A is the event that the student drives, and B is the event that the student went to the movies in the past month.
A Venn Diagram. One circle is labeled A (A and B Superscript C Baseline 0.06), another is labeled B (A Superscript C Baseline and B 0.22), and the shared area is labeled A and B (0.35). The area outside of the diagram is labeled A Superscript C Baseline and B superscript C Baseline 0.37.
Use the Venn diagram to answer the following questions.
What is the probability that a randomly selected student does not drive?
What is the probability that a randomly selected student went to the movies in the past month?
What is the probability that a randomly selected student drives or went to the movies in the past month?
Answers
If an event that "student-drives" is denoted by "A", and event "student go for movie" is denoted by B, then
(a) Probability that randomly selected student do not drive is 0.59,
(b) Probability for randomly selected student go for movie last-month is 0.57,
(c) Probability that randomly selected student "drives" or "go for movie past month" is 0.63.
(a) To find the probability that a randomly selected student does not drive, we can use the complement of event A, which is A'.
From the Venn-Diagram, We know that;
(A and [tex]B^{c}[/tex]) = 0.06, ([tex]A^{c}[/tex] and [tex]B^{c}[/tex]) = 0.37, (A and B) = 0.35, ([tex]A^{c}[/tex] and B) = 0.22,
We use the values of (A and [tex]B^{c}[/tex]) and (A and B) to calculate P(A):
P(A) = (A and [tex]B^{c}[/tex]) + (A and B) = 0.06 + 0.35 = 0.41;
So, P([tex]A^{c}[/tex]) = 1 - P(A) = 1 - 0.41 = 0.59,
The probability that randomly selected student do not drive is 0.59.
Part (b) : Probability that randomly selected student go for movies past month, is denoted by P(B).
So, P(B) = (A and B) + ([tex]A^{c}[/tex] and B) = 0.35 + 0.22 = 0.57.
The probability that randomly selected student go for movies past month is 0.57.
Part (c) : Probability that randomly selected student drives or go for movies past month, is denoted by union of events A and B, and We know that, P(A U B) = P(A) + P(B) - P(A and B);
Substituting the values,
We get,
= 0.41 + 0.57 - 0.35
= 0.63.
So, probability that randomly selected student drives or go for movies past month is 0.63.
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Related Questions
What are the 3 different types of solutions a 2 variable system can have?
Answers
The 3 different types of solutions a 2 variable system can have are a unique solution, no solution and many solutions.
There are 3 types of systems of linear equations which are as follows:
Dependent: The system has infinitely many solutions. The graphs of these equations represent the same lines.
Example: [tex]\left \{ {{2x + 2y = 4} \atop {4x + 4y = 8}} \right.[/tex]
The system has infinitely many solutions.
Independent: The system has exactly one solution. The graphs of these equations intersect at a single point.
Example: [tex]\left \{ {{x + y = 5} \atop {x - y = -1}} \right.[/tex]
The only solution to the system is (2, 3)
Inconsistent: The system has no solution. The graphs of these equations are parallel lines.
Example: [tex]\left \{ {{x + 2y = 9} \atop {2x + 4y = 7}} \right.[/tex]
The system has no solution.
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Julie wanted to match Lisa's obstacle course record of 68.2 seconds. She has already spent thirty-nine and one fourth seconds on wall climbing and 12.84 seconds on the ropes. How much time did she have left to match the record? 12.24 seconds 16.11 seconds 26.41 seconds 28.95 seconds
Answers
The time she has left to match the record is 16.11 seconds. The correct answer would be an option (B).
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
To match Lisa's obstacle course record of 68.2 seconds, Julie needs to complete the course in 68.2 seconds.
We know that she has already spent 39.25 seconds on wall climbing and 12.84 seconds on the ropes.
So, the time she has left to match the record is:
68.2 - (39.25 + 12.84) = 68.2 - 52.09 = 16.11 seconds
In the above step, use the arithmetic operations to solve.
Hence, the answer is 16.11 seconds.
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Which of the following ordered pairs is a solution to the inequality y is greater than one fourth times x plus 5? (12, 8) (11, 7) (8, 6) (4, 7)
Answers
The ordered pair that is a solution to the inequality:
y > (1/4)*x + 5
is (4, 7)
Which of the given ordered pairs is a solution for the inequality?Here we have the inequality:
y > (1/4)*x + 5
To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.
For example, for (12, 8)
We will get:
8 > (1/4)*12 + 5
8 > 3 + 5
8 > 8
This is false, so (12, 8) is not a solution.
The pair that is a solution is:
(4, 7)
7 > (1/4)*4 + 5
7 > 1 + 5
7 > 6
This is true.
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Convert this equation into standard form
Answers
The standard form of the given equation is expressed as; 3x + y = -1
How to write a Linear Equation is standard form?The standard form for linear equations in two variables is expressed as; Ax + By = C
We are given the equation as;
y - 5 = -3(x + 2)
Expanding the bracket gives us;
y - 5 = -3x - 6
Add 3x to both sides to get;
y - 5 + 3x = -6
Add 5 to both sides to get;
3x + y = -1
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How do you find the perpendicular bisector of a line segment?
Answers
The perpendicular bisector can be found by solving for the equation of the line and substituting the two points.
The perpendicular bisector of a line segment can be found by using the midpoint formula. The midpoint formula is used to find the midpoint of two points (x1,y1) and (x2,y2). The formula is:
Midpoint = (x1 + x2)/2, (y1 + y2)/2
Once the midpoint is found, the slope of the perpendicular line is found by using the negative reciprocal of the original line. The formula for the slope of the perpendicular line is y = -1/m * x + b, where m is the slope of the original line.
The equation of the perpendicular bisector is then found by substituting the slope and the midpoint into the equation of a line, y - y1 = m(x - x1).
Finally, the perpendicular bisector can be found by solving for the equation of the line and substituting the two points. The resulting equation is the equation of the perpendicular bisector.
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2. What is the new balance for the credit statement shown?
Billing
Date
Payments
& Credits
12/11/--
$70.94
Previous
Balance
$185.74
Finance
Charge
$2.71
New
Purchases
$49.80
New
Balance
Answers
So, here on solving the provided question, we can say that the New balance is as [tex]397.51[/tex]
What is balance ?A balance is the sum owing to an account in banking and accounting. The difference between the total debits and total credits posted to an account during an accounting period is referred to as a "balance" in accounting. The account will display a debit balance if the total of all debits exceeds the total of all credits.
Using the above data, first calculate the outstanding balance by using the formula below:
Previous balance-payments is as Unpaid balance
Unpaid balance is as [tex]95.85-45[/tex]
Unpaid balance is as [tex]50.85[/tex]
Finance charge is as [tex]50.85*1.5%[/tex]
Finance charge is as [tex]0.76[/tex]
New balance is as [tex]50.85+0.76+345.90[/tex]
New balance is as [tex]397.51[/tex]
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Please I’m gone faillll helpppooop
Answers
On solving the question of the polynomial The quotient = 3x+8 and remainder are and 2 respectively.
What are Polynomials ?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Polynomial long division is an extended variant of the well-known mathematical operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. Due to the fact that it breaks down a more difficult division issue into simpler ones, it may be completed quickly by hand.
Dividing 3x^3 - 2X^2 + 2x - 1 by x-1
= 3x+8
The quotient = 3x+8 and remainder are and 2 respectively.
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The cost of 1 cap and 1 wallet is
£28.
The cost of 2 caps and 1 wallet is
£45.
a) How much does 1 cap cost?
b) How much does 1 wallet cost?
Answers
Answer:
1 cap costs 17 dollars
1 wallet is 11
Step-by-step explanation:
45 - 28 = 17
The difference between one wallet and a cap and two caps and a wallet is 17, therefore each cap is 17 dollars
28 - 17 = 11
I hope this helps have a good day (:
Please help me with my work
Answers
Answer: 3k^2
Step-by-step explanation:
Find the equation of the line passing through the given point and perpendicular to the given line
Answers
Answer:
5x + y = 34
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - 5y = 8 ( subtract x from both sides )
- 5y = - x + 8 ( divide through by - 5 )
y = [tex]\frac{1}{5}[/tex] x - [tex]\frac{8}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute (5, 9 ) into the partial equation
9 = - 25 + c ⇒ c = 9 + 25 = 34
y = - 5x + 34 ← equation of perpendicular line in slope- intercept form
add 5x to both sides
5x + y = 34 ← equation in standard form
What is the area of a circle with a diameter of 5 m? use 3.14 for pi. round to the nearest tenth. responses a. 7.9 m² b. 15.7 m²c. 19.6 m² d. 78.5 m²
Answers
The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².
What is circle ?
A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.
The area of a circle is given by the formula A = [tex]\pi r^{2}[/tex], where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:
r = 5 m / 2 = 2.5 m
Then we can substitute this value of r into the formula for the area of a circle:
A = [tex]\pi r^{2}[/tex] = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²
So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².
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Answer:
The Area of a circle with a diameter of 5 m is 19.63 m² rounded to the Nearest tenth, it would be 19.6 m². the answer is c. 19.6 m².
Step-by-step explanation:
good luck to you
How many vectors are there in 3D Mcq?
Answers
There are three vectors in three-dimensional space, namely the X-axis, the Y-axis, and the Z-axis.
What is vector?Vector is a term used to describe a mathematical quantity that has both magnitude and direction, such as velocity, force, and acceleration. A vector can be represented by an arrow, with its length representing the magnitude and its direction indicating the direction. Vectors can be added together or scaled to create new vectors. Vector operations are essential in physics, engineering, and other fields of mathematics.
Each of these vectors has a magnitude and direction and can be used to represent any point in 3D space. All three axes intersect at the origin, which is the point (0,0,0). Vector algebra can be used to describe and calculate the relationships between these vectors in 3D space.
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How do you find the center of enlargement of a triangle?
Answers
To find the center of enlargement, draw line segments between corresponding vertices of pre-image and image triangles, the point where they intersect is the center of enlargement, check that all the line segments intersect at the same point, or use the coordinates of the triangle and the scale factor.
You can follow these steps:
Identify the pre-image triangle. This is the original triangle that will be enlarged.Identify the image triangle. This is the enlarged version of the pre-image triangle.Draw a line segment between the corresponding vertices of the pre-image and image triangles.The point where these line segments intersect is the center of enlargement.To check that you have the correct center of enlargement, you can draw a line segment between any other corresponding vertices of the pre-image and image triangles and check that they intersect at the same point.Another way to find the center of enlargement is to use the coordinates of the triangle and the scale factor. The center of enlargement is the point that remains the same distance from all points on the image and the pre-image. The center of enlargement is the point that the coordinates of the image triangle obtained from the coordinates of the pre-image triangle by multiplying each coordinate by the same scale factor greater than 1.
It's important to note that, the center of enlargement is the same as the center of dilation.
In both ways, it's important to have the pre-image triangle and the image triangle to find the center of enlargement.
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What is the surface area of a triangle having a base of 6m and 8m high?
Answers
Hi !
[tex]A= \frac{b \times h}{2} = \frac{6 \times 8}{2} = 24m {}^{2} [/tex]
Have a nice day ;)
A gym has soccer balls and basketballs. The ratio of soccer balls to basketballs is 3:2. The number of soccer balls at the gym is shown. How many basketballs does the gym have?
Answers
Answer: If the ratio of soccer balls to basketballs is 3:2, that means for every 3 soccer balls, there are 2 basketballs.
Let's say there are x soccer balls at the gym.
The ratio can be represented as 3x:2x
So the number of basketballs at the gym would be 2x.
So if you know the number of soccer balls at the gym, you can find the number of basketballs by multiplying the number of soccer balls by 2/3.
For example, if the gym has 18 soccer balls, the number of basketballs would be 2/3 * 18 = 12 basketballs
Step-by-step explanation:
How to solve
-y - 10=6x
5x + y= -10
Using the system by elimination
Answers
-y - 10 = 6x
5x + y = -10
First, we can add or subtract the equations in such a way that one variable is eliminated.
Add the equations :
-y - 10 + 5x + y = 6x + -10
5x = -20
x = -4
now we have x = -4 we can substitute this value in any of the equations we have.
let's substitute x = -4 in the first equation
-y -10 = 6*(-4)
-y = -40
y = 40
we have x = -4 and y = 40
we could check the solution by substitute x = -4 and y = 40 in the second equation
5*(-4) + 40 = -10
and we get 20+40 = -10, which is true.
therefore the solution for the system of equations is x = -4, y = 40
I need this asap because i will get in trouble if i don't pass this
Answers
-5+3(4)
-5+12
7
hope this helps
7
Explanation:
order of operations is PEMDAS
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
-5 + 3 (7.2 - 3.2)
First you need to do the math for what is inside the parenthesis.
7.2 - 3.2 = 4
there are no exponents so next step is to multiply.
So you need to multiply
3 x 4 = 12
then there is no division so next step is to add.
-5 + 12 = 7
that is the pest step since there is no subtraction
Is 0 0 an infinite solution?
Answers
Since 0 = 0 for any value of x, the system of equations has infinite solutions.
What is infinite solution?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".
What is an infinite number?
There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.
The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.
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9 gems will craft a diamond block what do you notice about the rate? write an equivalent ratio to represent this rate
Answers
The unit rate of the diamond block is 9
The equivalent ratio of the unit rate of the diamond block is 9/1
What is unit rate?A unit rate is the cost for only one of anything.
This is expressed as a ratio with a denominator of 1.
For instance, if you covered 60 meters in 10 seconds, you did so at an average speed of 6 meters per second.
Although both of the ratios 60 meters in 10 seconds and 6 meters in one second are rates, only the latter is a unit rate.
For the problem, 9 gems will craft a diamond block this means that
9 gems = 1 diamond block, hence for every diamond block 9 gems will be used
The unit rate is 9/1
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A system of linear equations with exactly one solution is a(n) __________ system.
Answers
Answer:
independent
Step-by-step explanation:
A system of linear equations with exactly one solution is a _independent system.
The local water slides have 70 employees, of which 40% are temporary. How many temporary employees are there?
Answers
Does anybody know what 5 1/3 minus 3 2/3 and 8 4/7 minus 7 5/7 is? And if possible try simplifying the answers.
Answers
Answer: 5 1/3 - 3 2/3 = 1 2/3. 8 4/7 - 7 5/7 = 6/7. Yes its simplified and 100% correct.
Step-by-step explanation:
The area of a rectangle is 14 1/2 sq cm and one side is 4 1/2 cm. how long is the other side?
Answers
Answer:
6cm*4.5cm = 27cm²
5cm*5cm = 25cm²
The first has a greater area - by 2 square centimeters.
Step-by-step explanation:
Answer:5 1/2
Step-by-step explanation:
4 1/2+4 1/2=9
14 1/2 -9=5 1/2
A bakery sells different packages of muffins. The number of muffins, , and the price in dollars, , of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
The bakery is considering adding a new package of muffins. Which of these combinations would make the relation NOT a function? Select TWO that apply.
Answers
A relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.
What are combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
You can choose the components of combos in any order.
Permutations and combinations can be mixed up.
So, given is the ordered pair:
(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)
All of the x-values in a relation must be distinct for it to be a function (i.e. no repetition)
The x values of choices (b) and (d) already exist in the ordered pair, namely (6,7) and (d), from the list of alternatives given (4,5)
Accordingly, (b) and (d) would prevent the relation from being a function.
Therefore, a relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.
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Correct question:
A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
{(1,2),(2,3),(4,5),(6,7),(12,13)}
The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.
a. (10,13)
b. (6,8)
c. (8,12)
d. (4,3)
e. (24,18)
Write an equation of the passes through the given point and has the given slope? 1.(10, -4); slope - 2/5
Answers
The equation of the line that passes through the point (10, -4) and has the slope -2/5 is y = 2/5 x
How to identify the equation of the lineThe slope, m of the linear function is given as -2/5.
The equation of the line that passes through point (10, -4) is calculated using the point slope formula which is given as:
x₁ = 10
y₁ = -4
m = -2/5
substituting in to the formula
(y - y₁) = m (x - x₁)
y + 4 = -2/5 (x - 10)
y + 4 = -2/5 x + 4
y = 2/5 x + 4 - 4
y = 2/5 x
The equation of the line is given as y = 2/5 x
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An
elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states (in alphabetical order, from
01 to 50), then uses a random number table to decide which states each kid gets. The random digits are 33874 64946 29977 66233.
a) Which two state numbers does the first student get?
b) Which two state numbers go to the second student?
Answers
Therefore , the solution of the given problem of combination comes out to be a) 45 and 10 b) 17 and 10
Define combination.Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.
Here,
Given :
Total students = 25
a) The first state is represented by the first two-digit number in the random digits, which is 45.
The following random two-digit number, which does not represent a state, is 92.
The following two-digit number in the random sequence is 10, which stands for the first student's second state.
b) The second student's initial state is represented by the following two-digit number (17) from the random digits.
Ten symbolizes the second state for the second state and is the first two-digit number of the random digits.
Therefore , the solution of the given problem of combination comes out to be a) 45 and 10 b) 17 and 10
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A number cube is rolled 50 times and the results are shown in the graph. Determine the experimental probability of rolling a 1.
Answers
Based on the information, we can conclude that we have a 5% chance (probability) of getting 1 in this test of throwing the dice 50 times.
How to calculate the probability of getting 1 according to the results?Taking into account the results of the graph, we can establish the probability of getting the number 1 in the 50 throws made. To do this, we must perform the following procedure:
50 / 100 = 0.50.5 * 10 = 5%In accordance with the above and based on the results of the test we can establish that we have a 5% probability of getting 1. This could be expressed as a 0.05 probability, in which 0 is not at all likely and 1 is very likely.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Image attached
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What is the factor theorem formula?
Answers
The Factor Theorem states that if a polynomial P(x) has a factor (x-a), then P(a) = 0. In other words, if x-a is a factor of the polynomial, then the value of the polynomial when x=a is equal to zero.
The factor theorem is a fundamental concept in algebra and polynomial functions. This can be useful for determining the roots of a polynomial equation.
Key points:
The factor theorem only applies to polynomials, not other types of functions.The factor (x-a) must be a factor of the polynomial, not just a term.The value of P(a) will be zero only if x-a is a factor of the polynomial, not if it is just a root.The factor theorem can be used to find the roots of a polynomial equation by setting P(x) = 0 and solving for x.The factor theorem is closely related to the remainder theorem, which states that if P(x) is divided by (x-a), the remainder is P(a).In summary, The Factor Theorem is a fundamental concept in Algebra and Polynomials, it helps us understand the relationship between the roots and the factors of a polynomial equation and how a root of a polynomial is related to the value of the polynomial evaluated at that point.
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Which set of numbers can represent the side lengths in inches of a right triangle?A. 8,12,15B. 10,24,26C. 12,20,25D. 15,18,20
Answers
The set B represent the side length in inches of a right triangle.
Now, According to the question:
Let's know:
What is Pythagoras Theorem?
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^2 + b^2 = c^2.[/tex]
Where a and b are the two legs of the triangle and c is the length of the hypotenuse [THE LONGEST SIDE].
We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.
A) [tex]8^2+12^2=15^2[/tex]
64 + 144 = 225
208 ≠ 225
This is not a right triangle.
B) [tex]10^2+24^2=26^2[/tex]
100 + 576 = 676
676 = 676
This is a right triangle.
C) [tex]12^2 + 20^2=25^2[/tex]
144 + 400 = 625
544 ≠ 625
This is not a right triangle.
D) [tex]15^2+18^2=20^2[/tex]
225 + 324 = 400
549 ≠400
This is not a right triangle.
Hence, The set B represent the side length in inches of a right triangle.
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A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is . The angle of elevation from sea level to the top of the lighthouse is . Find the height of the lighthouse from the top of the cliff. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale.
Answers
There is no numbers provided, but this is how you solve it.
We can use the tangent function to solve for the height of the lighthouse.
Let h be the height of the lighthouse from the top of the cliff.
tan(angle of elevation from sea level to the top of the lighthouse) = (h+ height of lighthouse from sea level ) / distance from the base of the cliff
tan( angle of elevation from sea level to the top of the lighthouse) = (h+x) / distance from the base of the cliff
tan(angle of elevation from sea level to the base of the lighthouse) = (h) / distance from the base of the cliff
By dividing the first equation by the second equation
(h+x) / distance from the base of the cliff = tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse)
(h+x) = (h) * (tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse))
h = (x * tan( angle of elevation from sea level to the base of the lighthouse)) / ( tan( angle of elevation from sea level to the top of the lighthouse) - tan( angle of elevation from sea level to the base of the lighthouse))
After plugging in the values into the equation, we get:
h = (x * tan( )) / ( tan( ) - tan( ))
Round to the nearest tenth
h = (x * tan( )) /