If sun A= 7/25 and cos B= 12/37 and angles A and B are in Quadrant 1, find the value of tan (A-B)
The value of tan (A-B) is -203/169, when angles A and B are in Quadrant 1.
What in trigonometry is the Pythagorean identity?In trigonometry, the Pythagorean identity is sin² + cos² = 1, where is an angle in a right triangle. The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle, is the source of this identity. Trigonometric identities and formulae are derived from the Pythagorean identity, which is a basic idea in the subject.
The trigonometric identity is given as
tan(A-B) = (tan A - tan B) / (1 + tan A tan B)
The value of tan A and tan B is calculated as follows.
sin A = 7/25, we can use the Pythagorean identity: sin² A + cos² A = 1 to find cos A:
cos A = √(1 - sin² A) = √(1 - (7/25)²) = 24/25
Therefore, tan A = sin A / cos A = (7/25) / (24/25) = 7/24.
Similarly, since cos B = 12/37, we can use the Pythagorean identity cos² B + sin² B = 1 to find sin B:
sin B = √(1 - cos² B) = √(1 - (12/37)²) = 35/37
Therefore, tan B = sin B / cos B = (35/37) / (12/37) = 35/12.
Substituting the values:
tan(A-B) = (tan A - tan B) / (1 + tan A tan B)
= ((7/24) - (35/12)) / (1 + (7/24) x (35/12))
= (-203/288) / (169/288)
= -203/169
Therefore, the value of tan (A-B) is -203/169.
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whats 2 + 2n is it 4n or 4 or something diffrent?
Answer:
it depends
Step-by-step explanation:
it depends on the value of n
for instance if n was = to 7 then
2+2n = 2+2(7) = 2+14 = 16
Answer: 2+2n
Step-by-step explanation:
The expression 2 + 2n can be simplified as follows:
2 + 2n = 2(1 + n)
So the expression 2 + 2n is equivalent to 2 times the quantity 1 plus n, or simply 2(1 + n). It cannot be simplified any further unless there is additional information or context provided.
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest form.
Answer:
67.5
Step-by-step explanation:
4 1/2x6= 27 27x2 1/2=67.5
This scatterplot shows data from Jillian's car trip.
Which equation best fits the data?
The linear function that best fits the data is given as follows:
y = 60x.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.When x = 0, y = 0, hence the intercept b of the line is given as follows:
b = 0.
When x increases by 5, y increases by 300, hence the slope m of the line is given as follows:
m = 300/5
m = 60.
Hence the equation is:
y = 60x.
Missing InformationThe points on the scatter plot are given as follows:
(0,0) and (5,300).
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use substitution to solve the system x-3y=10, x+5y=-22
Answer:
x = -2
y = -4
Step-by-step explanation:
Given equations:x - 3y = 10 --------------(1)
x + 5y = -22 -----------(2)
Taking Eq. (1)
x - 3y = 10
Add 3y to both sidesx = 10 + 3y ------------(3)
Put Eq. (3) in Eq. (1)10 + 3y + 5y = -22
Subtract 10 from both sides8y = -22 - 10
8y = -32
Divide 8 to both sidesy = -32/8
y = -4Put y = -4 in Eq. (3)x = 10 + 3(-4)
x = 10 - 12
x = -2[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\bf x=-2[/tex][tex]\bf y=-4[/tex]Step-by-step explanation:
To solve the given system, let's begin by solving for x in x- 3y=10:-
[tex]\tt x-3y=10[/tex]
Add 3y to both sides:-
[tex]\tt x-3y+3y=10+3y[/tex]
[tex]\tt x=10+3y[/tex]
Substitute x= 10+3y into x+5y=-22:-
[tex]\tt 10+3y+5y=-22[/tex]
Simplify:-
[tex]\tt 10+8y=-22[/tex]
Now, solve for y in 10+8y=-22:-
[tex]\tt 10+8y=-22[/tex]
Subtract 10 from both sides:-
[tex]\tt \tt 10+8y-10=-22-10[/tex]
[tex]\tt 8y=-32[/tex]
Divide both sides by -8:-
[tex]\boxed{\bf y=-4}[/tex]
Now, substitute y=-4 into x=10+3y:-
[tex]\tt x=10+3y[/tex]
[tex]\tt x=10+3\times-4[/tex]
Simplify:-
[tex]\boxed{\bf x=-2}[/tex]
Therefore, x=-2 and y=-4
_________________________
Hope this helps! :)
Do what the picture says.If the answer is right,I will give you brainilest!!!!
Answer:
63.25
Step-by-step explanation:
You need to calculate each figure separately.
The diameter of the circle = 4 + 3 + 3 = 10
=> radius = 5
area of 1/2 circle = 1/2πr^2 = 1/2π(5)^2 = 1/2(3.14)(25) = 39.25
area of the top rectangle = 3 x 6 = 18
area of the bottom rectangle = 2 x 3 = 6
total area = 39.25 + 18 + 6 = 63.25
Answer:Hi
Step-by-step explanation:
After spending 60 percent of his money , Joseph has a re 600. How much did he have in the beginning?
After spending 60% of his money Joseph has rs. 600., He has 1500 in the beginning.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Let the total amount be x
He spent 60% of his money
So, Money spent = 60% x=0.6x
Remaining amount = x- 0.6 x = 0.4x
We are given that Now he has Rs.600
[tex]0.4x=600\\\\x=\frac{600}{0.4}\\\\x=1500[/tex]
Hence He has Rs.1500 at the beginning
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What is the slope of the line through point B, and perpendicular to line k?
Answer:
To find the slope of the line through point B and perpendicular to line k, we need to first find the slope of line k.
If we have the equation of line k in slope-intercept form, y = mx + b, then the slope of line k is simply the coefficient of x, which is m.
Assuming we don't have the equation of line k, we can find its slope by using the slope formula, which is:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are two points on line k.
Let's say line k passes through points P and Q. Then we can write the slope of line k as:
m = (yQ - yP)/(xQ - xP)
Now, we want to find the slope of the line through point B and perpendicular to line k. We know that the product of the slopes of two perpendicular lines is -1. That is:
m1 * m2 = -1
where m1 is the slope of line k, and m2 is the slope of the line through point B and perpendicular to line k.
Therefore, we can write:
m2 = -1/m1
So we just need to find the slope of line k, and then we can use this formula to find the slope of the line through point B and perpendicular to line k.
Once we have the slope of the line through point B, we can write its equation in point-slope form:
y - yB = m2(x - xB)
where (xB, yB) is the point B.
Hope this helps with you with your question (it's not a direct answer, I think?) I'm sorry if it doesn't! If you need more help, ask me! :]
Factorise ax-a+x-1 By grouping terms in pairs
The factorized terms of the given expression ax - a + x - 1 by grouping the terms in pairs is given by (x - 1)(a + 1) .
Expression is equal to,
ax - a + x - 1
To factorize the expression ax-a+x-1 by grouping terms in pairs.
First group the first two terms and the last two terms together we get,
⇒ ax - a + x - 1 = ( ax - a ) + ( x - 1 )
Now factor out the common factor of 'a' from the first group.
And the common factor of '1' from the second group we get,
⇒ ax - a + x - 1 = a(x - 1) + 1(x - 1)
Both the groups have a common factor of (x - 1).
Take out common factor we have,
⇒ ax - a + x - 1 = (x - 1)(a + 1)
Therefore, the factorized expression is equal to,
ax - a + x - 1 = (x - 1)(a + 1)
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Calculate the distance between the points N and C in the coordinate plane.
Give an exact answer (not a decimal approximation)..... How would i solve something like this?
Applying the distance formula, the distance between points N and C in the coordinate plane is calculated as: 5 units.
How to Calculate the Distance between Two Points on a Coordinate Plane?To calculate the distance between two points on a coordinate plane, the distance formula can be applied which is given as:
d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the two points lie on the coordinate plane as the following coordinates:
N = (-8, 9)
C = (-4, 6)
Therefore, we will have:
d = √[(−4 − (−8))² + (6−9)²]
d = √[(4)² + (−3)²]
d = √(16 + 9)
d = √25
d = 5 units
Thus, the distance between points N and C is calculated as: 5 units.
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4x0 pls help i weally newd tis madly imb int da fiwst gwade
Answer:it’s 0
Step-by-step explanation:
In a mountain range of California, the percent of moisture that falls as snow rather than rain can be approximated by the function p(h) = 82 in (h) - 649.
where h is the altitude in feet and p(h) is the percent of an annual snow fall at the altitude h. Use the function to approximate the amount of snow at the
altitudes 3000 feet and 6000 feet
Approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.
According to the given function, the percent of annual snowfall at an altitude of h feet is given by p(h) = 82 in (h) - 649. To approximate the amount of snow at the altitudes of 3000 feet and 6000 feet, we can simply plug these values into the function and solve for p(h).
At an altitude of 3000 feet, we have:
p(3000) = 82 in (3000) - 649
p(3000) = 246000 - 649
p(3000) = 245351
Therefore, approximately 245351% of the annual moisture at an altitude of 3000 feet falls as snow.
Similarly, at an altitude of 6000 feet, we have:
p(6000) = 82 in (6000) - 649
p(6000) = 492000 - 649
p(6000) = 491351
Therefore, approximately 491351% of the annual moisture at an altitude of 6000 feet falls as snow.
It's important to note that these values represent percentages and not the actual amount of snowfall in inches. To convert these percentages to the actual amount of snowfall, we would need to know the total annual moisture at each altitude. Nonetheless, we can use the given function to approximate the percentage of snowfall at different altitudes in the mountain range of California.
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14. Using the credit card from question 13, if you have a good credit rating, how much must you pay at the end of the month to get the balance to the acceptable debt ratio percentage?
If the credit limit on the card is amount $1,000, then you should aim to keep the balance owing on the card at amount $300 or less.
It depends on the acceptable debt ratio. Generally, to maintain a good credit rating, it is recommended to keep a debt-to-credit ratio of 30% or less, meaning that you should have an amount owing on the card equal to or less than amount 30% of the credit limit.
If the credit limit on the card is $1,000, then you should aim to keep the balance owing on the card at $300 or less. So, if the balance owing at the end of the month is over $300, you would need to make a payment of at least the difference between the balance owing and the acceptable debt ratio.
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find the area of the shaded region of the given circle
diameter = 14cm
[tex]radius \: = \frac{d}{2} = \frac{14}{2} \\ = 7cm[/tex]
Area of circle ( A1 ) = [tex]\pi {r}^{2} [/tex]
[tex] = \frac{22}{7} \times 7 \times 7 \\ [/tex]
[tex] = 154 {cm}^{2} [/tex]
Area of Square ( A2 ) = l²
= ( 14 )²
= 196cm²
Area of shaded region = A2 - A1
= 196 - 154
= 42cm²
....Thank you !! :)
1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17 Calculate the upper limit
(Upper Bound) to determine if there are any outliers on the high
end.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
what is Median?
The median is a statistical measure that represents the central value of a dataset.
To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:
Upper Limit = Q3 + 1.5 * IQR
where Q3 is the third quartile, and IQR is the interquartile range.
First, we need to find the values for Q1, Q2 (median), and Q3:
1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17
Arranging the data in order:
1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17
The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:
Median = (7 + 8) / 2 = 7.5
To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:
Lower half: 1, 6, 6, 6, 7
Upper half: 8, 9, 10, 13, 17
Q1 is the median of the lower half, which is 6.
Q3 is the median of the upper half, which is 10.
Next, we can calculate the interquartile range:
IQR = Q3 - Q1 = 10 - 6 = 4
Finally, we can calculate the upper limit for outliers:
Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16
Any value above 16 can be considered a potential outlier on the high end of the data.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
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A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of � x. 136° x° Answer: � = x=
x°=46
Step-by-step explanation:
There are two methods of solving this question
Method 1:
x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"
x°=136°-90°
x°=46°
or
Method 2:
136° is on a straight line which is 180°
so, let the other side of the straight line be a.
therefore, 136°+a°=180° theorem {Angle on a straight line}
a°=180°-136°
a°=44°
so, in the triangle is the sum of 180°
a°+90°+x°=180° theorem {Sum of angles in a triangle}
44°+90°+x°=180°
x=180°-134°
x°=46°
B b) The diagram shows a circle centre O. A, B and Care points on the circumference. DCO is a straight line and DA is a tangent to the circle. Angle ADO = 34° a) Work out the size of angle AOD. (1) 34° Work out the size of angle ABC. Give a reason for your answer. D
let's recall that the point of tangency for a tangent line to a radius in a circle is alway a right-angle, also let's notice that ∡AOD as well as ∡ABC are both intercepting the same arc.
Check the picture below.
The quotient of 42 and the sum of a number and five equals seven 
Answer:
Step-by-step explanation:
[tex]\frac{42}{x+5} =7[/tex]
[tex]42=7(x+5)[/tex]
[tex]42=7x+35[/tex]
[tex]7x=-7[/tex]
[tex]x=-1[/tex]
a quadratic function has a discriminant with a value of -4 what type of solution does the quadratic equation have ?
Answer:
Complex or Imaginary solutions
Step-by-step explanation:
In the Quadratic Formula, the discriminant is the part that is inside of the radical (square root symbol).
So there are three cases, the discriminant can be:
-positive, OR
-zero, OR
-negative
If its positive, there are two real solutions.
If its zero, there is one real solution.
If its negative, there are two complex (imaginary) solutions.
a poll showed that 60.4% of americans say they believe that some people see the future in their dreams. what is the probability of randomly selecting someone who does not believe that some people see the future in their dreams.
The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
Probability is an area of mathematics that deals with the study of chance events.
We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.
Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:
P(A) = 1 - P(B)
Where,
P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.
P(B) = Probability of selecting someone who believes that some people see the future in their dreams.
P(A) = 1 - P(B)
⇒ 1 - 60.4/100
⇒39.6/100
⇒ 0.396 or 39.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
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Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in exponential form by filling in the boxes for exponents.)
*please can I get the numbers that go in the boxes*
Answer:
the GCF of 270 & 360 is 90
exponent form: 3³x 2 x 5 = 270 & 3²x 2³x 5 = 360
Step-by-step explanation:
3 x 3 x 3 x 2 x 5 = 270
3 x 3 x 2 x 2 x 2 x 5 = 360
The first number minus the second number equals to 26. When the first number is added to 3 times the second number, the result is 194. What are the two numbers
What is the best way to design a study to determine how much traffic there is during the morning rush
hour along a city street?
A. Send a survey to the local businesses surrounding the street, asking them how many times they
drive and how many times they take transit to work each year.
OB. Survey local car dealerships to see how many cars are sold in the area over the past year.
X
O C. Make video recordings of the street during rush hour every day for year and count the numbers
of vehicles that pass a certain point.
OD. Count the number of cars that pass a particular point during rush hour over 3 days, and then
take the average
The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.
The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.
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Select the correct answer. If x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3), then which statement is true?
The correct answer is:
x + 12 ≤ 5 − y ≤ 2(x − 3)
Explanation:
From the given inequalities:
x + 12 ≤ 5 − y ... (1)
5 − y ≤ 2(x − 3) ... (2)
We can see that 5 - y is common in both inequalities. We can isolate this term by subtracting 5 from both sides of (1) and (2):
x + 7 ≤ -y ... (3)
-y ≤ 2(x - 8) ... (4)
Multiplying (3) by -1, we get:
y - 7 ≥ x ... (5)
Substituting this value of x in (4), we get:
y - 7 ≤ -2(7 - y)
y - 7 ≤ -14 + 2y
y ≤ 7
Substituting this value of y in (5), we get:
0 ≤ x + 7 ≤ 14
Subtracting 7 from all sides, we get:
-7 ≤ x ≤ 7
Therefore, the statement x + 12 ≤ 5 − y ≤ 2(x − 3) is not true, but the statement -7 ≤ x ≤ 7 is true.
I dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:25 sticks
Step-by-step explanation:
1st=5 sticks
2nd=9 sticks
3rd=13 sticks
4th=17 sticks
5th=21 sticks
6th=25 sticks
The ratio of boys and girls in a class is 3:5. There are 32 students in the class.
How many students are girls?
Using ratios, we can find that the number of girls in the class are 20.
What are ratios?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalises two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls) There are 3 out of 4 girls and 1 out of 4 guys.
Now in the question, total students in class = 32.
The ratio between the boys and girls is 3:5.
So, total parts from the ratio = 3+5=8
Now 5/8 students in the class are girls.
= 5/8 × 32
= 5 × 4
= 20.
Therefore, the number of girls in the class are 20.
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The picture shows a container that Rene uses to freeze water:
A container is shown with a base diameter of 8 centimeters and a height of 10 centimeters.
What is the minimum number of identical containers Rene would need to make 2,000 cm3 of ice? (Use π = 3.14.)
a
2
b
4
c
1
d
12
The minimum number οf identical cοntainers Rene wοuld need tο make 2,000 cm³ οf ice is 4. Optiοn b is the cοrrect οptiοn.
What is a cylinder?A cylinder is a three-dimensiοnal sοlid in mathematics that maintains, at a fixed distance, twο parallel bases cοnnected by a curved surface. These bases typically have a circular shape (like a circle), and a line segment knοwn as the axis cοnnects the centers οf the twο bases.
The base οf a cοntainer is 8 centimeters. The height οf the cοntainer is 10 centimetres.
The radius οf a shape is half οf its diameter.
The radius οf cοntainer is 8/2 = 4 cm.
The vοlume οf a cylinder is πr²h.
The vοlume οf a cοntainer is π×4²×10
= 160 × 3.14
= 502.4 cm³
Assume that Rene needs x number οf cοntainers.
The vοlume οf x number οf cοntainers is 502.4 x.
Accοrding tο the questiοn:
502.4 x = 2,000
Divide bοth sides by 502.4:
x = 2000/502.4
x = 3.98
x ≈ 4
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Here are the first 6 terms of a quadratic sequence -5,1,11,25,43,65 find an expression, in terms of n, for the nth term of this sequence
The expression for the nth term of the sequence is, Tn = 3n^2 - 7n - 1
To find an expression for the nth term of a quadratic sequence, we need to find a quadratic function that describes the sequence.
Let the nth term of the sequence be denoted by Tn. We can use the method of finite differences to determine the degree of the quadratic function that describes the sequence.
The first differences between the terms are 6, 10, 14, 18, 22. The second differences between these first differences are all equal to 4. This tells us that the sequence is quadratic, since the second differences are constant.
To find the quadratic function that describes the sequence, we can use the formula for the nth term of a quadratic sequence,
Tn = an^2 + bn + c
where a, b, and c are constants to be determined.
We can use the first three terms of the sequence to form a system of three equations,
T1 = a + b + c = -5
T2 = 4a + 2b + c = 1
T3 = 9a + 3b + c = 11
Solving this system of equations, we get:
a = 3
b = -7
c = -1
Therefore, the expression for the nth term of the sequence is
Tn = 3n^2 - 7n - 1
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quadratic function in vertex form y=x^2+4x+6
Answer:
y = (x + 2)² + 2
Step-by-step explanation:
a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
y = x² + 4x + 6
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 4x
y = x² + 2(2)x + 4 - 4 + 6
= (x + 2)² + 2 ← in vertex form
Shuffle: Charles has seven songs on a playlist. Each song is by a different artist. The artists are Celine Dion, Phil Collins, Elton John, Mariah Carey, Joey Meintyre, Kavana, and Adam Rickilt. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Adam Rickitt and the second song is by Phil Collins? Write vour answer as a fraction or a decimal, rounded to four decimal places.
0.0002
The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.
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