Answer:
the probability of event B is approximately 0.48.
Step-by-step explanation:
P(A) = P(B) (given)
P(A∪B) = P(A) + P(B) - P(A∩B) (probability rule for the union of two events)
Since events A and B are independent, we know that P(A∩B) = P(A) × P(B).
Substituting the given values, we get:
0.63 = P(A) + P(B) - P(A) × P(B)
Since P(A) = P(B), we can substitute P(B) for P(A):
0.63 = 2P(B) - P(B)^2
Rearranging this equation, we get:
P(B)^2 - 2P(B) + 0.63 = 0
This is a quadratic equation that we can solve using the quadratic formula:
P(B) = [2 ± sqrt(4 - 4×0.63)] / 2
P(B) = [2 ± sqrt(1.48)] / 2
P(B) ≈ 1 or P(B) ≈ 0.48
Since probabilities must be between 0 and 1, we can discard the solution P(B) = 1, and the only possible solution is:
P(B) ≈ 0.48
Therefore, the probability of event B is approximately 0.48.
5 In a game that you are playing, your friend says that she has -6 points "give or take" 4 points. You currently have -3 points in the game. Can you say who is winning? Why or why not? Use a number line to explain.
Based on the information provided, it's not possible to say who is winning without knowing the specific game and how points are scored and awarded.
How to explain the informationThe statement "has -6 points give or take 4 points" doesn't provide a specific range of points that your friend could have, so we can't use this information to determine a winner.
Additionally, using a number line to compare two points of -3 and -6 is not helpful in determining who is winning in the game because it only shows their relative values, not the actual rules of the game and how points are scored.
It would be best to ask the friend to clarify their score and the rules of the game to determine who is winning.
Learn more about number line on:
https://brainly.com/question/24644930
#SPJ1
Find the explicit equation.
Answer:
f(n) = 10 + 3n
Step-by-step explanation:
Each of the expressions has 10 + a certain number of 3's
For example for n = 3 we have
f(3) = 10 + 3 threes = 10 + 3 x 3 = 10 + 9 = 19
For n = 4, we have
f(4) = 10 + 4 threes = 10 + 4 x 3 = 10 + 12 = 22
The others follow the same pattern
So the explicit equation is
f(n) = 10 + 3n
Testing on n = 6 we get
f(6) = 10 + 6n = 10 + 6 x 3 = 10 + 18 = 28
There are 4 grams of sugar in 1⁄2 of a liter of a new sports drink. How much sugar is in 3⁄4 of a liter of the sports drink?
Answer:
6 grams of sugar in 3/4 liter.
Explanation:
Recall that two 1/4 portions is equal to 1/2. So if 1/2 liter has 4 grams, 1/4 liter will have 2 grams of sugar.
Every 1/4 liter will have 2 grams of sugar.
Therefore, 3/4 liter will have 3 times as much sugar as 1/4 liter. The amount of sugar in 3/4 liter will be 3 times 2 grams or 6 grams of sugar in 3/4 liter
Why Eulerian path can be implemented in linear time, but not Hamiltonian path?
Eulerian path can be implemented in linear time because it follows a specific rule: a connected graph can have an Eulerian path if and only if it has either zero or two vertices of odd degree.
This means that the algorithm can quickly determine whether or not a graph has an Eulerian path by simply counting the number of odd degree vertices. This can be done in linear time, making the implementation of Eulerian path efficient and fast.
On the other hand, Hamiltonian path does not follow a specific rule, and there is no known efficient algorithm to determine whether or not a graph has a Hamiltonian path.
This means that the implementation of Hamiltonian path requires checking all possible paths in the graph, which can take a long time and is not efficient. Therefore, Hamiltonian path cannot be implemented in linear time like Eulerian path can.
To know more about Eulerian path click on below link:
https://brainly.com/question/27979322#
#SPJ11
Determine if the expression − � + 3 � 5 − � 2 −a+3a 5 −a 2 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
No, the expression − + 3 × 5 − 2 −a+3a 5 −a 2 is not a polynomial.
What is expression?In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers. Expressions can be complex, and often appear in the form of equations or formulas. Examples of expressions include equations, polynomials, functions, matrices and more.
A polynomial is an expression that is a sum of one or more terms, each of which is the product of a constant and a non-negative integer power of a variable. In the expression given, the exponent of the variable a is negative, which does not meet the criteria to be considered a polynomial.
To know more about expression click-
https://brainly.com/question/1859113
#SPJ1
A bowling alley charges $3+tax per shoe rental and $4+tax per person per game. If you and a friend bowl 3 games and each rent a pair of shoes, how much will it cost in all?
tax rate is - 13%
The total cost will be $21 for the bowling alley.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that a bowling alley charges $3 plus tax for each pair of shoes and $4 plus tax for each player every game. If you and a friend hire a pair of shoes and bowl three games.
The total cost will be calculated as:-
Cost = ( 3 + 4 ) x 3
Cost = 7 x 3
Cost = $21
Therefore, the total cost will be $21.
To know more about an expression follow
https://brainly.com/question/1859113
#SPJ9
i need help on this i would appreciate you soo much!!
Answer:
2(-3x+2)^2 -1
Step-by-step explanation:
so first you would find that f(g(x)) = f(-3x+2)
next plug in
f(-3x+2) = 2x^2-1
to every x
f(-3x+2) = 2(-3x+2)^2-1
Solve the given differential equation by using an appropriate substitution. The de is a bernoulli equation. X dy dx + y = 1 y2.
The Bernoulli equation of given differential equation Xdydx + y = 1y² is ln (1 - x/y - x) = c
Any equation with one or more derivates and one or more terms of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)
-1/y = u
y¹/y² = u¹
xy¹ - (1 + x)y = xy²
now take the y² on other side,
xy¹/y² - (1 + x)/y = c
now replace the values by u¹,
xu¹ + (1 + x)u = x
xu¹ + u + ux = x
xu = s ....[1]
Substitute the value of xu as s
u + xu¹ = s¹
s¹ + s = v
s - x = t
s¹ - 1 = t¹
t¹ + 1 + t = 0
Now take the integration of both the sides,
dt/dx = - ( 1 + t)
-∫ dt/1+t = ∫dx
-ln ( 1+ t ) = x + c
now ,put the value of t,
-in ( 1 + s - x ) = x + c
now put the value of s,
-ln ( 1 + xu - x ) = x + c
-ln ( 1 - x/y - x) = c.
Learn more about bernoulli equation here :-
https://brainly.com/question/9506577
#SPJ4
An army sergeant works as a trauma surgeon. Which two career clusters is she most likely a part of?
the Energy cluster and the Education and Training cluster
the Health Services cluster and the Energy cluster
the Government and Public Administration cluster and the Health Services cluster
the Education and Training cluster and the Government and Public Administration cluster
Both clusters are relevant to her career.
Why is it referred to as a cluster?Cluster is derived from the old english word clyster, which means a group. Cluster is now used as both a noun and a verb.
The army sergeant who works as a trauma surgeon is probably in the Health Services and Government and Public Administration clusters.
Health Services occupations include diagnosing, treating, and preventing illnesses and injuries, while Government and Public Administration occupations include planning, managing, and providing government functions and services. The individual is a member of the military, which is a government organisation, and a trauma surgeon, which is a part of the healthcare industry. As a result, both clusters are pertinent to her career.
To know more about Clusters visit:
https://brainly.com/question/30180321
#SPJ1
What is the value of 36celsius in fahrenheit?
The temperature conversion from Celsius to Fahrenheit is calculated using the following formula: Fahrenheit = (Celsius x 1.8) + 32. Increasing the Celsius temperature by 1 degree will result in an increase of 1.8 degrees Fahrenheit.
To convert a temperature of 36 degrees Celsius to Fahrenheit, we first multiply 36 by 1.8 to get 64.8, then add 32 to that result to get 96.8 degrees Fahrenheit. In other words, 36 degrees Celsius is equal to 96.8 degrees Fahrenheit. To better understand this conversion, it helps to remember that 0 degrees Celsius is equivalent to 32 degrees Fahrenheit. The two scales are offset by 32 degrees, meaning that for every degree Celsius, the equivalent Fahrenheit temperature is 1.8 degrees higher. For example, 10 degrees Celsius is equivalent to 50 degrees Fahrenheit (10 x 1.8 = 18 + 32 = 50). Thus, increasing the Celsius temperature by 1 degree will result in an increase of 1.8 degrees Fahrenheit.
Learn more about degrees here:
https://brainly.com/question/28162756
#SPJ4
The measure of central location most often reported for annual income and property value data is the__
A. Mode
B. Median
C. aggregate mean
D. weighted mean
What is the difference between AIC and BIC penalty?
The difference between AIC and BIC penalty lies in their approach to model selection.
AIC (Akaike Information Criterion) is a measure of the goodness of fit of a statistical model. It is used to compare different models and select the one that fits the data best. AIC is based on the principle of maximum likelihood, which means it is more focused on finding the model that fits the data best.
On the other hand, BIC (Bayesian Information Criterion) is a criterion for model selection based on the Bayesian approach. It is also used to compare different models, but it takes into account the complexity of the model. BIC tends to favor simpler models, and it is more focused on finding the model that is most likely to be true given the data.
In summary, AIC is more focused on finding the model that fits the data best, while BIC is more focused on finding the model that is most likely to be true given the data.
To know more about Akaike Information Criterion click on below link:
https://brainly.com/question/22238859#
#SPJ11
A triangle has sides with lengths of 4 miles, 6 miles, and 8 miles. Is it a right triangle?
yes or no
Answer:
scalene, right triangle
Step-by-step explanation:
Determine whether it is a triangle and the triangle's type:
Answer: scalene, right triangle
Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.
A. (8 * t) + (8 * 8) is equivalent to 8t + 64
B. 4t + 8 + 4t is equivalent to 8t + 8
C. 4(2t + 2) is equivalent to 8t + 8
D. 8t + 64 is equivalent to 8t + 64
E. 8t + 16 is equivalent to 8t + 16
F. (8 + t) + (8 + 8) is equivalent to 16 + t.
So the expressions that are equivalent to 8(t + 8) are B and C, the expression that is equivalent to 8t + 8 is E, and the expression that is neither is F.
In the given problem, we are comparing the given expressions to see if they are equivalent to 8(t + 8), 8t + 8, or neither.
Expression A: (8 * t) + (8 * 8) = 8t + 64
This expression is equivalent to 8t + 64, which is not the same as 8(t + 8) or 8t + 8.
Expression B: 4t + 8 + 4t = 8t + 8
This expression is equivalent to 8t + 8, which means that adding up 4t and 8, and then adding 4t again to the result is the same as multiplying 8 with t and adding 8 to the result.
Expression C: 4(2t + 2) = 8t + 8
This expression is also equivalent to 8t + 8, which means that multiplying 2t + 2 with 4 is the same as multiplying 8 with t and adding 8 to the result.
Expression D: 8t + 64 = 8t + 64
This expression is the same as 8t + 64, which is not equivalent to either 8(t + 8) or 8t + 8.
Expression E: 8t + 16 = 8t + 16
This expression is the same as 8t + 16, which is not equivalent to either 8(t + 8) or 8(t + 8).
Expression F: (8 + t) + (8 + 8) = 16 + t
This expression is not equivalent to either 8(t + 8), 8t + 8, or neither.
To know more on expression
https://brainly.com/question/28170201
#SPJ4
--The question is incomplete, answering to the question below--
"Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.
A. (8 * t) + (8 * 8)
B. 4t + 8 + 4t
C. 4(2t + 2)
D. 8t + 64
E. 8t + 16
F. (8 + t) + (8 + 8)"
Volume = 1243.44 in3
Height = 11 in
Solve this equation and you have the answer:
3.14 • 11 • r2 = 1243.44
Radius = in
The radius of the cylinder is approximately 5.88 inches.
What are equivalent equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
We can solve the given equation to find the radius of the cylinder using the volume and height information
3.14 * 11 * r² = 1243.44
First, divide both sides by 3.14*11 to isolate r²:
[tex]r^2 = 1243.44 / (3.14 * 11)[/tex]
r² ≈ 34.585
Taking the square root of both sides, we get:
r ≈ 5.88
Hence, the radius of the cylinder is approximately 5.88 inches.
To learn more about equivalent equations, Visit
https://brainly.com/question/2972832
#SPJ1
Vrite a cubic equation in standard form whose graph passes thr
1, 0), (2, 0), (0, -8), and (4, 0).
The cubic equation is given by A = x³ - 7x² + 14x - 8
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The coordinates of the points are A ( 1 , 0 ) , B ( 2 , 0 ) , C ( 0 , -8 ) , D ( 4 , 0 )
Now , the equation will be
f ( x ) = a ( x - 1 ) ( x - 2 ) ( x - 4 )
So , when x = 0 , the value of y = -8
-8 = a ( -1 ) ( -2 ) ( -4 )
-8 = a ( -8 )
8a = 8
Divide by 8 on both sides of the equation , we get
a = 1
Substitute the value of a in the equation , we get
f ( x ) = ( x - 1 ) ( x - 2 ) ( x - 4 )
f ( x ) = x³ - 7x² + 14x - 8
Hence , the equation is f ( x ) = x³ - 7x² + 14x - 8
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ9
Chapter 4 Lesson 3 Solving System of Equations Using Elimination
The solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54
by elimination are respectively:
x = -4, y = -4
x = 3, y = -1
x = 5, y = 1
x = -6, y = 4
How to evaluate for the solutions of the equations by eliminationwe shall write the equations as:
7x - 4y = -12...(1)
x - 2y = 4...(2)
multiply equation (2) by 7 to get equation (3)
7x - 14y = 28...(3)
subtract equation (1) from (3) to eliminate x
7x - 14y - 7x + 4y = 28 + 12
-10y = 40
divide through by -10
y = -4
put the value -4 for y in equation (2) to get y
x - 2(-4) = 4
x + 8= 4
x = -4
x - y = 4...(1)
2x + y = 5...(2)
Add equations (1) and (2) to eliminate y
2x + y + x - y = 5 + 4
3x = 9
divide through by 3
x = 3
put the value 3 for x in equation (1) to get y
3 - y = 4
y = -1
4x - 3y = 17...(1)
2x - 5y = 5...(2)
multiply equation (2) by 2 to get equation (3)
4x - 10y = 10...(3)
subtract equation (3) from (1) to eliminate x
4x - 3y - 4x - 10y = 17 - 10
7y = 7
divide through by 7
y = 1
put the value 1 for y in equation (2) to get y
2x - 5(1) = 5
2x - 5 = 5
x = 5
5x + 6y = -6...(1)
7x - 3y = -54...(2)
multiply equation (1) by 7 to get equation (3) and equation (2) by 5 to get equation (4)
35x + 42y = -42...(3)
35x - 15y = -270...(4)
subtract equation (4) from (3) to eliminate x
35x + 42y - 35x + 15y = -42 + 270
57y = 228
divide through by 57
y = 4
put the value for y in equation (1) to get x
5x - 6(4) = -6
5x + 24 = -6
x = -6
Therefore, the solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54
by elimination are:
x = -4, y = -4
x = 3, y = -1
x = 5, y = 1
x = -6, y = 4
Know more about elimination here:https://brainly.com/question/28405823
#SPJ1
Can someone pls help meeeeeee!!!
Answer:
For question 2, Ethan needs 3 cups of milk to make the batter for 3 times as many cakes.
For question 3, Isabella needs 5/4 of a gallon of the food to make 5 gallons of the mixture.
The sides of a triangle are 60, 68, and 32. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a=2.7 yards and b=1.6 yards, what is c? If necessary, round to the nearest tenth.
Answer:
[tex]\huge\boxed{\sf c = 3.1\ yards}[/tex]
Step-by-step explanation:
Given that,a = 2.7 yards
b = 1.6 yards
c = hypotenuse
Using Pythagoran Theorem:
[tex]c^2=a^2+b^2[/tex]
Put the given data.c² = (2.7)² + (1.6)²
c² = 7.29 + 2.56
c² = 9.85
Take square root on both sidesc = √9.85
c = 3.1 yards[tex]\rule[225]{225}{2}[/tex]
HELPPPPPPPP PLEASEEEE
algebra
Answer:
Your answer would be (x, y) = (0, 0)
Step-by-step explanation:
Please refer to the screenshot underneath.
What is the value of the next term in the following sequence
1, 5, 25, 125, 625 . . .
9. A helicopter is traveling at a speed of 44 meters per second in the direction of S 61° E. Find the
magnitude of the horizontal and vertical components.
The magnitude of the horizontal and vertical components are 21.33 m/s and 38.48 m/s
How to find the magnitude of the horizontal and vertical components.From the question, we have the following parameters that can be used in our computation:
Velocity = 44 meters per second
Direction = S 61° E
This means that
V = 44 and angle = 61°
The direction angle is 61° from the positive x-axis (E), so we can use the following trigonometric relationships to find H and V:
H = 44 * cos(61°) --- horizontal
V = 44 * sin(61°) --- vertical
Using a calculator, we can find that:
H = 21.33 m/s
V = 38.48 m/s
Read more about speed at
https://brainly.com/question/24571540
#SPJ1
Lee biked 11 1/4 miles in 3/4 of an hour. What is Lees biking speed?
Answer: First find your given information:
D=6 miles (3 miles there + 3 miles back)
T=1 hour
Vwind= 3 mph
We're going to assume that the wind's velocity is always in opposite direction to Mr. Lee so:
VFinal = VMr. Lee - Vwind
We also know that VFinal=D/T
So D/T = VMr. Lee - Vwind
Rearrange to get VMr. Lee = D/T + Vwind
Plug in your given info to get VMr. Lee = (6 miles)/(1 hours) + 4 mph or 10 mph
Tno wind= D/VMr. Lee or (6 miles/10 mph)
Tno wind=0.6 hours
Step-by-step explanation:
Answer:
15 mphStep-by-step explanation:
3 3/4 + 11 1/4 = 15
1/3 of 11 1/4 is 3.75 or 3 3/4. I added 3 3/4 to 11 1/4, and checked my answer, which was 15, by dividing it by four.
I know its confusing sorry, I hope you understand ^^
Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to angie how to solve this equation.
To solve the exponential equation 23^x = 6, take the logarithm base 23 of both sides to get x = log base 23 of 6.
Angie, to solve the exponential equation 23^x = 6, you need to find the value of x such that when you raise 23 to the power of x, you get 6. To do this, you can use logarithms.
In particular, you can use the logarithmic function log_23. The log_23 of a number y is the exponent x such that 23^x = y. So, to solve the equation 23^x = 6, you can take the log_23 of both sides:
log_23(23^x) = log_23(6)
x = log_23(6)
The right side of this equation can be evaluated using a calculator or logarithmic tables. Once you have the value of x, you will have solved the exponential equation.
To know more on exponential equation
https://brainly.com/question/29506679
#SPJ4
What is the division derivative rule?
Answer:
6
Step-by-step explanation:
ــــــ
-5
4
1
22
D) Where is Point A on the number line?
-3
1
-3
2
1
3-
2
2
2
2
2
A
||||
4
3
5
The Point A on the number line is 2 1/2
Where is Point A on the number line?From the question, we have the following parameters that can be used in our computation:
The number line
On the number line, we have
A = Halfway between 2 and 3
Using the above as a guide, we have the following:
A = (2 + 3)/2
Evaluate
A = 2 1/2
Hence, the position is 2 1/2
Read more about number line at
https://brainly.com/question/24644930
#SPJ1
What is the median of these numbers?
56, 65, 77, 81, 92
If needed, round your answer to the nearest tenth.
Answer:
74.2
Step-by-step explanation:
Median is another word for average amount.
So if you add the numbers 56, 65, 77, 81, and 92 you would end up with 371.
To get an average, or the median, you take the numbers, add them together, then divide the answer by how ever many numbers you had.
In this case, you had 5, so
56+65+77+81+92=371
then divide by 5 so
371/5=74.2
leading coefficient of -1 and a constant term of -20
The roots of the equation is x = -20
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The leading coefficient of the equation is -1
And , the constant term is -20
Now , according to rational root theorem ,
So , the equation is
-x - 20 = 0
Adding x on both sides of the equation , we get
x = -20
Therefore , the value of x is -20
Hence , the equation is x = -20
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ9
PLS HELP
If the difference of a number and nine is doubled, the result is eight more than the number. Find the number. Round your answer to the nearest integer, if necessary.