answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dominik [7]
2 years ago
14

How many ways are there to seat six different boys and six different girls along one side of a long table with 12 seats? how man

y ways if boys and girls alternate seats?
Mathematics
1 answer:
GaryK [48]2 years ago
3 0
Q1: 479 001 600 ways

Explanation:
You have 12 people, 12 seats, ¹²P₁₂ ways in arranging them, or essentially 12! ways

Q2: 1 036 800 ways

Explanation:
Let's break it up into two cases.

Case 1: BGBGBGBGBGBG
Case 2:GBGBGBGBGBGB

Let's deal with case 1, because case 2 will pop out. There are ⁶P₆ ways in sorting out the boys and ⁶P₆ ways in sorting out the girls, so for case 1, we'd have (⁶P₆)² ways in sorting out boys and girls in case 1.

This is exactly the same in case 2, so it'd be (⁶P₆)² ways in sorting out girls and boys in case 2.

So, (⁶P₆)² + (⁶P₆)² ways = 1 036 800 ways if they alternate
You might be interested in
Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five
kondaur [170]

Answer:

The last two terms of the expression are

  ----+8r^2s^4-3r^3s^3

Both the last terms has variable of degree equal to (2+4=6) and (3+3=6).So, the first term must have degree greater than 6.

Correct Options are

 1.\rightarrow 3r^4s^5\\\\2.\rightarrow -r^4s^6

3 0
2 years ago
The submarine is underwater. It’s position is 645 feet below sea level. It rises in the water 100 feet and then descends 100 fee
kolbaska11 [484]

Hello!

This submarine rose 100 feet (+100) and then descended (-100). Usually in an equation this would cancel out and make 0. Therefore, our answer is 0.

I hope this helps!

5 0
2 years ago
Read 2 more answers
A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well
kogti [31]

Answer:

Step-by-step explanation:

Hello!

To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:

<u>Group 1</u>: Ate healthy breakfast

X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.

n₁= 26

<u>Group 2: </u>Did not eat healthy breakfast

X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.

n₂= 20

After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:

p'₁= 0.50

p'₂= 0.40

The parameters of study are the population proportions, if the claim is true then p₁ > p₂

And you can determine the hypotheses as

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.05

Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }≈N(0;1)

pooled sample proportion: p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46

Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67

p-value: 0.2514

The decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.

At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.

So having a healthy breakfast doesn't seem to improve the grades of students.

I hope this helps!

5 0
2 years ago
A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by
Eddi Din [679]
The ABC sequence of points is clockwise in both figures, so there will be an even number of reflections or a rotation.

Rotation 90° clockwise about the point (-3, -3) would make the required transformation, but that is not an option. An equivalent is ...
   • reflection across the line x = -3
   • reflection across the line y = x
5 0
2 years ago
Read 2 more answers
A pizzeria charges $8 for a large cheese pizza, plus $2 for each topping. The total cost for a large pizza is given by the equat
Leni [432]
Slope is the rise and run of a point on the graph to the other 
the y intercept is where a line crosses the y axis for example, (0,5) so 5 is the y intercept

(0,8), (1,10), (2, 12), (3, 14), (4, 16), (5, 18)
7 0
2 years ago
Read 2 more answers
Other questions:
  • A Teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the seven groups in her class. She gives ea
    5·1 answer
  • How long is a distance of 8 km if measured on a map with a scale of 1:50,000
    10·1 answer
  •  if xy=c^2, prove that x^2 dx/dy+c^2=0
    12·1 answer
  • Kelly hiked in the woods it took her 1/14 hour to walk 1/4 mile after she snacked she walked another 1/6 mile in 1/16 hour
    10·2 answers
  • Determine the missing step for solving the quadratic equation by completing the square.
    6·2 answers
  • When Joseph first starts working at a grocery store, his hourly rate is \$10$10dollar sign, 10. For each year he works at the gr
    12·1 answer
  • Vanessa draws one side of an equilateral triangle ABC on the coordinate plane at points A(-2, 1) and B (4, 1). What are the two
    7·1 answer
  • Which statement about 6x2 + 7x – 10 is true?
    13·2 answers
  • A print shop manager is using the scale drawing shown below to make a rectangular banner the scale from the banner to the drawin
    14·1 answer
  • 311, 305,299,...Find the 32nd term.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!