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lakkis [162]
3 years ago
6

There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same sta

te. b How many ways can we choose a Senator from a chosen state? c How many ways can the 3-Senator committee be formed such that no two Senators are from the same state?
Mathematics
1 answer:
Morgarella [4.7K]3 years ago
6 0

Answer:

a) rCn = 1176

b) 2352

Step-by-step explanation:

a)Each committee should be formed with 3 members ( no two members could be of the same state) then

Let´s  fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then

rCn =  n! / (n - r )! *r!

rCn =  49!/ (49 - 2)!*2!

rCn =  49*48*47! / 47!*2!

rCn = 49*48 /2

rCn = 1176

So we can choose in 1176 different ways a senator for a given state

b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.

1176*2 = 2352

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kaheart [24]

Answer:

4x-15

Step-by-step explanation

You just multiply -5 and -3 to simplify this.

7 0
3 years ago
If ac =14 find the value of x then find ab and bc
Igoryamba

Answer:

If B is between A and C, AB = x, BC = 2x + 2, and AC = 14, find the value of x. Then find AB and BC.

Step-by-step explanation:

AB=x

BC = 2x + 2BC=2x+2

AC =14AC=14

Required

Determine x, AB and BC.

Since B is between A and C;

AB + BC = ACAB+BC=AC

Substitute x for AB; 2x + 2 for BC and 14 for AC

x + 2x + 2 = 14x+2x+2=14

3x + 2 = 143x+2=14

Collect Like Terms

3x = 14 - 23x=14−2

3x = 123x=12 '

x = \frac{12}{3}x=

3

12

x = 4x=4

Substitute 4 for x in

AB = xAB=x

BC = 2x + 2BC=2x+2

AB = 4AB=4

BC = 2(4) + 2BC=2(4)+2

BC = 8 + 2BC=8+2

BC = 10BC=10

3 0
2 years ago
If y(x) = 4x, what is x when y(x) = 4? <br><br> a.2<br> b.1.<br> c.4<br> d.0
zavuch27 [327]

Answer:

b. 1

Step-by-step explanation:

Step 1: Define

y(x) = 4x

y(x) = 4

Step 2: Substitute and Evaluate

4 = 4x

x = 1

8 0
3 years ago
If a man take one and a half mins to paint a door how much doors can he paint in seven half hour
sashaice [31]

Answer:

300 doors.

Step-by-step explanation:

1.5 minutes for 1 door.

7.5 hours for 300 doors.

7.5 hours = 450 minutes.

\frac{450}{1.5}=300

7 0
3 years ago
The vertices of a triangle are (-1,3) (6,3) and (-1,-4)
Travka [436]

Answer:

24.5 unit²

Step-by-step explanation:

Area of ∆

= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |

= ½ | -7 - 42 |

= ½ | - 49 |

= ½ (49)

= 24.5 unit²

<u>Method 2:</u>

Let the vertices are A, B and C. Using distance formula:

AB = √(-1-6)² + (3-3)² = 7

BC = √(-6-1)² + (-4-3)² = 7√2

AC = √(-1-(-1))² + (4-(-3))² = 7

Semi-perimeter = (7+7+7√2)/2

= (14+7√2)/2

Using herons formula:

Area = √s(s - a)(s - b)(s - c)

here,

s = semi-perimeter = (14 + 7√2)/2

s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2

s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2

s - c = (14+7√2)/2 - 7 = (7 + √2)/2

Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²

3 0
2 years ago
Read 2 more answers
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