An interest rate of 2.5 % is required to obtained a current capital of $ 143,000 after a period of 16 years.
How to find the interest rate of a deposit
In this problem we find that Jayden deposits an amount of money for a period of 16 years and such account is under composite interest, that is, that the account increases its capital continously in time. Compound interest model is shown:
C' = C · (1 + r / 100)ˣ
Where:
C - Initial capital, in monetary units.C' - Current capital, in monetary units. r - Interest rate, in percentage.x - Number of periods, in years.If we know that C = 97,000, C' = 143,000 and x = 16, then the interest rate is:
143,000 = 97,000 · (1 + r / 100)¹⁶
143 / 97 = (1 + r / 100)¹⁶
1.025 = 1 + r / 100
0.025 = r / 100
r = 2.5
The needed interest rate needed for a capital of $ 143,000 after a period of 16 years is equal to 2.5 %.
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Evaluate.
Remember Order of Operations!
(PEMDAS)
2+16÷2²-3×2
-2 1/3x = -1 3/4
I need it rn
Answer:2
Step-by-step explanation: To solve the equation -2 1/3x = -1 3/4, we need to isolate the variable x on one side and simplify the equation.
First, we need to convert both sides to have the same denominator. We can choose the least common multiple of 3 and 4, which is 12.
-2 1/3x = -1 3/4
-2 1/3 * 4/4 * x = -1 3/4 * 3/3
-8/3 x = -5 1/3
Next, we isolate x by dividing both sides by -8/3:
(-8/3) x / (-8/3) = -5 1/3 / (-8/3)
x = (5 1/3) / (8/3)
x = (5 1/3) * (3/8)
Finally, we simplify the fraction to get the final solution:
x = (5 1/3) * (3/8)
x = (5 * 3 + 1 * 3) / 8
x = 16 / 8
x = 2
Therefore, the solution to the equation -2 1/3x = -1 3/4 is x = 2.
Children 12 and under eat free at a local retaurant. If x repreent age, write an inequality to repreent the age of people who do not get a dicount
At a local eatery, children who is 12 or under 12, eat free. The inequality for non-discounted people is x > 12.
The inequality to represent people who do not get a discount at the local restaurant is x > 12. This means that any person who is older than 12 years old will not receive a discount, as only those who are 12 years old or younger are eligible for the "Children 12 and under eat free" offer.
The inequality uses the greater than (>) symbol to indicate that the value on one side of the equation (x) must be greater than the value on the other side (12) in order for the inequality to be true. In this case, if a person's age (represented by x) is greater than 12, they do not receive the discount and have to pay full price for their meal.
This question should be provided as follows:
Children 12 and under eat free at a local restaurant. If x represents age, write an inequality to represent the age of people who do not get a discount.
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please answer thanks
Step-by-step explanation:
This is a question where everyone's answer will be different. Here's my example answer.
Two goals for me:
A used car (2011 Honda Pilot is $11500)
A diamond necklace (14k white gold from Jared is $11900)
The used car would be a need because it would be my only way to get to work and school
The diamond necklace would be a want because I don't need it to stay alive and we'll, just to look good
The functions fand g are defined as follows.
g(x) = 2x³ +2
f(x) = 3x+4
Find f(-5) and g(-3).
Simplify your answers as much as possible.
f(-5) = 1
9(-3) =
010
X
Answer: f(-5)=-11 g(-3)=-52
Step-by-step explanation:
This figure is made up of two rectangular prisms.
What is the volume of the figure?
Enter your answer in the box.
cm³
Three-dimensional figure that could be formed by placing a smaller rectangular prism on top of a larger rectangular prism such that the widths of the prisms are the same. The larger bottom prism has a length of 22 centimeters, a width of 13 centimeters, and a height of 5 centimeters. The smaller top prism has a length of 6 centimeters and a height of 2 centimeters.
The volume of the given figure which is the sum of two rectangular prism would be = 1,490cm³
How to calculate the volume of a rectangular prism?The formula the is used to calculate the volume of a rectangular prism = v= length×width×height
There are two rectangular prism:
For the smaller prism;
where;
length= 6cm
height= 2cm
width= 5cm
volume = 6×2×5= 60cm³
For the larger prism;
length= 22cm
height= 5cm
width= 13cm
volume = 22×5×13 = 1,430cm³
The total volume of the figure = 1430 +60 = 1,490cm³
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When solving the equation, which is the best first step to begin to simplify the equation?
-2(x+3)=-10
O (-2)(-2)(x+3) =-10(-2)
0-3(-2)(x+3) --10-2)
{(x+3)-510
o Zo(x+3) = -10
The best first step to begin to simplify the equation -2(x + 3) = -10 is:
Dividing both sides of the equation by -2 to get x + 3 = 5
As per the given data, the equation is given by -2(x + 3) = -10
We have to determine the best first step in solving the equation:
-2(x + 3) = -10
Firstly we start by distributing -2 in the bracket (x + 3)
-2x - 6 = -10
Or
-2(x + 3) = -10
Also if we divide both sides of the equation by -2, we get
x + 3 = 5
Now, we can easily solve the equation.
Hence, the first best step to begin to simplify the equation -2(x + 3) = -10 is:
Distributing -2 in the bracket (x+3)
We get -2x -6 = -10
Or Dividing both sides of the equation by -2
We get x + 3 = 5
Here in options given x + 3 = 5
Hence option (c) is correct.
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PLS PLS PLS PLS PLS PLS BRAINLIEST WILL GIVE
A zoologist recorded the speed of two cheetahs. Cheetah A ran 18 miles in 16 minutes. Cheetah B ran 54 miles in 50 minutes. Which statement is correct?
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50.
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is less than 54 over 50.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Both cheetahs have the same ratio of miles per minute.
Answer:
A
Step-by-step explanation:
18/16=1.125
54/50=1.05
Therefore, Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50. So A is the correct answer.
Hope that helped!
Which i an example of a demand account?
aving account
invetment account
credit account
checking account
Saving account is an example of a demand account.
What sort of account may you use for Demat?For the purpose of purchasing and selling shares on the stock market, a Trading Account is typically kept in tandem with a Demat Account. One such 3 in 1 Account offered by HDFC Bank combines a trading account with a demat account and a savings account.Having shares and securities in an electronic format is made possible by a demat account. Also known as a dematerialized account, this type of account. Additionally, it is beneficial to retain accurate records of all investments made in bonds, mutual funds, ETFs, and shares in one location.To learn more about demand account refer to:
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What is the formula for torr to atm?
The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.
Given, that convert torr to atm.
Atmosphere (atm) and torr are both units of pressure measurement. Torr is a unit of pressure in the centimeter-gram-second (CGS) system, while atm is a unit of pressure in the International System of Units (SI).
The conversion from torr to atm involves multiplying the torr value by a conversion factor of 1/760. This is because 1 atm is equal to 760 torr.
For example:
To convert 2.77 atm to torr, multiply 2.77 by 760, which gives 2,108 torr. In conclusion, 2.77 atm is equal to 2,108 torr.
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Dani i collecting rainwater in a 1-litre jug. On Monday, he collect 220 ml of water. On Tueday, he collect a quarter of a litre of water. At the end of Wedneday, Dani ee he only need another 0. 1 litre until her jug i full. How much water did Dani collect on Wedneday?
Dani collecting rainwater in a 1 litre jug. So much water did Dani collect on Wedneday is 530 ml.
How much water did Dani collect on Wedneday?These are the specified parameters:
Monday = 220 ml
Tuesday = 1/4 litre
Wednesday = 0.1 litre
Fill the jug = 1 liter
A lot of water that has not been collected
= Fill the jug - (monday + tuesday + wednesday)
= 1 litre - (220 ml + 1/4 litre + 0.1 litre)
= (1 × 1000) ml - (220 ml + (1/4 × 1000) ml + (0.1 × 1000) ml)
= 1000 ml - (220 ml + 250 ml + 100 ml)
= 1000 ml - 570 ml
= 430 ml
Much water did Dani collect on Wedneday
= 0.1 litre + 430 ml
= 100 ml + 430 ml
= 530 ml
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Which expression is equivalent to
x2 − 2x − 5
x − 3
?
A) x − 5 −
20
x − 3
B) x − 5 −
10
x − 3
C) x + 1 −
8
x − 3
D) x + 1 −
2
x − 3
The expression which is equivalent to x² - 2x -5 /x-3 from the following is x+1 - 2/x-3.
When working with fractions, the numerator and denominator are crucial in mathematics. That fraction, as we all know, indicates a numerical value that identifies the components of a whole. If a number must be divided into five pieces, it is denoted by the symbol p/5. In this case, the fraction p/5 denotes the fifth of the integer p. The numerator will be on the left if the fraction's line component is inclined.
The denominator of a fraction is the fraction's divisor. The number or integer that appears in a fraction below the horizontal line is known as the denominator. whereas in a fraction, the numerator is above the line. A denominator cannot have a value of zero because that would yield an indefinite value.
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The graph below represents the value of a car, in thousands of dollars, with respect to the number of years since it was purchased.
Based on the graph, what was the initial value of the car (in thousands of dollars)?
Responses
0
0
10
10
12
12
15
Answer:154
Step-by-step explanation:
12+12=24 24+1=25 25-10=15
consider a facial recognition system that is used in an airport. this system has cameras that collect images of people's faces and analyzes them against a database of known criminals. how reliable does the facial recognition system have to be such that on average it does not observe more than 20 false positives within a sample of 10 million people processed? calculate the reliability as a percentage value. write your answer to 5 decimal places (e.g. 12.12345). (hint: reliability
Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767
There are several applications for facial recognition technology, including security and surveillance, access control, marketing, and social media. The most popular type of facial recognition technology makes use of biometrics, which track and examine the physical and behavioral traits of individuals.
When issuing identity documents, facial recognition is utilized, most frequently in conjunction with other biometric technology like fingerprints (preventing ID fraud and identity theft). At border crossings, face match is used to match the portrait on a digital biometric passport with the owner's face.
If the server needs all of the 10 million functioning to operate as intended, the overall reliability of the system is given by the product of each component's individual reliability:
S = [tex]c_{1} * c_{2} * c_{3} * c_{4} * c_{5} * c_{6} * c_{7} * c_{8} * c_{9} * c_{10} *[/tex]
If the system needs to have a reliability of 0.93, and all components have the same reliability, the required reliability for the components is:
20 = [tex]c^{10}[/tex]
c = [tex]\sqrt[10]{20}[/tex]
c = 1.34928284767
Therefore,
Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767
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Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767
There are several applications for facial recognition technology, including security and surveillance, access control, marketing, and social media. The most popular type of facial recognition technology makes use of biometrics, which track and examine the physical and behavioral traits of individuals.
When issuing identity documents, facial recognition is utilized, most frequently in conjunction with other biometric technology like fingerprints (preventing ID fraud and identity theft). At border crossings, face match is used to match the portrait on a digital biometric passport with the owner's face.
If the server needs all of the 10 million functioning to operate as intended, the overall reliability of the system is given by the product of each component's individual reliability:
S =
If the system needs to have a reliability of 0.93, and all components have the same reliability, the required reliability for the components is:
20 =
c =
c = 1.34928284767
Therefore,
Reliable does the facial recognition system have to be such that on average, then the reliability as a percentage value is C = 1.34928284767
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find the root of the question:
The root of the expression is 3/4
What are index forms?The index form of a number can be described as that number written in the nature of an exponential expression.
They are also forms that are written as a single numbers raised to another number.
Exponents explains the number of times to multiply the base of by itself to simply or evaluate the expression.
Note that the cube root of a number is the value which when multiplied by itself thrice gives the original value.
Given the expression;
[tex]\sqrt[3]{\frac{27}{y} }[/tex]
Find the cube root
3/4
Hence, the value is 3/4
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(4)i'm stuck with my math hw pls help me show all ur steps
Answer: x=7
Step-by-step explanation:
Find the circumference of the circle shown
The circumference of the circle is 54. 64 mm. Option B
How to determine the circumference of the circleIt is important to note that the formula for calculating the circumference of a circle is expressed as;
C = 2πr
Given that the parameters are;
C is the circumference of the circle2 is the constant valueπ takes the constant value 3.14 or 22/7r is the radius of the circleFrom the information given, we have that;
Circumference = 2 × 3.14 × 8.7
Now, multiply the values, we get;
Circumference = 54. 636
Approximate to two decimal place, we get;
Circumference = 54. 64 mm
Hence, the value is 54. 64 mm
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in a city of 190,000 people, there are 17,000 women. what is the probability that a randomly selected person from the city will be a woman?
The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.
1. Calculate the total number of women: 17,000
2. Calculate the total population of the city: 190,000
3. Divide the number of women by the total population: 17,000 / 190,000
4. The probability is approximately 0.089
The probability that a randomly selected person from the city will be a woman is 17,000 / 190,000, or approximately 0.089.
The probability that a randomly selected person from the city of Akron, Ohio will be a woman is 0.089. This means that out of every 100 people, approximately 8.9 of them will be female. The city has a population of 190,000 and 17,000 of them are female. This means that approximately 8.9 percent of the city's population is female.
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What is the product?
(2 x minus 1)(x + 4)
2 x squared minus 4
2 x squared + 4
2 x squared + 7 x minus 4
2 x squared minus 7 x minus 4
The product of the given expressions is 2x squared + 7x minus 4.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expressions are 2x - 1 and x + 4.
We have to multiply both the expressions.
(2x - 1) (x + 4) = (2x . x) + (-1 . x) + (2x . 4) + (-1 . 4)
= 2x² - x + 8x - 4
Adding the like terms together,
(2x - 1) (x + 4) = 2x² + 7x - 4
Hence the multiplication of the given expression gives the expression 2x² + 7x - 4.
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Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.) WebAssign Plot (a) f(−2) DNE Correct: Your answer is correct. (b) lim x→−2 f(x) DNE Correct: Your answer is correct. (c) f(0) 5 Correct: Your answer is correct. (d) lim x→0 f(x) 3.5 Incorrect: Your answer is incorrect. (e) f(2) DNE Correct: Your answer is correct. (f) lim x→2 f(x) 0.5 Correct: Your answer is correct. (g) f(4) 0 Correct: Your answer is correct. (h) lim x→4 f(x) DNE Correct: Your answer is correct.
f(-2) and f(2) does not exist. Limit when x tend to -2, 0 and 4 does not exist. f(0) = 5 and f(4) = -1. Limit when x tend to 2 converges to 0.5.
f(-2) does not exist as shown in the figure there is no definite value at -2. Also limit does not exist at x = -2 as right limit approaches positive infinity where left limit approaches negative infinity.
f(0) equals 5 and not 3.5 as we can see that at 3.5 it is a hole implying it is not defined, while at 5 it is a solid dot. Limit does not exist at f(0) as the left limit approaches 3.5 and the right limit approaches 5.
f(2) does not exist as there is a hole at that point in the graph. Limit as x tend to 2 approaches 0.5 as both right and left limit approaches 0.5.
f(4) equals -1 as the solid dot is at that point. As x tend to 4 the limit diverges to positive infinity implying the limit does not exist.
--The question is not readable, answering to the question below and graph attached--
"Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.)
(a) f(−2)
(b) lim x→−2 f(x)
(c) f(0)
(d) lim x→0 f(x)
(e) f(2)
(f) lim x→2 f(x) 0.5
(g) f(4)
(h) lim x→4 f(x) "
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What is diameter in math?
The length of the line through the center that touches two points on the edge of the circle.
Give an illustration of what diameter is?The spikes extending from one end to the other end through the center of a bicycle wheel are an illustration of diameter. We may compare this to the diameter of a circle, as the diameter is the line segment that runs from one end of the circle to the other, passing through the center.
The diameter of a circle goes from edge to edge and cuts through the center, whereas the radius travels from center to edge. The diameter of a circle divides the form in half.Every circle have infinite no. of diameter.
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One hose can fill a small swimming pool in 85 minutes. A larger hose can fill the pool in 40 minutes. How long will it take the two hoses to fill the pool working together?
Answer:
Below
Step-by-step explanation:
Rate1 = 1 pool / 85 min = 1/85
rate2 = 1 / 40
now find how long it will take with the combined rates
pool / (rates) = time
1 / ( 1/85 + 1/40) = 27.2 min
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the proportion. 16 50 = x 156 . 25 and please blow up before tonight I need it done quick please
The value of x in the given proportion is determined as 10.56.
What is the value of x in the given proportion?
The value of x in the given proportion is calculated by applying the following equation as shown below.
1650 = x ( 156.25 )
where;
x is the unknown variableThe value of x in the given expression is calculated as follows;
x = ( 1650 ) / ( 156.25 )
x = 10.56
Thus, the value of x in the proportion is obtained by dividing both sides of the equation by 156.25 and thereby making the unknown ( x ) the subject of the formula.
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Need help before Friday
The equation for the discounted price should be:
A' = $25*(1 - 20%/100%) = $20
How to find the discounted price?If we have an initial value A, and we decrease it by X (a percentage) then:
The discounted amount is:
D = A*(X/100%)
The new value is:
A' = A*(1 - X/100%)
So, if the initial value is $25 and there is a discount of the 20%, the new value of the item will be:
A' = $25*(1 - 20%/100%)
A' = $25*(1 -0.2)
A' = $25*0.8 = $20
That is the correctly discounted price.
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Find the area and the perimeter of a rectangle with the ide length of 4 1/5 in and 4 2/7 in
The Perimeter is 16.97 inch, and the Area is 18 square inch units.
Given, Length, l = 4 1/5 inch = 21/5 inch
Breadth, b = 4 2/7 inch = 30/7 inch
The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as the product of its length and width times two. As a linear measurement, the perimeter can be expressed in metres, centimetres, inches, feet, etc.
Perimeter of the rectangle = 2 (l + b) = 2 (21/5 + 30/7)
= (147 + 150)(2/35)
= 297 x 2/35 = 16.97 inch
The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes. To determine the area that these objects occupy, use the rectangle's area formula.
Area of the rectangle = l x b
= 21/5 x 30/7 = 18 inch square units
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The Perimeter is 16.97 inches, and the Area is 18 square inch units.
Given, Length, l = 4 1/5 inch = 21/5 inch
Breadth, b = 4 2/7 inch = 30/7 inch
The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as the product of its length and width times two. As a linear measurement, the perimeter can be expressed in meters, centimeters, inches, feet, etc.
Perimeter of the rectangle = 2 (l + b) = 2 (21/5 + 30/7)
= (147 + 150)(2/35)
= 297 x 2/35 = 16.97 inch
The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that can fit inside a rectangle is called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular shapes. To determine the area that these objects occupy, use the rectangle's area formula.
Area of the rectangle = l x b
= 21/5 x 30/7 = 18 inch square units
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Select all the values of P that are solutions for this inequality 10p-8>12
Answer: All values/solutions of P must be greater than 2 to be true to the inequality 10p-8>12
Step-by-step explanation:
When solving inequalities, we treat it like an equation, solving for the variable, in this case, p.
10p - 8 > 12
Lets isolate p
10p - 8 > 12
+8 +8
10p > 20
/10 /10
p > 2
After solving, we now know that all values of P must be greater than 2.
triangle sum and exterior angle theorem find the value of x. serious answers only, will give brainliest pls
The measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.
How to evaluate for the angles x for the trianglesquestion 19 has 2 isosceles triangles and the measure of x can be derived by equating one of the base angles of the smaller triangle to the sum of its 2 opposite angles as follows;
let y be one of the base angles of the smaller triangle so that;
2y = 180 - 56 {sum of interior angles of a triangle}
2y = 124
y = 62
hence;
62 = x + x {exterior angle of a triangle equals the sum of its two opposite angles}
2x = 62
x = 31°
For question 20, we first find the two opposite angles of x as follows;
180 -(62 + 50) = 68
180 - (53 + 80) = 47
x = 68 + 47
x = 115°
Therefore, the measure of angles for questions 19) and 20) are x = 32° and x = 115° respectively using the triangle sum and exterior angle theorem.
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2.8. the event that "a or b but not both" will occur can be written as (a∩b) ∪ (a ∩b) express the probability of this event in terms of p(a), p(b), and p(a∩b). True or false?
The event that "a or b but not both" P{(A∩B) ∪ (A ∩B)}
= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)
In this question, we will use the addition rule of the probability to calculate the required probability. The probability is a positive quantity from zero to one inclusively. The negative probability of an event does not exist
This is for independent events
P(A U B): This is A or B or both:
P(A n B): This is A and B.
P(A U B) = P(A) + P(B) - P(A n B)
P( A n B) = P(A) x P(B)
Hence:
A or B but not both:
P(A U B) = P(A) + P(B) - P(A n B) - P(A n B) = P(A) + P(B) - 2 x P(A n B)
can also be written in terms of the conditional probability P(A|B)
So we can write
P{(A∩B) ∪ (A ∩B)}
= P(A∩B) + P(A∩B) - P(A∩B∩A ∩B)
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In the figure below line k is parallel to line m? Find x
Answer:
corresponding Angles
Step-by-step explanation:
2x+16=3x-7
16-7=3x-2x
9=x
Answer:
x = 23
Step-by-step explanation:
The two angles shown in the diagram are corresponding angles. Therefore, the angles are congruent. 2x + 16 = 3x - 7; simplify to get x = 23
You enter a chess tournament where your probability of winning a game is 0. 3 against half the players (call them type 1), 0. 4 against a quarter of the players (call them type 2), and 0. 5 against the remaining quarter of the players (call them type 3). You play a game against a randomly chosen opponent. What is the probability of winning
The probability of winning chess tournament is 0.375.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Let A₁ be the event of playing an opponent of type i.
A₁ = playing the half of the opponent pool where the probability of winning
P (winning∣A₁) = 0.3
A₂ = playing the half of the opponent pool type 2, where the probability of winning P(winning∣A₂) = 0.4
A₃ = playing the half of the opponent pool type 3, where the probability of winning P(winning∣A₃) =0.5
By total probability theorem, we get,
P(winning)=P(A₁) P(winning∣A₁) +P(A₂) P(winning∣A₂) +P(A₃) P(winning∣A₃)
P(winning)=50%×0.3+25%×0.4+25%×0.5
P(winning)=0.375.
The probability of winning chess tournament is 0.375.
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The probability of winning the game depends on the type of opponent. If the opponent is of type 1, the probability of winning is 0.3; type 2, 0.4; and type 3, 0.5.
The probability of winning the game depends on the type of opponent. There are three types of opponents: type 1, type 2, and type 3. Against type 1 opponents, the probability of winning is 0.3. Against type 2 opponents, the probability of winning is 0.4. Against type 3 opponents, the probability of winning is 0.5. As the opponent is chosen randomly, the probability of winning is the average of all three probabilities. This means that the probability of winning the game is 0.4. To calculate this, we first add the probabilities of winning against each type of opponent: 0.3 + 0.4 + 0.5 = 1.2. We then divide this result by the number of opponent types (3): 1.2/3 = 0.4. This means that the probability of winning the game is 0.4.
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