In a school annual day function a variety programme was organised. It was planned that
there would be 3 short plays, 6 recitals and 4 dance programmes. However, the chief
guest invited for the function took much longer time than expected to finish his speech. To
finish in time, it was decided that only 2 short plays, 4 recitals and 3 dance programmes
would be perfomed, How many choices were available to them
Answers
Answer:
(a) 65318400
(b) 1080
(c) 311040
Step-by-step explanation:
I think you forgot to put the questions
(a) if the programmes can be perfomed in any order ?
(b) if the programmes of the same kind were perfomed at a stretch?
(c) if the programmes of the same kind were perfomed at a strech and considering the order of performance of the programmes of the same kind?
if you need the step by step solutions, visit
https://brainly.in/textbook-solutions/q-20-school-annual-day-function-variety-programme-3#q-20-school-annual-day-function-variety-programme-2
The number of choices available to them were \(65318400\) , \(1080\) and \(311040\).
What is combination ?Combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Combination \((^nC_{r} ) = \frac{n ! }{r!(n-r)!}\)
1.We have, to perform \(2\) short plays, \(4\) recitals and \(3\) dance programmes in any order.
So,
The number of ways to select \(2\) short plays out of \(3\) using the mentioned formula,
\((^3C_{2} ) = \frac{3 ! }{2!(3-2)!}\)
\(= \frac{3 *2*1 }{2*1*1}=3\)
Now,
The number of ways to select \(4\) recitals out of \(6\) using the mentioned formula,
\((^6C_{4} ) = \frac{6 ! }{4!(6-4)!}\)
\(= \frac{6*5*4 ! }{4!*2*1} =15\)
Now,
The number of ways to select \(3\) dance programs out of \(4\) using the mentioned formula,
\((^4C_{3} ) = \frac{4 ! }{3!(4-3)!}\)
\(= \frac{4*3 ! }{3!*1!}=4\)
Now,
The number of ways to arrange \(9\) program using the mentioned formula,
\((^9P_{9} ) = \frac{9 ! }{(9-9)!}\)
\(=9!\)
\(=9*8*7*6*5*4*3*2*1=362880\)
So, the total number of ways by multiplying the values
i.e. \(362880*4*15*3=65318400\)
So, the total number of ways to perform the programs are \(65318400\) .
2.We have, to perform the programmes of the same kind.
So,
The number of ways to arrange \(3\) different program using the mentioned formula,
\((^3P_{3} ) = \frac{3 ! }{(3-3)!}=3!=3*2*1=6\)
So, the total number of ways by multiplying the values,
i.e. \(6*4*15*3=1080\)
3.We have to perform, the programmes of the same kind and considering the order of performance of the programmes of the same kind.
So,
The number of ways to select \(2\) short plays out of \(3\) using the mentioned formula,
i.e. \((^3P_{2} ) = \frac{3 ! }{(3-2)!}=\frac{3!}{1!} =3*2=6\)
Now,
The number of ways to select \(4\) recitals out of \(6\) using the mentioned formula,
\((^6CP_{4} ) = \frac{6 ! }{(6-4)!}=\frac{6!}{2!} =\frac{6*5*4*3*2!}{2!} =360\)
Now,
The number of ways to select \(3\) dance programs out of \(4\) using the mentioned formula,
\((^4P_{3} ) = \frac{4 ! }{(4-3)!}=\frac{4!}{1!}=4*3*2=24\)
So,
The number of ways to arrange \(3\) different program using the mentioned formula,
\((^3P_{3} ) = \frac{3 ! }{(3-3)!}=3!=3*2*1=6\)
So, the total number of ways by multiplying the values,
i.e. \(6*24*360*6=311040\)
Hence, we can say that the number of choices available to them were \(65318400\) , \(1080\) and \(311040\).
To know more about Combination click here
https://brainly.com/question/9283678?
#SPJ3
Related Questions
Sofia wrote three numbers between 0.77 and 0.78 what numbers Sofia
Answers
Answer:
0.771, 0.772, 0.773
Step-by-step explanation:
three numbers between 0.77 and 0.78
0.77 = 0.770
and
0.78 = 0.780
So,
0.770, 0.771, 0.772, 0.773, 0.780
= 0.77, 0.771, 0.772, 0.773, 0.78
A relation that shows that one expression equals another expression is a(n) __________. equation function rate inequality
Answers
Answer:
Equation.
Step-by-step explanation:
The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.
Whereas if the two equation are not equal then it is known as inequality.
Thus, the given statement is correctly filled with equation.
A borrower wants to take a loan with a maximum effective monthly rate of 1%. What is the maximum APR with quarterly compounding that the borrower will accept from a lender?
Answers
The maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.
How to calculate APR?To convert the maximum effective monthly rate of 1% into an APR with quarterly compounding, we can use the formula:
\(APR = [(1 + \dfrac{r}{n})^n - 1] \times 4\)
Where r is the effective monthly rate and n is the number of compounding periods per year. In this case, we want to find the maximum APR with quarterly compounding that the borrower will accept, so we can substitute r = 1% and n = 3:
\(APR = ((1 + \dfrac{0.01}{3})^3 - 1) \times 4\)
APR = (1.0100333³ - 1) x 4
APR = 0.04033 x 4
APR = 0.16132 or 16.132%
Therefore, the maximum APR with quarterly compounding that the borrower will accept from a lender is 16.132%.
To know more about APR follow
https://brainly.com/question/2772156
#SPJ9
if you walk 200 meters in 1 minute, 400 meters in 4 minutes and 800 meters in 10 minutes find your average velocity for the whole walk
Answers
First, calculate each velocity:
\(v=\frac{distance}{time}\)so:
\(v1=\frac{200m}{1min}\)\(v2=\frac{400m}{4min}=\frac{100m}{min}\)\(v3=\frac{800m}{10min}=\frac{80m}{min}\)Now calculate the average between the 3 velocities:
\(av\text{ }v=\frac{200+100+80}{3}=\frac{126.67m}{min}\)The answer is 126.67 m per minute.
Identify the greatest common factor.
8y, -12x, 4xy
Answers
The greatest common factor, GCF, of 8y, -12x, and 4xy is 4
Determining the Greatest common factor (GCF) of expressionsFrom the question, we are to determine the greatest common factor of the given expressions.
The given expressions are 8y, -12x, and 4xy
To determine the greatest common factor, we will express each of the expressions as a product of their factors.
8y = 2 × 2 × 2 × y
-12x = 2 × 2 × 3 × -x
4xy = 2 × 2 × x × y
From above, we can observe that the greatest common factor is
2 × 2
= 4
Hence, the greatest common factor is 4
Learn more on Determining the greatest common factor here: https://brainly.com/question/28180346
#SPJ1
In how many ways can a class of nineteen students be divided into 3 sets so that 4 students are in the first set, 6 students are in the second set and nine students are in the third set?
Answers
Answer:
216
Step-by-step explanation:
5,10,15,20,25 what is the common difference
Answers
Answer:
The common difference in the given sequence is 5.
Step-by-step explanation:
The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15
What's 3.2rounded to the nearest tenth
Answers
Please look at the graphs in the photo. Thank you!
Answers
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
Read more on reflection here: brainly.com/question/27912791
#SPJ1
Write the letter of the definition next to the matching word as you work through the
lesson.
Answers
Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.
What is Hypotenuse?In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.
According to question:Altitude: In a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.Geometric mean: for two positive numbers, a and b, the positive number x that satisfies a/x = x/b.Hypotenuse: The side of a right triangle that is opposite the right angle and is always the longest side of the triangle.Leg: In a right triangle, either of the two sides forming the right angle.One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.
The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.
To know more about hypotenuse visit:
https://brainly.com/question/11958431
#SPJ1
There is a playground behind Jayden’s school where kids go outside for recess. The playground is 85 feet wide and 236 feet long. Jayden is curious if the playground has an area of more or less than 20,000 square feet. Does it? Show and explain how you know.
Answers
Answer:
Yes
Step-by-step explanation:
A = L x W
A = 236 x 85
A = 20,060
20,060 is more than 20,000 so yes
A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
A. 9
B. 4/3
C. 1/4
D. 3/4
Please select the best answer from the choices provided.
Answers
8+3+1=12
1-3/12=3/4
Find the area of the figure. 5in 2in 4in 5in
Answers
Answer: Your answer is 23.5in²
Hope it helped :D
Good Luck!
Find the average of the following numbers: 55.1, 67.9, 59.2, 64.1, 61.8, 62.7. Round
your answer to one decimal place *
Your answer
Answers
Answer:
61.8
Step-by-step explanation:
\( \frac{55.1 + 67.9 + 59.2 + 64.1 + 61.8 + 62.7}{6} \)
f(x)= a(x+p)² +q and g(x)= 0 3 3.1 x + p 1. The turning point of f is (1;4) and the asymptotes of g intersect at the turning point of f. Both graphs cut the y-axic at 3. 3.2 3.3 3.4 a 10 g +94 (1:4) Determine the equation of f Determine the equation of g Determine the coordinates of the x-intercept of g For which values of x will f(x) ≥ g(x)? [9]
Answers
Step-by-step explanation:
Let's solve the given questions step by step:
1. Determine the equation of f:
From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:
f(x) = a(x + p)^2 + q
Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:
4 = a(1 + p)^2 + q
This gives us one equation involving a, p, and q.
2. Determine the equation of g:
The equation of g is given as g(x) = 0.3x + p1.
3. Determine the coordinates of the x-intercept of g:
The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.
Setting g(x) = 0, we can solve for x:
0 = 0.3x + p1
-0.3x = p1
x = -p1/0.3
Therefore, the x-intercept of g is (-p1/0.3, 0).
4. For which values of x will f(x) ≥ g(x)?
To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.
f(x) = a(x + p)^2 + q
g(x) = 0.3x + p1
We need to find the values of x for which f(x) ≥ g(x):
a(x + p)^2 + q ≥ 0.3x + p1
Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.
To summarize:
We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).
For each ordered pair (x, y), determine whether it is a solution to the inequality y≤0.
(8,-43)
(4.-22)
(-3,25)
(-7,45)
Is it a solution?
Answers
Answer:
(8,-43)
(4,-22)
Step-by-step explanation:
In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.
For example:
(4,-22)
x=4 ; y=-22
Plug y into the inequality
y≤0
-22≤0
Since the statement is true, I know that (4,-22) must be a solution to the inequality.
Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
Answer:
Step-by-step explanation:
To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.
Let's check each ordered pair:
(8, -43):
The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.
(4, -22):
The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.
(-3, 25):
The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.
(-7, 45):
The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.
So, the solutions to the inequality y ≤ 0 are:
(8, -43) and (4, -22).
5 = g/8 g = what is the g
Answers
I run 3 miles in 20 minutes. What was my average speed in miles per hour?
Answers
Step by step
To get minutes to equal one hour, multiply by 3 ( 20 minutes x 3 = 60 minutes or 1 hour)
If you multiply 20 x 3, you will do the same to the miles
3 miles x 3 = 9 miles
Now we have 9 miles per 1 hour
Problem solved
The volume of a sphere is 4500cm. What is the surface area of the sphere to the nearest whole number?
Answers
The surface area of the sphere, to the nearest whole number, is 1318 cm².
How to determine the surface area of a sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
The surface area of a sphere is expressed as:
SA = 4πr²
Where r is the radius of the sphere and π is the mathematical constant pi.
Given that the volume V is 4500 cm³.
First, we solve for the radius:
Volume = (4/3)πr³
4500 = (4/3)πr³
4500 × 3 = 4πr³
13500 = 4πr³
r³ = 13500/4π
r = ∛( 13500/4π )
Now that we have the radius, we can calculate the surface area of the sphere using the formula:
SA = 4πr²
Substituting the radius we found:
SA = 4 × π × ∛( 13500/4π )²
SA = 1318 cm²
Therefore, the surface area is approximately 1318 cm².
Learn more about volume of hemisphere here: brainly.com/question/22886594
#SPJ1
By using a problem-solution structure, the author is able to show readers how people are hurting the planet. The structure also shows how we can change and what we can do to help solve the problems we have caused. It inspires people to take action
Answers
Answer:
One of the problems humans have made is a large amount of pollution.
And so some of the ways we can fix this is;
1- Using electric cars.
2- Using reusable packaging.
3- For the final one you could use stuff that easily and quickly to break down naturally materials.
Step-by-step explanation:
500 is what percent of 125?
Answers
Answer:
400
Step-by-step explanation:
Solution for 500 is what percent of 125:
500:125*100 =
(500*100):125 =
50000:125 = 400
Now we have: 500 is what percent of 125 = 400
Question: 500 is what percent of 125?
Percentage solution with steps:
Step 1: We make the assumption that 125 is 100% since it is our output value.
Step 2: We next represent the value we seek with \(x%\).
Step 3: From step 1, it follows that $100%=125$.
Step 4: In the same vein, $x%=500$.
Step 5: This gives us a pair of simple equations:
100%=125(1)
x%=500(2)
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left-hand side) of both equations have the same unit (%); we have
\(\frac{100\%}{x\%}=\frac{125}{500}\)
Step 7: Taking the inverse (or reciprocal) of both sides yields
\(\frac{x\%}{100\%}=\frac{500}{125}\)
\(\Rightarrow x=400\%\)
Therefore, 500 is 400% of 125
Hope this answer helps and answers your question! Have a great day/night!
Please help me with the simplifying
Answers
The key here is to not worry too much and just follow PEMDAS.
Here we have the expression \((5\cdot 7)^2\). Following PEMDAS, we complete the expression inside the parentheses first, or \(5\cdot 7 = 35\). This gives us \((35)^2\) or just \(35^2.\)
Hope this helps.
What is the product?
(-2d^2+s) (5d^2-6s)
A.) -10a^4+17a^2s-6s^2
B.) -10a^4+17a^4s-6s^2
C.) -10a^4-7a^2s-6s^2
D.) -10a^4+17a^2s+6s^2
Those are the only options as answers
Answers
Answer:
None of the above the answer is −
10d4+17sd2−6s2
Step-by-step explanation:
3. Compute the derivatives of the following functions. Do not simplify.
a) f(x)=tanx/e^3
b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)
Answers
Answer:
A im sure
Example
hope itz helpppp
help anyone please??
Answers
Answer:
I believe 3 ways based on what I see in the picture.
HELP, ILL GIVE BRAINLIEST BUT HELP ASAP WITH THIS!!
Answers
Answer:
proportional
Step-by-step explanation:
Question 1) A 6-pack of DVDs costs $10.80. What is the unit price? *
5 points
$1.08
$64.08
$64.80
$1.80
Answers
Answer:
the answer will might be A yeah I'm sure the answer is A
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
For more questions on algebraic expression:
https://brainly.com/question/29333936
#SPJ8
Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
The answers I have to choose from are:
A. When 7 3/8 is multiplied by a number greater than 1, the product is more than 7 3/8
B. When 7 3/8 is multiplied by a number greater than 1, the product is less than 7 3/8
C. When 7 3/8 is multiplied by a number less than 1, the product is more than 7 3/8
D. When 7 3/8 is multiplied by a number less than 1, the product is less than 7 3/8.
Answers
The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Explain about the term mixed fractions:Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.
Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.
We can convert the two fractions to decimal form in order to compare them.
7.375 is equivalent to 7 3/8, and
4/5 is equivalent to 0.8.
7.375 multiplied by 0.8 results in:
7.375 × 0.8 = 5.9
Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.
Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Know more about the term mixed fractions:
https://brainly.com/question/1055953
#SPJ1
How do I add fractions with different denominators?
Answers
Find the least common multiple (LCM) of the denominators. This is the smallest number that both denominators can divide into evenly.
Convert each fraction so that its denominator is the LCM found in step 1. To do this, you multiply both the numerator and denominator of each fraction by the same number.
Add the numerators of the two fractions together.
Simplify the resulting fraction, if possible, by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by that factor.
Here's an example:
Suppose you want to add 1/4 and 1/6.
Step 1: The LCM of 4 and 6 is 12.
Step 2: Convert the fractions to have a denominator of 12:
1/4 = 3/12 (multiply numerator and denominator by 3)
1/6 = 2/12 (multiply numerator and denominator by 2)
Step 3: Add the numerators:
3/12 + 2/12 = 5/12
Step 4: Simplify the fraction, if possible:
5/12 cannot be simplified further, so that is the final answer.
So, 1/4 + 1/6 = 5/12.