Section 2-Short Answer Question (5 marks) 2 marks) Suppose that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive. a. (1 mark) Find P(An B). Give the final answer: Show your calcu
Answers
P (A) = 0.4 and P (B) = 0.5 are provided, and it is also known that A and B are mutually exclusive. Hence, P(An B) can be calculated as: P(An B) = P(A) + P(B) - 2P(A ∩ B) (as mutually exclusive events have no intersection)
Thus, we have: P(An B) = P(A) + P(B) - 2P(A)P(B)P(A) = 0.4 and P(B) = 0.5; hence, substituting the values in the formula above, we get: P(An B) = 0.4 + 0.5 - 2(0.4)(0.5) = 0.4 + 0.5 - 0.4 = 0.5. Mutually exclusive events are those that cannot occur simultaneously, and they have a common property, i.e., P(A ∩ B) = 0. For instance, if A represents the occurrence of an event on a given day and B represents the non-occurrence of that event, the two events A and B cannot occur on the same day. In this case, it is provided that P(A) = 0.4, P(B) = 0.5, and that events A and B are mutually exclusive. We are to determine P (An B).P (An B) can be calculated using the formula: P(An B) = P(A) + P(B) - 2P(A ∩ B). Mutually exclusive events have no intersection; hence, the value of P(A ∩ B) is zero, and the formula becomes: P(An B) = P(A) + P(B) - 2P(A)P(B). Substituting the given values, we get: P(An B) = 0.4 + 0.5 - 2(0.4)(0.5) = 0.5. Thus, the probability of A and B occurring simultaneously is 0.5.
P(An B) has been calculated as 0.5, given P(A) = 0.4, P(B) = 0.5, and A and B being mutually exclusive events.
To know more about Mutually exclusive events visit:
brainly.com/question/29992365
#SPJ11
The probability of the intersection of A and B, denoted as P(A ∩ B), is equal to 0. This indicates that there is no overlap or common occurrence between events A and B.
In this case, since events A and B are mutually exclusive, it means that they cannot occur at the same time. Mathematically, this is represented by the fact that the intersection of A and B (A ∩ B) is an empty set, meaning there are no common outcomes between the two events.
Therefore, the probability of the intersection of A and B, denoted as P(A ∩ B), is equal to 0. This indicates that there is no overlap or common occurrence between events A and B.
To know more about probability, visit:
https://brainly.com/question/28974383
#SPJ11
Related Questions
Drawing a Cartesian coordinate system, plot an athlete running from point A (3,0) to point B (0,5) then
to point C (-4,-2) and ending at point D (3, -1). Be clear in marking your coordinate system and plotting
your athlete’s movement, using vector arrows depicting direction.
Answers
A Cartesian coordinate system is a coordinate system that employs a pair of perpendicular number lines, one horizontal axis and the other vertical axis.
Each point in the plane is defined by an ordered pair of numbers known as its coordinates. plot an athlete running from point A (3,0) to point B (0,5) then to point C (-4,-2) and ending at point D (3, -1) and clear marking of your coordinate system and plotting your athlete’s movement, using vector arrows depicting direction.
Step 1: Determine the maximum and minimum values on the x-axis and y-axis. Choose suitable values for both axes.
Step 2: Draw a horizontal x-axis and a vertical y-axis intersecting at the origin (0, 0). Ensure that the length of the axes is sufficient to accommodate the points.
Step 3: On the x-axis, mark the point A (3,0) which is located 3 units from the origin towards the right. Label the point A.
Step 4: On the y-axis, mark the point B (0,5) which is located 5 units from the origin towards the top. Label the point B.
Step 5: On the x-axis, mark the point C (-4,-2) which is located 4 units from the origin towards the left. Label the point C.
Step 6: On the y-axis, mark the point D (3,-1) which is located 1 unit from the origin towards the bottom. Label the pointD.
Step 7: Join the points A, B, C, and D to form a quadrilateral.
Step 8: Draw vectors (vector arrows) that depict the movement of the athlete in the order from A to B, from B to C, and from C to D. Repeat this for all the movements of the athlete from A to B, from B to C, and from C to D.
To know more about Cartesian coordinate visit:-
https://brainly.com/question/30637894
#SPJ11
find the determinant of the matrix. expand by cofactors using the indicated row or column. ([5 0 -4 4][5 11 5 -7][-1 0 6 5][7 5 0 3])
Answers
The determinant of the given matrix = 2455
To find the determinant of the given matrix using cofactor expansion, let's expand along the first row:
det([5 0 -4 4]
[5 11 5 -7]
[-1 0 6 5]
[7 5 0 3])
Expanding along the first row, we can use the cofactor expansion formula:
det(A) = a11 * C11 - a12 * C12 + a13 * C13 - a14 * C14
where aij represents the element at the ith row and jth column of the matrix, and Cij represents the cofactor of the element aij.
Calculating the cofactors for each element:
C11 = (-1)^(1+1) * det([11 5 -7][0 6 5][5 0 3])
= 1 * (11 * 6 * 3 + 5 * 5 * 0 + (-7) * 0 * 0 - 5 * 6 * 0 - (-7) * 5 * 3 - 0 * 0 * 5)
= 1 * (198 + 0 + 0 - 0 - (-105) - 0)
= 1 * (198 + 0 + 0 + 105 + 0)
= 1 * (303)
= 303
C12 = (-1)^(1+2) * det([5 5 -7][-1 6 5][7 0 3])
= -1 * (5 * 6 * 3 + (-7) * 0 * 7 + 5 * 5 * 3 - 7 * 6 * 5 - 5 * 0 * 3 - 5 * (-7) * 0)
= -1 * (90 + 0 + 75 - 210 - 0 - 0)
= -1 * (-75)
= 75
C13 = (-1)^(1+3) * det([5 11 -7][-1 0 5][7 5 3])
= 1 * (5 * 0 * 3 + (-7) * 5 * 7 + 11 * 5 * 3 - (-7) * 0 * 11 - 11 * 5 * 0 - 5 * (-7) * 3)
= 1 * (0 + (-245) + 165 - 0 - 0 - (-105))
= 1 * (-245 + 165 + 105)
= 1 * 25
= 25
C14 = (-1)^(1+4) * det([5 11 5][-1 0 6][7 5 0])
= -1 * (5 * 0 * 0 + 5 * 6 * 7 + 11 * 7 * 0 - 11 * 0 * 7 - 7 * 6 * 0 - 5 * 5 * 0)
= -1 * (0 + 210 + 0 - 0 - 0 - 0)
= -1 * (210)
= -210
Now, we can calculate the determinant using the cofactor expansion formula:
det(A) = a11 * C11 - a12 * C12 + a13 * C13 - a14 * C14
det(A) = 5 * 303 - 0 * 75 - (-4) * 25 - 4 * (-210) = 2455
To learn more about determinants visit : https://brainly.com/question/16981628
#SPJ11
find the marked angle of
Answers
Answer:
∠ C = 100°
Step-by-step explanation:
since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.
consider the angle inside the triangle to the left of 140°
this angle and 140° are a linear pair and sum to 180°
angle + 140° = 180° ( subtract 140° from both sides )
angle = 40°
then the angle on the left of the triangle = 40° ( base angles congruent )
the sum of the angles in a triangle = 180° , so
∠ C + 40° + 40° = 180°
∠ C + 80° = 180° ( subtract 80° from both sides )
∠ C = 100°
How do you know if a polynomial graph is positive or negative?
Answers
To determine if a polynomial graph is positive or negative, you need to look at the sign of the leading coefficient of the polynomial. If the leading coefficient is positive, the graph will be positive.
If the leading coefficient is negative, the graph will be negative. This is because the highest degree of the polynomial will determine the sign of the graph as the graph will either be increasing (positive) or decreasing (negative). To determine the leading coefficient, look at the polynomial expression and identify the term with the highest degree. The sign of this term will be the sign of the graph. For example, if the highest degree is 3, then the term would be ax^3, and the graph will be positive if a is positive, and negative if a is negative.
To know more about polynomials refer to the link brainly.com/question/20121808
#SPJ4
A wire, 24 meters in length, is attached from the top of a post to a stake in the ground. The measure of the angle that the wire makes with the ground is 36° Find to the nearest senth of a meter the distance from the stake to the foot of the post
Answers
given the information on the problem, we can draw the following diagram:
then, we can use the cosine function to find the distance from the stake to the foot of the post:
\(\begin{gathered} \cos (36)=\frac{\text{adjacent side}}{hypotenuse}=\frac{x}{24} \\ \Rightarrow x=24\cdot\cos (36)=19.4 \\ x=19.4 \end{gathered}\)therefore, the distance is 19.4 m
Work out the value of 5 to the power of a if it equal 1/125
Answers
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
NEED HELP ASAP! THANK YOU!
To get to Checkpoint C, Helena needs to run north 6 units, crawl through a 4-unit-long tube to the east, hopscotch south 3 units, jump 1 unit to the east, and run south 3 units.
1. Since she began at Checkpoint B, what are the coordinates for Checkpoint C?
2. What would be an easier way to get from Checkpoint B to Checkpoint C?
3. How might you be able to figure this out just by reading the description of the translations? (Hint: It may help you to plot these points on a graph or draw a picture.)
Answers
Helena's motions, including the 6 units north, 4 and 1, east, 3 and 3 south gives;
(5, 0)5 units to the southAdding the motions based on their directionsHow can the position of Helena be found?1. Let the coordinates of checkpoint B be (0, 0), using vectors, we have;
\(6 \times j \: + 4 \times i - 3 \times j \: + i - 3 \times j = 0 \times j \: + 5 \times i\)
The coordinates of checkpoint C is therefore; (5, 0)
2. The easier way to get to checkpoint C from point B is to go south 5 units.
3. How it is possible to figure out the shortest route is by taking the northwards and eastwards motions as positive numbers, and the motions to the south as negative.
The motions to the north can only be added to the motions to the south (motions in the same straight line) and the motions towards east are to be added to themselves.
Learn more about vectors here:
https://brainly.com/question/24855749
Answer:
5, 0
5 units south
adding motions based on direction
Step-by-step explanation:
What fractions and decimal forms match the long division problem?
Answers
Answer:
the answer b
Step-by-step explanation:because 2÷15 =0.13 (esitmated or black over the 3) or 2/15
The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?
O 16 feet
0 10 feet
12 feet
ОО
0 4 feet
Answers
Rocky has 2 1/4 cups of flour in her pantry. If she needs 1 /2 cups to make a batch of cupcakes, how many batches will she be able to make? Practice
Answers
Answer:if she has 2 1/4 and needs 1/2 as many times as possible the answer is she can make two batches since 1/2x2=2 leaving a remainder of 1/4
Answer:
\large 1\frac{1}{2}
Step-by-step explanation
if the measures, in degrees, of the three angles of a triangle are x,x 10, and 2x-6 the triangle must be ____
Answers
The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.
If the measures of the three angles of a triangle are x, x + 10, and 2x - 6, the triangle must be isosceles.
In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:
x + (x + 10) + (2x - 6) = 180
Combine the terms:
4x + 4 = 180
Subtract 4 from both sides:
4x = 176
Divide by 4:
x = 44
Now, we can find the measures of the other two angles:
x + 10 = 44 + 10 = 54
2x - 6 = 2(44) - 6 = 88 - 6 = 82
The three angles are 44, 54, and 82 degrees. Since two angles (44 and 44 degrees) have the same measure, the triangle is isosceles.
Learn more about angles here:
https://brainly.com/question/28451077
#SPJ11
I need help
The radius of a circle is 3 meters. What is the area of a sector bounded by a 180° arc?
Answers
I don’t understand c5 when c=2
Answers
Fill in the blank: \(\pi r2\) is the formula for finding ___ of a circle.
(Also happy pi day!!!! π!!!!! 3.14!!!!!!!!)
Answers
The formula\($\pi r^2$\) represents the area of a circle, where "r" is the radius of the circle and "\($\pi$\)" is a mathematical constant approximately equal to 3.14159.
How to use area of circle?The formula\($\pi r^2$\) represents the area of a circle, where "r" is the radius of the circle and "\($\pi$\)" is a mathematical constant approximately equal to 3.14159.
By using this formula, we can find the area of a circle given its radius. This is useful in many real-world applications, such as calculating the amount of space a circular object takes up, such as a circular table, a circular rug or a circular garden bed.
We can also use this formula to compare the areas of different circles. For example, if we have two circles with radii \($r_1$\) and \($r_2$\), we can find their areas using the formula \($\pi r_1^2$\) and \($\pi r_2^2$\) respectively, and compare them to see which circle has a larger area.
It is important to note that the formula only gives us the area of a circle, and not its circumference or diameter. For those, we would need to use other formulas, such as\($C = 2\pi r$\) for the circumference and D = 2r for the diameter.
To know more about Circle visit:
brainly.com/question/29142813
#SPJ1
Evaluate the expression −t/u+vw , where t = 2, u=−2/3 , v=−1 , and w=−1/3 .3 1/31 2/3−2 2/3
Answers
Answer:
The answer is 3 1/3
The value of the expression −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that,
The expression is:
= −t/u+vw
The values of t = 2, u=−2/3 , v=−1 , and w=−1/3
After pluggin the values of t, u, v, and w in the above expression we get:
= -2/(-2/3) + (-1)(-1/3)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
= 3 + 1/3
= 3 1/3 (in mixed fraction)
Thus, the value of the expression −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ2
3 1/3
The Ninoy Aquino International Airport (NAIA) and Singapore Changi Airport (SIN) are about 2,400 kilometers apart. A Singapore Airlines passenger plane leaves NAIA, traveling towards SIN at an average speed of 800 kilometers per hour. A Philippine Airline passenger plane leaves SIN at the same time, traveling toward NAIA, averaging 640 kilometers per hour. How long will it take them to meet?
Answers
The relative velocity of one plane with respect to the other plane is given
by the sum of the velocity of the two planes.
The time it would take the two planes to meet is \(\underline{1. \overline 6 \ km/hr}\)Reasons:
The distance between the two airports = 2,400 km
Speed of the plane from NAIA = 800 kilometer per hour
Speed of the plane coming from SIN = 640 kilometers per hour
Let t represent the time after which the two planes meet, we have;
800 × t + 640 × t = 2,400
\(\displaystyle t = \frac{2,400 \ km}{800 \ km/hr + 640 \ km/hr} = \frac{5}{3} \ km/hr = 1.\overline 6 \ km/hr\)
The time after which the two planes meet, t = \(\underline{1. \overline 6 \ km/hr}\)
Learn more here:
https://brainly.com/question/17228388
What does x equal 5x+2=16
Answers
Answer:
X = 2.8
Step-by-step explanation:
5x+2=16
5x=16-2
5x=14
x=14÷5
x=2.8
Hope that helps!
5+9 = 14+2 = 16
Please solve!!!
in a hurry!!!
(show work/explain answer)
Answers
Answer:y=4x+2
Step-by-step explanation:
-4x+y=2
−4x+y+4x=2+4x
y=4x+2
y=4x+2
Astrid is looking for a job at a call center. Call center A offers her 15 dollars per hour and call center B offers her 25 cents per minute.
Answers
Call center A and B offers equal wages.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
The formula for wages = P/t
First, P= 15 dollars
= 1500 cents
time= 1 hour= 60 minutes
then, the unit rate is
=1500/60
= 25 cents/ min
Second, P= 25 cents
time= 1 minutes
then, the unit rate is
=25/1
= 25 cents/ min
Hence, Call center A and B offers equal wages.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Miley earns $10 per hour babysitting. Is the amount of money earned proportional to the number of hours she spends babysitting? If it is proportional, find the constant of proportionality, explain what it means, and write an equation to represent the situation. Then find out how much she would make for babysitting 5.5 hours.
Answers
Answer:
think what constant of proportionality is
Step-by-step explanation:
Jason has a block of clay that is made up of two rectangular pieces of
different colors. Find the volume of the block of clay.
The measurements of the two clay blocks are:
6 cm
4 cm
3 cm
5 cm
Answers
Answer: 132 cubic centimeters
Step-by-step explanation:
To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.
The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).
The volume of A is:
Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters
The volume of B is:
Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters
So the total volume of the block of clay is:
Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters
Therefore, the volume of the block of clay is 132 cubic centimeters.
Suppose Shia has the utility function U(x 1
,x 2
)=6x 1
+(1/2)x 2
. a) Which of the following bundles, (x 1
,x 2
), do they rank the lowest?: (4,4),(4,2),(2,4), (8,4)(5,4) [PLEASE ENTER YOUR ANSWER AS "(#,\#)"] b) Suppose Shia had income of $150, faced prices of (x 1
,x 2
) which equaled p 1
=10 and p 2
=25, and had to pick among the five bundles in part (a). Which bundle would they pick? [PLEASE ENTER YOUR ANSWER AS "(#,\#)"]
Answers
Shia ranks the bundle (2,4) the lowest with a utility of 14.Given their income and prices, Shia would pick the bundle (4,2) as it maximizes their utility within their budget.
a) To determine the bundle that Shia ranks the lowest, we can calculate the utility for each bundle using the given utility function and compare the results.
Utility for each bundle:
U(4,4) = 6(4) + (1/2)(4) = 24 + 2 = 26
U(4,2) = 6(4) + (1/2)(2) = 24 + 1 = 25
U(2,4) = 6(2) + (1/2)(4) = 12 + 2 = 14
U(8,4) = 6(8) + (1/2)(4) = 48 + 2 = 50
U(5,4) = 6(5) + (1/2)(4) = 30 + 2 = 32
The bundle that Shia ranks the lowest is (2,4) with a utility of 14.
To determine the bundle Shia would pick given their income and prices, we need to calculate the expenditure for each bundle and find the bundle that maximizes their utility while staying within their budget.
Expenditure for each bundle:
Expenditure(4,4) = p1 * 4 + p2 * 4 = 10 * 4 + 25 * 4 = 160
Expenditure(4,2) = p1 * 4 + p2 * 2 = 10 * 4 + 25 * 2 = 90
Expenditure(2,4) = p1 * 2 + p2 * 4 = 10 * 2 + 25 * 4 = 120
Expenditure(8,4) = p1 * 8 + p2 * 4 = 10 * 8 + 25 * 4 = 200
Expenditure(5,4) = p1 * 5 + p2 * 4 = 10 * 5 + 25 * 4 = 165
Since Shia's income is $150, the bundle that Shia would pick is the one with the highest utility among the bundles that they can afford. In this case, Shia can afford the bundle (4,2) with an expenditure of $90, which is within their budget.
Therefore, Shia would pick the bundle (4,2).
Learn more about utility
brainly.com/question/31385674
#SPJ11
Subtract (-4x-2)-(13x-1)
Answers
Answer: -17x-1
Step-by-step explanation: Hope this help :D
Answer:
-17x-1
Step-by-step explanation:
A continuous random variable is a random variable: A. that is derived from a random population B. whose values are countable C. that is determined by random probability D. that can assume any value in one or more intervals
Answers
1) What is the sum of
\( \frac{1}{3} + \frac{3}4\)
A)
\( \frac{4}{7} \)
B)
\( \frac{1}{4} \)
C)
\(1 \times \frac{1}{12} \)
D)
\(1 \times \frac{1}{7} \)
Answers
Answer:
I believe its C 1 x 1/12. Hope this helps
Step-by-step explanation:
which of the following statements is true of random assignment and random sampling?
A. Random assignment is the same as random sampling
B. Random assignment, if effective, allows us to make sure the only difference between the various treatment groups is what we are studying
C. Random assignment allows us to obtain a sample representative of the population
D. All of the above
Answers
Answer:
Random assignment is necessary for internal validity, whereas random assignment is necessary for external validity
Step-by-step explanation:
(8.65x103)(9.3x10-23)
Answers
To multiply the given expressions (8.65 x 10^3) and (9.3 x 10^-23), we can apply the laws of exponents. In multiplication, we multiply the coefficients and add the exponents.
First, we multiply the coefficients:
8.65 * 9.3 = 80.295
Next, we add the exponents:
10^3 * 10^-23 = 10^(3 + (-23)) = 10^-20
Combining the coefficient and the exponent, we get:
80.295 x 10^-20
Thus, the final result of the multiplication is 80.295 x 10^-20.
In scientific notation, this can be written as 8.0295 x 10^-19, where the coefficient is 8.0295 and the exponent is -19.
This means that the product of (8.65 x 10^3) and (9.3 x 10^-23) is approximately 8.0295 x 10^-19. This result represents a very small value due to the negative exponent, indicating that the product is much smaller than 1.
To learn more about coefficients : brainly.com/question/1594145
#SPJ11
plz help me if you can
Answers
Answer:
Hey there!
These triangles can be proved congruent by the HL Theorem.
Hope this helps :)
Hey Mate!!
Your answer will be HL Theorem.
Because, Since the triangles overlap, their hypotenuses are the same side and therefore congruent by the reflexive property. This means the triangles are congruent by a hypotenuse, leg and right angle. This is known as HL.
☆ Good Luck ☆
♡ Comments down ♡
By ◇~Itsbrazts ◇~
Which is equivalent to 2^5?
Answers
Answer:
Are there certain options?
Step-by-step explanation:
2^5 is in other words 2x2x2x2x2
the answer to this is 32
Hope I helped?
Answer:
32
Step-by-step explanation:
What is the measure of ABC?
A. 126
B. 82
C. 44
D. 63
