an environmental organization has 32 members. each member will be placed on exactly 1 of 4 teams. each team will work on a different issue. the first team has 9 members, the second team has 6 members, the third team has 7 members, and the fourth has 10. in how many ways can these teams be formed?
Answers
Based on the team combination, the number of ways the team can be formed is 861,029,868,672 ways.
For the first team with 9 members, we need to select 9 members out of 32, which can be done in C(32, 9) ways.
Similarly, for the second team with 6 members, we need to select 6 members out of the remaining 32 - 9 = 23 members, which can be done in C(23, 6) ways.
For the third team with 7 members, we need to select 7 members out of the remaining 23 - 6 = 17 members, which can be done in C(17, 7) ways.
Finally, for the fourth team with 10 members, we need to select 10 members out of the remaining 17 - 7 = 10 members, which can be done in C(10, 10) ways.
Total number of ways = C(32, 9) × C(23, 6) × C(17, 7) × C(10, 10)
Using the combination formula C(n, r) = n! / (r! * (n - r)!), we can calculate the combinations:
Evaluating these expressions, we find:
C(32, 9) = 32,468,436
C(23, 6) = 1,352,128
C(17, 7) = 19,448
C(10, 10) = 1
Now, we can calculate the total number of ways:
Total number of ways = 32,468,436 × 1,352, 128 × 19,448 × 1
Total number of ways ≈ 861,029,868,672
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Related Questions
Which rays are part of line CF?
Answers
Answer:
A C and A F
Step-by-step explanation:
A C goes from A to C
A F goes from A to F
12 students are excellent students, they make up 37. 5% of the class. How many students is in the entire class?
Answers
If 12 students are excellent students and they make up 37.5% of the class, the total number of students in the class can be found using a proportion. The result is 32 students in the entire class.
If 12 students are excellent students and they make up 37.5% of the class, we can use the following proportion to find the total number of students in the class:
Number of excellent students / Total number of students = Percentage of excellent students as a decimal
Substituting the given values into the equation, we get:
12 / Total number of students = 0.375
To solve for the total number of students, we can isolate the variable by multiplying both sides of the equation by the reciprocal of 0.375, which is 2.6667 (rounded to four decimal places):
12 / 0.375 = Total number of students
Total number of students = 32
Therefore, there are 32 students in the entire class.
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(Likelihood MC)
The teacher gave a true and false quiz where P(true) = 0.7 for each question. Interpret the likelihood that the first question will be true.
Likely.
Unlikely.
Equally likely and unlikely.
This value is not possible to represent probability of a chance event.
Answers
The likelihood that the first question will be true in a true and false quiz where P(true) = 0.7 for each question is likely.
With a probability of 0.7 assigned to each question being true, there is a higher chance that the first question will be true compared to it being false.
However, it's important to note that this does not guarantee that the first question will be true, as probability represents the likelihood of an event occurring, not certainty.
Antonio is going to make a new summer drink. He needs 1/3 of a glass of orange juice and 2/4 of a glass of lime juice. The rest is water. To make one drink, what fraction of the glass will be water?
Answers
Answer:
1/6!!!! C
Step-by-step explanation:
Find common denominater. 12.
1/3 goes to 4/12.
2/4 goes to 6/12.
6/12+4/12 is 10/12
Remaining is 2/12!
That is 1/6 simplified!
a. 3/4 b.4/7 c.1/6 d. 5/
The model below represents an equation. Which value of x makes the equation
true?
Answers
Answer:
1,1,1,1
Step-by-step explanation:
I believe this is right
When a problem is said to be decidable or undecidable give an example of an undecidable problem?
Answers
Example of an undecidable problem is given by the problems in the system created by computer viruses.
What is decidable and undecidable problems?According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.
A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.
When is a problem said to be decidable or undecidable?
whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.
If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.
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If g(x) = x^2 + 3, find g(4).
11 19 16 8
Answers
Answer:
19
Step-by-step explanation:
g(x) = x^2 +3
substituing x for 4,
g(4) = 4^2 + 3
g(4) = 16 + 3
g(4) = 19
I put it in quadratic form but i don’t know where to go from there. I got X = -1/20y^2 + 4y +12
Answers
ANSWER:
p = -5
STEP-BY-STEP EXPLANATION:
We have that the form of the equation of the parabola is the following:
\((y-k)^2=4p\cdot(x-h)\)In this case we have the following equation, we convert it into its correct form, just like this:
\(\begin{gathered} \mleft(x-8\mright)=-\frac{1}{20}\cdot\mleft(y+2\mright)^2 \\ (y+2)^2=-20\cdot(x-8) \end{gathered}\)We compare and calculate the value of p, just like this:
\(\begin{gathered} 4p=-20 \\ p=-\frac{20}{4} \\ p=-5 \end{gathered}\)After a 40% markup, a tablet sells for $245. 0. What was the original price of the tablet?.
Answers
Answer: $175
Step-by-step explanation:
We can model this using an equation:
245 = 1.4x
We multiply the original price, x, by 1.4, because x must be 40% more to be 245.
From there we can simply solve for X.
245 = 1.4x
Divide by 1.4
175 = x
The measure of 3 angles of a triangle are 2x, 3x, and (x +60) what is the value of x?
Answers
Answer: angle x= 20 degrees
Step-by-step explanation: sum of angles in triangle is 180 degrees.
You count 2x + 3x +(x+60) = 180
6x=120
what is the step-by-step answer to
-3(X + 2)=-18
Answers
-3x - 6 = -18
-3x = -12
-x = -4
x = 4
Answer:
x = 4Step-by-step explanation:
Simplify both sides of the equation:−3 (x+2) = −18
(−3) (x) + (−3) (2) = −18 (Distribute)
−3x + −6 = −18
−3x −6 = −18
Add 6 to both sides:−3x −6 +6 = −18 + 6
−3x= −12
Divide both sides by -3:−3x/−3 = −12/−3
x = 4
The equations r = 5, x2 + y2 = 25, and x = 5 sin 3t, y = 5 cos 3t (0 ≤ t ≤ 2π) all have the same graph. Determine whether the statement is true or false.
Answers
The statement is true.Since all three equations represent a circle with radius 5 centered at the origin (0,0), they have the same graph.
Let's analyze each equation:
r = 5: This equation represents a circle with radius 5 centered at the origin (0,0). The points on this circle satisfy the equation x^2 + y^2 = 5^2 = 25.
x^2 + y^2 = 25: This equation also represents a circle with radius 5 centered at the origin (0,0). Any point that satisfies this equation lies on the circle with radius 5.
x = 5sin(3t), y = 5cos(3t): These equations represent parametric equations for a circle with radius 5 centered at the origin (0,0). The parameter t varies from 0 to 2π, tracing the entire circumference of the circle.
The x-coordinate is given by x = 5sin(3t), and the y-coordinate is given by y = 5cos(3t). As t varies from 0 to 2π, the point (x, y) traces the circle with radius 5.
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what is the inverse of the function f(x)=2x^2-3
Answers
Can some help someone help me
Answers
Answer:
they have different y-intercepts. the top one will be at pos 45 and the other one will be at -10
Step-by-step explanation: they parallel just far apart on the y int
any luck of help? this is rlly important just answer the ones u know leave the ones u don't I'll still be brainlisting !:)
Answers
Answer:
Hajj not connects us with khana kaeba.
Help, god help. I need to know ASAP in 9 days before april 1 HELP. One of the bases of a trapezoid has length $10$, and the height of the trapezoid is $4$. If the area of the trapezoid is $36$, then how long is the other base of the trapezoid?
Answers
The other base of the trapezoid is 8 units long.
Let's denote the other base of the trapezoid as 'x'. The formula for calculating the area of a trapezoid is given by A = (1/2)(b1 + b2)h, where b1 and b2 represent the lengths of the bases and 'h' represents the height. We are given that the length of one base (b1) is 10 units, the height (h) is 4 units, and the area (A) is 36 square units.
Using the formula for the area, we can plug in the given values: 36 = (1/2)(10 + x)(4). Simplifying the equation, we get 36 = (5 + 0.5x)(4). Further simplification yields 36 = 20 + 2x. By subtracting 20 from both sides of the equation, we obtain 16 = 2x. Dividing both sides by 2 gives us x = 8.
Therefore, the other base of the trapezoid is 8 units long.
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Write an equation in slope-Intercept form for the line with slope 2/5 and y- ntercept - 3 .
Answers
Answer:
y = \(\frac{2}{5}\) x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = \(\frac{2}{5}\) and c = - 3 , then
y = \(\frac{2}{5}\) x - 3 ← equation of line
Answer:
formula = y = mx + b
y = 2/5x - 3
Step-by-step explanation:
What is 67 kg in stones and pounds?
Answers
Kilograms (kg) is a unit of mass that is commonly used in the metric system. However, in some countries, such as the United Kingdom and the United States, the customary unit of measurement for weight is stone and pounds.
67 kg in stones is equivalent to approximately 147.71 pounds.
It's important to note that while the conversion from kilograms to stone and pounds is straightforward, the conversion is not exact due to rounding. However, this difference is generally small and can be ignored for most practical purposes.
Overall, understanding the conversion from kilograms to stone and pounds can be useful for students who are studying or traveling between countries that use different units of measurement for weight. Additionally, the process of converting from one unit of measurement to another can help reinforce important mathematical skills, such as division and rounding.
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A triangle has side lengths 7, 17, and x. Fill in the inequality for the possible
lengths of x below.
Answers
Answer:
9 < x < 25
Step-by-step explanation:
Write an equation of the line in slope intercept form
Answers
Answer:
Step-by-step explanation:
(0 - 4)/(0 + 3) = -4/3
y - 0 = -4/3(x - 0)
y = -4/3x
Fish management researchers estimate that approximately 60% of spawning Atlantic salmon are female (Sutterby and Greenhaigh, 2005). Suppose that a group of students takes a random sample of 10 salmon from a river where salmon are spawning. The number of females in the sample follows a binomial distribution with = 10 and p=0.60, where nequals the number of trials and p equals the probability of success on any given trial. Which histogram shows the distribution of the number of females in samples of size 10 when the population proportion of females is 0.00
Answers
Based on the given information, we can infer that you're looking for the histogram that shows the distribution of the number of females in samples of size 10 when the population proportion of females is 0.60.
To create this histogram, we'll use the binomial distribution with n=10 trials and p=0.60 success probability.
Step 1: Identify the range of possible outcomes
The range of possible outcomes for the number of females in a sample of 10 salmon can be from 0 to 10.
Step 2: Calculate the probabilities for each outcome
Using the binomial distribution formula, calculate the probability of each outcome from 0 to 10 females. The formula is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Step 3: Create the histogram
Plot the probabilities for each outcome (number of females) on the x-axis and their respective probabilities on the y-axis. This will give you a histogram that represents the distribution of the number of females in samples of size 10 when the population proportion of females is 0.60.
Note: As you didn't provide any specific histograms for comparison, we can't tell you which one matches this description. However, the explanation above should help you understand how to create and interpret the correct histogram.
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expand and simplify 3(x+3) - 2(x+2)
Answers
Step-by-step explanation:
3(x+3) - 2(x+2) =
3x + 9 - 2x - 4 =
x + 5
always remember the rules when combining signs and operations (therefore it is -4 at the end after doing the multiplications) :
++ = +
+- = -
-+ = -
-- = +
Explain what the intercepts mean in terms of the context and how to find them.
Answers
Answer:
Intercepts in terms of graphing are considered to be points at which a function crosses an axis. In the standard x and y graph (the Cartesian coordinate grid), one would find the intercepts by simply plugging in the value of 0 for either the x or the y to find either the y or x intercept respectively. For example, to find the y-intercept, you want to find (0,y) and to find the x-intercept, you want to find (x,0).
Cheers.
Riddle: The more you take the more you leave behind you. What is the answer?
Answers
Answer:
Footsteps
Step-by-step explanation:
When you take footsteps, you leave them behind as well.
For the second application, 3.2 MB has been downloaded. How much is left to download?
Answers
The amount of megabytes left to download is 6.8 mb
How to illustrate the expression?Mathematical operations include addition, subtraction, multiplication, and division. The expression x + y, for instance, consists of the terms x and y with an addition operator in between them.
In this situation, John wants to download an two applications that are 10 MB and the second application, 3.2 MB has been downloaded.
The application left to download will be:
= Total mb - mb download
= 10 - 3.2
= 6.8 mb
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Complete question
John wants to download an two applications that are 10 MB. For the second application, 3.2 MB has been downloaded. How much is left to download?
Three teachers shared 4/5 of a flat paper that was donated to the school. what fraction of the flat paper did each teacher receive
Answers
A math textbook has a length of 22 cm, a width of 27 cm, and a height of 3.5
cm. A science textbook has a length of 21 cm, a width of 27 cm, and a height
of 4 cm.
Which textbook has a greater volume?
OA. The science textbook, with a volume of 2376 cm³
OB. The math textbook, with a volume of 2464 cm³
OC. The math textbook, with a volume of 2079 cm³
OD. The science textbook, with a volume of 2268 cm³
Answers
The science textbook has a greater volume than the math textbook, so option D is correct, the science textbook, with a volume of 2268 cm³.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Using this formula, we can calculate the volumes of the math and science textbooks:
Math textbook:
V = 22 cm × 27 cm × 3.5 cm
= 2079 cm³
Science textbook:
V = 21 cm × 27 cm × 4 cm
= 2268 cm³
Therefore, the science textbook has a greater volume than the math textbook, so option D is correct, the science textbook, with a volume of 2268 cm³.
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I need help and I want to see if it’s none because I got 1+3-1+3
Answers
I need help please. I’m really desperate……….
Answers
Answer:
X=8
Step-by-step explanation:
Given that the Area is 36ft^2, and the formula for calculating the area of a triange is:
\(a_{t} =h_{b}b/2\)
we have:
\(36 = \frac{(x+1)*x}{2}\)
we can start solving for x through the quadratic formula, but that will take long.
Instead, we can try replacing x by some numbers.
\(36*2=(x+1)*x\)
\(72=(x+1)*x\)
After a while,
\(72=(8+1)8\\\\72=9*8\\\\72=72.\)
We find that x=8.
IMPORTANT: X can also be -9 in this case. But a negative measurement doesn't make sense in this context, I would say that x=8 in this problem.
The perimeter of a rectangular picture frame is 120 inches. The length of the picture frame is 10 inches more than the width. Find the length and width of the picture frame.
Answers
Answer:
Length is 35 width is 25
Step-by-step explanation: