We can derive the equations using the principle of optimality for Markov decision processes. This principle states that an optimal policy for a process must satisfy the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.
Let g(i) denote the total expected cost incurred by the DTMC until it visits state n starting from state i. We can express this as:
g(i) = c(i) + p(i, i+1)g(i+1) + p(i, i+2)g(i+2) + ... + p(i, n-1)g(n-1)
Here, p(i, j) denotes the transition probability from state i to state j. The first term c(i) represents the cost incurred by visiting state i for the first time, and the second term p(i, i+1)g(i+1) represents the expected cost of moving from state i to state i+1 and continuing optimally from state i+1. The same applies to the following terms, with the last term p(i, n-1)g(n-1) representing the expected cost of moving from state i to state n-1 and continuing optimally from state n-1 to state n.
To solve for g(n), we note that the expected cost to reach state n from state n is zero since we are already at the target state. Therefore, we have:
g(n) = 0
Now, we can use the principle of optimality to solve for the remaining g(i)'s. Specifically, we consider the expected cost of moving from state i to state i+1 and continuing optimally from state i+1. This can be expressed as:
c(i) + p(i, i+1)g(i+1)
The optimal decision is to minimize this cost, which can be achieved by choosing the state j that minimizes the cost of moving from state i to state j and continuing optimally from state j. Therefore, we have:
g(i) = c(i) + min_j{p(i, j)g(j)}, for 1 <= i < n
This equation states that the expected cost of visiting state i and continuing optimally to state n is the sum of the cost of visiting state i and the expected cost of moving from state i to the state j that minimizes the expected cost of moving from state i to state j and continuing optimally from state j.
Combining the two equations, we obtain the desired results:
g(n) = 0
g(i) = c(i) + min_j{p(i, j)g(j)}, for 1 <= i < n
To know more about optimality for Markov:
https://brainly.com/question/29764916
#SPJ4
(x - y) (x² - 2xy + y²)
On expanding the expression, we get -
{x³ - 2x²y + xy² - x²y + 2xy² - y³}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
(x - y) (x² - 2xy + y²)
The given expression is -
(x - y) (x² - 2xy + y²)
x {x² - 2xy + y²} - y {x² - 2xy + y²}
x³ - 2x²y + xy² - x²y + 2xy² - y³
Therefore, on expanding the expression, we get -
{x³ - 2x²y + xy² - x²y + 2xy² - y³}
To solve more questions on functions & expressions, visit the link below
brainly.com/question/17613163
#SPJ9
you have a toonie, a loonie, and three quarters. Hiw many different sums of money can you make?
The given sum of money in cents as 375 cents.
What is money?Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.
Given that, person has a toonie, a loonie, and three quarters.
1 Toonie = 2 dollars
1 Loonie = 1 dollar
3 quarters = 0.75 dollars
So, sum of money = 2+1+0.75
= 3.75 dollars
1 Toonie = 200 cents
1 Loonie = 100 cents
3 quarters = 75 cents
Sum of money = 200+100+75
= 375 cents
1 Toonie = 8 quarters
1 Loonie = 4 quarters
So, in quarters = 8+4+3
= 15 quarters
Therefore, the given sum of money in cents as 375 cents.
Learn more about money here:
https://brainly.com/question/22984856.
#SPJ9
Consider the following graph.
Determine whether the curve is the graph of a function of x.
Yes, it is a function.
No, it is not a function.
If it is, state the domain and range of the function. (Enter your answers using interval notation. If it is not a function, enter NAF in all blanks.)
domain
range
Reason: It fails the vertical line test. It is possible to pass a single vertical line through multiple points on this blue graph.
For instance, we can have a vertical line through x = 1. This vertical line intersects infinitely many points.
In other words, the input x = 1 leads to more than one output, which is a counter-example to show we do not have a function.
A function is only possible if each input in the domain leads to exactly one output in the range.
Since we don't have a function, you don't need to worry about filling in the domain and range boxes.
The graph is a function with a domain of (-infinity, infinity) and a range of (-infinity, infinity).
Explanation:The graph represents a function because for each value of x, there is exactly one corresponding value of y. As a result, the vertical line test is passed.
The domain of the function is the set of all x-values for which the function is defined. In this case, it appears that the graph extends from x = -infinity to x = infinity, so the domain is (-infinity, infinity).
The function's range is the set of all y-values that the function can yield. According to the graph, the y-values vary from y = -infinity to y = infinite, resulting in the range (-infinity, infinity).
Learn more about Function Graphs here:https://brainly.com/question/23573962
#SPJ2
Measurement scales match-up Aa Aa Select the measurement scale in the right column that best matches the description in the left column. Note that each scale (nominal scale, ordinal scale, interval scale, and ratio scale) will be used exactly once. The values of data measured on this scale can be rank ordered. In addition, the differences between two adjacent ranks are equal. The values of data measured on this scale can be rank ordered and have meaningful an absolute zero point. The values of data measured on this scale can be rank ordered. The values of data measured on this scale are labels or names. Interval Scale Nominal Scale differences between scale points. For this scale, there is also Ordinal Scale
The values of data measured on this scale are labels or names. -> Nominal Scale
The values of data measured on this scale can be rank ordered. -> Ordinal Scale. The values of data measured on this scale can be rank ordered and have meaningful an absolute zero point. -> Ratio Scale
The values of data measured on this scale can be rank ordered. In addition, the differences between two adjacent ranks are equal. -> Interval Scale
Nominal Scale: In the nominal scale, the values of data are labels or names used to categorize or classify items into mutually exclusive groups. Nominal data cannot be ordered, measured, or compared. Examples of nominal data include gender (male, female), eye color (blue, brown, green), or car brands (Toyota, Honda, Ford).
You can read more about Measurement scales at https://brainly.com/question/15998581
#SPJ4
Is every point of every open set E C R2 a limit point o E Answer the same question for closed sets in R2 is it the same?
Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.
Every point of every open set E in R2 is a limit point of E. This is because an open set is characterized by the fact that all of its boundary points are included in the set. Therefore, all of the points in the set are limit points because they are all on the boundary of the set.
For closed sets in R2, the answer is not the same. A closed set is characterized by the fact that it is determined by its boundary points and all of its interior points. Therefore, only the boundary points of a closed set are limit points, while the interior points are not.
Every point of an open set in R2 is a limit point, but only the boundary points of a closed set are limit points.
Learn more about limit point here:
https://brainly.com/question/29795597
#SPJ4
A committee is organizing a music festival in Jefferson County. The amount of time that the
venue has been reserved for determines the number of bands that will be able to play at the
festival.
t = the amount of time that the venue has been reserved for
b = the number of bands that will be able to play
The dependent and independent variables are b and t respectively.
A variable is a mathematical symbol, which do not have any fixed value, it can be a function, which changed according to the property given.
Given that, a committee is organizing a music festival in Jefferson County,
The time which reserved by venue, gives the number of band that will play at there,
We need to determine the dependent and independent variables,
Dependent variable :-
Dependent variable is a kind of variable which depends on the factors given, and do not change by its own.
Independent variables :-
The independent variable in the given study is the cause by which the dependent variable works, it does not manipulate by any other variable given.
Here,
The number of bands depends upon the amount of the time that the venue has been reserved for.
Therefore, the number of band is a dependent variable.
Hence, the dependent and independent variables are b and t respectively.
Learn more about variables, click;
https://brainly.com/question/17344045
#SPJ9
what is equivalant to - 2 ( -6x + 3y - 1)?
Based on the given option, the correct answer would be; C. 2x - 3y = 6 and 2x + y = -6
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
here, we have,
We are given the system of equations as;
2/3x - y = 2
x + 1/2 y = -3
Here multiply by 3 on both sides;
2x - 3y = 6
Now similarly;
x + 1/2 y = -3
2x + y = -6
The result would be C. 2x - 3y = 6 and 2x + y = -6
Learn more about equations here;
brainly.com/question/25180086
#SPJ9
All of the following statements are true about brake drum inside diameter measurements with a brake drum micrometer EXCEPT:A. The drum should be cleaned before measuring the diameter.B. If the drum diameter is less than specified, replace the drum.C. The diameter should be measured at two locations around the drum.D. The drum diameter variation should not exceed 0.035 in (0.009 mm).
The statement that is NOT true about brake drum inside diameter measurements with a brake drum micrometer is B.
If the drum diameter is less than specified, replace the drum. In fact, if the drum diameter is less than the minimum specified limit, the drum can be machined to a larger diameter to restore its proper dimension. This will depend on the manufacturer's recommendations, and the minimum thickness limits of the drum should also be checked to ensure it is within safe tolerances.
The other statements are true: A. The drum should be cleaned before measuring the diameter, to avoid errors due to dirt or rust. C. The diameter should be measured at two locations around the drum, usually at the top and bottom of the friction surface, to check for taper or out-of-roundness. D. The drum diameter variation should not exceed 0.035 in (0.009 mm), to ensure proper brake function and minimize vibration or noise.
For more such questions on Brakes
https://brainly.com/question/26962373
#SPJ4
If Steve drives 5 miles to school at 10 mph and returns home at 40 mph, what is his average speed?
Answer:
Step-by-step explanation:
To find the average speed for the round trip, we can use the formula:
average speed = total distance / total time
We know that Steve drives 5 miles to school and 5 miles back home, so the total distance is:
total distance = 5 miles + 5 miles = 10 miles
To find the total time, we need to calculate the time it takes for Steve to drive to school and the time it takes for him to return home. We can use the formula:
time = distance / speed
For the first part of the trip, Steve drives 5 miles at 10 mph, so the time it takes is:
time to school = 5 miles / 10 mph = 0.5 hours
For the second part of the trip, Steve drives 5 miles at 40 mph, so the time it takes is:
time to home = 5 miles / 40 mph = 0.125 hours
The total time for the round trip is the sum of the time to school and the time to home:
total time = time to school + time to home
total time = 0.5 hours + 0.125 hours
total time = 0.625 hours
Now we can calculate the average speed using the formula:
average speed = total distance / total time
average speed = 10 miles / 0.625 hours
average speed = 16 miles per hour (rounded to the nearest integer)
Therefore, Steve's average speed for the round trip is 16 mph.
Answer:
16 mph
Step-by-step explanation:
A random sample of 10 subjects have weights with a standard deviation of 10.3695 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
Answer:
Since we are given the standard deviation of the sample, we can use the formula:
variance = standard deviation^2
Substituting the given value:
variance = 10.3695^2 kg^2
Calculating:
variance ≈ 107.495 kg^2
Therefore, the variance of the weights of the 10 subjects is approximately 107.495 kg^2.
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
m∠A = 22 degrees
m∠B = 75 degrees
m∠F = _____ degrees
m∠G = _____ degrees
m∠H = _____ degrees
m∠C = _____ degrees
Answer:
Since triangle ABC is similar to triangle FGH, their angle measures are proportional. We can use the ratios of their angle measures to find the missing angle measures.
Let's call the missing angle measures x, y, z, and w, where x is m∠F, y is m∠G, z is m∠H, and w is m∠C.
From the given information, we have:
m∠A / m∠F = 22 / x
m∠B / m∠G = 75 / y
Since m∠A + m∠B + m∠C = 180 degrees, we can write:
w = 180 - (m∠A + m∠B)
m∠H / m∠C = z / w
Now we can use the ratios to find the missing angle measures:
x = 22 / (22 / x) = 22
y = 75 / (75 / y) = 75
z = m∠H / (m∠H / z) = m∠H
w = 180 - (22 + 75) = 83
So, the missing angle measures are:
m∠F = 22 degrees
m∠G = 75 degrees
m∠H = m∠H (unknown)
m∠C = 83 degrees
Suppose a die has been loaded so that a six is scored three times more often than any other score, while all the other scores are equally likely. Express your answers to three decimals.
Part a)
What is the probability of scoring a one?
Part b)
What is the probability of scoring a six?
a) The probability of scoring a one is 1/7, since a one is not the loaded number six and all other scores are equally likely.
b) The probability of scoring a six is 3/7, since a six is the loaded number and occurs three times as often as any other score.
Let p be the probability of scoring any number except six. Then the probability of scoring a six is 3p, since a six is scored three times more often than any other score. Since there are six equally likely possible scores on a die, we have:
p + 3p + p + p + p + p = 1
Simplifying, we get:
7p = 1
Dividing both sides by 7, we get:
p = 1/7
Therefore, the probability of scoring any number except six is 1/7, and the probability of scoring a six is 3/7. We can now answer the questions:
For more such questions on Probability
https://brainly.com/question/13604758
#SPJ4
Please Explain as well
Given f (x)=25-x² and g(x)=2x-9, determine the simplified form of the composite function f (g(x))?
Answer:
Step-by-step explanation:
[tex]25-(2x-9)^{2}[/tex]=[tex](25-2x+9)(25+2x-9)=(34-2x)(16+2x)=4(17-x)(8+x)[/tex]
Kristin had some paper with which to
make note cards. On her way to her room
she found seven more pieces to use. In
her room she cut each piece of paper in
half. When she was done she had 22
half-pieces of paper. With how many
sheets of paper did she start
The 22 half-pieces Kristin had from cutting the sheets she started with and the 7 pieces she found, indicates, that the solution to the word problem is that the number of sheets of paper Kristin started with are;
4 sheets of paperWhat is a word problem?A word problem is a mathematical question in which the scenario of the question is described using verbal terms, or complete sentences, rather than mathematical symbols or expressions, but which are solved using mathematical calculations.
Let x represent the initial number of paper Kristin had.
The extra number of papers Kristin found = Seven more pieces
The size in which Kristin cut each piece of paper = In half
The number of pieces she had after cutting the papers = 22 half-pieces
Therefore, the following equation can be used to find the number of sheets of paper, x, she started with;
2 × (x + 7) = 22
2 × (x + 7)/2 = 22 ÷ 2 = 11
x + 7 = 11
x = 11 - 7 = 4
The number of sheets of paper Kristin started with, x = 4 sheets of paper
Learn more on writing equations here: https://brainly.com/question/24628957
#SPJ1
HELPPPP
1.Use the given degree of confidence and sample data to construct a confidence interval for the population mean, . Assume that the population has a normal distribution.
The amounts (in ounces) of juice in eight randomly selected juice bottles are:
15.2 15.5 15.9 15.5 15.0 15.7 15.0 15.7
Construct a 90% confidence interval for the mean amount of juice in all such bottles.
Responses
A.(15.16, 15.72)
B.(15.21, 15.66)
C.(15.27, 15.61)
D.(15.08, 15.80)
2.Use the given degree of confidence and sample data to construct a confidence interval for the population mean, .
The monthly income of workers at a manufacturing plant are distributed normally. Suppose the mean monthly income is $2,150 and the standard deviation is $250 for a SRS of 18 workers. Find a 99% confidence interval for the mean monthly income for all workers at the plant.
Responses
A.(2096, 2204)
B.(1842, 2457)
C.(2144, 2155)
D.(1979, 2321)
Answer:
To construct a 90% confidence interval for the mean amount of juice in all such bottles, we first need to find the sample mean and sample standard deviation:
Sample mean, x = (15.2 + 15.5 + 15.9 + 15.5 + 15.0 + 15.7 + 15.0 + 15.7)/8 = 15.4375
Sample standard deviation, s = s = sqrt[((15.2-15.4375)^2 + (15.5-15.4375)^2 + (15.9-15.4375)^2 + (15.5-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2 + (15.0-15.4375)^2 + (15.7-15.4375)^2)/7] = 0.339
Using a t-distribution with degrees of freedom (n-1) = 7 and a 90% confidence level, we can find the t-value as 1.895.
The 90% confidence interval can then be calculated as:
x plus or minus (t-value)*(s/sqrt(n))
= 15.4375 plus or minus (1.895)*(0.339/sqrt(8))
= (15.16, 15.72)
Therefore, the answer is A.
To find a 99% confidence interval for the mean monthly income for all workers at the plant, we use the formula:
x plus or minus (z-value)*(σ/sqrt(n))
where x is the sample mean, σ is the population standard deviation, n is the sample size, and z-value is the critical value from the standard normal distribution for a 99% confidence level, which is 2.576.
Plugging in the given values, we get:
x plus or minus (z-value)*(σ/sqrt(n))
= 2150 plus or minus (2.576)*(250/sqrt(18))
= (2096, 2204)
Therefore, the answer is A.
Which expression has a value of 18?
5 × (40 – 25) – 50
6x (3212) (100 +50)
-
(6 + 18+6) + 15 + 10
07+ (16-7)+3+8
To determine which expression has a value of 18, we can evaluate each expression and see which one equals 18.
5 × (40 – 25) – 50 = 5 × 15 – 50 = 75 – 50 = 25, which is not equal to 18.
6x (3212) (100 +50) - (6 + 18+6) + 15 + 10 = 6 × 3212 × 150 - 30 + 25 = 29,021,770, which is not equal to 18.
07+ (16-7)+3+8 = 7 + 9 + 3 + 8 = 27, which is not equal to 18.
Therefore, none of the given expressions has a value of 18.
a bicycle was bought for R1489 and sold at a profit of R387. what was the selling price of the bicycle?
The selling price of the bicycle is equal to R1,102.
What is profit?In Mathematics, profit can be defined as a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.
Mathematically, the amount of profit made from selling a bicycle can be calculated by using the following function:
Profit made = Cost price - Selling price
Making selling price the subject of formula, we have:
Selling price = Cost price - Profit made
Selling price = R1489 - R387.
Selling price = R1,102.
Read more on profit here: brainly.com/question/1717365
#SPJ1
Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of life governed by the exponential distribution with mean 7 (with measurements in hundreds of hours).
(a)
Find the probability density function for the average length of life of the two components.
fU(u) =17e-u7, u ≥ 0,0 . , elsewhere
The probability density function for the average length of life of the two components is fU(u) = (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0
The length of life of each component is governed by an exponential distribution with a mean of 7, which means that the probability density function for the length of life of each component is given by:
fX(x) = (1/7)[tex]e^{(-x/7)}[/tex], x ≥ 0
The average length of life of the two components is given by:
U = (X1 + X2)/2
where X1 and X2 are the lengths of life of the two components.
To find the probability density function for U, we can use the convolution formula:
fU(u) = ∫fX(x)fX(2u-x)dx
where the limits of integration are from 0 to u if u ≤ 7, and from u-7 to 7 if u > 7.
Plugging in the expressions for fX(x) and fX(2u-x), we get:
fU(u) = ∫(1/7)[tex]e^{(-x/7)}[/tex](1/7)[tex]e^{-(2u-x/7)}[/tex]dx
= (1/49)∫[tex]e^{-(2u-2x/7)}[/tex]dx
= (1/49)∫[tex]e^{(-t/7)}[/tex]dt (where t = 2u - 2x)
= (1/49)(-7[tex]e^{(-x/7)}[/tex])|0 to 2u
= (1/7)[tex]e^{(-u/7)}[/tex], u ≥ 0
Read more about Probability Density Function from:
https://brainly.com/question/30403935
#SPJ4
Tell whether the angles are adjacent or vertical. Then find the value of x.
response - correct
The angles are vertical.
Question 2
x=
The angles are vertically opposite angles and the measure of x = 81
What are the angles formed by 2 intersecting lines?Two straight lines that intersect at the same location are said to be intersecting lines. The junction point is the place where two intersecting lines meet. Four angles are created when two lines cross. The four angles added together always equal 360 degrees.
Perpendicular lines are two straight lines that intersect and form right angles. When two perpendicular lines intersect, they form four right angles.
When lines intersect, two angle relationships are formed:
Opposite angles are congruent
Adjacent angles are supplementary
Given data ,
Let the first line be represented as m
Let the second line be represented as n
Now , the lines m and n intersect at point O and the resulting lines are formed
where ∠A = ∠B ( vertically opposite angles )
So , the measure of ( x + 3 )° = 84°
On simplifying , we get
x + 3 = 84
Subtracting 3 on both sides , we get
x = 81
Hence , the measure of angles are opposite angles
To learn more about angles formed by intersecting lines click :
https://brainly.com/question/16315358
#SPJ1
Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)
(a) 71st
(b) 29th
(c) 76th
(d) 24th
(e) 7th
You may need to use the appropriate table in the Appendix of Tables to answer this question.
(a) 0.52, (b) -0.54, (c) 0.68, (d) -0.71, (e) -1.44 - Percentiles for standard normal distribution using z-table.
(a) To find the 71st percentile, we search for the z-score that relates to a combined area of 0.71 to one side of the mean. From the standard typical circulation table, we find that the nearest z-scores are 0.67 and 0.72, with relating areas of 0.7486 and 0.7642, individually. To interject, we utilize the equation:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.71). Connecting the qualities, we get:
z = 0.67 + (0.72 - 0.67) * ((0.71 - 0.7486)/(0.7642 - 0.7486)) = 0.52
Consequently, the 71st percentile is z = 0.52.
(b) To find the 29th percentile, we search for the z-score that compares to a combined area of 0.29 to one side of the mean. From the standard ordinary conveyance table, we find that the nearest z-scores are - 0.53 and - 0.52, with relating areas of 0.2981 and 0.3050, individually. To add, we utilize the recipe:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.29). Connecting the qualities, we get:
z = - 0.53 + (- 0.52 - (- 0.53)) * ((0.29 - 0.2981)/(0.3050 - 0.2981)) = - 0.54
Consequently, the 29th percentile is z = - 0.54.
(c) To find the 76th percentile, we search for the z-score that relates to an aggregate area of 0.76 to one side of the mean. From the standard ordinary appropriation table, we find that the nearest z-scores are 0.73 and 0.77, with relating areas of 0.7673 and 0.7794, separately. To interject, we utilize the equation:
z = z1 + (z2 - z1) * ((p - p1)/(p2 - p1))
where z1 and z2 are the nearest z-scores in the table, p1 and p2 are the comparing regions, and p is the ideal total region (0.76). Connecting the qualities, we get:
z = 0.73 + (0.77 - 0.73) * ((0.76 - 0.7673)/(0.7794 - 0.7673)) = 0.68
Consequently, the 76th percentile is z = 0.68.
(d) The 24th percentile compares to a z-score of - 0.71, meaning 24% of the standard ordinary conveyance misleads its left.
(e) The seventh percentile relates to a z-score of - 1.44, meaning 7% of the standard typical conveyance misleads its left.
To learn more about percentiles, refer:
https://brainly.com/question/15113672
#SPJ4
i need help with this anwser
The missing side length of the figure is given as follows:
6 cm.
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that a segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.
For this problem, we have that:
The larger segment is of 16 cm.The smaller segment is of 10 cm.Hence the missing side length of the figure is obtained as follows:
16 - 10 = 6 cm.
More can be learned about the segment addition postulate at https://brainly.com/question/2134445
#SPJ1
A deck of cards contains RED cards numbered 1,2,3,4,5 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 5 is one of the outcomes in which of the following events? Select all correct answers.
The probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)
What is probability?Probability in mathematics is the process of finding chances of an event to happen.
Given that, a deck of card have,
Red cards = 1,2,3
Blue cards =1,2,3,4,5,6
Pr(R) = Drawing a red card = 3/9 = 1/3
Pr(B) = Drawing a blue card = 6/9 = 2/3
Pr(E) = Drawing an even card = 4/9
Pr(O) = Drawing an odd number card = 5/9
Probability of drawing the red 5 = P(red 5) = 1/9
From the options, we have :-
(A) R or O = Pr(R) + Pr(O) = 1/3 + 1/9 = 8/9 ≠ 1/9
(B) B and O = Pr(B) × Pr(O) = 2/3 × 5/9 = 10/21 ≠ 1/9
(D) R and O = Pr(R) + Pr(O) = 1/3 × 5/9 = 5/27 ≠ 1/9
(E) R'. E' = 1-Pr(R)-1-Pr(E) = 1-1/3 =2/3- 1-4/9 =5/9
= 2/3-5/9
= 1/9
Hence, the probability of drawing the red 5 is an example of the event shown in option E R'. E' = 1-Pr(R)-1-Pr(E)
Learn more about probability, click;
https://brainly.com/question/11234923
#SPJ9
Let A = {H, T}, B = {1, 2, 3, 4, 5}, and C = {red, green, blue}. Find the number indicated. HINT [See Example 5.]
n(B × C)
There are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.
Describe Cartesian Product?In mathematics, the Cartesian product is a binary operation that takes two sets and forms a set consisting of all possible ordered pairs of elements from the two sets. The resulting set is often denoted by A × B, where A and B are the two original sets.
Formally, if A and B are two sets, the Cartesian product A × B is defined as:
A × B = {(a, b) : a ∈ A and b ∈ B}
This means that the Cartesian product contains all possible ordered pairs (a, b) where a is an element of A and b is an element of B. For example, if A = {1, 2} and B = {x, y}, then A × B would be {(1, x), (1, y), (2, x), (2, y)}.
The Cartesian product B × C is the set of all ordered pairs (b, c) where b is an element of B and c is an element of C. Since B has 5 elements and C has 3 elements, there are 5 × 3 = 15 possible ordered pairs. Therefore, n(B × C) = 15.
To know more about product visit:
https://brainly.com/question/30340079
#SPJ1
stuck on this. pls do 2-6
All the areas of the circles are illustrated below.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The area of the circle is πr².
1. The area of the circle with a radius of 2.5 cm is,
= π(2.5)² sq cm.
= 19.625 sq cm.
2. The area of the circle with a radius of 11 in is,
= π(11)² sq in.
= 379.94 sq in.
3. The area of the circle with a radius of 3 mm is,
= π(3)² sq mm.
= 28.26 sq mm.
4. The area of the circle with a radius of 5 in is,
= π(5)² sq in.
= 78.5 sq in.
5. The area of the circle with a radius of 6.5 cm is,
= π(6.5)² sq cm.
= 132.665 sq cm.
6. The area of the circle with a radius of 7.2 yd is,
= π(7.2)² sq yd.
= 162.7776 sq yd.
learn more about circles here :
https://brainly.com/question/29142813
#SPJ1
If one of the 98 test subjects is randomly selected, find the probability that the subject had a positive test result GIVEN that the subject actually lied. O 0.962 O 0.654 O 0.784 O 0.456
The probability of a positive test result given that the subject actually lied is 0.962
In simple terms, probability is the measure of the likelihood of an event occurring. In this question, we are asked to find the probability of a positive test result given that the subject lied.
Let's break down the question and use the formula for conditional probability. Conditional probability is the probability of an event occurring, given that another event has already occurred.
P(A|B) = P(A and B) / P(B)
In this case, A represents the event of a positive test result, and B represents the event of the subject lying.
From the question, we know that 2% of the subjects lie, and 90% of those who lie test positive. This means that out of the 98 subjects, 2% or 1.96 subjects lied. And out of those 1.97 subjects, 90% or 1.78 subjects tested positive.
So, the probability of a positive test result given that the subject lied is
=> P(A|B) = 1.78/1.97 = 0.962.
To know more about probability here.
https://brainly.com/question/11234923
#SPJ4
Complete Question:
If one of the 98 test subjects is randomly selected, find the probability that the subject had a positive test result GIVEN
POSITIVE TEST RESULT 13 40
NEGATIVE TEST RESULT 34 11
that the subject actually lied.
A 0.962
B 0.654
C 0.784
D 0.456
Please help! What is the rate of change (slope) of the graph
The rate of change on a slope graph is 25.
How do you find the rate of change on a slope graph?
The rate of change for a line is the slope, the rise over run, or the change in over the change in. The slope can be calculated from two points in a table or from the slope triangle in a graph.
The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.
Given :
Y - variations = 0 , 25 , 50 ,75 , 100 , 125..........
X - variations = 0 , 1 , 2 , 3 , 4 , 5 , 6 .........
Thus , we can formulate the points as,
(0,0) , (1,25) , (2,50) , (3,75) and so on ...
for rate of change of graph with (x1 , y1) and (x2 , y2) as co-ordinate point we know that,
rate of change = (y2-y1)/(x2-x1)
Similarly ,by taking any two points(let (0,0) and (1,25)) from formulated points , we can say that
rate of change = (25-0)/(1-0)
rate of change = 25
Hence , the rate of change on a slope graph is 25.
Learn more about Slope at:
https://brainly.com/question/3493733
#SPJ1
The terminal ray of an angle with measure of 120 degrees intersect a unit circle at -1/2, square root of 3 /2. Find the EXACT VALUES for the sine and cosine of the given angle.
The Exact values for the sine and cosine of the given angles are : sin(120°) = √3/2, cos(120°) = -1/2
Given that the terminal ray of an angle with measure of 120 degrees intersects a unit circle at the point (-1/2, √3/2), we can use the definition of sine and cosine to find the exact values of these trigonometric functions for the given angle.
The sine of an angle is defined as the y-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the sine is:
sin(120°) = √3/2
The cosine of an angle is defined as the x-coordinate of the point on the unit circle that the terminal ray of that angle intersects. So, for this angle, the cosine is:
cos(120°) = -1/2
So, the exact values for the sine and cosine of the angle with measure of 120 degrees are:
sin(120°) = √3/2
cos(120°) = -1/2
To know more about sine and cosine:
https://brainly.com/question/3827723
#SPJ4
Convert the following number to Mayan notation. Show your calculations used to get your answers.
135 in Mayan notation is represented by one dot over four bars, followed by one dot over three bars, and then one dot over five dots.
To convert 135 to Mayan notation, we repeatedly divide by 20 and use the remainders to determine the number of dots and bars in each position. First, we divide 135 by 20 to get a quotient of 6 with a remainder of 15. The remainder of 15 corresponds to 1 dot over 5 dots and 2 bars (10 + 5).
Next, we divide 6 by 20 to get a quotient of 0 with a remainder of 6. The remainder of 6 corresponds to 1 dot over 3 bars (15). Finally, we have a quotient of 0 with a remainder of 6, which corresponds to 1 dot over 4 bars (20).
Putting these together, we get the Mayan representation of 135 as one dot over four bars, followed by one dot over three bars, and then one dot over five dots.
Complete question:
Convert the following numbers to Mayan notation. Show your calculations used to get your answers. 135?
Read more about Mayan notation:
https://brainly.com/question/882078
#SPJ4
. For every 16 games the football team won, they lost four.
Represent the ratio of games won to games played in fraction form and decimal form.
Select TWO correct answers.
The ratio of games won to games played is options A and E, 16/20 or 4/5 in fraction form and 0.8 in decimal form.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
For every 16 games the football team won, they lost four.
Games won = 16
Games lost = 4
Total games played = 16 + 4 = 20
Ratio of games won to total games in fractional form = 16 / 20 = 4/5
Ratio of games won to total games in decimal form = 0.8
The correct options are A and E.
Hence the ratio of games won to total games is 16/20 or 4/5 in fraction form and 0.8 in decimal form.
Learn more about Ratios here :
https://brainly.com/question/13419413
#SPJ9
Your question is incomplete. The complete question is given below.
Manchester Football team participates in a tournament. For every 16 games the football team won, they lost four. Represent the ratio of games won to games played in fraction form and decimal form.
Select TWO correct answers.
A. 4/5, 0.8
B. 1/2, 0.5
C. 2/4, 0.5
D. 1 /4, 0.25
E. 16/20, 0.8
A tin can has dimensions 2m ×1.5m×1m high. How many litres of kerosene oil can it hold?
Answer:
3000 liters
Step-by-step explanation:
To calculate the volume of the tin can, we can multiply its dimensions:
Volume = 2m × 1.5m × 1m = 3 cubic meters
Since a liter is equivalent to 0.001 cubic meters, we can convert the volume of the tin can to liters:
Volume (in liters) = 3 cubic meters × 1000 liters/cubic meter = 3000 liters
Therefore, the tin can can hold 3000 liters of kerosene oil.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ