In a lab experiment, the number of bacteria on a petri dish began at 7400 and is now increasing exponentially at a rate of 13% per hour. P(t) = [tex]7400(1 + 0.13)^t[/tex] is a function that may be used to represent the population of bacteria after t hours and in which a constant can be used to calculate the rate of change each minute. The rate of change in percentage is 0.21667% per minute.
The function to represent the population of bacteria after t hours can be expressed as:
P(t) = [tex]7400(1 + 0.13)^t[/tex]
where P(t) is the population of bacteria after t hours, 7400 is the initial population, and 0.13 is the growth rate per hour expressed as a decimal.
To find the rate of change per minute, we need to convert the growth rate per hour to a growth rate per minute. There are 60 minutes in an hour, so the growth rate per minute can be found by dividing the growth rate per hour by 60:
0.13/60 = 0.0021667 (rounded to seven decimal places)
So the growth rate per minute is approximately 0.0021667 or 0.21667% (rounded to two decimal places).
Therefore, the function to represent the population of bacteria after t hours is:
P(t) = [tex]7400(1 + 0.13)^t[/tex]
and the rate of change per minute is approximately 0.21667%.
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How can you check that your answer is correct?
Answer: Work out the problem. or input it in for check
Write 352,619 in expanded form and number names
Answer:
300,000 - Three hundred thousand - Hundred-thousandths place
50,000 - Fifty thousand - Ten-thousandths place
2,000 - Two thousand - Thousandths place
600 - Six hundred - Hundreds place
10 - Ten - Tens place
9 - Nine - Ones place
Step-by-step explanation:
The number is read, three hundred and fifty two thousand six hundred nineteen
the post office charges $0.55 to mail a standard-sized item that weighs an ounce or less. the charge for each additional ounce (up to 13 ounces), or fraction of an ounce, of weight is $0.15. at this rate, how much will it cost to mail a package that weighs 6.8 ounces?
Therefore, it will cost $1.42 to mail a package that weighs 6.8 ounces.
To mail a package that weighs 6.8 ounces, the amount it will cost can be calculated using the given information. The post office charges $0.55 to mail a standard-sized item that weighs an ounce or less, and the charge for each additional ounce (up to 13 ounces), or fraction of an ounce, of weight is $0.15.
Therefore, to mail a package that weighs 6.8 ounces, we can use the following formula:
Cost = $0.55 + (Number of additional ounces) x $0.15
We need to find the cost of mailing a package that weighs 6.8 ounces. We know that the first ounce costs $0.55, and the package weighs 6.8 ounces. Therefore, the number of additional ounces is:
6.8 - 1 = 5.8
We also know that the cost for each additional ounce is $0.15. Therefore, the cost of mailing a package that weighs 6.8 ounces can be calculated as:
Cost = $0.55 + (5.8) x $0.15
Cost = $0.55 + $0.87
Cost = $1.42
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nasa is conducting an experiment to find out the fraction of people who black out at g forces greater than 6 . in an earlier study, the population proportion was estimated to be 0.46 . how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 90% confidence level with an error of at most 0.03 ? round your answer up to the next integer.
NASA needs to select a sample of 749 people to estimate the proportion of people who black out at g-forces greater than 6 with a 90% confidence level and an error of at most 0.03, given the earlier study's estimated proportion of 0.46.
To determine the sample size required for the experiment, we need to use a formula that relates the proportion, confidence level, and margin of error. The margin of error is the amount by which the sample proportion is expected to differ from the true population proportion.
The formula for calculating the sample size required to estimate the proportion with a specified level of confidence and margin of error is:
n = (z² x p x q) / E²
Where: n = sample size z = the z-score associated with the confidence level (for a 90% confidence level, z = 1.645) p = estimated proportion (from the earlier study) q = 1 - p E = margin of error (0.03 in this case)
Substituting the values in the formula, we get:
n = (1.645² x 0.46 x 0.54) / 0.03²
n = 748.44
Rounding up to the nearest integer, we get the required sample size as 749.
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A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
The correct options are:
The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill.
The solution x = 60 represents the total food bill.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Since there are 8 friends and they decided to split the bill and tip evenly among themselves, each friend pays an equal share of the total bill, which is the food bill plus the tip. Let x be the food bill.
Then the total bill is x + 16 (the food bill plus the tip), and each friend's share is StartFraction 1 over 8 EndFraction (x + 16).
So, we have the equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction, which represents the situation where the total bill is $76 and there are 8 friends. Solving for x, we get:
StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction
x + 16 = 76
x = 60
Therefore, the total food bill is $60, which is the solution to the equation.
Each friend's share of the food bill and tip is StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 1 over 8 EndFraction (60 + 16) = $9.
The equation 8(x + 16) = 76 is not correct, as it assumes that the total bill is divided equally among 8 people without taking into account the food bill and the tip separately.
hence, The correct options are:
The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill.
The solution x = 60 represents the total food bill.
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What is the sum of a + cº?
The sum between angles a° and c° gives 300°.
How to get the sum of the two angles?Here we want to find the sum of the two angles a° and c°.
First, we can see that a is a plane angle, then:
a° = 180°
We also can see that c° plus the angle at its left which is 60° should be a plane angle, then we can write:
60° + c° = 180°
c° = 180° - 60°
c° = 120°
Now we know the values of c° and a°, then the sum will give:
a° + c° = 120° + 180° = 300°
That is the answer.
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14 Kawa rolls a fair number cube twice. What is the probability of rolling two 3's if the first roll is a 5? Explain.
Answer:
2/12
Step-by-step explanation:
There is a 1/6 chance of rolling a 3 once because there are six sides and only one 3, double that ratio if your want the probability of rolling that same number twice in a row.
eight children sit together at story time. seven children sit in a circle and one child sits in the middle to tell the story. in how many different ways can the children sit? (two seatings are considered identical if the same child is in the middle in both and each child on the outside has the same child on his or her right in both seatings.)
There are 8208 different ways that the children can sit.
There are 8 children in total, so we first need to choose one of them to sit in the middle. This can be done in 8 ways.
Once the child in the middle has been chosen, the remaining 7 children can sit in a circle around them. There are (7-1)! = 6! = 720 ways to arrange 7 children in a circle. However, due to the condition that "two seatings are considered identical if the same child is in the middle in both and each child on the outside has the same child on his or her right in both seatings", we need to divide by 7 to account for the fact that there are 7 equivalent circular arrangements.
Therefore, the total number of different ways that the children can sit is:
8 x (6! / 7) = 8 x 720 / 7 = 8208
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How many unit fractions of 1/10 are
in 100?
Answer:
100
Step-by-step explanation:
100 unit fractions of 1/10 are in 100.
The number of unit fractions of 1/10 in 100 is 1000.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
We have to find how many 1/10 s are in the number 100.
In order to find it, we have to divide 100 by the fraction 1/10.
Divide 100 by 1/10.
100 / (1/10) = 100 × 10 = 1000
Hence the number of unit fractions in the number 100 is 1000.
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Write an equation to describe the situation. 3x=2 1/4
A medical device company knows that the percentage
of patients experiencing injection-site reactions with the
current needle is 11%. A nurse will collect data by
performing injections with this type of needle until five
people experience injection-site reactions
Is it appropriate to use the geometric distribution to
calculate probabilities in this situation?
• Yes, the geometric distribution is appropriate.
• No. since each trial is not independent of the other
trials.
• No, because it is not looking for the first occurrence
of success.
• No, since the probability of success is not the same
for each of the trials.
Answer:
Yes, the geometric distribution is appropriate.
Step-by-step explanation:
a man traveled 1/3 of thr distance between 2 cities in 3/4 of an hour
It will take him 2[tex]\frac{1}{4}[/tex] hours to travel the entire distance between the two cities. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers are thought to be sufficiently described by the four basic operations, sometimes referred to as "arithmetic operations." The mathematical operations quotient, product, sum, and difference follow division, multiplication, addition, and subtraction.
It is given that a man traveled [tex]\frac{1}{3}[/tex] of the distance between 2 cities in [tex]\frac{3}{4}[/tex] of an hour.
So, using the multiplication, if he travels at the same rate, he will cover the entire distance in,
⇒ Time taken = [tex]\frac{3}{4}[/tex] * 3
⇒ Time taken = [tex]\frac{9}{4}[/tex]
⇒ Time taken = 2[tex]\frac{1}{4}[/tex] hours
Hence, it will take him 2[tex]\frac{1}{4}[/tex] hours to travel the entire distance between the two cities.
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How many real solutions does the equation 5x^2 + 8x - 1 = 0
Answer:
2 real solutions
Step-by-step explanation:
Currently, this quadratic equation is in standard form, which is:
[tex]ax^2+bx+c=0[/tex]
We can find the number of real solutions using the discriminant from the quadratic equation which is:
[tex]b^2-4ac[/tex]
When b^2 - 4ac > 0, there are 2 real solutions
When b^2 - 4ac = 0, there is 1 real solution
When b^2 - 4ac < 0, there are 0 real solutions
In the example, our a value is 5, our b value is 8 and our c value is -1:
[tex]8^2-4(5)(-1)\\64-20=44[/tex]
44 > 0, so there are 2 real solutions
If a ray QT bisects angle RQS, what would be the measure of one of the resulting answers? need answers asap please :)
If a ray QT bisects <RQS, then the measure of one m ∠TQS = 23.5°
Bisector:
In geometry, bisector is the division of something into two equal or equal parts (of the same shape and size). This usually involves a bisector, also called the midline. The most commonly considered bisectors are the bisector (the line passing through the midpoint of a given line segment) and the angle bisector (the line passing through the vertex of the angle, the bisector equal to the angle ).
According to the Question:
Given :
a ray QT bisects <RQS
∠PQR and ∠RQS is a linear pair . It makes and angle 180 degree
m ∠PQR + m ∠RQS = 180
From the diagram,
m ∠PQR = 3x-5, and m ∠RQS= x+1
Substitute the expression and solve for x
m ∠PQR + m ∠RQS = 180
⇒ 3x-5 + x+1 = 180
⇒ 4x -4 = 180
⇒ 4x = 184
⇒ x = 46
Now ,
m ∠RQS = x +1
= 46 +1
= 47
Given QT bisects <RQS. it means QT divides RQS equally
m ∠TQS = m ∠RQS/2
⇒ m ∠TQS = 47/2
⇒ m ∠TQS = 23.5
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When the angle of elevation of the sun is 32 degrees, a flagpole casts a shadow that is 10 feet long. In feet, how tall is the flagpole?
The flagpοle is apprοximately 5.88 feet tall.
What is the angle οf elevatiοn?The angle between an item abοve the hοrizοntal line οf sight and that line is knοwn as the angle οf elevatiοn.
This issue can be resοlved using trigοnοmetry. Let's denοte the flagpοle's height "h" Drawing a right triangle with the flagpοle as the vertical leg, the shadοw as the hοrizοntal leg, and the sun as the angle οppοsite the hypοtenuse is pοssible when the angle οf elevatiοn οf the sun is 32 degrees.
We knοw that the length οf the shadοw is 10 feet, sο that we can write:
tan(32 degrees) = h/10
Tο sοlve fοr "h," we can multiply bοth sides by 10 and simplify:
h = 10 tan(32 degrees)
h = 5.88 feet
Therefοre, the flagpοle is apprοximately 5.88 feet tall.
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5.
Solve each equation mentally. (from Unit 1, Lessor
a. 5/2 •x =1
b. x• 7/3 =1
c. 1 divided by 11/2= x
Answer:
b
Step-by-step explanation:
I need help with this for math
The answer based on graph as Square ABCD is reflected across the x-axis and then dilated by a scale factor of 2 centered at origin is Part A: A' = (2, -10), B' = (12, -10) , C' = (12, -2) , D' = (2, -2). and for Part B explanation is given below.
What is Scale factor?Scale factor refers to ratio of any two corresponding lengths in the two similar figures. In other words, it is the factor by which all the dimensions of an object are multiplied to transform it into a similar object. The scale factor is a dimensionless quantity and is represented by a ratio, a fraction, or a decimal.
Part A:
After reflecting square ABCD across the x-axis, the coordinates of the vertices become:
A = (1, -5)
B = (6, -5)
C = (6, -1)
D = (1, -1)
To dilate the square by a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each vertex by 2. So the new coordinates of the vertices of A'B'C'D' are:
A' = (2, -10)
B' = (12, -10)
C' = (12, -2)
D' = (2, -2)
Part B:
Square ABCD is congruent to square A'B'C'D'. This is because a dilation with a scale factor of 2 centered at the origin results in a figure that is twice as large as the original, but with the same shape and angles. Since square ABCD is reflected across the x-axis and then dilated by a scale factor of 2 centered at the origin to form square A'B'C'D', it retains its original shape and angles, and is therefore congruent to square A'B'C'D'.
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In a circle, an angle intercepts an arc of length 41.6. Find the angle in radians to the nearest 10th
Write ordinary number
A new car is purchased for 22400 dollars. The value of the car depreciates at 6. 75% per year. What will the value of the car be, to the nearest cent, after 9 years?
Use the formula V = P(1 - r)ᵗ, where V is the final value of the car, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the time in years. Substituting the given values, the value of the car after 9 years is approximately 10920.91 dollars.
To calculate the value of the car after 9 years, we can use the formula for exponential decay:
V = P(1 - r)ᵗ
where V is the final value of the car, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the time in years.
Substituting the given values, we get:
V = 22400(1 - 0.0675)⁹ ≈ 10920.91
Therefore, the value of the car after 9 years is approximately 10920.91 dollars.
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can someone help me solve
The number of hours,h,worked and the amount of money ,m,earned. I need help I didn't pay attention in class...
what is the question asking? independent and dependent?? if so h is independent and m is dependent. Explanation: Independent is the leader and dependent is the follower, in your question the amount of hours you work depend on the amount of money you make because say for example you can get paid $15 per hour and if you work for 2 days you'll only gain $30 bucks that day. hopefully that makes sense!
If it's not asking for dependent and independent, please reply to comment i'll be more than happy to help .
A gas cooker costing 450$
was increased by 10% how much is the gas cooker now
REPEATED REASONING
AB is divided into four congruent segments, each of which is the diameter of a semicircle.
The ratio of the area of the inscribed circle to the area of the square ABFE is π:2.
Define the term diameter of a semicircle?If AB is divided into four congruent segments, each of which is the diameter of a semicircle, then we can draw four semicircles such that each one has its diameter on AB and they all have the same radius. Let the radius of each semicircle is r.
Let's assume the radius of each semicircle to be "r" and AB to be equal to "4r" because AB is divided into four congruent segments. Let the center of the inscribed circle be "O". Draw radii from the center of the inscribed circle to the tangent points, and let the tangent points on the semicircles be "C" and "D", and the midpoint of AB be "M".
Since CM and DM are radii of semicircles, they each have a length of "2r". So, MC = MD = 2r. Additionally, since CMDO is a square (as opposite sides are parallel and equal in length), we have CM = MD = CO = DO = 2r.
By the Pythagorean theorem, we have MC² = MO² - OC². Substituting the values we have, we get:
(2r)² = MO² - (2r)²
4r² = MO² - 4r²
MO² = 8r²
The area of the inscribed circle can be calculated as πr², so substituting MO² = 8r², we get the area of the inscribed circle as 8πr².
The area of the square ABFE is (4r)² = 16r².
So, the ratio of the area of the inscribed circle to the area of the square ABFE is:
(8πr²) : (16r²) = π : 2
Therefore, the ratio of the area of the inscribed circle to the area of the square ABFE is π : 2.
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The complete question: AB is divided into four congruent segments, each of which is the diameter of a semicircle. If a circle is inscribed in the quadrilateral formed by connecting the endpoints of the semicircles, what is the ratio of the area of the inscribed circle to the area of the square ABFE?
For point S ( – 3 , 3 ) , where will the image of this point be located after applying the translation rule 3 units on the -axis and – 3 units on the -axis? ( 0 , 0 ) ( 0, 4 ) ( – 4 , 0 ) ( – 4 , 4 )
The image of the point after the transformation of 3 units on the x-axis and – 3 units on the y-axis is (0, 0)
Calculating the image of the point after the transformationGiven that the initial location of the point is
Point S = (-3, 3)
Next, we have the translation rule to be
3 units on the x-axis and – 3 units on the y-axis
Mathematically this can be expressed as
(x + 3, y - 3)
By substitution, we have
Image of point = (-3 + 3, 3 - 3)
Evaluate
Image of point = (0, 0)
Hence, the image is (0, 0)
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what is the unit rate, and which has the better value?
(PLEASE HELP)
17 oz for $2.98
or,
21 oz for $3.50
Answer:
we can see that the second option, 21 oz for $3.50, has the better value because it costs less per ounce compared to the first option.
Step-by-step explanation:
To calculate the unit rate for each option, we divide the price by the amount of ounces:
For 17 oz for $2.98:
Unit Rate = $2.98 ÷ 17 oz
Unit Rate = $0.175 oz^-1 (rounded to three decimal places)
For 21 oz for $3.50:
Unit Rate = $3.50 ÷ 21 oz
Unit Rate = $0.167 oz^-1 (rounded to three decimal places)
Comparing the two unit rates, we can see that the second option, 21 oz for $3.50, has the better value because it costs less per ounce compared to the first option.
List all possible rational zeros for the function. (Enter your answers as a comma-separated list.)
f(x) = 5x3 + 7x2 − 7x + 4
The possible rational zeros for [tex]$f(x) = 5x^3 + 7x^2 - 7x + 4$[/tex] are [tex]\pm 1, \pm 2, \pm 4, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}$.[/tex]
What is meant by rational zeros?
In algebra, rational zeros are possible values of the variable in a polynomial equation with rational coefficients, where the numerator and denominator of the value are integers that divide the constant term of the polynomial.
[tex]$f(x) = 5x^3 + 7x^2 - 7x + 4$[/tex]
To find the possible rational zeros, we need to look at the factors of the constant term and the factors of the leading coefficient.
The constant term is 4, so its factors are [tex]\pm 1, \pm 2, \pm 4$.[/tex]
The leading coefficient is 5, so its factors are [tex]\pm 1, \pm 5$.[/tex]
Now we can list all the possible rational zeros by taking all possible ratios of factors of the constant term over factors of the leading coefficient:
[tex]$$\pm 1, \pm 2, \pm 4, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}$$[/tex]
Therefore, the possible rational zeros for [tex]$f(x) = 5x^3 + 7x^2 - 7x + 4$[/tex] are [tex]\pm 1, \pm 2, \pm 4, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}$.[/tex]
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The shape above is a parallelogram. Find j and find k.
Answer:
j = 4.5k = 2Step-by-step explanation:
You want the values of the variables j and k in the parallelogram with the halves of one diagonal labeled (3j) and (5j-9), and the halves of the other diagonal labeled (6k) and (k+10).
DiagonalsThe diagonals of a parallelogram bisect each other. That means ...
5j -9 = 3j ⇒ 2j = 9 ⇒ j = 4.5
6k = k +10 ⇒ 5k = 10 ⇒ k = 2
The values of j and k are 4.5 and 2, respectively.
how to rewrite the mixed number as an improper fraction. draw please help me bc it do tomorrow PLEASE HELP PLEASE IT DO TOMORROW. for
3 2/4 and 4 2/5
Answer:
multiply the base number with the while number and add to the top number
Step-by-step explanation:
4 ×3+2 = 14/2 u can simplify
Answer:
Step-by-step explanation:
so for 3 2/4 you first multiply the whole number (the 3) with the bottom number of the fraction (the 4) that is 12. Then you add the top number (2) and get 14. That is the top number to your improper fractions. The bottom number is 4 because the bottom number will be the same as the original fraction. this is called the c method. Multiply the denominator by the whole number then add the numerator. Same method applies for 4 2/5
two teams are playing in the world series. assuming each team has an equal likelihood of winning each game, what is the probability that one team wins in exactly five games?
The probability that one team wins in exactly five games assuming each team has an equal likelihood of winning each game is 0.29.
Algorithm World Series(n, p)
//Computes the odds of winning a series of n games
//Input: A number of wins n needed to win the series and probability p of one particular team winning a game
//Output: The probability of this team winning the series
q ← 1 − p
for j ← 1 to n do
P[0, j] ← 1.0
for i ← 1 to n do
P[i, 0] ← 0.0
for j ← 1 to n do
P[i, j] ← p ∗ P[i − 1, j] + q ∗ P[i, j − 1]
return P[n, n]
Both the time efficiency and the space efficiency are in Θ(n2) because each entry of the n + 1-by-n + 1 table (except P[0, 0], which is not computed) is computed in Θ(1) time
a. Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series. If team A wins the game, which happens with probability p, A will need i − 1 more wins to win the series while B will still need j wins. If team A looses the game, which happens with probability q = 1 − p, A will still need i wins while B will need j − 1 wins to win the series.
This leads to the recurrence
P(i, j) = pP(i − 1, j) + qP(i, j − 1) for i, j > 0
The initial conditions follow immediately from the definition of P(i, j):
P(0, j)=1 for j > 0, P(i, 0) = 0 for i > 0
b. Here is the dynamic programming table in question, with its entries rounded-off to two decimal places. (It can be filled either row-by-row, or column-by-column, or diagonal-by-diagonal.)
i/jj 0 1 2 3 4
0 1 1 1 1
1 0 0.40 0.64 0.78 0.87
2 0 0.16 0.35 0.52 0.66
3 0 0.06 0.18 0.32 0.46
4 0 0.03 0.09 0.18 0.29
Thus, P[4, 4] ≈ 0.29.
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Complete question:
World Series Odds. [20 marks total] Consider two teams, A and B, playing a series of games until one of the teams wins n games. Assume that the probability of A winning a game is the same for each game and equal to p and the probability of A losing a game is q = 1 − p. (Hence, there are no ties.) Let P(i, j) be the probability of A winning the series if A needs i more games to win the series and B needs j more games to win the series.
(a) Set up a recurrence relation for P(i, j) that can be used by a dynamic programming algorithm. Hint: In the situation where teams A and B need i and j games, respectively, to win the series, consider the result of team A winning the game and the result of team A losing the game.
(b) Find the probability of team A winning a seven-game series if the probability of it winning a game is 0.4. Hint: Set up a table with five rows (0 ≤ i ≤ 4) and five columns (0 ≤ j ≤ 4) and fill it by using the recurrence derived in part (a).
(c) Write C/C++ pseudocode for a dynamic programming algorithm to solve this problem and determine its time and space efficiencies. Hint: Your pseudocode should be guided by the recurrence you set up in part (a).