Answers
Using Cramers Rule, X = 10.34, Y = 0.85. See the computations below.
What is Cramers Rule?Cramer's rule is an explicit formula in linear algebra for solving a system of linear expressions with as many equations as unknowns, and it is true whenever the system has a unique solution.
Given:
10x - 4y = 100; ..................1) and
8x - 100y = -2; ...................2)
First things first, let's pick off the variables we will need for Cramer's equation:
Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f. Therefore:
a = 10, b = -4, c = 100, d = 8, e = -100, f = -2
Step 1, calculate the denominator Delta (Δ):
Δ = a * e - b * d
Δ = (10 * -100) - (-4 * 8)
Δ = -1000 - -32
Δ = -968
Step 2, calculate the numerator for x
Numerator(x) = c * e - b * f
Numerator(x) = (100 * -100) - (-4 * -2)
Numerator(x) = -10000 - 8
Numerator(x) = -10008
X = Numerator (x) / Δ
x = -10008/-968
x = 10.338842975207
x [tex]\approx[/tex] 10.34
y = Numerator(y)/Δ
y = -820/-968
y = 0.84710743801653
y [tex]\approx[/tex] 0.85
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Related Questions
I need help on this problem pleaseeeeeeeeeee
Answers
A. Y=7.65x+50
B . 149.45-50= 99.45. 99.45/7.65=13 13 Hours
C. Y=7.65x48= $376.20 For 2 Days
Please give me Brainlyiest
Enter the denominator of the fraction is simplest form that is equal to 0.7
Answers
The simplest form of the fraction equivalent to 0.7 is 7/10
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, to show the denominator of the fraction in the simplest form that is equal to 0.7
To convert 0.7 into a fraction, we have to write it in p/q form, where p and q are positive integers.
we can write .7 as 0.7/1
now to remove the decimal point we will multiply and divide by 10
therefore,
0.7/1 × 10/10 = 7/10
Hence, the simplest form of the fraction equivalent to 0.7 is 7/10
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you shuffle a standard deck of cards, then draw four cards.(a) what is the probability all four are the same suit? (b) what is the probability all four are red? (c) what is the probability each has a different suit?
Answers
a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105
Total number of cards =52
No. of cards for each suit =13
Total types of four suit =4 (heart, spades, diamonds, clubs)
Total numbers of ways = [tex]^{52}C_4[/tex] =270,725 ways
a) number of ways choosing four cards of the same suit
= [tex]^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4[/tex]
= [tex]4 \times ^{13}C_4\\[/tex]
= [tex]4 \times \frac{13!}{4!(13-4)!}[/tex]
=2860 ways
Probability that all four are the same suit is 2860/270,725 = 0.0106
b) Number of ways all four cards are red
=[tex]^{26}C_4[/tex]
= 4,950 ways
Probability that all four are red = 4950/270,725 =0.055
c) Number of ways each card has a different suit
=[tex]^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1[/tex]
= 28,561 ways
Probability each has a different suit is 28561/270725 = 0.105
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I really need help! Can you help??
Answers
Answer:
To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.
Step-by-step explanation:
In what time will the simple interest on Rs7560 be Rs1102. 50 at 25/4% per annum
Answers
The simple interest on Rs 7560 will be Rs 1102.50 at a rate of 25/4% per annum after approximately 1 month (0.09 years).
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, and not on any accumulated interest. It is usually calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.
We can use the formula for simple interest to solve this problem:
Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)
We know that the principal is Rs 7560, the rate is 25/4% per annum, and the interest is Rs 1102.50. Substituting these values into the formula, we get:
1102.50 = 7560 x (25/4) x T
Simplifying:
1102.50 = 47250T/4
Multiplying both sides by 4 to eliminate the fraction:
1102.50 x 4 = 47250T
4410 = 47250T
Dividing both sides by 47250:
T = 4410/47250
T = 0.093 or approximately 0.09 years.
To convert this to months or days, we can multiply by 12 or 365, respectively.
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car rental company a charges an $80 service fee plus $22 per day. car rental company b does not have a service fee and charges $32 per day. which equation will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b? responses 32d
Answers
Equation that will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b is [tex]\frac{80+22d}{d} = 32d[/tex]
For finding the equation we will first form separate equations of both company a and company b and then we will equate the formed equation to find the number of days.
Let the number of days be d.
For company a, we will first add the service charges and per day charge multiplied with number of days, and then divide the sum with number of days.
= [tex]\frac{80+22d}{d}[/tex]
For company b, we will multiply the per day charges with the number of days.
= [tex]32d[/tex]
Now, we will equate both the formed equation
[tex]\frac{80+22d}{d} = 32d[/tex]
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choose the best data type for each of the following so that any reasonable value is accommodated but no memory storage is wasted. give an example of a typical value that would be held by the variable, and explain why you chose the type you did.
Answers
a. The best data type for the number of siblings would be an integer.
An example of a typical value for this variable would be 3, as someone might have 3 siblings. An integer is the best data type because the number of siblings is a whole number and can never be a fraction or a negative number.
b. The best data type for the final grade in this class would be a floating-point number. An example of a typical value for this variable would be 85.5, as a final grade may include decimal points. A floating-point number is the best data type because a final grade can have a decimal point and may include fractions.
c. The best data type for the population of Earth would be a long integer. An example of a typical value for this variable would be 7,794,798,739, as of the year 2020. A long integer is the best data type because the population of Earth is a large number and cannot be expressed using a regular integer.
d. The best data type for the population of a U.S. county would be an integer. An example of a typical value for this variable would be 100,000, as the population of a county can vary greatly. An integer is the best data type because the population of a county is a whole number and can never be a fraction or a negative number.
e. The best data type for the number of passengers on a bus would be an integer. An example of a typical value for this variable would be 20, as a bus can carry a varying number of passengers. An integer is the best data type because the number of passengers on a bus is a whole number and can never be a fraction or a negative number.
f. The best data type for one player's score in a Scrabble game would be an integer. An example of a typical value for this variable would be 45, as a score in Scrabble is calculated in whole numbers. An integer is the best data type because a score in Scrabble is a whole number and can never be a fraction or a negative number.
g. The best data type for one team's score in a Major League Baseball game would be an integer. An example of a typical value for this variable would be 7, as a team's score is calculated in whole numbers. An integer is the best data type because a team's score is a whole number and can never be a fraction or a negative number.
h. The best data type for the year a historical event occurred would be an integer. An example of a typical value for this variable would be 1776, as the year the United States declared independence. An integer is the best data type because a year is a whole number and can never be a fraction or a negative number.
i. The best data type for the number of legs on an animal would be an integer. An example of a typical value for this variable would be 4, as many animals have four legs. An integer is the best data type because the number of legs an animal has is a whole number and can never be a fraction or a negative number.
j. The best data type for the price of an automobile would be a floating-point number. An example of a typical value for this variable would be $25,000.50, as a price for a car can include decimal points. A floating-point number is the best data type because the price of a car can have a decimal point and may include fractions.
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A 3 inch radius circle is drawn inside a 7 inch radius circle. If you throw a dart at these circles, what is the probability AS A PERCENT that you land inside the smaller circle? Round to the nearest whole percent. Use 3.14 for pi.
Answers
Answer:
Step-by-step explanation:
What information is in the text but not in the graph?
Answers
Answer:
B. More money was given than expected in 1994
Step-by-step explanation:
Nowhere is it mentioned what amount was expected as donations. Only actual amounts received are shown on the graph
Hence this is an assumption and not necessarily fact
Each of these graphs of residuals is from the same set of data using different lines to fit the data. Which graph is most likely to represent the residuals from the best fit line?EXPLAIN YOUR REASONING.
Answers
The graph which is most likely to represent the residuals from the best fit line is Option C.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that from the graphs of residuals is the same set of data using different lines to fit the data.
The best fit line is the line that minimizes the sum of the squared residuals.
In other words, it is the line that has the smallest sum of the squared differences between the actual data points and the predicted values from the line.
The residuals represent the differences between the actual data points and the predicted values, and any systematic pattern in the residuals would suggest that the line is not a good fit for the data.
Hence, Option C is correct, the graph which is most likely to represent the residuals from the best fit line.
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Fatima has a total of $8 to spend to make fruit smoothies. She will use two types of fruit. The table to the right shows the cost of each type of fruit per cup.
For the mango and pineapple mixture, find a linear equation in standard form that models how much mango and pineapple she can buy, where x is cups of mango and y is cups of pineapple.
Mango=0.50
Pineapple=0.75
Strawberry=1.00
Answers
Answer:
0.75y + 0.5x = 8.00
Step-by-step explanation:
QUESTION FOR FOR LIH04
Answers
how many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? how many of these are odd numbers? how many are greater than 330?
Answers
By using the concept of combinations, we have determined that there are 210 three-digit numbers that can be formed using the digits 0-6 without repeating any of them. Among them, there are 90 odd numbers and 120 numbers greater than 330.
Combinations are a fundamental concept in mathematics, particularly in the field of combinatorics, which deals with counting and arranging objects.
To solve this problem, we can use the concept of combinations, which is a way of counting the number of ways we can choose k items from a set of n items. In this case, we want to find the number of three-digit numbers we can form from the set {0, 1, 2, 3, 4, 5, 6}, without repeating any of the digits.
First, we can determine the number of ways we can choose the first digit. Since there are seven digits to choose from, we have 7 options for the first digit.
Next, we can determine the number of ways we can choose the second digit. Since we have already used one of the digits, we only have 6 options left for the second digit.
Finally, we can determine the number of ways we can choose the third digit. Since we have used two of the digits, we only have 5 options left for the third digit.
Therefore, the total number of three-digit numbers we can form is given by the product of the number of choices for each digit:
7 x 6 x 5 = 210
So there are 210 different three-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6, without repeating any of the digits.
To find the number of odd numbers, we need to consider that the last digit must be either 1, 3, or 5, since these are the only odd digits in the set. We can choose the first two digits in the same way as before, and then choose one of the three odd digits for the last digit. Therefore, the number of odd three-digit numbers is:
6 x 5 x 3 = 90
To find the number of three-digit numbers greater than 330, we need to consider that the first digit must be either 3, 4, 5, or 6. We can choose the first digit in 4 ways, and then choose the remaining two digits as before. Therefore, the number of three-digit numbers greater than 330 is:
4 x 6 x 5 = 120
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Which of the following sequences is an arithmetic sequence?
O {1, 2, 4, 7,...}
O {1, -2, 4, -8,...}
O {1, 4, 7, 10, ...}
O {1, 3, 9, 27,...}
Answers
Answer:
The third option
Step-by-step explanation:
The third option, {1, 4, 7, 10, ...} is an arithmetic sequence because you add 3 to get from 1 to 4, and then you add 3 to get to 7, and then you add another 3 to get to 10.
which of the following are true statements? select all that apply: 1. a 95% confidence interval is a random interval that contains the true parameter 95% of the time 2. the true parameter is a random value that has 95% chance of falling in the 95% confidence interval 3. i perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. there is a 95% probability that the true parameter is between 0.4 and 0.5. 4. the true parameter (unknown to me) is 0.5. if i sample data and construct a 95% confidence interval, the interval will contain 0.5 95% of the time. answer :
Answers
Among the following statements, The true statements are:
Option (1) a 95% confidence interval is a random interval that contains the true parameter 95% of the time, (2)the true parameter is a random value that has 95% chance of falling in the 95% confidence interval, (3) i perform a linear regression and get a 95% confidence interval from 0.4 to 0.5. there is a 95% probability that the true parameter is between 0.4 and 0.5, (4) the true parameter (unknown to me) is 0.
A 95% confidence interval is a random interval that contains the true parameter 95% of the time.
The true parameter is NOT a random value, and it is not correct to say that it has a 95% chance of falling in the 95% confidence interval.
If you perform a linear regression and get a 95% confidence interval from 0.4 to 0.5,
it means that if you repeated the same experiment many times, 95% of the resulting confidence intervals would contain the true parameter.
It is not correct to say that there is a 95% probability that the true parameter is between 0.4 and 0.5 because the true parameter is either in the interval or not.
If the true parameter is 0.5 and you sample data and construct a 95% confidence interval, the interval may or may not contain 0.5.
The 95% confidence interval is a statement about the probability of the interval containing the true parameter, not about the probability of the true parameter being any specific value.
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Simplify.
(5x-2+3x²)+(4x+3)
O 3x² +9x-1
O 12x4 +1
O 3x²+x+5
O 3x² +9x+1
Answers
Answer:
3x² + 9x + 1
Step-by-step explanation:
5x - 2 + 3x² + 4x + 3
= 9x - 2 + 3x² + 3
= 9x + 1 + 3x²
= 3x² + 9x + 1
For what values of x and y must ABCD be a parallelogram?
Answers
The correct answer is,
x = 39
y =21
What is Parallelogram ?A different type of quadrilateral known as parallelogram has both pairs of its opposite sides parallel and equal.
The figure shows a parallelogram ABCD with the parameters AB II CD and AD II BC. Furthermore, AB = CD and AD = BC.
In a parallelogram, the opponent angles are equal.. So it means that side /A is equal to side /C, let's equate the two angles and solve for x;
5y - 3 = x + 3y
2y - x = 3 ........(1)
Also, consecutive angles of a parallelogram are supplementary,
therefore,
/C + /D = 180
x + 3y + 2x = 180
3x + 3y = 180
x + y = 60 .......(2)
Now, add equations (1) and (2)
(2y-x) + (y+x) = 3 + 60
3y = 63
y = 21
now put this value of y in (2) we get,
x + y = 60
x + 21 = 60
x = 39
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Which expressions are equivalent to 4 � 4b4, b ? Choose all answers that apply: Choose all answers that apply: (Choice A) A � + 2 ( � + 2 � ) b+2(b+2b)b, plus, 2, left parenthesis, b, plus, 2, b, right parenthesis (Choice B) B 3 � + � 3b+b3, b, plus, b (Choice C) C 2 ( 2 � ) 2(2b)
Answers
B=3b-b
C= 2b expressions are equivalent to 4 � 4b4, b .
b+2(b+2b)=b+2(3b)=b+6b=7b
3b+b=4b
2(2b)=4b Option B and C produce the outcome 4b. They are the expressions that are comparable to 4b as a result. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value. If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4. Of course, both sides of the equation can be made simpler. Constants x=2x+7+4 on the left side cancel each other out. If two systems of equations have the same solution, they are equivalent (s). In algebra, two equations are said to be equivalent if their roots or solutions are the same. The same number, symbol, or expression must be added to or subtracted from both sides of an equation to produce an equivalent equation.
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2.5 pounds of meat for 2 dogs x pounds of meat for 7 dogs
Answers
There are 8.75 pounds of meat for 7 dogs
How to find the value of x?
Ratio is used to compare two or more quantities. It is used to indicate how big or small a quantity is when compared to another.
Since 2.5 pounds of meat for 2 dogs x pounds of meat for 7 dogs. We can write:
2.5/2 = x/7
2*x = 2.5*7
2x = 17.5
x = 17.5/2
x = 8.75
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The population of rabbits on an island is growing exponentially. In the year 2000, the population of rabbits was 950, and by 2003 the population had grown to 1000. Predict the population of rabbits in the year 2013, to the nearest whole number.
Answers
The population of rabbits in the year 2013 is 1186.
How to predict the population of rabbits in the year 2013?
To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:
P = P₀ * e^(rt)
where:
P = final population
P₀ = initial population (950)
r = the growth rate (we need to find this)
t = time elapsed (13 years)
We can use the data from 2003 to find the growth rate:
1000 = 950 * e^(r * 3)
1000 = 950 * e^(3r)
1000/950 = e^(3r)
ln (1000/950) = 3r
r = (ln(1000 / 950)) / 3
r = 0.0171
Now that we have the growth rate, we can use it to find the population in 2013:
P = 950 * e^(0.0171 * 13)
P = 1186
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2. 20 m 24 m 24 26 m
Answers
Note that the body starts "with an initial velocity and moves with uniform acceleration."(Option C)
What is Acceleration?In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.
The distance covered by the particle in nth second
Sₙ = u + a/2(2n-1)
S₈ = 20m
S₈ = u + a/2(2x(8-1)
20 = u + 7.5a ...................()
S₉ = 22 = u + a/2(2*9-1)
22 = u + 8.5a ..................(2)
By solving equations 1 and 2 we have :
u=5m/s , a=2m/s²
Thus,
S₁₀ = u+ a/2(2*10-1)
S₁₀ = 5 + 1/2 * 2 (2 * 10-1)
S₁₀ = 5 + 19
S₁₀ = 24m
Thus, it is correct to state that the body starts with the initial velocity and moves with uniform acceleration, and the correct option is C.
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Full Question:
A body covers 20 m, 22 m, 24 m, in 8th, 9th, and 10th seconds respectively. The body starts:
from rest and moves with uniform velocity.
from rest and moves with uniform acceleration.
with an initial velocity and moves with uniform acceleration.
with an initial velocity and moves with uniform velocity.
Help me with this math homework pls!
Rewrite every expression underneath, while replacing every sign "x" implied.
23 + 8b = .......
㎡ - 5g = .......
⅛ q + 7a/3 = .....
12k (g+h) =......
(2x + 3)(2 - 5x) = ......
Answers
The following expressions rewritten below;
23 + 8bm² - 5g(3q + 56a) / 2412kg + 12kh -10x² -11x + 6How to write algebraic expressions?23 + 8b
No common terms or factors
= 23 + 8b
㎡ - 5g
No common terms or factors
= m² - 5g
1/8 q + 7a/3
= (3q + 56a) / 24
12k (g+h)
= 12kg + 12kh
(2x + 3)(2 - 5x)
= 4x - 10x² + 6 - 15x
combine like terms
= -10x² -11x + 6
Therefore, algebraic expressions are solved by multiplying and combining like terms.
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Please help (will mark as brainlest)
Answers
Answer:
TRIANGLE PROBLEM:
area : 6a^4
perimeter : 12a^2
SIMPLIFY problem:
-40c^2+26a^2+30ac
EVALUATE & FACTOR:
(q^2 - p) ( p^2 - q)
and the solved form is 240
hope it helps :)
Step-by-step explanation:
lol im an rsm kid too. but i hope these are right,
first i'm gonna start with 263 c.
AREA = 4a^2 * 3a^2 divided by 2.
12a^4 divided by 2 = 6a^4.
AREA = 6a^4
Perimeter you can find with the pythag. th.
(4a^2) ^2 + (3a^2 ) ^2 = c^2
16a^4 + 9a^4 = c^2
, the missing side is 5a^2
therefore the perimeter is 4a^2 + 3a^2 + 5a^2 = 12a^2
ok next, im gonna do 266
the answer is -40c^2+26a^2+30ac
make sure to check this w/ symbo or mthway
ok last one!!
factored form is (q^2 - p) ( p^2 - q)
and the solved form is 240
NEED HELP
Solve for x.
X=
Answers
The measure of the angle x would be 25.2°.
What is a circle theorem?
The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.
By using the circle theorem, we can write
5x-7 = 119
5x = 119 + 7
5x = 126
x = 126/5
x = 25.2°
Hence, the measure of the angle x would be 25.2°.
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there 10 cars in a race. in how many ways can three cars finish the race as the 1st, 2nd, and the 3rd places?
Answers
There are 10 cars in a race, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
An arrangement of particulars in a specific order is appertained to as a permutation. Then, the factors of sets are arranged in a direct or successional order. For case, the set A = ,6 has a permutation of 2, which is. There's no other way to organise the factors of set A, as you can see.
There are 10 cars in the race,
Three cars finish the race in the 1st ,2nd and 3rd order
1st finish the race have 10 chances
P(A) = 10
2nd finish the race have 9 chances
P(B) = 9
3rd finish the race have 8 chances
P(C) = 8
The number in which this can be put,
= P(A) x P(B) x P(C)
= 10*9*8
=720 ways
Therefore, in 720 ways can three cars finish the race as the 1st, 2nd, and the 3rd places.
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1 13. In the first few days of its life, the length of an earthworm I is thought to be proportional to the square root of the number of hours n which have elapsed since its birth. If a worm is 2 cm long after 1 hour, how long will it be after 4 hours? How long will it take to grow to a length of 14 cm?
Answers
The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.
What is meant by Proportion?Proportions are defined when two or more ratios are made to be equal to each other.
Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.
If a is proportional to b, we denote it as a ∝ b.
Given,
Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.
l ∝ √n
l = k √n, for some constant k.
If a worm is 2 cm long after 1 hour, we can write it as,
2 = k × √1
⇒ k = 2
So the proportionality constant is 2.
After 4 hours,
l = k √4
l = 2 × 2 = 4 cm
If the length is 14 cm,
14 = 2 √n
√n = 14 / 2
√n = 7
n = 7² = 49 hours
Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.
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Step 3: Apply the slope formula: m =
2-3
-1-6
m=
(1/5)
(-1/7)
(1/7)
32-).
X2 X1
Answers
The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line and m is the slope of the line. To use the formula, you need to know the coordinates of two points on the line. If you have the coordinates of two points, you can substitute them into the formula to find the slope.
take your time in 2-6
Answers
Sketch and graph please
Answers
We have drawn the graph for the given inequality.
What is inequality?
Inequality is a mathematical statement that compares two values or expressions and shows their relative size. It is represented by the symbols >, <, ≥, or ≤, which respectively mean "greater than", "less than", "greater than or equal to", and "less than or equal to". Inequalities can also include variables and can be used to describe a range of possible values for that variable.
For the given inequality y ≤ 3/5x-5
we can draw the graph as shown below:
Hence, we have drawn the graph for the given inequality.
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the probability that it will rain tomorrow is 0.3. if it rains tomorrow, the probability that it will rain on the following day is 0.9. if it does not rain tomorrow, the probability that it will rain on the following day is 0.08. round your answers to three decimal places.
Answers
the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.
Given the probabilities, you can use Bayes' theorem to calculate the probability that it will rain on the following day, given that it rained tomorrow. Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B)
Where: P(A|B) is the likelihood that event A will occur assuming event B has already happened. P(B|A) is the probability of event B given that event A has occurred. The prior probability of event A is P(A). The prior probability of event B is P(B).
In this case, let A be the event that it rains on the following day and B be the event that it rains tomorrow.
So, P(A|B) = P(B|A) * P(A) / P(B) = 0.9 * 0.3 / P(B)
To calculate P(B), you can use the total probability theorem:
P(B) = P(B|A) * P(A) + P(B|~A) * P(~A) = 0.9 * 0.3 + 0.08 * 0.7 = 0.327
Now, you can substitute the values into the formula for P(A|B) to get:
P(A|B) = 0.9 * 0.3 / 0.327 = 0.75
So, the probability that it will rain on the following day, given that it rained tomorrow, is 0.75. Rounded to three decimal places, the answer is 0.750.
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