in how many ways can you give three baseball tickets, three soccer tickets, and three opera tickets, all general admission, to nine friend so each gets one ticket?
Answers
The total number of ways to distribute the tickets among the 9 friends, which is 9P3 * 6P3 * 3P3 = 987 * 654 * 1 = 84,600.
The ways how nine friends can get one ticket each?
The number of ways to distribute 3 baseball tickets, 3 soccer tickets, and 3 opera tickets among 9 friends, with each friend getting one ticket, is given by the permutation formula:
9P3 * 6P3 * 3P3 = 9!/(9-3)! * 6!/(6-3)! * 3!/(3-3)! = 9!/(6!3!) * 6!/(3!3!) * 3!/(0!3!) = 84,600
Therefore, there are 84,600 ways to distribute the tickets among the 9 friends.
To explain this answer, we can break it down into three parts.
First, there are 9 friends to choose from for the first baseball ticket, then 8 friends to choose from for the second baseball ticket, and 7 friends to choose from for the third baseball ticket. This gives us 9P3, or 9 factorial divided by (9-3) factorial, which is equal to 9!/(6!) = 987.
Next, there are 6 friends left to choose from for the first soccer ticket, then 5 friends left to choose from for the second soccer ticket, and 4 friends left to choose from for the third soccer ticket. This gives us 6P3, or 6 factorial divided by (6-3) factorial, which is equal to 6!/(3!) = 654.
Finally, there are 3 friends left to choose from for the first opera ticket, then 2 friends left to choose from for the second opera ticket, and 1 friend left to choose from for the third opera ticket. This gives us 3P3, or 3 factorial divided by (3-3) factorial, which is equal to 3!/(0!) = 1.
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Related Questions
If the property of a sample of matter depends on the amount of matter present, it is a(n) ____________ property.
Answers
If the property of a sample of matter depends on the amount of matter present, it is an extensive property.
Extensive properties of a substance depend on the amount or size of the substance being measured. Examples of extensive properties include mass, volume, and heat capacity.Examples of extensive properties are weight, length, volume, size, surface area, and charge. The extensive property of a substance or material varies proportionally to its size or amount. The greater the quantity or size of the substance, the greater the extent of the substance's extensive property.Therefore, it can be said that if the property of a sample of matter depends on the amount of matter present, it is an extensive property.
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Which is the solution set of the inequality 15y-9 < 36? A. y> 9/5B. y< 9/5C. y< 3D. y> 3
Answers
15y - 9 < 36
add 9 to both-side of the equation
15y < 36 + 9
15y < 45
Divide both-side of the equation by 15
y < 3
Determine the general solution for sin(x-30°) = cos 2 x
Answers
x-30=90-2x + 360k , where k= 0,1,2,3.......
3x= 120+360k
x= 40+120k
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x?
18x+5y=6
4x+3y=6
A)
subtract 2 times the second equation from 9 times the first equation
B)
subtract 9 times the second equation from 2 times the first equation
C)
subtract 3 times the second equation from 5 times the first equation
D)
subtract 5 times the second equation from 3 times the first equation
Answers
find the vertex of y=(x-3)^2+2
Answers
Answer:
Vertex: ( 3 , 2 )
Step-by-step explanation:
Rewrite in vertex form and use this form to find the vertex ( h , k ) .
Axis of Symmetry: x = 3
Vertex: ( 3 , 2 )
Graph: in pic
(Hope this helps can I pls have brainlist (crown)☺️)
someone please help and explain. i need this rnnn.
Answers
Answer:
x=8
Step-by-step explanation:
63+90+2x+11=180
Answer:
B
Step-by-step explanation:
Add 63 and 90 to find the left angle. Then subtract by 180.
Since that answer is 27, add it to 90 and subtract by 180 to find the last angle in the middle. then finally the angle in the corner should equal 27 since the triangles are congruent.
7. Given f(x) = ln x, a) Find the Taylor polynomial of degree 4 for f(x) about the point x = 1. b) Use the result of (a) to approximate f (0.9) and f (1.1). c) Use the Taylor remainder to find an erro
Answers
(a) The Taylor polynomial of degree 4 for f(x) about the point x = 1 is P4(x) = (x - 1) - (x - 1)^2/2 + (x - 1)^3/3 - (x - 1)^4/4. (b) Approximations for f(0.9) and f(1.1) using the Taylor polynomial P4(x) are f(0.9) ≈ -0.105 and f(1.1) ≈ 0.095. (c) The error bound for both approximations f(0.9) and f(1.1) using the Taylor polynomial P4(x) is approximately 0.00012.
a) To find the Taylor polynomial of degree 4 for f(x) about x = 1, we'll use the formula for the Taylor series expansion:
Pn(x) = f(a) + f'(a)(x - a) + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ... + fⁿ(a)(x - a)^n/n!
For the given function f(x) = ln(x), let's calculate the derivatives up to the fourth order:
f(x) = ln(x)
f'(x) = 1/x
f''(x) = -1/x²
f'''(x) = 2/x³
f⁴(x) = -6/x⁴
Now, substitute x = 1 and a = 1 into the formula to get the Taylor polynomial of degree 4:
P4(x) = ln(1) + (1/1)(x - 1) + (-1/1²)(x - 1)²/2! + (2/1³)(x - 1)³/3! + (-6/1⁴)(x - 1)⁴/4!
Simplifying the terms, we get:
P4(x) = (x - 1) - (x - 1)^2/2 + (x - 1)^3/3 - (x - 1)^4/4
(b) To approximate f(0.9) and f(1.1) using the Taylor polynomial P4(x), we substitute the respective values of x into P4(x):
For f(0.9):
f(0.9) ≈ P4(0.9)
= (0.9 - 1) - (0.9 - 1)^2/2 + (0.9 - 1)^3/3 - (0.9 - 1)^4/4
Calculating the expression gives f(0.9) ≈ -0.105.
Similarly, for f(1.1):
f(1.1) ≈ P4(1.1)
= (1.1 - 1) - (1.1 - 1)^2/2 + (1.1 - 1)^3/3 - (1.1 - 1)^4/4
Calculating the expression gives f(1.1) ≈ 0.095.
(c) The Taylor remainder formula allows us to estimate the error between the actual function and its Taylor polynomial approximation. For the Taylor polynomial P4(x), the remainder term R4(x) is given by:
R4(x) = (x - a)⁵/f⁵(c)(5!)
Where a = 1 (the point of expansion) and c is some value between 1 and x.
To find the error bound, we need to evaluate the fifth derivative of f(x) = ln(x):
f⁵(x) = 24/x⁶
To find the maximum value of f⁵(c) for c between 1 and x, we consider the interval [0.9, 1.1]. The maximum value occurs at x = 0.9:
f⁵(c) = 24/0.9⁶
Calculating this expression, we find that f⁵(c) ≈ 379.08.
Now, substituting the values into the remainder formula, we have:
R4(x) = (x - 1)⁵/(379.08)(5!)
For both f(0.9) and f(1.1), the error bound for both approximations f(0.9) and f(1.1) using the Taylor polynomial P4(x) is approximately 0.00012.
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help me pleaseeeeeeeee
Answers
Answer:
Angles on a straight line add up to 180 degrees so for the 129 degrees you will take 180 - 129 = 51. In the triangle you will add 51 and 55 = 106 but remember in a triangle all angles should be equal to 180. So 180 - 106 = 74. X=74degrees
Since the exterior angle is 129 degrees, the other angle supplementary to it would equal 51.
After you know that, add 51 + 55 = 106
180 - 106 = 74, so the measure of x is 74 degrees.
COMPATIBLE
Activity 3
Solve each problem. Write your solution and answer in your activity notebook.
1
Mr Raciles ordered lunch amounting to Php 500. 00 in a restaurant. If there is a
service charge of 10%, how much should he pay in all?
2. On a test with 50 items, Shiela answered 62% of items correctly. What percent of
the questions did she miss?
3. Jana paid PhP 420. 00 for a dress similar to Queenie's. Queenie said that this is 105%
of what she paid. How much did Queenie pay?
4. Among the 920 students of Princess Urduja Elementary School, 90% are walking
to school. How many are walking to school? How many are riding to school?
5. The total number of voters of Barangay San Isidro is 3,050. If 60% are males, how
many are females?
6. There are 50 households in Barangay Magtulongan. If 65% of them received
financial help, how many families received financial aid?
7. John deposited his PhP 10,000. 00 savings in a bank. It has a 2% interest every
month. How much is the interest of his money after a month?
8. Sarah Geronimo's concert sold 2 million worth of tickets, the 80% gain will be
given to a charitable institution. How much is the share of the charitable institution?
9. Jason answered 98% of his test correctly. If there were 50 items in the test, how
many items did he answer correctly?
10. There are 50 students in a class. If 90% of them were present, how many attended
the class?
Answers
1. So, Mr. Raciles should pay Php 500.00 + Php 50.00 = Php 550.00 in all.
1. To calculate the total amount Mr. Raciles should pay, we need to add the service charge to the original amount. The service charge is 10% of Php 500.00, which is:
10% of Php 500.00 = 0.10 x Php 500.00 = Php 50.00
2. To determine the percent of questions Shiela missed, we subtract her correct answers from the total number of questions and find the percentage. Shiela answered 62% of the 50 items correctly, which means she missed:
100% - 62% = 38%
So, Shiela missed 38% of the questions.
3. Jana paid Php 420.00 for a dress, which is 105% of what Queenie paid. To find the amount Queenie paid, we need to divide Php 420.00 by 105%:
Queenie's payment = Php 420.00 / 105% = Php 400.00
Therefore, Queenie paid Php 400.00.
4. Among the 920 students, 90% are walking to school. To find the number of students walking and riding to school, we can calculate it as follows:
Number of students walking to school = 90% of 920 = 0.90 x 920 = 828 students
Number of students riding to school = Total students - Students walking = 920 - 828 = 92 students
Therefore, 828 students are walking to school, and 92 students are riding to school.
5. If 60% of the voters in Barangay San Isidro are males, the remaining percentage represents the females:
Percentage of females = 100% - 60% = 40%
To find the number of females, we multiply the percentage by the total number of voters:
Number of females = 40% of 3,050 = 0.40 x 3,050 = 1,220 females
So, there are 1,220 females in Barangay San Isidro.
6. If 65% of the households received financial help, we can calculate the number of families that received aid as follows:
Number of families received financial aid = 65% of 50 = 0.65 x 50 = 32.5
Since we cannot have a fraction of a family, we round down to the nearest whole number. Therefore, 32 families received financial aid.
7. John's savings of Php 10,000.00 earns a 2% interest every month. To calculate the interest after a month, we multiply his savings by the interest rate:
Interest = 2% of Php 10,000.00 = 0.02 x Php 10,000.00 = Php 200.00
So, the interest on John's savings after a month is Php 200.00.
8. The total worth of tickets sold for Sarah Geronimo's concert is Php 2 million. The 80% gain given to the charitable institution can be calculated as follows:
Share of the charitable institution = 80% of Php 2,000,000.00 = 0.80 x Php 2,000,000.00 = Php 1,600,000.00
Therefore, the share of the charitable institution is Php 1,600,000.00.
9. If Jason answered 98% of the test correctly and there were 50 items, we can calculate the number of items he answered correctly as follows:
Number of items answered correctly = 98% of
50 = 0.98 x 50 = 49
Jason answered 49 items correctly.
10. If 90% of the 50 students in the class were present, we can calculate the number of students who attended the class as follows:
Number of students attended = 90% of 50 = 0.90 x 50 = 45
Therefore, 45 students attended the class.
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Which of the following coordinate points have undergone an enlargement and reduction? Select all that apply.Group of answer choices(5, -1) --> (10, 2) --> (20, 4)(1, 1) --> (6, 6) --> (1, 1)(4, 9) --> (20, 34) --> (20/45, 1)(3, 0) --> (9, 0) --> (18, 0)(0, -5) --> (0, 5) --> (0, 30)
Answers
By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.
If there is a reduction, then 0 < k < 1.
If there is an enlargement, then k > 1.
\((x,y)\rightarrow(kx,ky)\)So, you have
\(\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)\(\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow(\frac{1}{6}\cdot6,\frac{1}{6}\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}\)\(\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot\frac{34}{9})=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}\)\(\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}\)\(\begin{gathered} (0,-5)\rightarrow(-1\cdot0,-1\cdot-5)=(0,5) \\ \text{ In this case, k = -1, and by definition k > 0} \end{gathered}\)Therefore, the correct answer is
\(B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)\)Simplify the expression -4x(6x − 7).
Answers
Answer: -24x^2+28x
Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x
QUESTION 7 Introduce los factores dentro del radical. Da. √1280 x 10y7 b. 7/1280x 24 y 7 Oc7/285x63y7 d. 7/27x 10y8 QUESTION 8 2x³y 10x3
Answers
The main answer is √1280x10y7 = 8√10xy³.
How can the expression √1280x10y7 be simplified?The expression √1280x10y7 can be simplified as 8√10xy³. To understand this, let's break it down:
Within the radical, we have √1280. To simplify this, we can factor out perfect squares. The prime factorization of 1280 is 2^7 * 5. Taking out the largest perfect square, which is 2^6, we are left with 2√10.
Next, we have x and y terms outside the radical. These terms can be simplified separately. In this case, we have x^1 and y^7, so we can rewrite them as x and y^6 * y.
Combining these factors, we get the simplified expression 8√10xy³. This means we have 8 times the square root of 10, multiplied by x, and multiplied by y cubed.
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Simplify: I3 - 6| - (12 ÷ 6 + 1)3
Answers
Solution
The question would like us to evaluate the following expression
\(|3-6\left|-(12\div6+1\right)^2\)- We should deal with the modulus and bracket separately.
- After that, we can then perform the subtraction operation on the results of the modulus and bracket.
- This is done below:
\(\begin{gathered} |3-6|=|-3\left|\right? \\ |-3\left|\right?=3\text{ \lparen Because the modulus always returns a positive number\rparen} \end{gathered}\)Also,
\(\begin{gathered} \lparen12\div6+1)^2 \\ By\text{ the rules of PEDMAS,} \\ Division\text{ comes before Addition, thus, we should perform the division operation first} \\ 12\div6=2 \\ \\ \lparen2+1)^2=3^2=9 \end{gathered}\)Thus, combining both results, we have:
\(\begin{gathered} 3-9 \\ =-6 \end{gathered}\)Final Answer
The answer is -6
Answer:
-6 hope it helps
thank you
A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation $4x+6y=48$ models this situation, where $x$ is the number of cars and $y$ is the number of vans
Answers
The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
Given the equation that models the situation expressed as:
4x + 6y = 48
We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.
If there are no cars i.e. at when x = 0
4(0) + 6y = 48
0 + 6y = 48
6y = 48
y = 48/6
y = 8
One of the solution is (0, 8)
If there are 3 cars, i.e. at when x = 0
4(3) + 6y = 48
12 + 6y = 48
6y = 48 - 12
y = 36/6
y = 6
The second solution will be (3, 6)
If there are 6 cars, i.e. at when x = 6
4(6) + 6y = 48
24 + 6y = 48
6y = 48 - 24
y = 24/6
y = 4
The third solution will be (6, 3)
If there are 9 cars, i.e. at when x = 9
4(9) + 6y = 48
36 + 6y = 48
6y = 48 - 36
y = 12/6
y = 2
The fourth solution will be (9, 2)
Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)
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This is very confusing for me, please help
Answers
Answer:
Math: Deals 6710 - 9506 fire damage and combustion to the second weakest enemy and 2 random enemies.
Step-by-step explanation:
wra
Which fraction and decimal forms match the long division problem?
Answers
Answer: C
Step-by-step explanation: C
2 divided into 9 parts is 2/9.
Let's' explain this visually
Take this pizza, (image below)
Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.
Now 2/9=0.2 repeating!
This is how I got my answer sorry for the vague explanation
Which of the following is equal to the opposite of -45?
O-(-45)
O-45
O-1-451
O-145!
Answers
Step-by-step explanation:
A o option
-(-45)
hope it helps
Could yall help me PLEASE
estimate the circumference of a quarter whose diameter measures 1.205 inches.
7.6 in.
1.9 in.
2.4 in.
3,6 in.
Answers
Answer: 3.6
Step-by-step explanation:
(Not the best at math but I am an above level student)
C= pi x diameter
C= pi x 1.205
C= 3.7
NEED HELP PLEASE!!! Lionel created a scatter plot and drew a line of best fit, as shown.
What is the equation of the line of best fit that Lionel drew?
Answers
Answer: A.
Y=-2x+16
Step-by-step explanation:
You gotta find the pretty points on the line of the linear function. Then you have to find the slope (rise over run) with those pretty points. Then you have to use a coordinate (I used 6,4) to find the y intercept. Then you solve the equation, by plugging in all the numbers :) hope this helps.
William is 11 years old. One day, his granddad took him and his younger brother to a basketball game. The tickets for the game were priced at $17 for adults (`a`) and $13 for children (13 years and younger) (`c`). What is the expression for the total cost of the tickets for William’s family and what was the total cost?
Answers
Answer:
43$
Step-by-step explanation: Three tickets total.
2 tickets cost 13$ =26
1 ticket 17 = 43 total
Hope this helped! God Bless!!
The total cost of the tickets for William’s family with 1 adult and 2 children is $43.
William's age = 11 years
Price for an adult = $17
Price for a child = $13
What will be the total number of tickets be bought?The total number of tickets to be bought will be 3 i.e. William, His Granddad, and William's younger brother i.e. 1 adult ticket and 2 children tickets.
Total price = price of 1 adult ticket + price for 2 children's ticket
Total price =17+2*13
Total price =17+26
Total price =$43
Therefore, the total cost of the tickets for William’s family is $43.
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Divide. Write your answer in simplest form.
7
— /8
6
Answers
Answer:
7/64
Step-by-step explanation:
7/6÷8=7/6*1/8=7/64
Hope this helps :)
Multiply and simplify the product.
–12i × 3i
Answers
Answer:
36
Step-by-step explanation:
Which graph represents the function
f(x)=√x+3-4
Answers
Answer:
I believe it is the last option but I'm not completely sure because the pic is blurry. But if the beginning of the graph is at (-3, -4) then the last option is definitely correct.
Step-by-step explanation:
Remember h controls horizontal movement k controls vertical movements.
always remember to take the opposite of h.
;)
0.32 divided 38.9 please and thank you
Answers
Answer:
The correct answer has a lot of decimals, but the correct answer is 0.008226221. If you want to simply the alternative answer is 0.008
Step-by-step explanation:
HAVE A GOOD DAY!
please help asap what is the answer to this no links please or telling me to download it u will be reported...
Answers
The origin is where the x-axis and the y-axis intersect
How is scientific notation used in the real world?l
Answers
Answer: Scientific notation is used in the real world to make writing very large numbers, like the distance of a star from Earth or the weight of our oceans, much simpler and easier, especially when writing them in things like reports or scientific papers.
Step-by-step explanation: For example, the distance of the Sun from Neptune is somewhere around 4,500,000,000km. Writing this number takes time, and when you have to write this over and over, it wastes time, so instead, you would write 4.5 × 10⁸, which is much shorter and saves time when writing it down in a scientific report/paper many times.
Sorry for the really long explanation, I'm pretty sure just the 'Answer' bit should be fine, but you can include the 'Step-by-step explanation' bit if you want.
Hope this helps!
Jane spent $40 on flowers. Each small flower cost $2, and each large flower cost $3. Write an equation that describes the relationship between cost and number of flowers purchased, where X is the number of small flowers and Y is the number of large flowers.
Answers
Answer:
Step-by-step explanation:
he small ones cost $2 and the bigger ones cost $3. So to get the answer you will need to multiply the number of flowers with the cost. In this case 2 times x and 3 times y. x represents the small flowers and y represents the big flowers.
Answer:
2x + 3y = 40
Step-by-step explanation:
Help please I don’t understand how to do these types of problems
Answers
he mean salary of 150 employees of an organization was found to be Rs 22500 per month.Later on ,after disbursement of salary it was found that salary of two employees was wrongly entered as Rs 25760 and Rs 19590. The correct salaries were Rs 27760 and Rs 18590.Calculate the correct mean salary paid to employees .
Answers
The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532.
150 x 22,500 equals the total salary before correction, or Rs.
After rectification, the total salary equals
(150-2)*22500 + 25760 + 18590, or Rs. 339060.
Correct mean pay is equal to Rs. 339060 / 150, or Rs. 22532.
Initial reports stated that the mean wage for 150 workers was Rs. 22500 per month. Further examination revealed, however, that two employees' salary had been put incorrectly as Rs 25760 and Rs 19590, respectively. The two employees' actual pay were Rs. 27760 and Rs. 18590. The total salary before rectification was therefore 150*22,500, or Rs. 337,000. After two employees' pay were adjusted, the total salary was (150-2)*22500.The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532 (150-2)*22500 + 25760 + 18590 = Rs339060. Consequently, it was determined that Rs339060 / 150 = Rs22532 was the proper mean wage paid to employees. After correcting the two incorrectly reported salaries, the average monthly wage for the organization's employees came to Rs22532.
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The Panthers did not score more points than the Tigers. The Tigers scored fewer points than the Lions. The Lions scored fewer points than the Wolverines but more points than the Panthers. Which team scored more points, the Wolverines or the Panthers?
Answers
Answer:Wolverines
Step-by-step explanation:
The panthers < tigers Tiger 1
Tigers < Lions Lions 2
Lions< wolverines Panthers 0
Lions> Panthers Wolverines 1
Even though the lions scored more wolverines scored more than the panthers since the panthers didn't score a single point according to my calculations