Answer:
\(33\%\)
Step-by-step explanation:
To work out the percentage of the circle shaded blue, we first must work out the area of the whole circle.
Area of the whole circle = \(\pi r^2\)
\(r=4+3+3\\\pi * (4+3+3)^2=\pi*10^2=100\pi\)
Now we need to work out the area of the blue 2d torus, by finding out the area of the blue circle, then subtracting the area of the innermost white circle.
Blue shaded area = \(\pi(r_{0}{^2}-r_{1}{^2})\)
\(r_0=4+3\\r_1 = 4\\\pi ((4+3)^2-(4)^2)= \pi (7^2-4^2)=33 \pi\)
Now we have the total areas of each, we can work out the fraction of blue to non blue by dividing the blue area by the total area, and then working out the percentage by multiplying by 100.
\(\frac{33\pi}{100\pi}*100=\frac{33\pi}{\pi}=33\%\)
What is the Slope of the line?
Answer:
1/2
Step-by-step explanation:
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A super sundae ice cream cone has a radius of 0. 5 in and a depth of 4 in. A wonderful waffle cone has a radius 0. 9 in and a depth of 3 in. Which cone holds more ice cream?
The wonderful waffle cone holds more ice cream than super sundae cone.
In this question,
The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.
Volume of ice cream cone = volume of hemisphere + volume of cone
Volume of ice cream cone = \(\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h\)
Volume of super sundae cone:
Radius of hemisphere = height of hemisphere = 0.5 in
Depth of the ice cream cone = 4 in
Volume of super sundae cone = \(\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)\)
⇒ \(\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)\)
⇒ 0.2616+1.0466
⇒ 1.3082 ≈ 1.31 cubic in.
Volume of wonderful waffle cone:
Radius of hemisphere = height of hemisphere = 0.9 in
Depth of the ice cream cone = 3 in
Volume of wonderful waffle cone = \(\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)\)
⇒ \(\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)\)
⇒ 1.526+2.5434
⇒ 4.0694 ≈ 4.07 cubic in.
Thus volume of wonderful waffle cone > volume of super sundae cone.
Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.
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Choose the correct graph of the function y = x +1
Answer:
No answer
Step-by-step explanation:
y=x+1 is a LINE
Which option below is not a potential risk of purchasing a used car?
used cars can require repairs sooner
Shorter lifespans of the engine and transmission
used cars can have lower initial cost
unexpected issues may arise
Answer:
used cars can have a lower initial cost
Step-by-step explanation:
it is not a risk/hinder to purchasing a used car
A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
The graph of the coordinate points of the vertices of ABCD indicates;
Part A The perimeter of ABCD ia approximately 61.2 units
Part B. The area of ABCD is 199.5 square units
What is the perimeter of a figure in geometry?The perimeter of a figure is length of the line that goes round the figure.
A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;
AB = √((21-11)²+(11-(-1))²) ≈ 15.6
BC = √((21-26)²+(11-(-1))²) = 13
CD = √((26-2)²+(-1-(-8))²) = 25
AD = √((2-5)²+(-8-(-1))²) ≈ 7.6
The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2
The polygon has a perimeter of approximately 61.2 unitsB. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD
The base length of triangle ΔABC = 26 - 5 = 21
The height of triangle ΔABC = 11 - (-1) = 12
The area of triangle ΔABC = 0.5 × 21 × 12 = 126
Base length of triangle ΔADC = 21
Height of triangle ΔADC = -1 - (-8) = 7
Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5
Area of the composite figure is therefore;
A = 126 + 73.5 = 199.5
The area of the figure is therefore; 199.5 square units
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James is travelling to South Korea.
The conversion from pounds to South Korean
won is £1 = 1500
He buys a train ticket for 30 000
How much does James pay in pounds?
Answer:
2.03
Step-by-step explanation:
Answer:
£20
Step-by-step explanation:
1500*20= 30000
1*20=£20
PLEASE HELPI GIVE 20 POINTS
Answer:
D) 4 7/12
Step-by-step explanation:
55 divided by 12 is
4 remainder 7/12
so
4 7/12 which is D
The fare charged for a rideshare service is a function of
the distance traveled. However, the fare differs
according to the time of day, availability, and other
variables. The distance and fares for 10 rides are shown
in the table. The equation of the least-squares regression
line is ý = 5.21 +2.33x, where y is the predicted fare and
x is the distance.
What is the residual for the rideshare cost with a
distance of 5 miles?
O -0.34
O 0.34
2.33
O 5.21
The observed fare for a 16-mile journey is 53.84; therefore, the residual is 53.84 - 42.49, or 11.35. Hence, the solution is 11.35.
What is the distance?Distance is the sum of an object's movements, regardless of direction.
The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
So, the equation of the least-squares regression line and the observed fare for that distance can be used to determine the residual for the rideshare cost with a distance of 16 miles.
The discrepancy between the actual value and the expected value is referred to as the residual.
In the equation of the least-squares regression line, = 5.20 + 2.33x, we may swap 16 for x to get the anticipated fare for a journey of 16 miles.
We get = 5.20 + 2.33 * 16 = 42.49 from this.
53.84 is the observed fare for a 16-mile trip, so the residual is equal to 53.84 - 42.49, or 11.35. The answer is 11.35 as a result.
Therefore, the observed fare for a 16-mile journey is 53.84; therefore, the residual is 53.84 - 42.49, or 11.35. Hence, the solution is 11.35.
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Correct question:
The fare charged for a rideshare service is a function of the distance traveled. However, the fare differs according to the time of day, availability, and other variables. The distance and fares for 10 rides are
shown in the table. The equation of the least-squares regression line is ý = 5.20 +2.33x, where y is the predicted fare and x is the distance.
Distance
(Miles)
1
3
5
8
10
12
15
16
56
Mark this and return
Fare
(Dollars)
1.91
13.68
16.52
24.15
24.79
39.87
40.24
53.84
What is the residual for the rideshare cost with a
distance of 16 miles?
2.33
5.21
11.35
42.49
Determine if the triangles are similar by side-angle-side similarity
Answer:
Step-by-step explanation:
note that all adjacent triangles will share an angle.
for 13 and 14 this is the case.
for 13 and 14 the adjacent sides are also multiples of each other proportionately. find this by dividing one side by the other for both triangles. if equal they are proportionately larger.
13 and 14 are both similar
for 15 and 16 the same logic can be applied to the side lengths. however, we are not given any information on the angles and cannot determine the angles mathematically.
for 17 and 18 the same logic can be applied again for the sides and given that the angles are confined within each other, the angles are the same.
for 17 and 18 you must add the side lengths for each side together and divide to determine the ratio and compare that to the ratio of the initial triangle
a fair die is rolled n times. what is the probability that at least 1 of the 6 values never appears?
Answer:
5/6 to the power of n but whole fraction to the power
Step-by-step explanation:
in a factory ,12 machines are used to produce an assignment of nailsin ninie days. if 6 machines are added to step up the production,find out how many days it will take to complete the assignment
A school trip to a museum cost $2,056. A total of 125 chaperones and students went on the trip. Adult admission to the museum costs $23, and student admission costs $16. How many chaperones and students went to the museum?
Answer:
117 students, 8 adults
Step-by-step explanation:
Let's say a adults went and s students went.
Total cost for adults = 23 for each a = 23a
Total cost for each student = 16s
Number of adults and students = a + s = 125
Total cost = 23a + 16s = 2056
a + s = 125
23a + 16s = 2056
We can solve this by solving for a and then plugging that into the other equation, making it so that there is only one variable
subtract s from both sides in the first equation
a = 125 - s
plug that into the second equation
23(125 - s) + 16s = 2056
2875 - 23s + 16s = 2056
2875 - 7s = 2056
subtract 2875 from both sides to isolate s and its coefficient
-7s = -819
divide both sides by -7 to isolate s
s = 117
a = 125 - s = 125 - 117 = 8
Answer:
Answer:
Chaperones = 8 and Student = 117
Step-by-step explanation:
Let,
Chaperones = x
Student = y
x + y = 125
=> x = 125 - y (1)
23x + 16y = 2056
=> 23(125 - y) + 16y = 2056
=> 2875 - 23y + 16y = 2056
=> 2875 - 7y = 2056
=> 2875 - 2056 = 7y
=> 819 = 7y
=> 819/7 = y
=> 117 = y
From 1
=> x = 125 - 117
=> x = 8
The ratio of boys to girls is 4:5 if there are 20 boys in the class find the number of girls. Show workings
Answer:
25 girls
Step-by-step explanation:
We Know
The ratio of boys to girls is 4:5. For every 4 boys, there are 5 girls.
To get from 4 to 20, we multiply by 5.
We Take
5 x 5 = 25 girls
So, there are 25 girls in class.
Answer: 25 girls are in the class
Step-by-step explanation: You can set up the ratio 4:5 as a fraction, \(\frac{4}{5}\) to find your answer. You are given the fact that 20 boys are in the class so now you can solve 2 ways.
Option 1 - Set up the equation algebraically as \(\frac{20}{x}\), where x = number of girls and set that equal to \(\frac{4}{5}\). This way allows you to see that the fraction must have the same ratio as 4:5. You can see that 4 x 5 = 20, so the multiple factor is 5. The variable x must equal 5 x 5, so x = 25.
Option 2 - Multiply the amount of boys given to you by the reciprocal of the ratio. Instead of using \(\frac{4}{5}\), you have to use \(\frac{5}{4}\) because there are more girls than boys in the class. This allows you to finish the problem by multiplying 20 x \(\frac{5}{4}\) to get the result of \(\frac{100}{4}\), which you may know simplifies into 25.
I’ll give the Brainliest to who answers this question with a reasonable explanation.
Find the best buy between 6.2 oz. for $2.97 or 8 oz. for $3.47.
A) Buying 8 oz for $3.47 is the better buy.
B) Buying 6.2 oz for $2.97 is the better buy.
Thank you!
please help due today;/
cos³x+C 3. Using the substitution x=2 tane where <<. dx is equal z +C b. 2744 +C C. 2x d. √2244 2x²³ +1 gives + C +C
The integration of ∫ (2/(√[x² + 4])³) dx using the substitution x = 2 tan θ is x/(2 √[x² + 4]) + C, where C is the Integrating Constant.
Hence the correct option is (B).
Given the integral is,
I = ∫ (2/(√[x² + 4])³) dx
We have to do substitution x = 2 tan θ so,
Differentiating, dx = 2 sec² θ dθ
I = ∫ (2/(√[(2 tan θ)² + 4])³) (2 sec² θ dθ)
I = ∫ (2/(√[4 tan² θ + 4])³) (2 sec² θ dθ)
I = ∫ (2/(8√[tan² θ + 1]) (2 sec² θ dθ)
I = ∫ (1/(2√[sec² θ]) (sec² θ dθ) , since tan² θ + 1 = sec² θ
I = (1/2) ∫ (sec² θ/sec³ θ) dθ
I = (1/2) ∫ sec θ dθ
I = (1/2) ∫cos θ dθ
I = (sin θ)/2 + C, where C is Integrating constant
I = 1/(2 cosec θ) + C
I = 1/(2 √cosec² θ) + C
I = 1/(2 √[1 + cot² θ]) + C
I = 1/(2 √[1 + (2/x)²]) + C, since x = 2 tan θ
I = x/(2 √[x² + 4]) + C
Hence the correct option is (B).
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The question is incomplete. The complete question is -
Using the Incenter P, find the measure of ∠ZPX.
117°
140°
64°
129°
42°
132°
Answer:
The measure of ∠ZPX is 63°
Step-by-step explanation:
The given parameters are;
The incenter of the triangle = P
m∠KXP = 31°, m∠PYJ = 27°, \(\overline {ZP}\) = 20 feet
Given that the segment \(\overline {XJ}\) from the vertex, X, passes through the incenter of the triangle, we have;
The segment \(\overline {XJ}\) bisects ∠KXL to form ∠KXP and ∠LXP
Therefore, ∠KXP = ∠LXP = 31°
∠KXL = ∠KXP + ∠LXP = 31° + 31° = 62°
∠KXL = 62°
Similarly;
The segment \(\overline {YL}\) bisects ∠KYJ to form ∠PYJ and ∠PYK
Therefore, ∠PYJ = ∠PYK = 27°
∠KYJ = ∠PYJ + ∠PYK = 27° + 27° = 54°
∠KYJ = 54°
In ΔXYZ, we have, ∠LZJ + ∠KYJ + ∠KXL = 180° based on the sum of the interior angles of a triangle postulate
∴ ∠LZJ = 180° - (∠KYJ + ∠KXL) = 180° - (54° + 62°) = 64°
∠LZJ = 64°
The segment \(\overline {ZK}\) bisects ∠LZJ to form ∠PZL and ∠PZJ
Therefore, ∠PZL = ∠PZJ
∠LZJ = ∠PZL + ∠PZJ = 2 × ∠PZL = 64°
∠PZL = 64°/2 = 32° = ∠PZJ
In ΔZPX, we have;
∠PZL + ∠LXP + ∠ZPX = 180° based on the sum of the interior angles of a triangle postulate
∠ZPX = 180° - (∠PZL + ∠LXP) = 180° - (32° + 31°) = 63°
∠ZPX = 63°
The measure of ∠ZPX = 63°
You have $20 to spend for cupcakes. If each cupcake costs $4, write and solve an inequality to show the maximum number of cupcakes you can buy.
the list shows the weight in pounds of 6 puppies at birth. 3, 1.6, 2.8, 2.5, 1.7, 2.8 what is the mean absolute deviation of these numbers?
John spent 30 minutes developing an estimate for a job. The job itself took 2 hours, 45 minutes to
complete. What is the ratio of the time spent on the job estimate to the total time spent (including the time
spent calculating the estimate) on this job?
Answer:
Ratio is 11 : 13
Step-by-step explanation:
We are given;
Time to develop estimate = 30 minutes
Time to do the job = 2 hours 45 minutes = (2 * 60) + 45 = 165 minutes
Total time to develop and do job = 165 + 30 = 195 minutes
Thus;
Ratio of time spent on job to total time = 165 : 195
Whrn this is broken further, we have; 11 : 13
The integral S/2 sin? (x) cos® (x) dx is equivalent to which of the following integrals? (A) SÓ (1 – 22)uº du (B) Só u? (1 – u?) du (C) Só –22 (1 – 2°) du (D) Si' -u? V1 – u? du (E) Sou du
The integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.
To determine the equivalent integral of S/2 sinθ(x) cos²(x) dx, we can use the trigonometric identity:
cos²(x) = (1 + cos(2x))/2
Substituting this into the integral, we have:
S/2 sinθ(x) cos²(x) dx = S/2 sinθ(x) (1 + cos(2x))/2 dx
Now, we can distribute the sinθ(x) term:
= S/4 [sinθ(x) + sinθ(x) cos(2x)] dx
Using the trigonometric identity sinθ(x) cos(2x) = (1/2)sin(2x)sinθ(x), we get:
= S/4 [sinθ(x) + (1/2)sin(2x)sinθ(x)] dx
Factoring out sinθ(x), we have:
= S/4 sinθ(x) [1 + (1/2)sin(2x)] dx
Now, comparing this with the given options, we can see that the equivalent integral is:
(E) S u du
Therefore, the integral S/2 sinθ(x) cos²(x) dx is equivalent to the integral (E) Sou du.
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Vibrations of harmonic motion can be represented in a vectorial form. Analyze the values of displacement, velocity, and acceleration if the amplitude, A=2+T, angular velocity, ω=4+U rad/s and time, t=1 s. The values of T and U depend on the respective 5th and 6th digits of your matric number. For example, if your matric number is AD201414, it gives the value of T=1 and U=4.
The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).
Harmonic motion is a motion that repeats itself after a certain period of time.
Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.
The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.
Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.
Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.
A simple harmonic motion is a projection of uniform circular motion in a straight line.
The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.
Let's now calculate the values of displacement, velocity, and acceleration.
Displacement, s = A sin (ωt)
Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)
So, s = 3 sin (8 x 1) = 2.68 m (approx)
Velocity, v = Aω cos(ωt)
Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)
Acceleration, a = -Aω2 sin(ωt)
Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)
Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
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Suppose that f(1) = 1, f(4) = 5, f '(1) = 3, f '(4) = 3, and f '' is continuous. find the value of 4 1 xf ''(x) dx.
Answer: b
Step-by-step explanation:
I think
rite the equation for the logarithmic function that has the following
ansformations from the parent logarithmic function. The function will
ave a base of 10. You will not have to write the 10. It is assumed.
- Shifted 3 units left
Vertical compression by a factor of 2
Reflected across the y-axis
Shifted down 5 units
The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Given the parent function with base 10.
We want to find the given transformations.
The given parent function is y=log(x)
Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get
y=log(x+3)
Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get
y=2log(x+3)
Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get
y=2log(-x+3)
Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get
y=2log(-x+3)-5
Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
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The scale of a map says that 8 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 8 kilometers?
Answer:
40 cm
Step-by-step explanation:
We have that the distance on the map (in centimeters) represents an actual distance of 8 kilometers
x=12.8cm
From the question we are told
The scale of a map says that 8 cm represents 5 km. What distance on the map (in centimeters) represents an actual distance of 8 kilometers?
Generally the equation for the statement is mathematically given as
8cm=5km
x=8km
Therefore
\(x=\frac{8*8}{5}\\\\x=64//5\\\\x=12.8cm\)
Therefore
the distance on the map (in centimeters) represents an actual distance of 8 kilometers
x=12.8cm
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Find the length of CD.
To determine the length of CD, we need additional context or information. Without any specific details about the geometric configuration or diagram, it is challenging to provide an exact answer.
However, we can discuss the concept of determining lengths in various scenarios.
In geometry, CD could refer to a line segment, a chord, or a diagonal of a polygon. The length of CD would depend on the particular shape, such as a circle, triangle, quadrilateral, or more complex polygon.
Additionally, the dimensions, angles, or relationships of the surrounding elements are crucial in finding the length accurately.
If CD represents a line segment, it can be measured directly by using a ruler or any other suitable measuring tool. This method is precise and provides an exact length.
However, if CD refers to a more complex shape, such as a chord or diagonal, mathematical calculations or formulas specific to that shape would be required to determine the length accurately.
To solve such problems, it is necessary to understand and apply relevant geometric principles and formulas.
These may include the Pythagorean theorem, trigonometric ratios, properties of similar triangles, or the Law of Cosines, among others.
By utilizing these concepts and the given information about the shape or diagram, one can calculate the length of CD.
In conclusion, without further details or a specific geometric scenario, it is impossible to determine the length of CD accurately. However, by employing appropriate formulas and concepts, one can calculate the length by considering the specific shape and relevant measurements or relationships.
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Triangle LMN has vertices at L(0, 0), M(0,4), and N(-3,0). The triangle will be rotated 270° counterclockwise about the origin. What will
be the coordinates for point N'?
A (-3,0)
B. (0,-3)
C (0, 3)
D (3, 0)
\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)
Actually Welcome to the Concept of the mirror reflection.
Since the image of triangle is reflected along Y-axis,hence the coordinates of N after 270° rotation are
N ==> ( 3,0)
===> Option D.) is correct
Answer:(3,0)
Step-by-step explanation:
D
There at least 8 slices of bread left in the bag. Use p as your variable
Answer:
your P will be equal to 8 x
A particularly long traffic light on your morning commute is green 20% of the time that you approach it. assume that each morning represents an independent trial. 1. over five mornings, what is the probability that the light is green on exactly one day? 2. over 20 mornings, what is the probability that the light is green on exactly four days? 3. over 20 mornings, what is the probability that the light is green on more than four days?
The probability that the light will turn green on one certain day is 0.4096.
What is probability?Probability is a tool used to assess the likelihood of occurrence. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
The probability mass function of X has the following formula:
P(X=k)
=(k n)\(0.2^{k}\)×\(0.8^{n-k}\) where k=0,1,…,n
(a) Set n where 5 n=5
P(X=1)
=( 5 1 )\(0.2^{1}\)\(0.8^{4}\)
= 0.4096
(b) Set n = 20
P(X=4)
=(20 4 )×\(0.2^{4}\) x \(0.8^{16}\)
= 0.218
P(X ≥ 4) =1 − P(X ≤ 4)
=1−P(X = 0)−P(X = 1 )−P(X = 2)−P(X = 3)−P(X = 4)
=0.37
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Kristen's financial advisor has given her a list of 8 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this?
The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.
If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:
nPr = n!/{(n - r)!}.
In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.
Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.
Substituting n = 8, and r = 4 in the formula, we get:
8P4 = 8!/{(8 - 4)!}
= 8!/4!
= 5 * 6 * 7 * 8
= 1680.
Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
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