Use the image below to answer the questions. Answers should be fractions in lowest terms.
(a) Find the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid
(b) Find the probability that a point chosen randomly inside the rectangle and is outside the Triangle
The probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, area of a rectangle = Length×Breadth
= 15×8
= 120 square units
Area of a triangle = 1/2 ×Base×Height
= 1/2 ×(√10²-6²)×6
= 0.5×8×6
= 24 square units
Area of a trapezium = 1/2 (Sum of parallel sides)×Height
= 1/2 ×(5+7)×2
= 12 square units
Area of a square = side² = 2²
= 4 square units
(a) Probability of landing in trapezium or Square = 12/120 + 4/120
= 16/120
= 2/15
(b) Probability of landing inside the rectangle but outside the triangle = 16/120
= 2/15
Therefore, the probability that a point chosen randomly inside the rectangle and is inside the Square or Trapezoid is 2/15.
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Linda is discussing her interior design ideas for a children’s playroom with her client. What type of drawing will be useful to express her ideas to her client?
Linda can represent the different kinds of spaces she has planned for the playroom through a _________ diagram.
Answer:
A floor plan diagram would be useful for Linda to express her ideas to her client.
please help will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
4. The surface area of a cube is 486 in. Find the volume inside the cube but outside of
an inscribed sphere. Round to the nearest tenth.
Answer:
Let s be the length of a side of the cube, then its surface area is given by 6s^2. We know that the surface area of the cube is 486 in^2, so we can set up the equation:
6s^2 = 486
Solving for s, we get:
s^2 = 81
s = 9
Therefore, the length of a side of the cube is 9 in. The radius of the inscribed sphere is half the length of a side, so it is r = 4.5 in. The volume inside the cube but outside of the sphere is equal to the volume of the cube minus the volume of the sphere:
V = s^3 - (4/3)πr^3
V = 9^3 - (4/3)π(4.5)^3
V ≈ 328.8 in^3
Rounding to the nearest tenth, the volume inside the cube but outside of the inscribed sphere is approximately 328.8 in^3.
y greater then or less than 8
The equivalent value of the inequality is y > 8 and y < 8
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
A = y greater then or less than 8
On simplifying the equation , we get
y > 8 and y < 8
Hence , the inequality is y > 8 and y < 8
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Your gross income is $4,520.00/month. Your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. How much is the total interest earned between both accounts in 60 days?
a)$44.31
b)$59.06
c)$39.27
d)$41.19
Answer:
C
Step-by-step explanation:
First, we need to calculate the net income after deductions:
FICA = 7.65% x $4,520.00 = $346.38
Federal tax withholding = 11.75% x $4,520.00 = $531.40
State tax withholding = 8.5% x $4,520.00 = $384.20
Total deductions = $346.38 + $531.40 + $384.20 = $1,262.98
Net income = $4,520.00 - $1,262.98 = $3,257.02
Next, we need to calculate the amount allocated for fixed expenses:
Fixed expenses = 30% x $3,257.02 = $977.11
The remaining amount that is available for savings is:
Savings = $3,257.02 - $977.11 = $2,279.91
The emergency fund is equal to 5 months' worth of fixed expenses, which is:
Emergency fund = 5 x $977.11 = $4,885.55
The amount placed in the CD is 75% of the emergency fund, which is:
CD = 75% x $4,885.55 = $3,664.16
The amount placed in the regular savings account is:
Savings account = $4,885.55 - $3,664.16 = $1,221.39
To calculate the interest earned in the CD in 60 days, we use the formula:
Interest = Principal x Rate x Time
where the rate is annual percentage rate (APR) divided by 365 (number of days in a year)
Interest earned in the CD = $3,664.16 x (5.25%/365) x 60 = $21.97
To calculate the interest earned in the regular savings account, we use the formula:
Interest = Principal x Rate x Time
where the rate is annual percentage yield (APY) divided by 365 (number of days in a year)
Interest earned in the regular savings account = $1,221.39 x (3.8%/365) x 60 = $17.30
Therefore, the total interest earned between both accounts in 60 days is:
$21.97 + $17.30 = $39.27
So the correct answer is (c) $39.27.
which range contains the value of √4(4+3)
a: between 2.6 and 2.7
b: between 4.3 and 4.5
c: between 5.2 and 5.4
d: between 7.4 and 7.6
[tex]\sqrt{4(4+3)}[/tex] is between 5.2 and 5.4.
Answer:
Step-by-step explanation:
Here first look at the quantity which is [tex]4(4+3)=16+12=28[/tex]. So the nearby largest possible of square root which gives us integer is 25. So [tex]5=\sqrt{25} < \sqrt{28}[/tex] is satisfied.
So now looking at the options we can say that [tex]5.2^{2}=27.04[/tex] and [tex]5.4^{2}=29.16[/tex]. We can see that [tex]27.04 < 28 < 29.04[/tex].
Final Answer: So the answer is b)between 5.2 and 5.4.
The charter of a corporation provides for the issuance of 110,000 shares of common stock. Assume that 51,000 shares were originally issued and 4.100 were subsequently reacquired. What is the number of
shares outstanding?
Oa. 55.100
Ob. 46.900
Oc. $1.000
Od. 4.100
Answer:
A
Step-by-step explanation:
I'm assuming it is A since it said the 51,000 were originally issued and then adding on the 4,100, you get 55,100.
Jacob recently graduated from college and is starting a new job where he will have to commute to work by car. He shares an
apartment with a roommate and his share of rent and utilities comes to $700 per month. His other necessary monthly
expenses include $400 per month for food, $400 per month in student loan repayments and $200 per month in personal
expenses. His take-home pay from work is $2,000 per month. If auto insurance and repairs for his new vehicle are expected
to be $200 per month, what is the greatest amount he can commit for a monthly vehicle payment with no safety margin?
Answer:
Step-by-step explanation:
Begin with monthly his take-home pay (after taxes and other withholdings): $2,000
Subtract all necessary monthly expenses.
$2,000 monthly take-home pay
- $700 rent & utilities
- $400 food
- $400 student loan payment
- $200 personal expenses
- $200 auto insurance & repairs
= $100, which is the maximum amount that Jacob can commit to monthly expenses for his vehicle.
After totaling his monthly necessary expenses ($1,900), it is evident that Jacob could allocate up to $100 per month towards a vehicle payment without having a safety margin, given his monthly take-home pay of $2000.
Explanation:To calculate the maximum amount Jacob can commit for a monthly vehicle payment, we need to subtract all his necessary monthly expenses from his monthly take-home pay. Jacob's current expenses include:
Rent and utilities: $700 Food: $400 Student loan payment: $400 Personal expenses: $200 Auto insurance and repairs: $200Adding these expenses together, Jacob spends $1,900 on necessary expenses each month. Therefore, if we subtract this from his monthly take-home pay of $2,000, we find that Jacob could theoretically allocate as much as $100 per month ($2000 - $1900) towards a vehicle payment with no safety margin.
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anushka and arushi are friends. they have equal amount of money. anushka gives arushi 1/3 as a gift. then arushi spends half of her total money, if the money arushi has left is 1600 then whats the amount gifted to arushi. give answer with steps
Answer: Rs. 3200
Step-by-step explanation:
Let's assume the amount of money they both had before Anushka gives Arushi a gift as "M".
After Anushka gives Arushi 1/3 of her money, Arushi has 1/3 of Anushka's money, which is (1/3)×M.
Then, Arushi spends half of her total money, which means she spends (1/2)×[(1/3)×M] = (1/6)×M.
So now Arushi has (1/3)×M - (1/6)×M = (1/6)×M left.
According to the problem statement, (1/6)×M is equal to 1600. So we can set up an equation:
(1/6)×M = 1600
Multiplying both sides by 6, we get:
M = 9600
So the total amount of money they both had initially was Rs. 9600.
We know that Anushka gave 1/3 of this money to Arushi, which is:
(1/3)×9600 = 3200
Therefore, the amount gifted to Arushi was Rs. 3200.
The area of triangle G is 8 square centimeters. What is the Area of triangle H?
Answer:
The answer is 32cm²
Step-by-step explanation:
Area of triangle G=8cm²
A=1/2×xy=8cm²
Area of triangle H=?
A=1/2×4x×4y
A=4×area of triangle G
A=8×4=32cm²
Please help me !!!!! And show work
Answer:
I have alredy answered this for you. You posted it twice
Step-by-step explanation:
Given the severity and unusual circumstances of both the Great Recession and the COVID-19 recession, the Fed had to not only implement traditional monetary tools, but also come up with new ways to stimulate the economy. For each of the following policy actions, indicate whether the Fed implemented it during both recessions or just the COVID-19 recession.
Sort each into Covid-19 or Both:
A. purchase long-term corporate bonds B. purchase long-term Treasuries C. eliminate the requirement that banks hold reserves D. purchase mortgage-backed securities E. support lending to smaller nonfinancial firms F. cut the federal funds rate to near zero
During both the Great Recession and the COVID-19 recession, the Fed implemented policies to purchase long-term bonds and mortgage-backed securities, as well as cutting the federal funds rate to near zero.
The Fed implemented some policy actions during both the Great Recession and the COVID-19 recession, while others were implemented only during the latter. Let's take a closer look:
A. Purchase long-term corporate bonds: Both
During both recessions, the Fed implemented a policy of purchasing long-term corporate bonds. This is a form of quantitative easing, where the central bank buys bonds to increase the money supply and lower long-term interest rates. By lowering borrowing costs for businesses, the Fed aims to encourage investment and boost economic growth.
B. Purchase long-term Treasuries: Both
Similar to the purchase of long-term corporate bonds, the Fed also implemented a policy of purchasing long-term Treasuries during both recessions. This has the same goal of increasing the money supply and lowering long-term interest rates, making it cheaper for the government to borrow money and for individuals and businesses to finance investments.
C. Eliminate the requirement that banks hold reserves: COVID-19
During the COVID-19 recession, the Fed eliminated the requirement that banks hold reserves. This meant that banks could lend more money to individuals and businesses, which could help stimulate the economy.
D. Purchase mortgage-backed securities: Both
During both recessions, the Fed implemented a policy of purchasing mortgage-backed securities. This was done to support the housing market and make it easier for people to obtain mortgages and refinance their homes.
E. Support lending to smaller nonfinancial firms: COVID-19
During the COVID-19 recession, the Fed implemented a policy of supporting lending to smaller nonfinancial firms. This was done to help small businesses, which are often hit hardest during economic downturns, access credit and stay afloat.
F. Cut the federal funds rate to near zero: Both
During both recessions, the Fed cut the federal funds rate to near zero. This is the interest rate that banks charge each other for overnight loans, and it affects other interest rates throughout the economy. By cutting the federal funds rate, the Fed aims to make borrowing cheaper and stimulate economic activity.
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can someone please solve #7
The solution to the composite function f(a) + f(h) is f(a) + f(h) = a² - 5a + h² - 5h + 6
Calculating the composite function f(a) + f(h)From the question, we have the following parameters that can be used in our computation:
f(x) = x² - 5x + 3
Using the above as a guide, we have the following:
f(a) = a² - 5a + 3
f(h) = h² - 5h + 3
When these functions are added together, we have
f(a) + f(h) = a² - 5a + 3 + h² - 5h + 3
So, we have
f(a) + f(h) = a² - 5a + h² - 5h + 6
Hence, the solution is f(a) + f(h) = a² - 5a + h² - 5h + 6
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pls help me i will mark brainly
After considering the given set of options we conclude that the number of options that do justify the given question are s+2.3=6.8, s-2.3-6.8 then Options D and E apply.
Here we have to apply the principle of subtraction
Dean ran 2.3 fewer kilometers than Sam. So, we can say that Sam ran 2.3 km more than Dean. We can represent the distance Dean ran as d and the distance Sam ran as s.
So, we can place the equation as s-2.3=6.8 because Dean ran 6.8 km and we know that he ran 2.3 km less than Sam.
To evaluate out how far Sam ran, we need to solve for s. We can do this by adding 2.3 to both sides of the equation:
s-2.3+2.3=6.8+2.3
s=9.1
So Sam ran 9.1 km
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The complete question is
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
Select all that apply.
A) You know the difference in the distances the boys ran , so this is a subtraction problem.
B) You are finding the total distance the boys ran, so this is an addition problem.
C) Dean ran part of the distance Sam ran, so this is a multiplication problem.
D) The correct equation is: s+2.3=6.8.
E) The correct equation is s-2.3-6.8.
F) The correct equation is 2.3-6.8.
Jim is in a gambling casino that charges $4 per chance to roll
an honest die. He will be paid, in dollars, the number of dots
on the face of the die. Find his mathematical expectation.
Round to the nearest penny.
Answer:
$3.50
Step-by-step explanation:
There are six equally likely outcomes when rolling a fair die, with each outcome having a probability of 1/6. Let X be the random variable representing the amount Jim wins, then:
X = 1, 2, 3, 4, 5, or 6, each with probability 1/6.
The mathematical expectation (or expected value) of X, denoted E(X), is the sum of each outcome multiplied by its probability:
E(X) = (1)(1/6) + (2)(1/6) + (3)(1/6) + (4)(1/6) + (5)(1/6) + (6)(1/6)
= 21/6
= 3.5
Therefore, Jim's mathematical expectation is $3.50 per roll, which means on average he can expect to win $3.50 per roll in the long run.
Can somebody help me with this please
R₁-->43(R₁)+9(R₂) is the row operation we apply to make 1 in the 1st row and a column.
The given matrix is [tex]\left[\begin{array}{ccc}9&4&-9\\-43&-19&44\end{array}\right][/tex]
We have to make 1 in row 1 and column 1
We have to apply a row operation to make 1 in the row 1 and column 1
R₁-->43(R₁)+9(R₂)
[tex]\left[\begin{array}{ccc}0&1&9\\-43&-19&44\end{array}\right][/tex]
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1. Find the area of the triangle.
5.7 m
4 m
4 m
5 m
3 m
Answer:
28m^2
Step-by-step explanation:
According to the information we can infer that the area of the triangle is 14.25 square centimeters.
How to find the area of triangle?To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))where s is the semi-perimeter of the triangle, calculated by:
s = (a + b + c) / 2In this case, the side lengths of the triangle are given as 5.7 cm, 7 cm, and 5 cm. Let's calculate the area using Heron's formula:
s = (5.7 + 7 + 5) / 2 = 8.35 cmNow, we can substitute the values of s, a, b, and c into the formula:
Area = √(8.35(8.35-5.7)(8.35-7)(8.35-5))Calculating the expression inside the square root:
Area = √(8.35 × 2.65 × 1.35 × 3.35)Area = √(64.3966375)Area ≈ 8.02 cm²Rounding to two decimal places, the area of the triangle is approximately 8.02 square centimeters.
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Seventy percent of the children went on the excursion. If 27 stayed at school, how many went?
By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.
We are given that,
No. of children who stayed at school is 27,
Also, 70% of the children went on an excursion.
Suppose, the total number of children in percentage is 100%
Out of which 70% went on an excursion
Thus, the children who stayed at school is 100% - 70% = 30%
By using the Unitary method, we can find out the number of 70% of children.
If 30% of the children are 27
Then 70% of the children are = 27 × 100
30
= 63
∴ the total no. of children in the school = 27 + 63
= 90
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Simplify the expression.
0.4×6
Answer:
2.4 Hope it helped! It was so easy!
A store has two types of animal feed available. Type A contains 5 pounds of oats and 7 pounds of corn per bag. Type B contains 6 pounds of oats and 4 pound
of corn per bag. A farmer buys both types and combines them so that the resulting mixture has at least 150 pounds of oats and at least 140 pounds of corn.
The store only has 20 bags of type A feed and 25 bags of type B feed in stock. Let x be the number of type A bags purchased. Let y be the number of type B
bags purchased. Shade the region corresponding to all values of x and y that satisfy these requirements.
PO
B
X
Ś
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The region that satisfy the requirements in this situation is added as an attachment
Here, we have,
Identifying the region that satisfy the requirements in this situation
From the question, we have the following parameters that can be used in our computation:
Type A
5 pounds of oats and 7 pounds of corn per bag.
Type B
6 pounds of oats and 4 pounds of corn per bag
This means that
Oats = 5x + 6y
Corn = 7x + 4y
Using the resulting mixtures, we have
5x + 6y ≥ 150
7x + 4y ≥ 140
For the bags available, we have
0 ≤ x ≤ 20 and 0 ≤ y ≤ 25
See attachment
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Solve the equation e' = 120. Then find the approximate value of the solution
using a calculator.
The approximate value of the solution to the equation e' = 120 is e ≈ 120.the value of e by rounding it to a Reasonable number of Decimal places.
The given equation is e' = 120, where e represents some variable.
To solve for e, we can start by dividing both sides of the equation by the coefficient of e, which is 1:
e' / 1 = 120 / 1
Simplifying the right-hand side, we get:
e' = 120
This means that the value of e is equal to 120. So the solution to the equation e' = 120 is e = 120.
To find the approximate value of e, we can use a calculator to evaluate the expression. Since e is a variable, we cannot substitute it directly into the calculator. However, we can estimate the value of e by rounding it to a reasonable number of decimal places.
In this case, since e' is given as 120, we can assume that e is also in the same units. So we can round e to the nearest whole number:
e ≈ 120
Therefore, the approximate value of the solution to the equation e' = 120 is e ≈ 120.
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44 multiplied by 3.5
Answer:
154
Step-by-step explanation:
Because that is right.
*WILL GIVE BRAINLIEST*
Unit 5 circles unit test
What does x = ?
The calculated value of x in the unit circle is 81
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The circle
The sum of angles on a circumference of a circle is 360 degrees
using the above as a guide, we have the following:
x + 69 + x + 49 + 80 = 360
When the like terms are evaluated, we have
2x = 360 - 80 - 49 - 69
Evaluate
2x = 162
So, we have
x = 81
Hence, the value of x is 81
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Ava spent 1 1/6hrs writing her English composition and 1 3/10hrs working on her mathematics assignment. How much time did Ava spend on her homework altogether?
Answer:
2 hours and 28 minutes
Step-by-step explanation:
English = 1 1/6 hrs = 1hr 10min (1/6×60 to obtain the minutes part)
Maths = 1 3/10hrs = 1hr 18min (3/10×60)
Total time = 2hrs 28 mins
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equation which have same value as 3/5 (30x - 15) = 72 are 18x- 9 = 72 and 3(6x- 3) = 72
We have,
3/5 (30x - 15) = 72
Now, simplifying the equation we get
3/5 (30x) - 3/5(15) = 72
18x - 9 = 72
Now, add both side 9 we get
18x- 9 +9 = 72 + 9
18x = 81
Now, divide both side by 18 we get
18x/ 18 = 81
x = 4.5
So, the equation which have same value as 3/5 (30x - 15) = 72 are 18x- 9 = 72 and 3(6x- 3) = 72
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the question is attached
The exponential equations in the question indicates that solution for the equation are;
The solution to the system of equations y = f(x) and g(x) are (0, 7), and (2, 4). The solution of the system of equation f(x) = g(x) are 0 and 2
What is a system of equation?A system of equation is a set of equations that share the same variables.
The solution of the graphical equations are the points where the graph intersects the x-axis.
The solution are therefore; y = f(x) = 0 = 4(2)⁻ˣ + 3
4(2)⁻ˣ = -3
(2)⁻ˣ = -3/4
-x·ln(2) = ln(-3/4)
x = -ln(-3/4)/ln(2) (No real solution)
However, the solution of the system of equation is the points where the graphs of the equations intersect. The graph indicates that the solution points are (0, 7), and (2, 4)
Therefore, the x-values of the solution are; x = 0, and x = 2
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Cone A is similar to Cone B. The ratio of the surface area of Cone A to Cone B is 16:1. Find the ratio of the radius of Cone A to Cone
Answer:
Step-by-step explanation:
its 4:1 because 16 divided by 4 is 4.
The ratio of the radius of cone A to cone B is 4:1.
We are given that;
The ratio = 16:1
Now,
If we divide the surface area of cone A by the surface area of cone B, we get:
[tex]SA_A / SA_B = (πr_A(r_A + l_A)) / (πr_B(r_B + l_B)) SA_A / SA_B = (r_A(r_A + l_A)) / (r_B(r_B + l_B))[/tex]
Simplify this equation by using the fact that[tex]r_A / r_B = l_A / l_B = k,[/tex]where k is a constant. We get:
[tex]SA_A / SA_B = (r_A(r_A + k r_A)) / (r_B(r_B + k r_B)) SA_A / SA_B = (r_A^2(1 + k)) / (r_B^2(1 + k)) SA_A / SA_B = (r_A^2) / (r_B^2)[/tex]
Take the square root of both sides to get:
[tex]sqrt(SA_A / SA_B) = r_A / r_B[/tex]
Substitute the given ratio of 16:1 for SA_A / SA_B and simplify to get:
[tex]sqrt(16/1) = r_A / r_B 4/1 = r_A / r_B 4:1 = r_A : r_B[/tex]
Therefore, by the ratio the answer will be 4:1.
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need help will give brainlist
Answer:
B) 1 - (-6) / -2 -4
Step-by-step explanation:
The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
For the points (4, -6) and (-2, 1), we can choose (4, -6) as (x1, y1) and (-2, 1) as (x2, y2), or vice versa. It doesn't matter which point we choose as (x1, y1) and which one we choose as (x2, y2), as long as we're consistent in our choice.
Let's choose (4, -6) as (x1, y1) and (-2, 1) as (x2, y2). Then we can write:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-6)) / (-2 - 4)
Simplifying this expression, we get:
m = 7 / (-6)
So the correct way to set up the slope formula for the line that passes through the points (4, -6) and (-2, 1) is:
B) 1 - (-6) / -2 -4
m = (1 - (-6)) / (-2 - 4) = 7 / (-6)
WEATHER Paola’s weather app tells her that there is a 20% chance of rain on Tuesday and a 50% chance of rain on Wednesday. What is the probability that it will rain on both Tuesday and Wednesday?
The probability that it will rain on both Tuesday and Wednesday is 60%.
Let A represents the event of raining on Wednesday and B represents the event of raining in Tuesday,
Then according to the question,
P(A) = 20% = 0.2,
P(B) = 50% = 0.4,
Here, A and B are independent events,
So, P(AB) = P(A) × P(B),
⇒ P(A∩B) = 0.2 × 0.5 = 0.10
We know that,
P(A∪B) = P(A) + P(B)
The probability it rains on Wednesday or Tuesday, P(A∪B) = 0.2 + 0.5 - 0.10
= 0.60
= 60%
Hence the probability that it will rain on both Tuesday and Wednesday is 60%.
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