for the second one.
The first one has an outlier of 50 at the start, so the median would be most appropriate for this.
The last one is basically equal for each value, so the mean would best describe the center for this one.
The point (2, -3) is the midpoint of segment JK . Point K is located at (-6, -3). What is the length of segment JK ?
Answers
Answer:
16
Step-by-step explanation:
The distance from the midpoint to [tex]K[/tex] is [tex]|-6-2|=8[/tex].
By definition, this is half the length of [tex]\overline{JK}[/tex], meaning [tex]JK=16[/tex].
What is the equation in point − slope form of the line passing through 1 2 and 2/5 )? 5 points?
Answers
The equation in point-slope form of the line passing through [tex](1,2)[/tex] and [tex](2,5)[/tex] is [tex]y=3x-1[/tex]
To find the slope of the line is
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{5-2}{2-1} \\m=\frac{3}{1} \\m=3[/tex]
The equation of the line is given by
[tex]y=mx+c.........(1)[/tex]
We have to use one point form to find the equation
The point [tex](1,2)[/tex] satisfies the equation
plug in the value of m, the equation becomes
[tex]2=3(1)+c\\2=3+c\\c=2-3\\c=-1[/tex]
Put the value of m,c in (1) equation
[tex]y=3x-1[/tex]
The equation of the line is [tex]y=3x-1[/tex].
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What is the value of the expression 1/2 + 2/3 when b = -5?
-17/6
-1/6
23/6
I don't know.
Answers
Answer:
1st answer is correct
Step-by-step explanation:
[tex]\sf \frac{1}{2} +\frac{2b}{3}[/tex]
Given that,
b = -5
To find the value of the above expression, replace b with -5.
[tex]\sf \frac{1}{2} +\frac{2b}{3}\\\\\sf \frac{1}{2} +\frac{2*(-5)}{3}\\\\\sf \frac{1}{2} +\frac{-10}{3}[/tex]
Now, to solve the above fractions, you have to make the denominator the same.
For that, multiply both the numerator and denominator of (1/2) & (-10/3) by 3 & 2 respectively.
Let us solve it now.
[tex]\sf \frac{1}{2} +\frac{-10}{3}\\\\\sf \frac{1}{2} -\frac{10}{3}\\\\\sf \frac{1*3}{2*3} -\frac{10*2}{3*2}\\\\\sf\frac{3}{6} -\frac{20}{6} \\\\\sf\frac{-17}{6}[/tex]
coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 in3/min. (a) how fast is the level in the pot rising when the coffee in the cone is 5 in deep?
Answers
The level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
Here the variables are the height of the coffee in the filter hf , the radius of the top of the coffee in the filter rf , and the height of the coffee in the pot hp:
We allowed Vp to represent the volume of coffee in the pot. We are interested in the instant when
hf = 5 in and dVp/dt = 10 in³/min.
The question is dhp/dt =? when dVp/dt = 10 in³/min and hf = 5 in
We need to relate hp to the other variables. In the pot (idealized as a cylinder), we have the volume Vp as Vp = π(3)²hp = 9πhp in³(since the volume of a cylinder of radius r and height h is V = πr²h).
Differentiation of Vp with respect to time gives dVp/dt = 9πhp/dt or
dhp/dt = (1/9π).(dVp/dt)
When dVp/dt = 10 in³/min and hf = 5 in, we have
dhp/ dt = 1/9π(10)
= 10/9π in/min
dhp/ dt ≈ 0.35 in/min (notice that the answer here is independent of hf ).
Hence, the level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
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Find the perimeter and area of the figure.
Answers
The ratio of roses to lilles in a garden is 3 to 2 what percentage of the gardens flowers are roses
Answers
Answer:
To find the percentage of roses in the garden, we first need to determine the total number of flowers in the garden. We can do this by adding the number of roses and lilies, and then multiplying that number by the ratio of roses to lilies. For example, if there are 3 roses and 2 lilies in the garden, the total number of flowers would be 5 (3 + 2 = 5). To determine the percentage of roses, we would then divide the number of roses by the total number of flowers, and multiply by 100. In this case, the percentage of roses would be 60% (3 / 5 * 100 = 60).
Pls help a girl out
Answers
The statement that best describes how income levels have changed in the United States is given as follows:
C. High-income earners are making more, but most people have only seen limited gains.
How to obtain the correct statement?Recently, in the entire world, an especially in the United States, inflation has been a problem, and thus people's income has not followed the pattern, staying mostly stagnant while inflation happens. This has happened even though the economy has improved from the 2008 global crisis.
However, high-income earners are making more, as the number of millionaires and billionaires increase, increasing the gap between high and low income earners. Thus option C is the correct option.
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