Answer:
a) Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.
b) Hay 720 secuencias posibles existen para las seis ciudades designadas.
Step-by-step explanation:
a) Se llama combinaciones de m elementos tomados de n en n a todas las agrupaciones posibles que pueden hacerse con los m elementos de forma que no entran todos los elementos , no importa el orden y no se repiten los elementos. La combinación se calcula como:
[tex]C=\frac{m!}{n!*(m-n)!}[/tex]
En este caso m corresponde a las 10 ciudades en el área geográfica que va a visitar, mientras que n corresponde a las 6 ciudades que debe visitar un representante de venta durante un viaje.
Entonces:
[tex]C=\frac{10!}{6!*(10-6)!}=\frac{10!}{6!*4!}[/tex]
Considerando que el factorial ! indica que se deben multiplicar todos los números enteros y positivos que hay entre el número que aparece en la fórmula y el número 1, entonces la combinación dará como resultado:
C= 210
Hay 210 grupos diferentes de seis ciudades que el representante de ventas podrá seleccionar.
b) Se llama permutación de n elementos a cada una de las diferentes ordenaciones que se pueden hacer con esos elementos.
Si se tiene un grupo de n objetos distintos, el número de maneras diferentes que podemos tomar un número r de objetos (r < n) del grupo, está dado por la fórmula de la permutación:
[tex]P=\frac{n!}{(n-r)!}[/tex]
Si m=n para calcular el total de permutaciones se utiliza la fórmula:
P= n!
En este caso se utiliza esta última expresión, ya que se desea calcular las permutaciones de 6 ciudades en 6 posiciones:
P=6!
P=720
Hay 720 secuencias posibles existen para las seis ciudades designadas.
7 × 105 − 5,100 whats the answer
Answer:
-4,365
Step-by-step explanation:
f(x) = x + 9, g(x) = x2 − 4x, h(x) = x4 + 2x3
What is the degree of (f º g º h)(x)?
7
8
21
24
Answer:
the degree of the function is 8
Step-by-step explanation:
(f º g º h)(x) = [tex]f(g(h(x)))[/tex]
first lets evaluate g(h(x))
[tex](x^4 + 2x^3)^2 - 4(x^2 + 2x^3)[/tex]
simplify
[tex]x^8 + 4x^3 + 4x^6 - 4x^4 -8x^3[/tex]
[tex]x^8 + -4x^3 + 4x^6 - 4x^4[/tex]
you can easily see that the highest power term is 8 meaning the degree of the function is 8
Answer:
its 8 :)
Step-by-step explanation:
For a sledding trip you randomly select one of your four hats- red, blue with stripes, purple, or black. Write a ratio that compare the number of red hats to the number of total hats.
what is the answer please help
Answer:
B: 22.5 degrees
Step-by-step explanation:
The interior angles of a pentagon add up to 540 degrees
(if you dont believe me you can turn a pentagon into three triangles, 3x180 = 540)
So you have four same angles say measure "x" degrees, and one final one that measures "5x" degrees, so 9x = 540, and x = 60
Unless I read the problem wrong, 60 degrees is the answer which is not an option :P
Edit: Yea I read it wrong, the final angle is 5 times the other four angles COMBINED, so that angle measures "20x" degrees.
The total would be 24x = 540, and so x = 22.5
b/4+2=-1
b=?
answer please
Answer:
b=−12
Step-by-step explanation:
When are two distinct lines parallel?
Answer:
if the line keeps going and theynever touch
Step-by-step explanation:
Answer:
Two lines are parallel when are side by side and if the lines kept on going, they would never collide with each other
Step-by-step explanation:
There are 3072 books in the school library if 96 students reads the same number of books how many books would each student need to read?
Answer:
32 books each
Step-by-step explanation:
Simplify the expression:
10t - 40 + 3t + t
Answer:
Your correct answer is 14t - 40
Step-by-step explanation:
Combine like terms:
10t + 3t + t = 14t
Since there are no other integers, just tag on the -40:
14t - 40
**please mark brainliest!!
Which equation represents a line that passes through the two points in the
table?
X Y
3 3
6 5
Answer: The slope is 2/3, y=2/3x+1
Step-by-step explanation: The 2 points, (3,3) and (6,5), use the method y2-y/x2-x1. Then you find the slope that way, then use point slope form for the slope intercept form: y-y1=m(x-x1), then substitute and solve to get y=2/3x+1
mr bob the baker made 24 pies on monday and 48 on wednesday how many pieces did he made in all
Answer:
72 pies
Step-by-step explanation:
24 pies + 48 pies = 72 pies
Farmer Simpson was collecting eggs and noticed that each of his 6 hens laid the same
number of eggs this week. If Farmer Simpson collected 78 eggs, how many eggs did each
hen lay?
15
7
13
18
The graph of linear function f passes through the point (4,–2) and has a slope of –1.
What is the zero of f ?
Answer: 2
Step-by-step explanation:
y=mx + b
plug in known values
-2= (-1)(4) + b
b= 2
Equation: y= -x+2
graph and locate the x-intercept
Which number can each term of the equation be multiplied by to eliminate the decimals before solving?
–m + 0.02 + 2.1m = –1.45 – 4.81m
0.01
Answer:
Multiply by 100
Step-by-step explanation:
The equation is given as:
-m + 0.02 + 2.1m = -1.45 - 4.81m
To eliminate the decimals from all the terms, we must multiply by a number that make all the coefficients integers.
The decimal coefficients and independent terms are
0.02, 2.1, 1.45, 4.81
Note the maximum number of decimals found in all of them is 2. Thus, multiplying by 100 all the decimals will vanish as follows:
100(-m + 0.02 + 2.1m) = 100(-1.45 - 4.81m)
-100m + 2 + 210m = -145 - 481m
Now all terms have integer coefficients as required.
Answer: Multiply by 100
Jana uses 20 cards to play a memory game the cards are either animal cards or fruit cards. The ratio of animal cards to fruit cards is 2:3 How many if the 20 cards are animal cards? Of the fruit cards, 1/3 have bananas on them. How many cards have bananas on them. Show or explain your work.
Given that,
Total no of cards = 20
The ratio of animal cards to fruit cards is 2:3
No of animal cards = 20
Solution,
Let there are 2x animal cards and 3x fruit cards. ATQ,
2x+3x = 20
5x = 20
x = 4
Animal cards = 2x
= 2(4)
= 8
Fruit cards = 3x
= 3(4)
= 12
It is also mentioned that, of the cards, 1/3 have bananas on them. It means,
[tex]B=\dfrac{1}{3}\times 12\\\\=4[/tex]
Hence, 4 cards have bananas on them.
HELPPPPP ITS VERY URGENT!!!!!!
Answer:
LN i think.. i'm not sure tho
Step-by-step explanation:
The domain on which the following function is increasing
The domain on which of the following function is increasing is [0,4].
Given:
The graph of a function.
To find:
The domain on which of the following function is increasing.
Domain is the set of x-values or input values.
From the given graph it is clear that the vertex of the given function is at (4,75).
Before the point (4,75) the graph is increasing and after the point (4,75) the graph is decreasing.
The function is defined for 0≤x≤9 .
Since the graph is increasing when 0≤x≤4 , therefore the function is increasing over the interval [0,4].
Therefore, the domain on which of the following function is increasing is [0,4].
What is domain?
The domain is the value that x can take from a given function and codomain is the value of y from a function.
Learn more about domain here:https://brainly.com/question/10547118
#SPJ9
Identify the angle relationship
2
Answer:
which angle relarion send angle photo also
The map of a community shows that a lake is 6 inches away from a library. The scale of the map is 14 inch represents 3.5 meters. How far apart are the actual lake and library? A. 42 m A. 42 m, , B. 84 m B. 84 m C. 49 m C. 49 m D. 14 m D. 14 m
Answer:
Real distance = 84 meter
Step-by-step explanation:
Given:
Map distance = 6 inches
Map scale 1/4 inch = 3.5 m
Computation:
0.25 inches = 3.5 m
Computation:
Real distance = 6/0.25[3.5]
Real distance = 24[3.5]
Real distance = 84 meter
if 4-3(2-x)<10+x what is the greatest possible integer value of x?
Answer:
4-3(2-x) < 10+x
4 -6 +3x< 10 + x
-2 +3x< 10 +x
2x< 12
x<6
↣ First we solve the Inequality.
[tex]4-3(2-x)<10+x[/tex]
[tex]4-6+3x<10+x[/tex] ↣ Distribute -3 in (2-x) for easier in solving.
[tex]3x-2<10+x\\3x-x<10+2\\2x<12\\x<6[/tex]
Thus, the answer is x < 6.
↣ Therefore, the greatest possible Integer value of x is 5.
Which of the following can be used to prove that triangle ABC is congruent to triangle DEF?
Answer:
SAS congruence theorem
Step-by-step explanation:
since we are given the two congruent sides and the right angle. We know all right angles are congruent and the right angle is an angle that is between the two sides which is why it is SAS. hope this helps :))
Grant spent half of his weekly allowance. Then he earned $5 back by doing the dishes. What is his weekly allowance if he ended with $15?
Answer:
Grant's weekly allowance is $20.
Step-by-step explanation:
We know that Grant ended with $15. We can say that Grant's weekly allowance is x.
x/2 + 5 = 15
Now to solve:
x/2 + 5 - 5 = 15 - 5 (subtract 5 from both sides to isolate the x/2)
x/2 = 10
x/2 * 2 = 10 * 2 (multiply both sides by 2 to isolate the x)
x = 20
Grant's weekly allowance is $20.
PLEASE HELP I HAVE 6 MINUTES LEFT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:the answer is D
Step-by-step explanation:
5 ( x + 3 - 5x)
PLZ WHAT IS THIS IN SIMPLEIST FORM WILL GIVE BRAINLIEST
Answer:
-20x + 15
Step-by-step explanation:
Answer: -20x + 15
Step-by-step explanation:
5(x + 3 - 5x)
5(-4x +3)
5(-4x +3)
(Resolve) -12 x 5 = 07 60 -60 0-7
Answer:
-60
Step-by-step explanation:
braincells
WILL GIVE BRAINLEST IF RIGHT
Which expression is equivalent to this expression?
34(4h – 6)
A. 3h – 92
B. 4h + 92
C. 3h – 6
D. 4h + 6
Answer:
C. 3h - 6
Step-by-step explanation:
__Na2O + __ H2O → __NaOH
Answer:
Na20+H20 -> 2NaOH
Step-by-step explanation:
Lucy cuts 4 squares with side length x in. from the corners of a 6 in. by 9 in. cardboard rectangle. She folds the remaining cardboard to make a tray that is x in. high. Write and simplify a polynomial function for the volume V of the tray in terms of x.
Answer:
Lucy cuts 4 squares with side length x in. from the corners of a 6 in. by 9 in. cardboard rectangle. She folds the remaining cardboard to make a tray that is x in. high. Write and simplify a polynomial function for the volume V
Step-by-step explanation:
9v
The polynomial function for the volume V of the tray in terms of x will be;
⇒ 4x³ - 30x² + 54x
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
Lucy cuts 4 squares with side length x inch from the corners of a 6 inch by 9 inch cardboard rectangle.
She folds the remaining cardboard to make a tray that is x inch high
Now,
By the give condition we get;
Length of tray = 9 - 2x
Width of tray = 6 - 2x
Height of tray = x
So., The volume of the tray is expressed as;
Volume = x (9 - 2x) (6 - 2x)
= x (54 - 18x - 12x + 4x²)
= x (54 - 30x + 4x²)
= 4x³ - 30x² + 54x
Thus, The polynomial function for the volume V of the tray in terms of x will be;
⇒ 4x³ - 30x² + 54x
Learn more about the volume visit:
https://brainly.com/question/12410983
#SPJ2
I need help with this one
Answer:
c
Step-by-step explanation:
please help i need slope! algebra 1
Answer:
slope: -1/3 y intercept: 2
Step-by-step explanation:
I'm also in Algebra 1 and I'm not completely sure.
what is (5.91 x 10^-3) - (8.7 x 10^10) written in a scientific notation? Please answer asap thank you :))
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
[tex]\left(5.91\times \:10^{-3}\right)-\left(8.7\times \:10^{10}\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=5.91\times \:10^{-3}-8.7\times \:10^{10}[/tex]
as
[tex]5.91\times \:10^{-3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=5.91\times \frac{1}{10^3}[/tex]
[tex]=\frac{5.91}{1000}[/tex]
[tex]=0.00591[/tex]
similarly
[tex]8.7\times \:10^{10}[/tex]
Convert element to a decimal form
[tex]10^{10}=10000000000[/tex]
so
[tex]=10000000000\times \:8.7[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:8.7\times \:10000000000=87000000000[/tex]
[tex]=87000000000[/tex]
Thus, the expression becomes
[tex]\left(5.91\times \:\:10^{-3}\right)-\left(8.7\times \:\:10^{10}\right)=5.91\times \:\:10^{-3}-8.7\times \:\:10^{10}[/tex]
[tex]=0.00591-87000000000[/tex]
[tex]=-86999999999.9941[/tex]
Hence,
converting -86999999999.9941 in a scientific notation
In order to make our job easier we will remove the sign "-" from number -86999999999.9941 (we will write "-" at the final solution). So after this step we have:
−86999999999.9941 ⟶ 86999999999.9941
In order to write number 86999999999.9941 in scientific notation, we need to move the decimal point from its current location (black dot) to the new position such as:
8.6999999999.9941
So, we need to move the decimal point 10 places to the right.
This means that the power of 10 will be positive 10.
Now we have that the
Number part = 8.69999999999941 and
Exponent part = 10
Thus, we conclude that:
−86999999999.9941 = − 8.69999999999941 × 10¹⁰