Find the number of ways that 9 people can be divided into 2 groups such that the first group has 5 people and the second group has 4 people.

Answers

Answer 1

Answer:

126 ways

Step-by-step explanation:

To find the number of ways to divide 9 people into two groups, with 5 people in the first group and 4 people in the second group, we can use the concept of combinations.

The number of ways to choose 5 people out of 9 to be in the first group is given by the combination formula:

C(9, 5) = 9! / (5! * (9 - 5)!) = 9! / (5! * 4!) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126

This represents the number of ways to select 5 people from a group of 9 to be in the first group.

Once we have determined the first group, the remaining 4 people automatically form the second group.

Therefore, there are 126 different ways to divide 9 people into 2 groups such that the first group has 5 people and the second group has 4 people.

Related Questions

What is the solution to this equation?
3x + 8 = 2x - 8

Answers

Step-by-step explanation:

$ \tt{3x + 8 = 2x - 8}$

We want to get all the constants on the right hand side of the equation. So , Add 8 on both sides of the equation.

⤏ $ \tt{3x + 8 + 8= 2x - 8 + 8}$

⤏ $ \tt{3x + 16 = 2x}$

Move 2x to left hand side and change it's sign. Similarly , Move 16 to right hand side and change it's sign :

⤏ $ \tt{3x - 2x = - 16}$

Since , 3x and 2x are like terms , they can be added or subtracted. Subtract 2x from 3x :

⤏ $ \sf{x = - 16}$

$ \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{x = - 16}}}}}}}$

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2. Ms. Fallis wants to tile a kitchen counter that has an area of 2 square meters. She has 2000 square tiles with 3-centimeter sides. Does she have enough tiles to cover the counter?

Answers

Fallis has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

To find out if Ms. Fallis has enough tiles to cover the counter, we need to calculate how many tiles are required to cover an area of 2 square meters.

Since the tiles have a side length of 3 centimeters, we need to convert the area of the counter to square centimeters.

1 square meter = 10000 square centimeters (cm²)

So, 2 square meters = 20000 square centimeters (cm²)

Now, we need to calculate the area of each tile:

Side length of each tile = 3 centimeters (cm)

Area of each tile = $(side length)^2$ = $(3 cm)^2$ = 9 square centimeters (cm²)

To cover the counter, we need to divide the total area of the counter by the area of each tile:

Number of tiles required = (Total area of counter) / (Area of each tile)

= 20000 cm² / 9 cm²

= 2222.22

Since we cannot have a fraction of a tile, we need to round up to the nearest whole number of tiles. So, Ms. Fallis needs at least 2223 tiles to cover the counter.

Since she has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

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if s is the subspace of r 3 containing only the zero vector, what is s ⊥ ? if s is spanned by (1, 1, 1), what is s ⊥ ? if s is spanned by (1, 1, 1) and (1, 1, −1), what is a basis for s ⊥?

Answers

Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

What is a basis for s ⊥?

The question involving the terms "subspace," "containing," and "spanned."

If s is the subspace of R³ containing only the zero vector, s⊥ (the orthogonal complement of s) is the entire R³ space. This is because all vectors in R³ are orthogonal to the zero vector.

If s is spanned by (1, 1, 1), to find s⊥, we need a vector that is orthogonal to (1, 1, 1). We can use the dot product to determine orthogonality. For a vector (x, y, z), the dot product with (1, 1, 1) should be zero:

(1, 1, 1) · (x, y, z) = 0
x + y + z = 0

One possible vector that satisfies this equation is (-1, 1, 0). So, s⊥ is the subspace spanned by (-1, 1, 0).

If s is spanned by (1, 1, 1) and (1, 1, -1), to find a basis for s⊥, we need a vector orthogonal to both given vectors. We can use the cross product of the given vectors to find the orthogonal vector:

(1, 1, 1) × (1, 1, -1) = (-2, 2, 0)

Thus, a basis for s⊥ is the set {(-2, 2, 0)}.

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A bee flies at 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 18 minutes, and then flies directly back to the hive at 4 feet per
second. It is away from the hive for a total of 20 minutes
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive

Answers

Answer: T=x+y

T=600 ft

Step-by-step explanation:

T=Total distance

a. x=distance in feet/second traveled from hive to flowerbed

y=distance in feet/second traveled to hive

20*60=1200 seconds

18*60=1080 seconds

T=x+y ==> equation

b. x/6=y/4=60 seconds ==> 1 min

x/6=60

x=360 feet

y/4=60

y=240 feet

x+y=

360+240=600 ft

Protractor postulate: given any angle, we can express its measure as a unique ______________ number from 0 to 180 degrees.

Answers

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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It is known that X has a uniform distribution with μ=0.5 minutes and σ=0.29 minutes. Suppose a random sample of 64 people is selected. The shape of the sampling distribution of X
ˉ is: Uniform Approximately Normal Normal not enough information to determine

Answers

In this scenario, the shape of the sampling distribution of X-bar is approximately normal.

The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.

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3p + q = 8 and
3p - q = 10
then p+q is?

Answers

Answer:

Step-by-step explanation:

3p + q = 8 and

3p - q = 10

then p+q is?

--------

add up side-by-side:

6p=18 ⇒ p=3

q=8-3p= 8 - 9= -1

p+q= 3-1=2

Answer:

Step-by-step explanation:

3p + q = 8

3p - q = 10

→ Minus the two equations away from each other which would cancel out 3p

2q = -2

→ Divide both sides by 2 to isolate q

q = -1

→ Substitute q = -1 back into 3p + q = 8

3p - 1 = 8

→ Add 1 to both sides to isolate p

3p = 9

→ Divide both sides by 3 to isolate p

p = 3

⇒ The question asks us to find p + q so,

3 + - 1

→ Remember the minus cancels out the plus

3 - 1 = 2

there is a busy intersection between two one-way streets main street and 1st street avenue. Cars passing through the intersection can only pass through one at a time. When multiple cars arrive at the intersection at the same time, two queues can build up -- each for one street complete the function getResult

Answers

The program that van be used to illustrate the information is given below.

How to illustrate the program?

The program that depicts the cars will be:

def getResult(arrival, street):

# Write your code here

result = []

# The first car arrives on Main Street at time 0. The first car arrives on 1st Avenue at time 0. The second car arrives on Main Street at time

1. The third car arrives on 1st Avenue at time 5.

time = 0

main_street_queue = []

first_avenue_queue = []

while len(main_street_queue) > 0 or len(first_avenue_queue) > 0:

if len(main_street_queue) == 0:

car_to_add_to_result = first_avenue_queue.pop(0)