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e-lub [12.9K]
3 years ago
5

The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How man

y different teams made up of two girls and two boys could be chosen?
Mathematics
1 answer:
melamori03 [73]3 years ago
7 0

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

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The linear function f(x) = 0.9x + 79 represents the average test score in your math class, where x is the number of the test tak
Levart [38]

Given:

The linear function for average test score in your math class is

f(x)=0.9x+79

where x is the number of the test taken.

The linear function g(x) in the given table represents the average test score in your science class, where x is the number of the test taken.

To find:

Part A: The test average for your math class after completing test 2.

Part B: The test average for your science class after completing test 2.

Part C: Which class had a higher average after completing test 4?

Solution:

Part A:

We have,

f(x)=0.9x+79

Put x=2 in the above function, to find the test average for your math class after completing test 2.

f(2)=0.9(2)+79

f(2)=1.8+79

f(2)=80.8

Therefore, the test average for your math class after completing test 2 is 80.8.

Part B:

From the given table it is clear that g(x) =79 at x=2.

Therefore, the test average for your science class after completing test 2 is 79.

Part C:

Put x=4 in f(x), to find the test average for your math class after completing test 4.

f(4)=0.9(4)+79

f(4)=3.6+79

f(4)=82.6

From the table it is clear that the value of g(x) is increased by 1 as x is increased by 1. So, the value of function g(x) at x=4 must be 1 more than 80.

g(4)=81

It is clear that,

82.6>81

Therefore, math class had a higher average after completing test 4.

3 0
3 years ago
Solve the system by graphing.
igor_vitrenko [27]

Answer:

Hi There the correct answer is {x,y} = {-1,-10}  

 

System of Linear Equations entered :

  [1]    3x - y = 7

  [2]    4x - 2y = 16

Graphic Representation of the Equations :

   y + 3x = 7        -2y + 4x = 16  

 

 

Solve by Substitution :

// Solve equation [1] for the variable  y  

 

 [1]    y = 3x - 7

// Plug this in for variable  y  in equation [2]

  [2]    4x - 2•(3x-7) = 16

  [2]    -2x = 2

// Solve equation [2] for the variable  x  

  [2]    2x = - 2  

  [2]    x = - 1  

// By now we know this much :

   x = -1

   y = 3x-7

// Use the  x  value to solve for  y  

   y = 3(-1)-7 = -10  

Solution :

{x,y} = {-1,-10}  

Hope it helps!

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Answer:

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Step-by-step explanation:

If you divide 52 by 65 you will get a decimal, then multiply by 100% to get the equivalent.

52/65 = 0.8

0.8 x 100 = 80%

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2 years ago
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box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box (in cm) that minimize the am
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Answer:

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Step-by-step explanation:

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The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

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Answer:

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