Answers
Answer:
3 square units
Step-by-step explanation:
You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).
TriangleThe plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.
AreaThe area formula for a triangle is ...
A = 1/2bh
For base b=3 and height h=2, the area is ...
A = 1/2(3)(2) = 3 . . . . . square units
The area of the triangle is 3 square units.
Related Questions
Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off 1/3 of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 1/2 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.
Answers
The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches
How to find the original length of fabric ?Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :
= 1 / 3 x
The equation would then be :
x - 1 / 3 x - 10 - 5 = 35 + 1 / 2
x - 1 / 3 x - 10 - 5 = 35 . 5
The length of the original fabric is:
2 / 3x = 35. 5 + 10 + 5
x = 50. 5 ÷ 2 / 3
x = 50. 5 x 3 / 2
x = 75 .75 inches
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Pls help me do this its kinda hard for me sense im not in a higher grade
Answers
So this is what you can do
X+110=180
X=180-110
X=70
The angles is 70 degrees.
Select ALL the ordered pairs that are solution to the following system. (There are several correct answers. Find them all.) Select the ordered pair that are solution to the following system:
2x + 3y>10
y≥ -3x + 2
(ordered pairs)
(15, -1) (0, 0) (-6, 1) (-2, 8) (15,-20) (0,4) (10, 30) (8,-2) (5, 5) (1, 10)
Answers
The ordered pairs that are solution to the system are (15, -1) (0,4) (10, 30) (5, 5) (1, 10)
How to determine the ordered pair that are solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x + 3y>10
y≥ -3x + 2
Represent properly
2x + 3y > 10
y ≥ -3x + 2
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the coordinates in the shaded area are
(15, -1) (0,4) (10, 30) (5, 5) (1, 10)
None of the options represent the shaded area (see attachment)
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Please read the photo
Answers
The average rate of change is 2.The rate of change of the function is its gradient or slope.
How is the average rate determined?To get the average rate of change, divide the change in y-values by the change in x-values.Knowing the average rate of change is necessary to detect changes in observable metrics like average speed or average velocity.
What is the average change rate?It displays the typical rate of change of the function for each unit during that time. It is determined using the slope of the line connecting the ends of the interval in the function graph.
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Find the equation of the line that passes through (1,3) and is perpendicular to
y=2x-1.
Leave your answer in the form ax+by=c
Where a, b and c are integers.
Answers
Answer:
Equation of perpendicular line:
[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]
Step-by-step explanation:
Generalized lope-intercept form of a line is y = mx + b [1]
where
m = slope
b = y-intercept
Equation of the given line is y = 2x - 1 [2]
We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)
Reciprocal of [tex]\mbox{\larg \displaystyle 2 = \displaystyle \dfrac{1}{2}}[/tex]
Negative of [tex]\dfrac{1}{2}[/tex] = [tex]-\dfrac{1}{2}[/tex] and this is the slope of the perpendicular line
The products of the slopes ⇒ [tex]2 \times -1/2 = - 1[/tex]
Therefore the equation of the perpendicular line is of the form
[tex]y = -\dfrac{1}{2}x + b[/tex]
where b is the y-intercept of this line
Since it passes through the point (1, 3), x= 1 and y = 3 is a solution point on this line
Plugging y = 3, x = 1
[tex]3 = -\dfrac{1}{2} \times 1 + b\\\\3 = -\dfrac{1}{2} + b\\\\3 + \dfrac{1}{2}= b\\\\b = 3 \dfrac{1}{2}= -\dfrac{7}{2}= 3.5[/tex]
What is the area of KELP, h = 52.6, b1 = 47.8, b2 = 39.1 *
A diagram with Trapezoid KELP and Circle C is shown. Given the dimensions, find the
area of each figure and complete the table. Round to the nearest hundredth if
necessary.
Answers
The area of the trapezoid KELP is approximately 2285.47 square units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The formula to find the area of a trapezoid is -
A = (1/2) × h × (b1 + b2)
where -
A is the area of the trapezoid.
h is the height of the trapezoid.
b1 and b2 are the lengths of the parallel bases of the trapezoid.
Using the given values, we can substitute them into the formula and solve for the area -
A = (1/2) × h × (b1 + b2)
A = (1/2) × 52.6 × (47.8 + 39.1)
A = 2285.47
Therefore, the area value is 2285.47 square units.
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Find the sine of Z.
7
X
√26
Z
√21
Y
Answers
The sine of Z is 0.834.
How to calculate sine of an angle?Assume that "α" is the angle in a right triangle XYZ. The sine formula is then given as Sin = Opposite side/ Hypotenuse.
Using the Pythagorean theorem, we can find the length of side Y:
Y² = X² + Z²
Y² = 7² + ( √(21) )²
Y² = 49 + 21
Y² = 70
Y = √(70)
Now we can use the definition of sine:
sin(Z) = opposite/hypotenuse
sin(Z) = X / Y
sin(Z) = 7 / √(70)
sin(Z) = (7 / 10) √(70)
So the sine of Z is (7 / 10) √(70), or approximately 0.834.
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Malik just got hired for a new job and will make $96, 000 in his first year. Malik was
told that he can expect to get raises of $5,000 every year going forward. How much
money in salary would Malik make in his 11th year working at this job?
Answers
The amount of money Jamar will make in his 18th year working at this job is = $107,500
What is salary outcome?A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis.
here, we have,
Calculation of yearly salary outcome
The amount of money Jamar made in his first year= $48,000
The salary rise per year = $3,500
The amount of money he will make for the extra 17 years is
= 17 × $3,500
= $59,500
Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500
= $107,500
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tyler drove 138miles, and brittney drove 116miles. what is the ratio of tyler's miles to brittney's miles? write your answer as a simplified fraction.
Answers
Tyler drove 138miles, and brittney drove 116miles, the ratio of tyler's miles to brittney's miles is 69/58.
The ratio of Tyler's miles to Brittney's miles can be found by dividing Tyler's miles by Brittney's miles.
Ratio of Tyler's miles to Brittney's miles = Tyler's miles / Brittney's miles
Ratio of Tyler's miles to Brittney's miles = 138 miles / 116 miles
Simplifying the ratio by dividing both numbers by their greatest common factor, which is 2, we get:
Hence,
Ratio of Tyler's miles to Brittney's miles = 69/58
This means that for every 69 miles Tyler drove, Brittney drove 58 miles.
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if a, b, and c are boolean variables, then the value of !(a & !(b & !c)) is the same as which of these expressions: !a || (!b || c) !a || (b & !c) (!a || b) & !c
Answers
The value of the expression is the same as the second option: !a || (b & !c).
What are boolean variables?Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.
The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:
!(a & !(b & !c)) = !a || (b & !c)
Therefore, the value of the expression is the same as the second option: !a || (b & !c).
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You started a savings account by depositing $4,200. The savings account earns 2.1% APY, compounded monthly. What was the balance in the account after 2 months?
1=Prt
Answers
4214.7 is the balance in the account after 2 months .
What does compound and simple interest mean?
A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.
Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.
P = $4200
R = 2.1% = 2.1/100 = 0.021 =
T = 2 month = 2/12 = 1/6
I = PRT
= 4200 * 0.021 * 1/6 = 14.7
Amount = P + I = 4200 + 14.7 = 4214.7
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A factory has 1,254 tires each new car needs 4 tires how many new cars can be made
Answers
The total number of new cars made by a factory from 1,254 tires as each car required four tires is equal to 314 ( round off to nearest whole number ).
Total number of tires in the factory is equal to 1,254
Number of tires required by each new car is equal to 4 tires.
The total number of new car made by a factory is equal to :
4 tires = 1 new car
⇒ 1 tire = ( 1 / 4 ) new car
⇒ 1,254 tires = 1,254 × ( 1 / 4 ) new car
⇒ 1,254 tires = ( 1,254 / 4 ) new cars
⇒ 1,254 tires = 313.5 new cars
But number of new cars cannot be in the decimals or fraction.
Round off to the nearest whole number .
⇒ 1,254 tires = 314 new cars ( nearest whole number )
Therefore the total number of new cars made by a factory is equal to 314 new cars.
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Maxine is pre-heating the oven to bake a pie. The temperature of the oven increases at a constant rate.
How long will it take the oven to reach a temperature of at least 375
degrees?
Responses
Answers
It will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.
What is Approximation?
Approximation is the act of estimating or finding a value that is close to the true or exact value, but not necessarily identical to it. In other words, an approximation is a rough calculation or an educated guess that is used when the exact value is not known or is too difficult to calculate. Approximations are commonly used in mathematics, science, engineering, and many other fields where exact values are often difficult to obtain or not required. The level of accuracy of an approximation depends on the method used and the degree of precision needed for the particular situation.
Let's use the information given to find the rate of temperature increase per minute.
Between the first two data points, the temperature increased by 3 degrees in 1 minute. Between the next two data points, the temperature increased by (112.5 - 3) = 109.5 degrees in (5 - 1) = 4 minutes. So the rate of temperature increase is (109.5/4) = 27.375 degrees per minute.
To find out how long it will take the oven to reach 375 degrees, we can use the formula:
time = (final temperature - initial temperature) / rate of temperature increase
In this case, the initial temperature is 3 degrees and the final temperature is 375 degrees. Substituting these values and the rate of temperature increase we calculated earlier, we get:
time = (375 - 3) / 27.375 = 12.96 minutes (rounded to two decimal places)
So it will take approximately 12.96 minutes for the oven to reach a temperature of at least 375 degrees.
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Samir bought snacks for his team's practice. He bought a bag of popcorn for $1.67 and a 24-pack of juice bottles. The total cost before tax was $31.19. Write and solve an equation which can be used to determine
x, how much each bottle of juice cost.
Answers
Answer:
Step-by-step explanation:
is this in deltamath or bigideas? lol
(31.19-1.67)/24=x
"/" means divide.
help I need help somebody help
Answers
The expression to represent the total volume of the two storage spaces is s³+12.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, the edge of the large cube s feet and the volume of the small cube is 12 ft³.
We know that, the formula to find the cube is side³.
Volume of large cube = s×s×s
= s³
Total volume of the two storage spaces =s³+12
If edge of large cube is 4 feet long, then the volume is
4³ = 64 ft³
Therefore, the expression to represent the total volume of the two storage spaces is s³+12.
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Expand and simplify
(3x + 4)(2x + 3)
Answers
Answer:
6x^2 + 17x + 12
Step-by-step explanation:
(3x + 4)(2x + 3) - Distribute
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
Let f(x) = 2√3x and g(x) = -4√3x. Find (f-g)(x), then evaluate when x = 12.
Answers
The function operation (f-g)(x) in the functions f(x) = 2√3x and g(x) = -4√3x is 6√3x and the value of (f-g)(12) is 36.
What is the function operation (f-g)(x) and value of (f-g)(12)?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = 2√3xg(x) = -4√3x(f-g)(x) = ?(f-g)(12) = ?First, set up the function;
(f - g)(x) = f(x) - g(x)
Replace the function designators with the actual function.
(f - g)(x) = f(x) - g(x)
(f - g)(x) = 2√3x - (-4√3x)
(f - g)(x) = 2√3x + 4√3x
(f - g)(x) = 6√3x
Now, we evaluate when x = 12.
(f - g)(x) = 6√3x
Replace x with 12
(f - g)( 12 ) = 6√3(12)
(f - g)( 12 ) = 6√36
(f - g)( 12 ) = 6 × 6
(f - g)( 12 ) = 36
Therefore, the function operation (f-g)(x) is 6√3x and (f-g)(12) is 36.
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33.3% and 0.3 as a fraction
Answers
0.3 as a fraction would be 3/10
33.3 would be 333/10
To check it so 3 ÷ 10 and 333 ÷ 10
It will give you the decimal again.
Step-by-step explanation:You're welcome.
Answer: the answer is 33.3 is 33 3/10 and 0.3 is 3/10
Step-by-step explanation:
you welcome (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the plane and x represents the number of minutes the plane has been decending: y = -128x + 3,840
Part A: Create a table for the values when x + 0, 5, 8, 10, 30. Include worked-out equations used to identify the values within the table.
Part B: Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
Answers
The altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.
What is the altitude?
The height of an object or point in relation to sea level or ground level.
Part A:
To create a table for the given equation, we substitute the given values of x in the equation and calculate the corresponding values of y:
x y = -128x + 3,840
0 3,840
5 3,200
8 2,624
10 2,304
30 0
Part B:
To find the altitude after 5 minutes, we substitute x = 5 in the given equation:
y = -128(5) + 3,840
y = 3,200
So the altitude of the airplane after 5 minutes of descending is 3,200 feet.
To find the altitude after 30 minutes, we substitute x = 30 in the given equation:
y = -128(30) + 3,840
y = 0
The altitude of the airplane is decreasing as time (x) increases, as given by the negative slope (-128) of the equation.
At 5 minutes, the airplane has descended to an altitude of 3,200 feet, which is still relatively high.
At 30 minutes, the altitude has decreased to 0, which means the airplane has landed on the ground.
Hence, the altitude of the airplane after 30 minutes of descending is 0 feet, which means the airplane has landed.
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A second hand car dealer bought a car for R85 000. The costs related to the transaction amount R250. He sells the car for R93 000. Calculate the profit he made on the deal
Answers
The profit made on the transaction by the dealer was Rs. 7,750.
To calculate the profit made by the second hand car dealer, you can subtract the cost of buying the car and the transaction costs from the selling price.
Profit = Selling Price - Cost of Car - Transaction Costs
Profit = 93,000 - 85,000 - 250
Profit = 7,750
So the dealer made a profit of Rs. 7,750 on the transaction.
Profit and Loss (P&L) is a statement that summarizes a company's revenues and expenses over a specific period of time, typically a quarter or a year. The purpose of a P&L statement is to show a company's ability to generate revenue, as well as the cost of doing so. The difference between a company's total revenue and total expenses is referred to as net profit or net loss
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weinstein, mcdermott, and roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies. one part of the study asked students to prepare for a test by reading a passage. in one condition, students generated and answered questions after reading the passage. in a second condition, students simply read the passage a second time. all students were then given a test on the passage material and the researchers recorded the number of correct answers. a. identify the dependent variable for this study. b. is the dependent variable discrete or continuous?
Answers
a. The dependent variable for this study is the number of correct answers on the test given.
b. The dependent variable in this study is a discrete variable.
a. The dependent variable for this study is the number of correct answers on the test given to the students after they prepared for the test by either generating and answering questions or reading the passage a second time.
b. The dependent variable in this study is a discrete variable because the number of correct answers can only take on whole numbers (e.g., 0, 1, 2, 3, etc.). It is not possible to have fractional or continuous values of correct answers on the test.
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Find the value of x in 3x + 4y = 12 and 9x - 4y = 24.
A.-3
B.3
C.0.75
D.-0.75
Answers
Answer:
B. x=3
Step-by-step explanation:
3x+4y=12
9x-4y=24
Add 9x and 3x
Subtract -4y from 4y which will cancel out
Add 12 and 24
12x=36
divide both sides by 12
x=3
Kim bought a birdhouse that originally cost $36. She used a coupon that took 25% off the price. How much money did Kim save?
Answers
Kim saved $9 by using the coupon.
How to find Original price?
The MSRP (i.e., Manufacturer's Suggested Retail Price) set the original price, which is the cost. In the majority of cases, the original price would have been less expensive than the current price, though this is not always the case. Finding an item's original price and knowing the price after a discount are both made possible by original price.
Original price = Sales price/(100%-Discount%)
To find out how much money Kim saved, we need to first find out how much the birdhouse cost after the coupon was applied.
The coupon took 25% off the original price, so the birdhouse cost 100% - 25% = 75% of its original price.
So, the new price of the birdhouse would be:
36 * 75% = $27
Kim saved 36 - 27 = $9 by using the coupon.
Therefore, Kim saved $9 using the coupon.
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Number 4: Would the product change if 30 and 5 on the left side of the area model were changed to 20, 10, and 5? Explain.
Answers
No, if the figures on the left side of the area model were changed to 20, 10, and 5, the product would retain the same.
Area model multiplication is what?
The area model approach is based on the straightforward equation that may be used to calculate the area of a rectangle: LxW=A. As this anchor chart from Primary Punch illustrates, students typically begin by learning basic arrays for one-digit multiplication. When we multiply each digit of one number by each digit of another number while maintaining the place value of each digit, the resulting numbers are called partial products.
According to the supplied query,
30 and 5 on the left side of the area model are altered to 20,10, and 5
Thus, after multiplying partial products, we obtain:
First row = 20×100+20×20+8×20
= 2000+400+160 = 2560
Second row = 10×100+10×20+10×8
= 1000+200+80 = 1280
Third row = 5×100+5×20+5×8
= 500+100+40 = 640
Adding all the rows we get,
2560+1280+640 = 4480
The item we receive when the dimensions are 30 and 5 is the same as this. In each instance, the area product stays the same.
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Solve for x *
04
45
O x = 50
Ox=8
x = 48.2
x = 40.5
20
S
18
R
Answers
Answer:
x = 40.5
Step-by-step explanation:
SQ is an angle bisector and divides the opposite side into segments that are proportional to the other two sides, that is
[tex]\frac{PS}{RS}[/tex] = [tex]\frac{PQ}{RQ}[/tex] ( substitute values )
[tex]\frac{20}{18}[/tex] = [tex]\frac{45}{x}[/tex] ( cross- multiply )
20x = 18 × 45 = 810 ( divide both sides by 20 )
x = 40.5
In the figure below, B is between A and C, and C is between B and D. If AD=13, BD=7, and BC=3, find AC.
AC =
Answers
The length of segment AC is equal to 9.
How to Find the Length of a Segment?Since B is between A and C, we can use the fact that AB + BC = AC. Similarly, since C is between B and D, we can use the fact to state the lengths of the following segments that: CD + BC = BD.
Substituting the given values, we get:
AB + BC = AC
CD + BC = BD
We are given segments BD = 7 and BC = 3, so we can substitute these values:
CD + 3 = 7
Solving for CD, we get:
CD = 7 - 3
CD = 4
Now we can use the fact that AD = AC + CD to solve for the length of segment AC:
AD = AC + CD
13 = AC + 4
AC = 9
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Someone help me with this equation please!!
Answers
The given proof follows the symmetric property of angle congruence. Therefore, option C is the correct answer.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that,
Statements Reasons
1. ∠ABC≅∠DEF 1. Given
2. m∠ABC=m∠DEF 2. Definition of congruent angles
3. m∠DEF=m∠ABC 3. Symmetric property of equality
4. ∠DEF≅∠ABC 4. Definition of congruent angles
The symmetric property says that if one geometric shape is congruent to another, than the second shape is also congruent to the first. The symmetric property of congruence says that for any angles A and B, if ∠A≅∠B then ∠B≅∠A.
Therefore, option C is the correct answer.
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in a particular region during a 1-year period, there were 1000 deaths. it was observed that 321 people died of a renal failure and 460 people had at least one parent with renal failure. of these 460 people, 115 died of renal failure. calculate the probabil ity of a person that he dies of renal failure if neither of his parents had a renal failure
Answers
The probability of a person dying of renal failure if neither of their parents had renal failure is 0.056 or about 5.6%.
To solve this problem, we can use Bayes' theorem, which states that:
P(A|B) = P(B|A) * P(A) / P(B)
where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this case, we want to find the probability of a person dying of renal failure given that neither of their parents had renal failure. Let's define the following events:
R: death due to renal failure
P: at least one parent with renal failure
NP: neither parent has renal failure
We are given the following information:
Total deaths = 1000
Deaths due to renal failure (R) = 321
People with at least one parent with renal failure (P) = 460
Deaths due to renal failure among people with at least one parent with renal failure = 115
Using this information, we can calculate the probabilities as follows:
P(R) = 321/1000
P(P) = 460/1000
P(R|P) = 115/460
To find the probability of a person dying of renal failure given that neither of their parents had renal failure (i.e., P(R|NP)), we need to use Bayes' theorem. We can start by finding the probability of neither parent having renal failure (i.e., P(NP)):
P(NP) = 1 - P(P) = 1 - 0.46 = 0.54
Next, we can use the law of total probability to find the probability of dying of renal failure among people with neither parent having renal failure:
P(R|NP) = P(R) * P(NP|R) / P(NP)
We can find P(NP|R) using the formula:
P(NP|R) = P(NP ∩ R) / P(R)
To find P(NP ∩ R), we can use the formula:
P(NP ∩ R) = P(R|NP) * P(NP)
Substituting the values, we get:
P(R|NP) = P(R) * P(NP|R) / P(NP)
= 321/1000 * (1 - 115/460) / 0.54
= 0.056
This calculation shows how conditional probabilities can be calculated using Bayes' theorem and the law of total probability.
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What value of x makes the equation true
3(2x-5+8x)=5(2x+5)
Answers
The value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2
How to evaluate for the value of x for the equationWe shall evaluate for the value of x to know what makes the algebraic equation true as follows;
3(2x - 5 + 8x) = 5(2x + 5)
3(10x - 5) = 5(2x + 5)
30x - 15 = 10x + 25 {expand bracket}
30x - 10x = 25 + 15 {collect like terms}
20x = 40
x = 40/20 {divide through by 20}
x = 2
Therefore, the value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2.
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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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