Usando técnicas de conteo, se encuentra que
1. Un cliente puede ordenar una comida de 784 formas.
2. 420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
3. 840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
4. 10 partidos distintos se pueden realizar.
5. Pueden colocarse de 3,628,800 formas.
6. 1260 señales distintas pueden indicarse.
Item 1:
La técnica usada es el principio fundamental de conteo, que afirma que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] maneras de seren realizadas, el número total de maneras de ser realizadas es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema, [tex]n_1 = 14, n_2 = 8, n_3 = 7[/tex], por eso:
[tex]T = 14 \times 8 \times 7 = 784[/tex]
Un cliente puede ordenar una comida de 784 formas.
Item 2:
El orden es importante, ya que TECN es una palabra diferente de NCET, por lo tanto, la fórmula de permutaciones se usa para resolver este problema.
Fórmula de permutaciociones:
El número de permutaciones de x elementos en un conjunto de n elementos es dada por:
[tex]P_{n,x} = \frac{n!}{(n - x)!}[/tex]
En este problema, 4 letras de 7, enconteces:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
La letra C se repite dos veces, o sea:
[tex]T = \frac{P_{7,4}}{2} = \frac{840}{2} = 420[/tex]
420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.
Item 3:
Permutaciones de 4 dígitos de 7, sin repeticiones, o sea:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.
Item 4:
El orden no es importante, ya que Time 1 x Time 2 es la misma partida de Time 2 x Time 1, por lo tanto, la fórmula de combinaciones se usa para resolver este problema.
Fórmula de combinaciones:
El número de combinaciones de x elementos en un conjunto de n elementos es dada por:
[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]
En este problema, combinaciones de 2 elementos de un conjunto de 5, entonces:
[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
10 partidos distintos se pueden realizar.
Item 5:
El número de arreglos de n elementos viene dado por
[tex]A_n = n![/tex]
En este problema, arreglo de 10 elementos, o sea:
[tex]A_{10} = 10! = 3628800[/tex]
Pueden colocarse de 3,628,800 formas.
Item 6:
El número de arreglos de n elementos, con repeticiones de [tex]n_1, n_2, \cdots n_n[/tex] elementos viene dado por
[tex]A_n^{n_1,n_2,\cdots,n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
En este problema, [tex]n = 9, n_1 = 3, n_2 = 2, n_3 = 4[/tex], por eso:
[tex]A_9^{3,2,4} = \frac{9!}{3!2!4!} = 1260[/tex]
1260 señales distintas pueden indicarse.
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At football practice on Monday, Brandon threw a football into the target 5 times. The next Monday, he tripled the number of targets he hit. On the following Monday, his hits double that of the week before. Write and evaluate a numerical expression to find how many times he hit the target during those three weeks.
Enter the correct answers in the boxes.
Expression:
Answer:
try using a different app, it helps with all types of mathematical equations
In a math class, the teacher asked the students to find the approximate value of one of the x-coordinates of a point of intersection of two functions: f(x) = 2x2 − 3x + 4 g(x) = 5x − 1 Her students gave her different answers. Which answer is the most accurate?
A.
0.8
B.
0.9
C.
1.9
D.
1.1
Answer:
A. 0.8Step-by-step explanation:
An easy way is to substitute values into both equations and compare:
A. x = 0.8
f(x) = 2(0.8)² - 3(0.8) + 4 = 2.88g(x) = 5(0.8) - 1 = 3B. x = 0.9
f(x) = 2(0.9)² - 3(0.9) + 4 = 2.92g(x) = 5(0.9) - 1 = 3.5C. x = 1.9
f(x) = 2(1.9)² - 3(1.9) + 4 = 5.52g(x) = 5(1.9) - 1 = 8.5D. x = 1.1
f(x) = 2(1.1)² - 3(1.1) + 4 = 3.12g(x) = 5(1.1) - 1 = 4.5As we see the most accurate one is A
Let's graph both function(Attached)
Let's round 0.775
[tex]\\ \sf\longmapsto 0.775[/tex]
[tex]\\ \sf\longmapsto 0.77[/tex]
[tex]\\ \sf\longmapsto 0.8[/tex]
Option A is correct
The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated
coffee in the morning. How long will it take for only 60% of the caffeine to remain in his body?
We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.
We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.
So we can define the proportion of coffee that Jeremiah has in his body as:
P(t) = 1*e^{k*t}
Such that:
P(4.8 h) = 0.5 = 1*e^{k*4.8}
Then, if we apply the natural logarithm we get:
Ln(0.5) = Ln(e^{k*4.8})
Ln(0.5) = k*4.8
Ln(0.5)/4.8 = k = -0.144
Then the equation is:
P(t) = 1*e^{-0.144*t}
Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:
P(t) = 0.6 = 1*e^{-0.144*t}
Again, we use the natural logarithm:
Ln(0.6) = Ln(e^{-0.144*t})
Ln(0.6) = -0.144*t
Ln(0.6)/-0.144 = t = 3.55
So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.
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Task 1:
Taxi Cab Company A: $8 per ride and $0.35 per mile
• Write an equation in slope intercept form to represent the cost of a
taxi ride using company A.
Hint: use y=mx+b
OY =
• What does the y-intercept mean in the context of this problem?
Hint: What do you pay to step into the cab?
Using the slope - intercept form to represent the scenario described, the equation obtained would be y = 0.35x + 8
The cost per ride represents the intercept = $8
The cost per mile represents the slope = $0.35
The slope - intercept form of a linear equation is expressed as :
y = bx + c b = slope ; c = interceptTherefore, the slope intercept form for the cost of taxi ride is y = 0.35x + 8
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Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.
Use this to help you:
Air travel time: 12 hours
Destination: 2,184 miles
182.00 miles per hour
y = 182x will be the equation to represent one way you can find how many miles Emily's plane flew each hour.
What is the equation?A formula that expresses the connection between two words on each side of an indication. A calculation with an integer multiple is referred to as an equation. Algebra is widely used in equations. In performing calculations but unsure of the precise amount, algebra is utilized.
The information that is provided is
the air travel time is 12 hours
The destination miles will include 2,184 miles
Assuming the values of x and y
x = number of hours n
y = distance covered
The equation that will be made will be:
y = (2184 / 12)x
y = 182x
Therefore, the equation will be y = 182x.
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A scale model of a bicycle has a scale of 1 : 25. The real bicycle has a length of 1.75 m. What is the length of the model in cm?
Answer:
It's 7 I just did this question today and got it right
show work plz!!!!!!!!!!!!!
Here, we have been asked to find the order of rotational symmetry of a symmetry of a regular pentagon. First let us learn about rotational symmetry and some basic terms related to it.
1. Rotational Symmetry: -
It is the property a shape has when it looks the same after some rotation by a partial turn. For example: - an equilateral triangle will look the same after a partial rotation of 120∘
2. Centre of rotation: -
The fixed point around which the rotation occurs is called the centre of rotation. For example: - the centre of rotation of a fan is the centre of the fan from which its blade originates.
3. Angle of Rotational Symmetry: -
The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself. For example: - the angle of rotation of an equilateral triangle is 120∘
4. Order of Rotational Symmetry: -
The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. For example: - an equilateral triangle can be rotated 3 times around a full circle, each time at the angle of 120∘
, so its order of rotation will be 3.
In general, a regular polygon having n – sides have ‘n’ lines of symmetry and their order of rotational symmetry is ‘n’.
Now, let us come to the question. We have to find the order of rotational symmetry of a regular pentagon.
We know that a regular pentagon has 5 sides.
Hence, it will have 5 lines of symmetry and its order of rotational symmetry will be 5.The sum of two numbers is 65. The larger number is 5 more than the smaller number. What are the numbers?
Answer:
30 and 35
Step-by-step explanation:
Put this question into equation form:
Let x be the smaller number, if the larger number is 5 more and the total is 65:
x + 5 + x = 65
2x + 5 = 65
Subtract 5 from both sides
2x + 5 - 5 = 65 - 5
2x = 60
Divide both sides by 2:
2x ÷ 2 = 60 ÷ 2
x = 30
As the larger number is 5 bigger:
30 + 5 = 35
So the two numbers are 30 and 35.
Hope this helps!
Answer:
Small number 30
Large Number 35
Step-by-step explanation:
The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:
x + y = 65
The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:
x - y = 5
Now solve equation B for x to get the revised equation B:
x - y = 5
x = 5 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 65
5 + y + y = 65
5 + 2y = 65
2y = 60
y = 30
Now we know y is 30. Which means that we can substitute y for 30 in equation A and solve for x:
x + y = 65
x + 30 = 65
X = 35
Therefore the large and small number us 35 and 30 respectively.
what is 3/4 divided by 11/20
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11
❗❗CORRECT ANSWER+EXPLANATION=BRAINLIEST❗❗
Simplify: (question in the pic)
The simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]
Functions and equationGiven the following function as shown:
[tex]f(x)=\frac{x^2-9}{x^2-3x}[/tex]
This can be factorized as:
[tex]f(x)=\frac{x^2-3^2}{x(x-3)}\\f(x)= \frac{(x+3)(x-3)}{x(x-3)} \\[/tex]
Cancel out the common terms:
[tex]f(x) = \frac{x+3}{x}[/tex]
Hence the simplified form of the function is [tex]f(x) = \frac{x+3}{x}[/tex]\
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Hi Phoenix! :)
I'm much late lol.
Answer:
[tex]\boxed{ \cfrac{x + 3}{x}} [/tex]
Step-by-step explanation:
Given:
[tex] \cfrac{x {}^{2} - 9}{x {}^{2} - 3x } [/tex]
Solution:
[Here the best option is to factorise the expression.]
Rewrite the numerator of the expression as
[tex] \cfrac{x {}^{2} - 3 {}^{2} }{x {}^{2} - 3x} [/tex]
It can be seen that the numerator is like an algebraic identity:
> a² - b² = (a+b)(a-b)
ATP, numerator : a = x² and b = 3²
[tex] \cfrac{(x + 3)(x - 3)}{ {x}^{2} - 3x} [/tex]Now in the denominator take x common:
[tex] \cfrac{(x + 3)(x - 3)}{x(x - 3)} [/tex](x-3) in the denominator and (x-3) in the numerator gets canceled.
[tex] \cfrac{(x + 3) \cancel{(x - 3)}}{x \cancel{(x - 3)}} [/tex][tex] \boxed{\cfrac{x + 3}{x} }[/tex]Welp,Done, that's it! :D
Last year, Dante had $10,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account
that paid 8% simple interest per year. After one year, he received a total of $730 in interest. How much did he invest in each account?
a = amount invested at 7%
b = amount invested at 8%
we know that total that he invested was 10000, therefore a + b = 10000.
hmmm how muich is 7% of "a"? well (7/100) * a => 0.07a.
how much is 8% of "b"? well (8/100) * b => 0.08b.
After a year he received in interest $730, so we know that at simple interest rate, 0.07a + 0.08b = 730.
[tex]\begin{cases} a+b=10000\\ 0.07a+0.08b=730\\[-0.5em] \hrulefill\\ b = 10000 - a \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{0.07a+0.08(10000-a) = 730} \\\\\\ 0.07a+800-0.08a=730\implies 0.07a-0.08a=-70\implies -0.01a=-70 \\\\\\ a=\cfrac{-70}{-0.01}\implies \boxed{a = 7000} ~\hfill \stackrel{\textit{we know that}}{b = 10000 -a}\implies \boxed{b = 3000}[/tex]
phone company offers to monthly plans. Plan a cost $11 plus an additional $.19 for each minute of calls. Plan B cost $16 plus an additional $.15 for each minute of calls
Answer:
whats the question I can't help without a question
Second Graph problem! Can anybody please help me out with this? (Almost done for today) (Algebra graph problem)
Answer:
x = -2
Step-by-step explanation:
The expression f(x) = 1 corresponds to the point on the graph that is 1 unit above the x-axis. You can locate that horizontal line and see where it intersects the graph. That point of intersection is 2 grid squares to the left of the y-axis, where x = -2.
f(-2) = 1
x = -2
Please take a look at the picture
Step-by-step explanation:
option c is correct answer
Answer:
A) -11/-4
Step-by-step explanation:
-11/-2=11/4
Rewrite the fraction.
-(-11/4)
=11/4
Hope this helps :)
Exercise #14: The mile and the kilometer are relatively close in size. Can you convert 1 mile into an equivalent
in kilometers? Here's what I'll give you. There are 2.54 centimeters in an inch, 5,280 feet in a mile, 100
centimeters in a meter, and 1000 meters in a kilometer. All else you should be able to do for yourself. Round
your answer to the nearest tenth of a kilometer. This takes quite a string of multiplications, but you can do it!
The equivalent of 1 mile to kilometres is approximately 1.6 km.
2.54 cm = 1 inch
5280 ft = 1 mile
100 cm = 1 m
1000 m = 1 km
Using the information let's convert 1 mile to kilometre.
1000 m = 1 km
Therefore,
1 m = 0.000621371 miles
1000 m(1 km) = ?
cross multiply
length = 1000 × 0.000621371 = 0.621371 miles
Therefore,
0.621371 miles = 1 km(1000 m)
1 miles = ?
length in km = 1.60934449789 km
Therefore,
1 miles = 1.6 km
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Hey everybody! Can anybody help me out with this algebra problem? I would really appreciate it if you can!
The following relation is a variation. Which description best represents the relation?
Answer:
x and y are directly related because y = -3x
Step-by-step explanation:
HELP ME OUT PLEASE
A die was rolled six times. The polls were 1,2,3,3,4 and 5. What is the mean deviation for this data!
A) 3/5
B) 1
C) 2
D) 6
Answer:The mean deviation of the given data is;
Option B: 1
Step-by-step explanation:
Σ(x - x¯)/n
Now, x¯ is the mean = (1 + 2 + 3 + 3 + 4 + 5)/5
x¯ = 3
Thus;
1 - 3 = -2
2 - 3 = -1
3 - 3 = 0
3 - 3 = 0
4 - 3 = 1
5 - 3 = 2
Mean deviation is usually a positive value. Thus;
Σ(x - x¯) = 2 + 1 + 0 + 0 + 1 + 2
Σ(x - x¯) = 6
Thus;
Σ(x - x¯)/n = 6/6
Σ(x - x¯)/n = 1
help me out guys I don't get this ?!
Answer:
B: (-2,-3)
Step-by-step explanation:
The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.
Find the equation of the line passing through the points 7,2 and 9,1
9514 1404 393
Answer:
y = -1/2x +11/2
Step-by-step explanation:
The slope of the line is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -2)/(9 -7) = -1/2
The y-intercept is ...
b = y -mx
b = 2 -(-1/2)(7) = 11/2
Then the slope-intercept equation is ...
y = -1/2x +11/2
_____
Alternative solution
A general form equation for the line can be ...
(y1 -y2)(x -x1) -(x1 -x2)(y -y1) = 0
(2 -1)(x -7) -(7 -9)(y -2) = 0
x-7 +2y -4 = 0
x +2y -11 = 0 . . . . . general form equation
x +2y = 11 . . . . . . . standard form equation
Note that we want the x-coefficient to be positive, so we chose the order of the points to make that be the case.
Rewrite 2/3 and 1/15 as a unit rate
Answer:
10:1
Step-by-step explanation:
Answer:
Step-by-step explanation:
The unit rate is found by dividing.
2/3 = 0.(6)
1/15 = 0.(6)
A rectangular field is 350 meters long and 200 meters wide. What is the area of the field in square kilometers? Do not round your answer. Be sure to include
the correct unit in your answer.
0
km
km2
km
The area of the rectangular field is 0.07 square kilometers (km²).To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers.
To find the area of the rectangular field in square kilometers, we need to convert the given dimensions from meters to kilometers and then calculate the area.
Given:
Length of the field = 350 meters
Width of the field = 200 meters
To convert from meters to kilometers, we divide the measurements by 1000, since there are 1000 meters in a kilometer.
Length in kilometers = 350 meters / 1000 = 0.35 kilometers
Width in kilometers = 200 meters / 1000 = 0.2 kilometers
Now that we have the dimensions of the field in kilometers, we can calculate the area.
Area of the field = Length in kilometers * Width in kilometers
Area of the field = 0.35 kilometers * 0.2 kilometers
Multiplying the values, we get:
Area of the field = 0.07 square kilometers
Therefore, the area of the rectangular field is 0.07 square kilometers.
It's important to include the correct unit in the answer, which is "square kilometers" (km²). This represents the unit for measuring the two-dimensional area. In this case, the area of the field is 0.07 km².
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ASAP
which of the following values of 'x' is the equation 4(x-2)-3x
= x +2 true?
A. -1
B. All Real Numbers
C. The equation has no solution
D. 3
E. 2
Answer: A
Step-by-step explanation:
The student government snack shop sold 64 snacks this week. 8 of the snacks sold were fruit cups. What percentage of all snacks sold were fruit cups?
Rewrite the equation as a division equation.
Answer:
8/64 = 0.125 = 12.5%
Step-by-step explanation:
8/64 = 0.125 = 12.5%
Solve the following equation for x: 5x-3 1/2 = 9x+4 Enter answers as a decimal with no variable, no spaces, and no equal sign. DO NOT ROUND.
Answer:
− 1.875
Step-by-step explanation:
Do you want an explanation?
f(x) = 3x + 1 and f-1 = f-1 = x-1 / 3
then f -'(7) =
Answer:
2
Step-by-step explanation:
f^-1 (7) = [tex]\frac{x-1}{3}[/tex] = [tex]\frac{7-1}{3}[/tex] = [tex]\frac{6}{3}[/tex] = 2
WHAT is the next sequence
Answer: its 21
Step-by-step explanation:
the sequence goes up by 1 each time
Answer:
21
Step-by-step explanation:
a1=1
a2=a1+2
a3=a2+3
a4=a3+4
...
a(n)=a(n-1)+n
if 6sinx=3cosx the value of tanx is
Step-by-step explanation:
tanx=sinx/cosx=3/6=1/2
range of the function f(x) = -x^2 - 5
Answer:
Step-by-step explanation:
Circle the multiplication problem that does not belong with the other three. explain 12×8=,22×4=,42×2=,33×3=
Answer: 12 x 8
Step-by-step explanation: The other three are not the basic multiplication facts from 0 - 12.
If you own a car with an assessed value of 23,300 in the state of West Virginia, which has a 1.66% tax rate, what would your property taxes be for your vehicle
Answer:
Average County Tax Rate
0.520%
(Mercer County)
Property Taxes
$121
(Annual)
Step-by-step explanation: I'm assuming this is the answer, if you can please can you mark me Brainliest.