if we have a class of 15 students and we want to choose a committee of 5 students, their order and position don't matter, how many different ways are there of creating a 5-person committee among the 15 students?
Answers
if we have a class of 15 students and we want to choose a committee of 5 students, their order and position don't matter, 3003 many different ways are there of creating a 5-person committee among the 15 students.
What is combination formula?The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
Since order and position doesn't matter in this problem, use the combination formula.
The combination formula is: n! / (n-r)! r!
where n is the total number of items (15 in this case) and r is the number of items being selected at once (5 in this case)
Plugging our numbers into the formula:
= 15! / (15-5)! 5!
= 3003 ways.
So, there are 3003 ways of picking 5 people from a group of 15.
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Related Questions
suppose someone offers max the following gamble: with probability 0.50 he will win $10 and with probability 0.50 he will lose $8. the expected value of this gamble is
Answers
The expected value of this gamble is $1.
The expected value of this gamble is the weighted average of all possible outcomes where the weights are the probabilities of each outcome happening.
The formula for expected value (EV) is as follows:
Expected Value = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost)
Hence, substituting the values:
Expected Value = (0.5 × $10) − (0.5 × $8)
Expected Value = $5 - $4
Expected Value = $1
Therefore, the expected value of this gamble is $1.
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Solomon is planning to recover a lampshade. How much fabric does he need?
a.912 cm^2
b.1,056 cm^2
c.768 cm^2
d.2,304 cm^2
Answers
Area of fabric needed to cover the lampshade is 768 \(cm^2\)
What is Fabric?
Fabric can be either a cloth made by weaving or knitting, or it can be the framework of a construction. Some individuals use twisting, felting, or braiding to create fabrics. When I remark that termites are "gradually eating away at the fabric of the building," I'm referring to either the floor or the walls.
The phrase may also be used to refer to the fundamental framework or organization of society. For instance, "the fabric of society" refers to its fundamental structure, which includes all of its practices and beliefs.
I'm referring to the body of the car when I remark, "I heard clanking noises in the fabric of the car." This phrase can also be used to describe the body of an aircraft.
Length= 16 cm
Breath= 12 cm
Area= 4(16*12) \(cm^2\)
Area=768 \(cm^2\)
Hence, Fabric needed is 768 \(cm^2\)
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How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers probability?
Answers
The total number of possible 7-place license plates are 67600000.
Given: A 7-plate license plate. 2 places are for letters and 5 places are for numbers. To find how many different 7-plate license plates are possible
Let's solve the given problem:
The license plate has 7 places. 2 places are for letters and the remaining 5 places are for numbers.
Combination of letters: As there are no restrictions given in the question, so the first letter can be any alphabet out of the 26 alphabets (A, B, C, D, ......... Z). So the first place for the letter can be filled in ²⁶C₁ ways that are 26 ways. Also for the second place, as the letters can repeat so it can be filled in ²⁶C₁ ways too which are 26 ways. Therefore, the possible ways in which the place for two letters can be filled is 26 × 26 ways = 676 ways.Combination of numbers: As there are no restrictions given in the question so the first number can be any of the numbers out of the 10 numbers (10, 1, 2, 3, ....... 9). So the first number can be filled in ¹⁰C₁ = 10 ways. Similarly, as the numbers can repeat so the 2nd, 3rd, 4th and 5th numbers can be filled in ¹⁰C₁ ways that all the other places can be filled in 10 ways each. Therefore the total number of ways in which the place for 5 numbers can be filled is 10 × 10 × 10 × 10 × 10 ways = 100000 ways.Therefore, the total number of ways in which the 7-place license plate can fill are: Total possible ways in which the two letters can be filled × Total possible ways in which the 5 number places can be filled
= 676 × 100000
= 67600000 ways
Hence the total number of possible 7-place license plates are 67600000.
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can anyone help with math thanks
Answers
Answer:
Step-by-step explanation:
50 - 5 - 18 = 27
27 ÷ 3 = 9
x = 9
Which of these statements is true for f(x) = 2.3*?
OA. The y-intercept is (0, 1).
OB. The domain is x > 0.
OC. The y-intercept is (0, 2).
OD. It is always decreasing.
Answers
The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).
How to determine the true statement?The function is given as:
f(x) = 2(3)^x
Set x = 0 to determine the y-intercept
f(0) = 2(3)^0
Evaluate
f(0) = 2
This means that the y-intercept of f(x) = 2(3)^x is (0,2)
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Angle E and angle F are supplementary if m angle E =62 find m angle F
Answers
If Angle E and angle F are supplementary to each other, and (∠E = 62°), then the measure of ∠F will be 118°.
As per the question statement, Angle E and angle F are supplementary to each other, and (∠E = 62°),
Then we are required to calculate the measure of ∠F.
To answer this question, first we need to understand the concept of supplementary angles. "Two angles are said to be supplementary to each other, if their sum is equal to 180°".
That, if Angle E and angle F are supplementary to each other, then
[(∠E + ∠F) = 180°],
Or, [(62° + ∠F) = 180°]...[∵(∠E = 62°), given]
Or, [∠F = (180 - 62)°]
Or, (∠F = 118°)
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2) At age 22, Joseph places $4,500 in a retirement account with a fixed annual interest rate 7%,compounded continuously. He never places any additional money in the account. What will hisbalance be at age 55 ?
Answers
lets remember what it means compound continuously,
the interest never stopped, the balance is earning interest at all time
Joseph is 22 and he wants to know how much money he will have at 55
55-22=33
his balance will gain interest for 33 years, this is our time
there is a 7% rate
the formula is
P(t)= P(0) e ^rt
our t is 33
rate=7%
Joseph will have a balance at age 55, 45,334.99 dollars
Chris bought 12.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closetsto the number of liters of gasoline Chris bought? A 11.44 L B 2.74 L C 47.12 L D 14.20 L2
Answers
Answer:
C 47.12 L
Step-by-step explanation:
1 gallon = 3.8 liters
12.4 gallons = x
Cross Multiply
= 12.4 × 3.8
47.12 liters
Option C is correct
Find an equation of the plane perpendicular to the line where plane 4x-3y +27=5 and plane 3x+2y=Z+11=0 meet after passing a point (6,2,-1).
Answers
To find an equation of the plane perpendicular to the line of intersection between the planes 4x - 3y + 27 = 5 and 3x + 2y + z + 11 = 0, passing through the point (6, 2, -1),
The normal vector of the first plane is (4, -3, 0), and the normal vector of the second plane is (3, 2, 1). Taking their cross product, we get the direction vector of the line as (3, -12, 17). This vector represents the direction in which the line extends. Next, using the point (6, 2, -1),
we can substitute its coordinates into the general equation of a plane, which is ax + by + cz = d, to determine the values of a, b, c, and d. Substituting the point coordinates, we obtain 3(x - 6) - 12(y - 2) + 17(z + 1) = 0. This equation represents the plane perpendicular to the line of intersection between the given planes, passing through the point (6, 2, -1).
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A rectangle with a width of 4.6 inches has an area of 23 inches squared. What is the length?
Answers
Answer:
length = 5
Step-by-step explanation:
area = length × width
23 = length × 4.6
23 ÷ 4.6 = length
5 = length
mhm help me please thanks
Answers
Answer:
19
Step-by-step explanation:
Sorry if wrong :> Hope i helped! Have a awesome day!!! You're a great hooman ^_^ Please mark brainliest !!
Directions: Read the problem. Then calculate the final price you would pay for the item, including tax
This is a Lamborghin[Veneno. The asking price for one of these is $4.5 million. It is the most expensive
production car in the world. The dealer will give you a 35% discount on the car. The tax rate is 7.75%.
What is the final price of the car, including tax? You may use a calculator, but you need to show your work
(what numbers and operations are you doing on your calculator?)
Final Price:
Answers
Answer:
Get to know the easy procedure on how to find 4500000 minus 35% is what along with steps by referring further.
As per the given data inputs P% = 35%, X= 4500000
We need to figure out the value of Y i.e. result obtained on subtracting 4500000 minus 35%
Substitute the given inputs in the formula i.e. Y= X(1-P%)
On substituting we get the data as under Y =4500000(1-35%)
Determine the value of 35% in decimal by simply dividing with 100 i.e. 35/100 =0.35
Replace the decimal value in terms of 35% in the equation.
Thus, we get the equation as Y = 4500000(1-0.35)
On simplifying it further by performing basic maths operations we get Y =4500000(0.65)
Finally, we get the value of Y as 2925000
Therefore 4500000 minus 35% is 2925000
plus 7.75%
total answer: 3151687.5
Step-by-step explanation:
(TR)546 - (TR)540
pls help!
Answers
The computation of (TR)546 - (TR)540 will give a value of 3261.
How to compute the value?
TR(546) = 546(546 + 1)/2 = 273 * 547
TR (540) = 540(540 + 1)/2 = 270 * 541
273 * 547 = (270 + 3)(541 + 6)
= 270*541 + 270*6 + 541 *3 + 18
= 270*541 + 1620 + 1623 + 18
= 270*541 + 3261
TR(546) -TR (540) = 270*541 + 3261 - 270 * 541
= 3261
TR(546) -TR (540) = 3261
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Rufus and Cody went from living in the country to living in the city. How would you feel If your parents decided they’d rather have a life on a farm than stay in the city any longer. What would your feelings be and why?
AT LEAST 6 SENTENCEs
WILL RECIEVE BRAINLIST AND EXTRA POINTS
Answers
Answer:
-In my opinion- I tried hope you like this!
Step-by-step explanation:
I would feel Average because, I already lived in the country. I could go visit the city when I grow up anytime. I can also find new things I never knew about in the farm that wasn't in the country. in addition, I would also go discover how farmers do it like for example how they take care of their crops and their animals like all the basics. Living in the city isn't a need it's a choice if my parents would decide to live in the Farm I would be happy with their choice. My feelings towards this choice would be Happy and curious because you never know what would happen in the farm you might like it , if I don't then I would talk with my parents about what I dislike, I'm pretty sure they would understand.
Find the constant of variation when y=6 varies directly with x=3
Answers
Answer:
The constant of variation is 2
Step-by-step explanation:
The equation of the direct variation is y = k x, where k is the constant of variation
Let us solve the question
∵ x and y are in the direct variation
→ Use the form of the equation above
∴ The equation of variation is y = k x
∵ x = 3
∵ y = 6
→ Substitute them in the equation above
∴ 6 = k (3)
∴ 6 = 3k
→ To find k divide both sides by 3
∵ \(\frac{6}{3}\) = \(\frac{3k}{3}\)
∴ 2 = k
∵ k is the constant of variation
∴ The constant of variation is 2
Subtract
1/13
31
55
62
110
2
3/5
55
7
10
-
3
22. Simplify the answer.
Answers
When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.
To subtract 3 from 22, we can perform the subtraction operation as follows:
22
3
19
We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.
Therefore, the simplified answer is 19.
The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.
By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.
In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.
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jack wants to buy a pair of trousers for $60.When he went to the store he found that the price was marked down by 20%. how much do they cost
Answers
Answer:
$48
no idea how working out would go
Answer: $48
Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.
Then multiply 60 x 0.20 which equals 12.
Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.
I hope this helps!! Good Luck!
Huey can wash 6 cars or mow 3 lawns in one hour. Dewey can wash 3 cars or mow 3 lawns in one hour. Louie can wash 3 cars or mow 6 lawns in one hour. They each work 8 hours per day. If two of them wash cars and one mows lawns then at most they can wash cars and mow lawns. Enter whole numbers.
Answers
At most, they can wash 96 cars and mow 96 lawns.
To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.
Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.
Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.
Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.
Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.
The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.
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someone please help meeeee! I don't know what the solution is!
Answers
Answer:
(2,4)
Step-by-step explanation:
Answer:
(2,4)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation
Answer this please I’m not sure of the answer
Answers
Answer:
50
Step-by-step explanation:
All angles in a triangle add to 180 so C would be 65 and we just do 180-65-65 and we get 50.
how many fifths are in 2? PLEASE HELP
Answers
Answer:
10/5 ten fifths are in two
Step-by-step explanation:
10/5 = 2
7x + 3 = 4x - 5x + 12
Answers
Answer:
x=1.125
Step-by-step explanation:
Answer:
1.125
Step-by-step explanation:
7x + 3 = 4x - 5x + 12
7x + 3 = -x + 12
+x +x
8x + 3 = 12
-3 -3
8x = 9
x = 1.125
At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes.
The typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of new machine set ups are completed in less than 25 minutes?
A. Approximately 25%
B. Approximately 68%
C. Approximately 22.7%
D. Approximately 77,3%
Answers
The correct option is (D). Approximately 77.3% of new machine set ups are completed in less than 25 minutes.
Given a local manufacturing plant, employees must complete new machine set ups within 30 minutes.
The new machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. The typical worker needs five minutes to adjust to their surroundings before beginning their duties.
To find the percentage of new machine set ups completed in less than 25 minutes, we need to calculate the z-score. For this, we will use the formula:
z = (X - μ) / σ
where X = 25 minutes, μ = 22 minutes, and σ = 4 minutes
z = (25 - 22) / 4z = 0.75
We can now look up the percentage of the area under the normal distribution curve that corresponds to z = 0.75. Using a standard normal distribution table, we find that the area to the left of z = 0.75 is approximately 0.7734.
So, the percentage of new machine set ups completed in less than 25 minutes is approximately 77.34%.
Therefore, the correct option is (D).Approximately 77.3% of new machine set ups are completed in less than 25 minutes.
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find the equation of the line in slope-intercept form. e through (−5, 6) with slope = 3
Answers
Answer:
Step-by-step explanation:
y - 6 = 3(x + 5)
y - 6 = 3x + 15
y = 3x + 21
What is the solution
-3x + y = 2
y = x + 4
Answers
Answer:
to find the solution, we substitute y = x + 4 into the other equation.
-3x + (x + 4) = 2
-3x + x + 4 = 2
-2x = 2 - 4
-2x = -2
x = 1
to find y, we substitute x to the x variable in the y equation.
y = 1 + 4
y = 5
therefore, when combined, it is (1,5).
5sinA=4, find the value of tanA.
Answers
Answer: tan A=4/3
Step-by-step explanation:
Theo đề ta có: 5sinA=4 suy ra: sinA=4/5, mà ta đã biết là: sinA= cạnh đối/cạnh huyền, suy ra: cạnh đối của góc A =4, cạnh huyền =5
Áp dụng định lí py ta go ta đc:
5^2=4^2+x^2
=) x=3
Vậy cạnh kề của góc A=3
Mà tanA = cạnh đối/cạnh kề
Vậy giá trị của tanA=4/3
(bạn vẽ hình ra thì có thể nhìn rõ hơn đấy, cảm ơn bạn đã tham khảo câu trả lời của mik)
16 x \(\frac{1}{8}\)
Answers
Answer:
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A compound X contains 63.3 percent manganese (Mn) and 36.7 percent O by mass. When X is heated, oxygen gas is evolved and a new compound Y containing 72.0 percent Mn and 28.0 percent O is formed. Determine the empirical formulas of X and Y.
Answers
The empirical formula of compound X is MnO₂.
The empirical formula of compound Y is Mn₃O₄.
We have,
To determine the empirical formulas of compounds X and Y, we need to find the ratio of the elements present in each compound.
For compound X:
The percentage of manganese (Mn) is 63.3%, which corresponds to 63.3 grams out of 100 grams.
The percentage of oxygen (O) is 36.7%, which corresponds to 36.7 grams out of 100 grams.
To find the empirical formula of X, we need to determine the ratio of Mn to O. To simplify the ratio, we can divide both values by their respective atomic masses.
The atomic mass of Mn is approximately 54.94 g/mol, and the atomic mass of O is approximately 16.00 g/mol.
For Mn: (63.3 g) / (54.94 g/mol) ≈ 1.15 mol
For O: (36.7 g) / (16.00 g/mol) ≈ 2.29 mol
The ratio of Mn to O is approximately 1.15:2.29, which simplifies to approximately 1:2.
Therefore, the empirical formula of compound X is MnO₂.
Now, let's calculate the empirical formula of compound Y using a similar approach:
The percentage of Mn in Y is 72.0%, which corresponds to 72.0 grams out of 100 grams.
The percentage of O in Y is 28.0%, which corresponds to 28.0 grams out of 100 grams.
Using the atomic masses mentioned earlier:
For Mn: (72.0 g) / (54.94 g/mol) ≈ 1.31 mol
For O: (28.0 g) / (16.00 g/mol) ≈ 1.75 mol
The ratio of Mn to O in compound Y is approximately 1.31:1.75, which simplifies to approximately 3:4.
Therefore, the empirical formula of compound Y is Mn₃O₄.
Thus,
The empirical formula of compound X is MnO₂.
The empirical formula of compound Y is Mn₃O₄.
Learn more about empirical formulas of compounds here:
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A jacket is on sale for 10% off including the discount and 7% tax the sales price of the jacket is $115.56 what is the price of the jacket before the discount and tax
Answers
Answer:
120.00
Step-by-step explanation:
Let x be the original price
The price is 10% off, or we pay 90% of the original price
.9 x
Then we have to pay 7% sales tax
.9x * 7%
.9x * .07
.063x is the tax
Add this to the .9x we have to pay for the jacket
.9x + .063x = .963x
This is the cost of the jacket
.963x = 115.56
Divide each side by.963
.963x/.963 = 115.56/.963
x =120.00
The cost of the jacket before discount and tax is 120.00
1) Find the value of k in the equation x2 – 3x + k = 0 if its roots are real, irrational and not equal.
2) Find the value of k in the equation x2 – 2x + k – 1 = 0 if this equation has two equal roots.
3) The graph of 2x2 – 8x + k = 0 crossed the x- axis twice. What is the value k?
4) Find the value of k in the equation 4x2 – 6x + 4 (k – 1) = 0 if it has only one solution.
5) Find the value of k in the equation afdahx2 – 4x + k + 1 = 0 if this quadratic equation has no solution.
with solution.
Answers
Answer:
b^2-4ac(formula for finding the roots )
Step-by-step explanation:
1)9-4k=0
k=9/4(roots are real )
2)4-4k+4=0
8-4k=0
k=2(the roots are real )
3)64-8k=0
k=8
4)36-16k+16=0
52-16k=0
k=52/16=13/8
16-4k+4=0
k=5