events A and B in some sample sapce each have a probability 0.5 of occuring, while the probability that both occur (simultaneously) is 0.25. what is the probability that neither of A or B occurs? this is the work i did, can i please get some guidance
=============================================
Explanation:
I appreciate you showing your work so far, and your thought process.
Your steps are correct because the events [tex]A \cup B[/tex] and [tex](A \cup B)'[/tex] are complementary, aka opposite. One or the other must happen. It's like a coin flip heads vs tails.
The last thing you need to do really is simplify 1-0.5-0.5+0.25 to get the final answer 0.25
-------------------
This is what I would do as an approach.
P(A u B) = P(A) + P(B) - P(A n B)
P(A u B) = 0.5 + 0.5 - 0.25
P(A u B) = 0.75
So,
P( (A u B)' ) = 1 - P(A u B)
P( (A u B)' ) = 1 - 0.75
P( (A u B)' ) = 0.25
-------------------
Another approach:
Imagine we had 100 people.
50 are in set A to give P(A) = 50/100 = 0.50
50 are in set B to give P(B) = 0.50
25 are in both A and B to get P(A n B) = 25/100 = 0.25
50+50-25 = 75 people are in either A, or B, or both
That leaves 100-75 = 25 in neither set
25/100 = 0.25
I recommend to draw out the Venn Diagram.
What is the slope of this line? and can you provide me with the formula for the slope of the line too please?
Answer:
slope = 1/2
Step-by-step explanation:
The slope formula:
The slope of a line that passes through points [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] is
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
To find the slope, we find two easy-to-read points. Easy-to-read points are usually on grid line intersections.
Points (0, 0) and (2, 1) are on grid line intersections and are easy to read.
We will now input the information from our two points into the slope formula to calculate the slope.
[tex] slope = m = \dfrac{1 - 0}{2 - 0} = \dfrac{1}{2} [/tex]
21•15 equals
(20+1)•15
The value of 21•15 equals (20+1)•15. This is true.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of 21•15 will be:
= 21 × 15
= 315
Also (20+1)•15 will be:
= 21 × 15
= 315
Therefore, they're equal.
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Complete question
The value of 21•15 equals (20+1)•15. True or false?
Need asap will give brainlist!
Answer:
10,37
Step-by-step explanation:
for EF= [tex]\sqrt{17^{2} -14^{2} } =10[/tex]
for D= we have 2 knowns which are 53 and 90, so we need to minus them from each other to get D. 90-53=37
there i 2 worker, one can make a houe in 2 day the other one can make houe in 3 day, if they work together how much day it take them to make a houe
The time taken by both the workers working together, which is 2 days.
The time taken to build a house by two workers working together can be calculated using the formula T = (1/W1 + 1/W2)^-1, where W1 and W2 are the working speeds of each worker. In this case, W1 = 2 days and W2 = 3 days. So, the time taken to build a house by both workers together is calculated as follows:
T = (1/2 + 1/3)^-1 = (3/6)^-1 = 6/3 = 2 days
Therefore, both the workers working together will take 2 days to build a house. This is because when two workers work together, the total work done in a given time is equal to the sum of the work done by each worker separately in that given time. In this case, both the workers will take 2 days and 3 days respectively to build the house when working separately, so when they work together the total work done in a given time will be 5 days. This is equal to the time taken by both the workers working together, which is 2 days.
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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
8x²³-21²-67x-24?
2x²-x-21
The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
Which expression represents the correct form for the quotient and remainder?(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To learn more about partial fractions refer to:
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can someone help me with this question?
The final balace in Tracy's bank account is $ 361.80.
How to follow transactions in a bank account
In this question we must pay attention to every movement in a bank account and determine final balance within. The hint is having an active reading in the meaning of translating every Tracy's movement in additions and subtractions, First, we translate very sentence into numbers and signs:
Tracy's checking account: + $ 300.00
Tracy bought new sneakers: - $ 63.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 17.75
Tracy wrote a check: - $ 9.45
Tracy made a withdrawal at her bank: - $ 20.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 18.00
Tracy made a withdrawal at another bank: - $ 20.00 - $ 1.50
Tracy deposited her birthday money: + $ 125.00
Second, calculate the final balance in Tracy's account:
x = 300.00 - 63.00 + 43.25 - 17.75 - 9.45 - 20.00 + 43.25 - 18.00 - 20.00 - 1.50 + 125.00
x = 361.80
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Calculate the theoretical mass of precipitate produced if calcium chloride solution was reacted with excess sodium bicarbonate
If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.
The theoretical mass of precipitate produced in a reaction between calcium chloride and sodium bicarbonate can be calculated by using the balanced chemical equation for the reaction. The balanced equation for this reaction is given as follows:
CaCl₂ + NaHCO₃ → CaCO₃ + NaCl + H₂O
In this reaction, one mole of calcium chloride reacts with one mole of sodium bicarbonate to produce one mole of calcium carbonate precipitate, one mole of sodium chloride solution, and one mole of water.
The mass of the precipitate can be calculated by multiplying the molar mass of calcium carbonate by the number of moles of calcium carbonate produced.
So, to calculate the theoretical mass of precipitate produced, you need to know the amount (in moles) of calcium chloride and sodium bicarbonate used in the reaction. If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.
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Find the logarithmic function f(x) = log a (x-h) that describes the graph *image included*
The logarithmic function that describes the graph is given as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
How to define the logarithmic function?The parent logarithmic function is defined as follows:
f(x) = log(x).
Which, no matter the base, has the vertical asymptote given as follows:
x = 0.
The vertical asymptote of the graphed function is given as follows:
x = -1.
Hence:
[tex]f(x) = \log_a{(x + 1)}[/tex]
When x = 3, f(x) = 2, hence the base a is obtained as follows:
[tex]2 = \log_a{(4)}[/tex]
Meaning that:
a² = 4.
a = 2.
And the function is then defined as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
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A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can bee loaded into the container is 26000 kilograms. Other shipments weighing 11300 kilograms have already been loaded into the container. Write an inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container
An inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container: c ≤ 98
We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .
It is an unequal relation between two algebraic expressions.
Here, the greatest weight that can be loaded into the container = 26,000 kilograms
the weight of each crate = 150 kilogram
and the weight of other shipment = 11300 kilograms
Let c be the total number of 150-kilogram crates that can be loaded.
So, we get an inequality:
150 c + 11300 ≤ 26,000
150 c ≤ 26,000 - 11300
150 c ≤ 14700
c ≤ 98
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Determine which of the lines, if any, are parallel or perpendicular.
The line a and line c are perpendicular to each other.
How to find parallel and perpendicular lines?Lines are known if they are parallel or perpendicular by there slopes.
Therefore, parallel lines have the same slopes and perpendicular have slopes that are negative reciprocals of one another.
The slope of a line is the change in the dependent variable to the change in the independent variable.
Therefore, let's find the slopes of each line.
line a:
slope = -3 - 1 / 6- 0 = - 4 / 6 = - 2 / 3
line b:
slope = -2 - 0 / 3 + 3 = - 2 / 6 = - 1 / 3
line c:
slope = 7 + 2 / 2 + 4 = 9 / 6 = 3 / 2
Therefore, line a and c are perpendicular
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Let N(t) represent the number of people in line at a BBQ truck, t hours after the food truck opens. Interpret each of the following statements in context.
Each of the given statements are interpreted in context below.
What is the quadratic equation?
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The solutions of the equation are the values of x that make the equation true.
a. N(1) = 11: This statement represents that 1 hour after the food truck opens, there are 11 people in line.
b. N(0) = N(3): This statement represents that at the time the food truck opens, the number of people in line is the same as 3 hours after the food truck opens.
c. N(4) > N(6): This statement represents that at 4 hours after the food truck opens, the number of people in line is greater than at 6 hours after the food truck opens.
d. N(R) = 34: This statement represents that the number of people in line at an unspecified time R is 34. The letter "R" can be any value for time, it is only a placeholder for any arbitrary value.
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Select the correct answer.
What is the y-intercept of function f?
(-3x - 2,
-∞ <
-x + 1,
-2 ≤ x ≤ 3
2x + 5,
3 ≤ x < 00
f(x)
=
OA. -1
OB. 5
O C. 1
OD. -2
< -2
Answer:
The correct answer is C. 1
Need help for math k12
Answer:
9y^8
Step-by-step explanation:
15/5 = 3
y^6 / y^2 = y^4
so you are looking at basically (3y^4)² = 3y^4 * 3y^4 = 9y^8
How to do this question? I don't really know what the lines next to 2t are, or are they just brackets?
Answer:
- 14
Step-by-step explanation:
the bars around 2t , indicate the absolute value of 2t
the absolute value function always gives a positive value , that is
| - a | = | a | = a
so for example
| - 4 | = | 4 | = 4
given
[tex]\frac{2}{3}[/tex] p - | 2t | - s² ( substitute values for p, t and s into the expression )
= [tex]\frac{2}{3}[/tex] × 12 - | 2(- 3) | - (- 4)²
= 2 × 4 - | - 6 | - 16
= 8 - 6 - 16
= 2 - 16
= - 14
How do you solve the equations that is listed to the right? (8x-9)-(3x-1)
Answer: The answer is 5x-8.
Step-by-step explanation: The equation we have is (8x-9)-(3x-1). The first step is to write the equation as shown:
8x-9-(3x-1)
After that step, next is to apply the distributive law:
8x-9-3x+1
Then, group/combine like terms:
8x-3x-9+1
Then adding similar elements:
5x-9+1
And finally, solving:
5x-8
Use a model to solve t+4=5.
The model to solve t + 4 = 5 is that John hast number of oranges and got 4 more making 5 oranges.
How to explain the model?A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modeling is the process of creating a mathematical model.
To make a prediction or offer insight, mathematical modeling is the process of creating a mathematical representation of a real-world scenario.
The equation t + 4 = 5 can be solved by subtracting 4 from both sides of the equation:
t + 4 = 5
t = 5 - 4
t = 1
So t = 1 is the solution to the equation
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Find the zeros of the function.
Enter the solutions from least to greatest.
f(x) = 8x² - 800
lesser x =
greater x =
The zeros of the function are -10 and +10
lesser x = -10
greater x = +10
What are zeros of a quadratic equation?The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. . The zeros of quadratic equation will always have two values.
f(x) = 8x²- 800
f(x) = y
y = 8x²-800
when the graph crosses x axis the value of y = 0
therefore 0 = 8x²-800
divide both sides by 8
0 = x² - 00
x² = 100
x= √100
x= ±10
therefore lesser x = -10
greater 10 = +10
therefore the zeros of the quadratic equation f(x) = 8x²- 800 = +10 and -10
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The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
Answer:
Step-by-step explanation:
a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525
b) Overestimate
the maked pieceof a t shirt is 220. a discount of 20% is announced on sales. then the selling price is
In this case, the marked price of 220 is the cost price and discount of 20% is announced on sales, so the selling price is 176.
How is this determined?The t-shirt costs $166.5 to purchase. To do this, multiply the listed price (220) by the discount rate (20%) stated as a decimal. This will give you the amount of the discount (0.20).
220*0.20 =44
The selling price is then determined by deducting the discount (44) from the marked price (220):
220-44 =176
Before applying any markups or reductions, the retailer paid the item's cost price, commonly referred to as the wholesale price. The price a consumer pays to purchase an item is known as the selling price. The selling price will be less than the advertised price if a discount is being offered, and the difference between the two represents the discount.
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A cruise line ship left port A and traveled 80 miles due west and then 150 miles due north at this point what is the shortest distance from the cruise to port A in miles
Answer:
170 miles
Step-by-step explanation:
Use 80 miles and 150 miles as the legs of a right triangle, and find the length of the hypotenuse using the Pythagorean theorem.
a² + b² = c²
80² + 150² = c²
6400 + 22500 = c²
c = √28900
x = 170
Answer: 170 miles
Which list orders the decimal numbers 1.47, 4.01, 1.4, and 4.1 from least to greatest?
Answer:
Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.
Least to greatest is 1.4, 1.47, 4.01, and 4.1
Carlos solved the equation below incorrectly.
13(12x−9)=12(x+18) 16x−3=12x+9 14x−3=9 14x=12 x=48
Identify Carlos' error and then solve the equation correctly. (3 points)
Enter your answer and your work or explanation in the space provided.
Answer: Please see explanation column for answer.
x= -36
Step-by-step explanation:
Step 1
from the attachment, Carlo solving is given as
1/3 (1/2x- 9) = 1/2 (x+18)
1/6x-3= 1/2x+9
1/4x-3=9
1/4x=12
x=48
Carlos error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.
Solving correctly, we have that
1/3(1/2x-9) = 1/2(x+18)
1/6x -3= 1/2x+ 9
taking like terms to like terms
1/6x-1/2x= 9+3
(1-3)/6x= 12
-2/6x= 12
-1/3x= 12
multiplying both sides by -3
-1/3x X -3 = 12 X -3
x= -36
Three years ago,a father was three times as old as his so.in five years time,the father will be twice as old as his son,what will be the sum of their ages in four years
let f = father's present age, let s = son's
:
write an equation for each statement, simplify
:
Three years ago a father was thrice as old as his son
f - 3 = 3(s-3)
f - 3 = 3s - 9
f = 3s - 9 + 3
f = 3s - 6
in 5 years time the father will be twice as his son
f + 5 = 2(s+5)
f + 5 = 2s + 10
f = 2s + 10 - 5
f = 2s + 5
replace f with 3s - 6, from the 1st statement
3s - 6 = 2s + 5
3s - 2s = 5 + 6
s = 11 yrs is the son's age
find the fathers age
f = 3(11) - 6
f = 33 - 6
f = 27 yrs is the father's age
:
what will be the sum of their age in four years
27+4 + 11+4 = 46
have been generated by a linear function?
Answer:
no.................,.............
Mia and her children went into a bakery that sells cupcakes for $2.50 each and donuts for $1.25 each. Mia has $30 to spend and must buy no less than 14 cupcakes and donuts altogether. If � x represents the number of cupcakes purchased and � y represents the number of donuts purchased, write and solve a system of inequalities graphically
Answer:
2.50x + 1.25y ≤ 30
x + y ≥ 14
x ≤ 10 and y ≤ 24
Step-by-step explanation:
we can by elimination if we multiply the second inequality by -2.5, we get:
-2.50x - 2.5y ≥ -35
if we add the first inequality to the above we get:
2.50x + 1.25y ≤ 30
+ -2.50x - 2.5y ≥ -35
-1.25y = -5
divide each side by -1.25 to get:
y = 4
therefore, x = 10
if you graph each system you must look for the area where the shading of each inequality overlaps
upon graphing, the solution is x ≥ 10 and y ≤ 24
what is right! its either a or c
Answer: I believe it is A
Make x the subject of m=n+x/p
Answer:
x = p(m-n)
Step-by-step explanation:
we can eliminate the 'p' in the denominator by multiplying each side of the equation by 'p' to get:
mp = np + x
now we can subtract 'np' from each side to get:
mp - np = x
we can further simplify it as:
p(m-n) = x
Answer:
X=n-p×m
Step-by-step explanation:
m=n-x/p
p×m=n-x
n-p×m=n+x-n
X=n-p×m
(1/5 x 5)^5 this is the problem
The problem involving exponents (1/5 x 5)⁵ is calculated to get 1
How to solve the problem involving exponentsInformation made available in the question is an equation of the form
= (1/5 x 5)⁵
The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved using parenthesis first
= (1/5 x 5)⁵
= (1)⁵
Then exponents
= (1)⁵
= 1 * 1 * 1 * 1 * 1
= 1
The solution is 1
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HURRY PLEASE!!! What are the marginal
column totals?
The marginal column total for the given data is option D: 39; 16.
What is marginal total?
A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.
The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.
The number of men who prefer to eat fish = 11
The number of women who prefer to eat fish = 6
The number of men who prefer to eat red meat = 28
The number of women who prefer to eat red meat = 10
So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -
11 + 28 = 39
The marginal column total for the number of women who prefer to eat fish and red meat collectively is -
6 + 10 = 16
Therefore, the marginal total is 39, 16.
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