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Andreas93 [3]
4 years ago
12

There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selectin

g 7 students from student council. How many possible committees can be formed?
Mathematics
2 answers:
Anarel [89]4 years ago
5 0
Since the students are to be selected at random, the concept used is Combination. The combination is 20C7 which means that "combination of 20 taken 7". The numerical value of the combination is 77520. Thus, there are 77520 ways of choosing the members of the student council. 
kolezko [41]4 years ago
5 0

Answer:

77520

Step-by-step explanation:

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(1/3) + (1/2)

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Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)
MakcuM [25]

The average value of f over the region D is 243/4

To answer the question, we need to know what the average value of a function is

<h3>What is the average value of a function?</h3>

The average value of a function f(x) over an interval [a,b] is given by

\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx

Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).

x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9

So, \frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ =  \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0}  \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\=  \frac{81}{2} X3 X \frac{1}{2} \\=  \frac{243}{4}

So, the average value of f over the region D is 243/4

Learn more about average value of a function here:

brainly.com/question/15870615

#SPJ1

8 0
2 years ago
Solve 2(x+3)3/2=54 x = <br>show your work
hjlf

Answer:

x=15

Step-by-step explanation:

Step 1: Multiply both sides by 2.

Step 2: Simplify both sides of the equation.

6x+18=108

Step 3: Subtract 18 from both sides.

6x+18−18=108−18

6x=90

Step 4: Divide both sides by 6.

x=15

6 0
3 years ago
ecn 221 The sodium content of a popular sports drink is listed as 206 mg in a 32-oz bottle. Analysis of 14 bottles indicates a s
spayn [35]

Answer:

H_{0}: \mu = 206\text{ mg}\\H_A: \mu \neq 206\text{ mg}

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =  206 mg

Sample mean, \bar{x} = 217.5 mg

Sample size, n = 14

Sample standard deviation, s = 14.9 mg

Claim:

The mean sodium content for the sports drink is not 206 mg. It is different than 206 mg.

Thus, we design the null and the alternate hypothesis

H_{0}: \mu = 206\text{ mg}\\H_A: \mu \neq 206\text{ mg}

We use two-tailed t test to perform this hypothesis.

     

3 0
3 years ago
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