what is C(8,5) in factorial notation?
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Answer:
The formula for the number of combinations of n objects taken r at a time is given by:
C(n, r) = n! / (r! * (n-r)!)
In this case, we have:
C(8, 5) = 8! / (5! * (8-5)!)
Simplifying the denominator:
C(8, 5) = 8! / (5! * 3!)
Writing 5! and 3! in expanded form:
C(8, 5) = 8! / (5 * 4 * 3! * 3 * 2 * 1)
Cancelling out the 3! terms:
C(8, 5) = 8! / (5 * 4 * 3 * 2 * 1)
Writing 8! in expanded form:
C(8, 5) = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1)
Cancelling out the 5 * 4 * 3 * 2 * 1 terms:
C(8, 5) = 8 * 7 * 6 / (3 * 2 * 1)
Simplifying:
C(8, 5) = 56
Therefore, C(8, 5) = 56 in factorial notation.
Related Questions
let f:A=B such that f(x)=y and g:B=C such that g(y)=z.name the function defined from A to C.
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Answer:
since g:B→C is onto
suppose z∈C,there exists a pre-image in B
Let the pre-image be y
Hence y∈B such that g(y)=z
similarly f:A→B is onto
suppose y∈B,there exists a pre-image in A
Let the pre-image be x
Hence x∈A such that f(x)=y
Now gof(x)=g(f(x))=g(y)=z
So for every x in A,there is an image z in C
A amusement park charges an admission fee of 25.00 and 5.50 for each ride Andy wrote an expression to find the total amount he spent after x number of rides what does the constant term in the expression represent
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Answer:
The admissions fee($25)
Step-by-step explanation:
No matter what, the admissions fee stays the same. Your coefficient($5.50) is multiplied by the amount of rides taken(x)
A computer costs £968. A tax of 16.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.
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The amount of tax that is added to the cost of the computer is 159.72
How to determine the amount of tax that is added to the cost of the computer.From the question, we have the following parameters that can be used in our computation:
Computer cost = 968
Tax percentage = 16.5%
Using the above as a guide, we have the following:
Tax amount = Computer cost * Tax percentage
substitute the known values in the above equation, so, we have the following representation
Tax amount = 968 * 16.5%
Evaluate
Tax amount = 159.72
Hence, the amount of tax that is added to the cost of the computer is 159.72
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Will mark brainliest if you help!!!!!
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Answer:
.70
Step-by-step explanation:
5 and up round up so it would round to .7
A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use the fact that water weighs 62.5 lb/ft3. (Round your answer to the nearest whole number.) 3 ft6 ft12 ft A frustum of a cone with a spout is given. The smaller radius is 3 ft, the larger radius is 6 ft, and the height is 12 ft.
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The work required to pump the water out of the spout is approximately 64,307,077 ft-lb
To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.
First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.
Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:
V = (1/3)π(12)(9 + 36 + 18) = 270π ft³
Now, we can calculate the weight of the water using the density of water:
Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb
Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):
Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²
Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:
Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft
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Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neither. If it is either arithmetic or geometric, give the next term in the sequence. 4096, 1024, 256, 64, 16,...
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Answer: geometric series
Step-by-step explanation:
If it is arithmetic, the difference from each term to the next will always be the same.
4096 - 1024 = 3072; 1024 - 256 = 768
3072 ≠ 768. so not arithmetic
If it is geometric, the ratio of each term to the next will always be the same.
4096/1024 = 4
1024/256 = 4
256/64 = 4
64/16 = 4
This is a geometric series. Each term (after the first) is (1/4) of the term before.
Hope this helps.
Consider the linear second-order differential equation:
d^2y/ dx^2 + a1(x)dy/dx +ao(x)y(x)=0
Note that this equation is linear because y(x) and its derivatives appear only to the first power and there are no cross terms. It does not have constant coefficients, however, and there is no general, simple method for solving it like there is if the coefficients were constants. In fact, each equation of this type must be treated more or less individually. Nevertheless, because it is linear, we must have that if y1(x) and y2(x) are any two solutions, then a linear combination.
y(x)=c1y1(x)+c2y2(x) where c1 and c2 are constants, is also a solution. Prove that y(x) is a solution.
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Answer:
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Step-by-step explanation:
Please awnser asap I will brainlist
Answers
The members of the given set in this problem are given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
How to obtain the union and intersection set of two sets?The union and intersection sets of multiple sets are defined as follows:
The union set is composed by the elements that belong to at least one of the sets.The intersection set is composed by the elements that belong to at all the sets.The intersection of the sets Y and Z for this problem is given as follows:
Y ∩ Z = {0, 6, 23, 26}
(which are the elements that belong to both of the sets).
The union of the above set with the set X is given as follows:
X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}
(elements that belong to at least one of the sets).
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Two cups of flour make 23 batch of bread. How many cups of flour make 1 batch?
Answers
SCL1501 ASSIGNMENT 1 2023_0 X + 20kay/Documents/2023%20assessments/SCL 1501%20ASSIGNMENT%201%202023_0adc3afa3db59caacea862 QUESTION 5 Jane Doe purchased a Range Rover last week for R790 500 (VAT incl). While driving from the Dube Port area along the N2 Road in Durban, she collides with John Wick, who is the owner-driver of a Porshe Cayenne. Doeriş is 23% negligent, whereas Wick is 33% negligent. The damage to the Range Rover is estimated at R175 000.00. It is uneconomical to repair the Porsche, but its salvage value is R125 000.00. The pre-accident value of Porsche was R985 000.00. Regarding the damages to Doe and Wick's motor vehicles, calculate who must pay whom and what would be the amount in damages. (4)
Answers
Dοe must pay Wick R506 398.00 - R71 872.50 = R434 525.50 in damages.
What is the basic mathematical οperatiοns?The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.
Tο calculate the damages, we need tο find οut the prοpοrtiοn οf negligence fοr each driver and apply it tο the damages.
Let D represent Dοe and W represent Wick.
Dοe's negligence = 23%
Wick's negligence = 33%
Tοtal negligence = 23% + 33% = 56%
Therefοre, Dοe is 23%/56% = 0.4107 οr 41.07% liable, and Wick is 33%/56% = 0.5893 οr 58.93% liable.
Damage tο Range Rοver = R175 000
Dοe's liability = 41.07% οf R175 000 = R71 872.50
Wick's liability = 58.93% οf R175 000 = R103 127.50
Salvage value οf Pοrsche = R125 000
Pre-accident value οf Pοrsche = R985 000
Lοss οf value οf Pοrsche = R985 000 - R125 000 = R860 000
Wick's liability fοr lοss οf value = 58.93% οf R860 000 = R506 398.00
Therefοre, Dοe must pay Wick R506 398.00 - R71 872.50 = R434 525.50 in damages.
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1) Which statement below is equivalent to - 15 - 12? Ex choice. a) - 15 + 12=-3 b) -15 +-12=-27 c) 15 - 12=3 d) 15--12=-27 ANSWER: EXPLAIN:
Answers
It’s equivalent to -15-12
Using the integers −9 to 9 at most one time each, place a digit in each box ( ___ , ____) and. ( ___ , ____) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3)
Answers
Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).
To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:
(x₁ + x₂)/2 = 1
(y₁ + y₂)/2 = 3
We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:
(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2
(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6
Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:
x₁ + (2-x₁) = 2 => x₁ = 1
y₁ + (6-y₁) = 6 => y₁ = 3
So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.
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Simplify the expression below using the distributive property:
6(32)
Answers
Answer: 192
Step-by-step explanation:
192
Answer:
6(32)
6x32
192
explanation:
It is known that the number of hours a student sleeps per night has a normal distribution. The sleeping time in hours of a random sample of 8 students is given below. See Attached Excel for Data. 8.6, 8.3, 7.6, 6, 7.1, 5.6, 5.1, 6 Compute a 98% confidence interval for the true mean time a student sleeps per night and fill in the blanks appropriately. We have 98 % confidence that the true mean time a student sleeps per night is between and hours. (round to 3 decimal places)
Answers
We have 98 % confidence that the true mean time a student sleeps per night is between 6.2928 hours and 7.1832 hours.
Mean = (8.6 + 8.3 + 7.6 + 6 + 7.1 + 5.6 + 5.1 + 6)/ 8 = 6.7875
Standard deviation = √Σ(x - mean)²/n
Σ(x - mean)² = (8.6 - 6.7875)^2 + (8.3 - 6.7875)^2 + (7.6 - 6.7875)^2 + (6 - 6.7875)^2 + (7.1 - 6.7875)^2 + (5.6 - 6.7875)^2 + (5.1 - 6.7875)^2 + (6 - 6.7875)^2
Standard deviation : \(\sqrt{11.82875}/8\)
s = 0.42991
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
sample standard deviation
number of samples
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 8 - 1 = 7
Since confidence level = 98% = 0.98, α = 1 - CL = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
the area to the right of z0.01 is 0.01 and the area to the left of z0.01 is 1 - 0.01 = 0.99
Looking at the t distribution table,
z = 2.998
Margin of error = 2.998 × 0.42/√8
= 0.4452
The lower limit of this confidence interval is
6.738 - 0.4452 = 6.2928
The upper limit of this confidence interval is
6.738 + 0.4452 = 7.1832
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An arrow is shot from 3 ft above the top of a hill with a vertical upward velocity of 108 ft/s. If it strikes the plain below after 9.5 s, how high is the hill?
If the arrow is launched at t0, then write an equation describing velocity as a function of time?
Answers
The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),
To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:
h = h0 + v0t + 1/2at^2
where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).
In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.
At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:
v = v0 + at
we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:
0 = 108 - 32.2t
t = 108/32.2 ≈ 3.35 s
Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.
Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:
h_hill = h0 + v0t + 1/2at^2 - h_top
where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:
h_top = h0 + v0^2/2a
Plugging in the given values, we get:
h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft
Plugging this into the first equation, we get:
h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78
h_hill ≈ 25.73 ft
If the arrow is launched at t0, the equation describing velocity as a function of time would be:
v(t) = v0 - gt
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A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she descended 60.4 feet. How many feet had she been below sea level, if she was 126.7 feet below sea level after she descended?
Answers
The Depth of the Scientist before dropping is: 66.3 ft
How to calculate sea level elevation?It is pertinent to note that sea level is usually considered zero level. Thus, one is either above the sea level (positive sign) or below the sea level.
Now, we are told that the scientist was already below the sea level before she dropped 60.4 ft.
Now, if after dropping 60.4 ft, she is now 126.7 ft below sea level, then it means that the depth she was at before dropping 60.4 ft is:
Depth before dropping 60.4 ft = 126.7 - 60.4
Depth before dropping = 66.3 ft
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The tax on a $80 item is $3.20.
Find the tax on a $140 item.
What is the tax?
Answers
Tax in the $140 item is $5.60
(0.04x140)
A density graph for all of the possible times from 50 seconds to 300 seconds
can be used to find which of the following?
A. The probability of a time from 75 seconds to 350 seconds
B. The probability of a time from 25 seconds to 250 seconds
C. The probability of a time from 150 seconds to 350 seconds
D. The probability of a time from 75 seconds to 250 seconds
Answers
Answer: D. took quiz :)
Step-by-step explanation:
Answer: d. the probability of a time from 75 seconds to 250 seconds
Step-by-step explanation:
Melanie placed 5 packs of fruit squishes in a picnic basket. Find the
weight (in ounces) of all the packs, if each pack weighs 15.75 ounces
Answers
Answer:
Your answer is 78.75 oz.
Step-by-step explanation:
15.75 * 5 = 78.5 oz.
Hope this helps.
Answer:
78.75 oz
Step-by-step explanation:
okay I'm not sure, but I think the question is each pack weighs 15.75 how many does it weigh in all like all 5 packs if so all you have to do is do multiplication 15.75 and 5 (15.75 to represent what each pack weigh) ( and 5 to represent each pack) to get the answer of 78.75 in total.
hope i helped
4. Uncle Royce is 42. What is his target heart rate range?
O 120-180 beats per minute
O 150-200 beats per minute
O116-160 beats per minute
O170-236 beats per minute
Answers
Step-by-step explanation:
70 to 85 % of his maximum
Maximum is estimated to be 220 - age = 220 - 42 = 178
70% of this is 125
85 % is 89 151
I believe I would go with the third choice 116-160 bpm
Find the missing numbers
Answers
Based on the information provided, the missing number would be number 6.
How to find the missing numbers?When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.
In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.
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What is the x-intercept for h(x) = (x+1) ^2 - 4
Answers
Solution
Given
\(h(x)=(x+1)^2-4\)setting h(x) = 0
\(undefined\)verify each identity \( \frac{ \cos^{2}x }{ \csc{}^{2}x } = \frac{ \sin ^{2}x }{ \sec ^{2}x } \)
Answers
Answer:
Verified
Explanation:
Given the identity:
\(\frac{ \cos^{2}x }{ \csc{}^{2}x }=\frac{ \sin^{2}x }{ \sec^{2}x }\)We apply the following identity:
\(\begin{gathered} \csc =\frac{1}{\sin}\implies\sin =\frac{1}{\csc } \\ \sec =\frac{1}{\cos}\implies\cos =\frac{1}{\sec } \end{gathered}\)Therefore:
\(\begin{gathered} \frac{\cos^2x}{\csc{}^2x}\stackrel{?}{=}\frac{\sin^2x}{\sec^2x} \\ \cos ^2x\times\frac{1}{\csc{}^2x}\stackrel{?}{=}\sin ^2x\times\frac{1}{\sec ^2x} \\ \cos ^2x\times\sin ^2x\stackrel{?}{=}\sin ^2x\times\cos ^2x \\ \implies\sin ^2x\cos ^2x=\sin ^2x\cos ^2x \end{gathered}\)Thus, the identity is verified since both sides of the identity are equal.
which of the following is not a reason that the process being monitored with the chart should be investigated?
Answers
By using the concept of control chart, it can be concluded that
A large number of plots are on or near the centerline.
Third option is correct.
What is control chart?
Control chart is used to show how a process changes over time.
There are three lines in a control chart.
They are the central line for the average, upper line for the Upper Control Limit (UCL) and a lower line for the Lower Control Limit (LCL)
It is known that the highest performance of a process is obtained when it is between the LCL and the UCL.
That means to get the best result, samples needs to be concentrated near the centerline.
So the third option is correct
A large number of plots are on or near the centerline.
Third option is correct.
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Complete Question
Quality control charts usually have a central line and upper and lower control limit lines. Which of the following is not a reason that the process being monitored with the chart should be investigated?
A sudden and sustained shift in the plots toward the upper or lower control limit
There is an upward trend in the plots
A large number of plots are on or near the central line
A single plot falls outside of the control limits
Determine the surface area and volume. Note: The base is a square.
Answers
Answer:
volume=60cm3, surface area=96cm2
Step-by-step explanation:
volume=1/3×(6×6)×5
=60cm3
surface area= 4(1/2×6×5)+(6×6)
=96cm2
What is the value of the digit in the ones place?
2,615
A. 50
B. 5
OC. 2,000
OD. 100
Answers
Calculate the down payment percent using the following information: (2 points)
Purchase price: $281,700
Closing costs: 2.6% of purchase price
Total move-in costs: $52,396.20
15%
16%
17%
18%
Answers
The down payment percentage for down payment of $52,396.20 and purchase price of $281,700 is option D: 18%.
What is down payment?
A down payment is a quantity of money that a buyer pays at the beginning of a pricey good or service purchase. A portion of the entire purchase price is covered by the down payment, and the buyer frequently takes out a loan to cover the balance.
The purchase price is - $281,700
The down payment is - $52,396.20
Let the down payment percentage be x.
The formula for down payment is -
Down Payment = Down Payment Percentage × Purchase Price
Substitute the values into the equation -
52,396.20 = x% × 281,700
x% = 52,396.20 / 281,700
x% = 0.186
x = 0.186 × 100
x = 18.6 ≈ 18%
Therefore, the down payment percentage is 18%.
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There are 2 rows of oranges on a table. Each row has 4 oranges. How many oranges are there in all?
Answers
Answer:
8
Step-by-step explanation:
2 rows with 4 oranges each -> 2*4 = 8
are the ratios 2:1 and 20:10 equivalent
Answers
Yes, there is an analogous ratio between 2:1 and 20:10.
What ratio is similar to 2 to 1?We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.
By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.
As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.
The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:
20 ÷ 10 : 10 ÷ 10
= 2 : 1
As a result, both ratios have the same reduced form, 2:1, making them equal.
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Whats the value of the dimes?