Suppose that a large family has 14 children, including two sets of identical triplets, three sets of identical twins, and two individual children. How many ways are there to seat these children in a row of chairs if the identical triplets or twins cannot be distinguished from one another

Answer:

First, assume that we have 14 seats in a row.

Let's count the total number of combinations assuming that the 14 kids are differentiable.

In the first seat, we can sit only one child, the number of options is (14)

In the second seat, we can sit another child, in this case, the number of options is 13, because one child is already seated.

For the third seat, we will have 12 options.

for the fourth seat we will have 11 options, and so on.

The total number of permutations is equal to the product between the numbers of options for each case.

Then the total number of permutations is:

P = 14*13*12*11*...*3*2*1 = 14!

Now, we need to discount the permutations of the two sets of identical triplets:

a triplet has 3 elements, then the permutations of each set of triplets is:

p = 3*2*1 = 3!

Then if we discount two sets of triplets, we need to divide by:

d = 2*(3!)

We also have 3 sets of twins, the permutations for each set of twins is:

p = 2*1 = 2!

Then if we discount the 3 sets of twins, we need to by:

q = 3*(2!)

Then the total number of different combinations will be:

[tex]P = \frac{14!}{2*(3!)*3*(2!)} = 1,210,809,600[/tex]

A 30-foot ladder was put up against a building. The ladder makes a 64° angle with the ground. How high up
on the wall does the top of the ladder reach?

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kimtoya travels from New York to Florida by airplane. She pays a total of $402 for her flight. This includes a base price of $285 for the ticket plus a fee for each of her 3 pieces of checked baggage. To figure out how much the fee per bag is, she adds $402 to $285 and then divides this total by 3 to get $173. Is Kimtoya correct? Include all necessary work to support your answer.​

According to the National Beer Wholesalers Association, U.S. consumers years and older consumed gallons of beer and cider per person during . A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers years and older in Milwaukee will be taken, and the sample mean beer and cider consumption will be used to test the following null and alternative hypotheses: : : a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee

Jeff and Kathy are in a walking race. Kathy is faster and walks 3 meters per second. Jeff walks 2 meter
per second. Jeff gets a 24 meter head start.
At what time are Kathy and Jeff at the same distance in the race
1. 3 seconds
2. 30seconds
3. 36 seconds
4. 24 seconds

Olive is allowed to bring one friend on a
She does not want to play favorites.
trip with her.
What is NOT a random method of choosing a friend?

If x=2 and y=5 Evaluate this expression: 6x +5 y

Name:
Date:
Class:
Test: Lessons 18-1 Slicing Solids and 18-2 Lateral and Surface Area of Prisms
Circle the term or phrase that best completes each sentence.
1. The figure on the left is a ...
triangular prism.
triangular pyramid.
2. The figure on the right is a...
three-dimensional figure.
two-dimensional composite figure.
3. Another name for the shapes that make up any three-dimensional
figure is ...
faces.
edges.
4. For any three-dimensional figure, the sum of the areas of all its
faces is its ...
surface area.
area.

9. Are there any outliers in the data from question #7?
A. Yes; Week 10 is an outlier since it is the greatest data point.
B. Yes; Week 1 is an outlier since it is the lowest data point.
C. Yes; Week 7 is an outlier since it does not fit the general trend of the data.
D. No; there are not any outliers in the data.

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 13 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Match each term with its notation.

___________ The number of treatment conditions
___________ The number of scores in each treatment.
___________ The total number of scores in the entire study.
___________ The sum of the scores for each treatment condition.
___________ The sum of all of the scores in the research study.
___________ The F-ratio

1. n
2. F
3. G
4. N
5. k
6. T

the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?

Three times Francis' age plus five times Earl's age is 230. Earl is also four times Francis age. How old is Earl?

Twenty percent of 56 is 11.2

TRUE OR FALSE


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pls help me forgot how to do this
find the value of x

use the 3 digits 5, 3, and 2 only once in each number how many 3 digit numbers can you make?

Which expression can be used to simplify this expression? -2 divided by 1 and 3/4

Please help
i will give brainleist
Screen shot down below⬇⬇⬇

Vx
What is the percent decrease when the balance in a bank account goes from $300 to $60?
O The percent decrease is 20%.
O The percent decrease is 25%.
O The percent decrease is 80%.
O The percent decrease is 87%

Which of these expressions are equivalent to [tex]\frac{p}{3}[/tex]
A. [tex]p-\frac{2}{3} p[/tex]
B.[tex]\frac{1}{3}p[/tex]
C.[tex]p-3[/tex]
D. 3 ÷ p
E. [tex]\frac{3p}{9}[/tex]
F. [tex]\frac{1}{3}p + \frac{1}{3}p + \frac{1}{3}p[/tex]

CAN YOU GUYS HELP ME FOR #10

A likely amount of vanilla in a batch of cookies is 1/2 fluid Ounces. True or False?
I need it fast if you can!

22, 17. 12, 7... O Arithmetic
O Geometric
O Neither

6
Uzupełnij zdania, wykorzystując podane
w nawiasach wyrazy w odpowiedniej formie.
Nie zmieniaj kolejności podanych wyrazów,
jednak - jeżeli jest to konieczne - dodaj
inne wyrazy. W każdą lukę możesz wpisać
maksymalnie cztery słowa, wliczając w to
wyrazy już podane.
1 We couldn't make an omelette because we
(have /no/egg)
2 You cooked a delicious meal, so let (1 / wash/
dish)
3 My uncle is a chef, so everyone (listen / he /
advice)
about cooking.
4 Claire is trying (not/ eat / sweet)
5 I only (drink/bit)
the coffee because it was too strong.​

PLEASE HELP, 80 POINTS!!!!

1. Write as a function of an acute angle. sec(11 pi/4)
A): sec45
B): -sec45
C): -sec(-45)
D): sec(-45)

2. If cot0=5.671, find a point on the terminal side of 0.
A): (5.671, 1)
B): (1, 5.671)
C): (5.671, -1)
D): (-1, 5.671)

3. Convert to degrees. 2^R
A): 360
B): 180
C): 114.592
D): 1.570

An unknown number y is 12 more than an unknown number x. The number y is also x less than 17. The equations to find x and y are shown below.

y = x + 12
y = −x + 17

Which of the following statements is a correct step to find x and y? (4 points)

a
Multiply the equations to eliminate y.

b
Write the points where the graphs of the equations intersect the x-axis.

c
Write the points where the graphs of the equations intersect the y-axis.

d
Add the equations to eliminate x.

Which expression is equivalent to 7(a+2) when a= 6?
O 7(6)
O 9(6)
O 7(6)+2
O 7(6)+14

A traffic fanatic wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He assumes that each car is 17 feet long, travels at speed s, and follows the car in front of it at a safe distance for that speed. He finds that the number N of cars that can pass a given spot per minute is modeled by the function
N(s) 87s/19 + 19 (s/24)2|
At what speed can the greatest number of cars travel safely on that road?

Please help me not sure