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.
Un problema similar es dado en https://brainly.com/question/19022577
Out of the 25 students in Mrs. Green's class, 15 have a pet. What percent of the students in Mrs. Green's class have a pet?
A company generally purchases large lots of a certain kind of electronic device. A method is used that rejects a lot if 4 or more defective units are found in a random sample of 100 units. ​(a) What is the probability of rejecting a lot that is ​3% ​defective? ​(b) What is the probability of accepting a lot that is ​4% ​defective?
Using the binomial distribution, it is found that there is a:
a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.
For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem, the sample has 100 units, hence [tex]n = 100[/tex].
Item a:
3% of the pieces are defective, hence [tex]p = 0.03[/tex].
The probability is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]
[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]
[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]
[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]
0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
Item b:
4% of the pieces are defective, hence [tex]p = 0.04[/tex].
Lot is accepted if less than 4 units are defective, hence:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]
[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]
[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]
[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]
0.4295 = 42.95% probability of accepting a lot that is 4% defective.
A similar problem is given at https://brainly.com/question/24863377
An aircraft factory manufactures airplane engines. The unit C(the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made , then the unit cost is given by the function C (x) = 0.9x^2-306x+34,590. What is the minimum unit cost?
Describe the transformation of g(x)=4|x|
[tex]g(x) = 4 |x| = x = 0[/tex]
Sally must have at least $200 in her savings account to avoid a
fee. She currently has $850 in her account, but plans to spend
$75 per week. Write an inequality to determine the number of
weeks she can spend money and avoid a penalty.
Answer:
675$
Step-by-step explanation:
got it right
The diameter of a circle is 6.8 m. Find the circumference to the nearest tenth
Answer:
21.4m
Step-by-step explanation:
Circumference : x diameter
is approximately 3.142
3.142 x 6.8 = 21.3656
Nearest tenth = 21.4m
Mr. Reyes baked 4 batches of muffins for his class each batch had 12 muffins. if Mr. Reyes Has 24 students, How many muffins will each student receive?
Answer:2 muffins
Step-by-step explanation: First you have to see how many muffins he baked. 12x4 = 48 thus giving us the amount of muffins he baked. 48 muffins. If each student gets the same amount of muffins 48/24 = 2.
So each person would get 2 muffins.
Hope this helps :)
I don't know the answer to this & I don't understand how to get it.
Answer:
i thank it h
Step-by-step explanation:
Answer:
Well your answer is (F)
Step-by-step explanation:
?
ABCD is a parallelogram.the length of AB is 15 what is the the length of CD
rhombus opposite sides are equal.
So, CD = 15
Also do the line pass through the origin? Explain.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad \qquad m = -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{-3}(x-\stackrel{x_1}{4})\implies y+1=-3(x-4) \\\\\\ y+1=-3x+12\implies \stackrel{\textit{slope-intercept form}}{y=-3x+11}[/tex]
does it pass through the origin? well, we could draw it, or we can just check that, the origin is at 0,0, or namely when x = 0, y = 0, let's see if that's true, let's make x = 0, let's see what we get for "y".
y = -3(0) + 11 => y = 11
woops, no dice, y ≠ 0, so nope, doesn't pass through the origin.
The result of a division problem is the a ) divisor . b ) quotient . c ) factor . d ) remainder .
Answer:
b) quotient
Step-by-step explanation:
divisor is the number/value you are dividing with.
A remainder is a number that remains after you divide.
A factor is a number that can divide into a number or numbers without leaving a remainder
There are 1,000 students in Sharon's high school. 65% of the students are taking Spanish. How many students are taking Spanish?
Answer:
650 students are spanish.
Step-by-step explanation:
just say 1,000 people = 100%
then 650 students would = 65%
Hope I helped
HELP ME PLEASE!! I DONT WANT TO FAIL THIS AGAIN.
Answer:
A.
Step-by-step explanation:
You can see that the rate of change of function A is 3. because that's the slope (M) in y=mx+b
5 is slope for B because unit rate is 5 ( 1 to 3 change is +10 so unit rate is 5)
Please answer the 4 questions :)
Step-by-step explanation:
The lines or plains which contain R:
1. Parallel to SP ⇒ segment RQ2. Perpendicular to SP ⇒ segment RS3. Skew to SP ⇒ segment RK4. Plane parallel to KLM ⇒ plane RSPwork out the value of 10²-4³ give ypur answer as a power of 6
Answer: 36
Step-by-step explanation: 10^2 is 100 and 4^3 is 64, and 100-64=36
Will mark as brain list if answered correctly
Answer:
The answer is 3
Step-by-step explanation:
I am sure.
Answer: i think it is 3
Step-by-step explanation:
What integer is equivalent to 25 3/2?
Answer:
[tex]25\frac{3}{2} =26.5[/tex]
Step-by-step explanation:
This mixed number can be separated into 25 and [tex]\frac{3}{2}[/tex]. Convert the fraction to a decimal by plugging it into a calculator, then add 25.
If you meant what whole number is equivalent, that does not exist.
There are 900 3-digit integers, the integers between 100 and 999, inclusive. What percent of these integers contain only odd digits
Each digit can be one of {1, 3, 5, 7, 9}, so there are 5 choices for each. Then there are 5•5•5 = 5³ = 125 integers containing only odd digits, which means they make of 125/900 ≈ 14% of them.
The annual rainfall in a town has a mean of 51.84 inches and a standard deviation of 8.05 inches. Last year there was rainfall of 63 inches. How many standard deviations away from the mean is that
It is 1.39 standard devaitions away from the mean.
Since the mean x = 51.84 inches and the standard deviation, σ = 8.05 inches.
The amount of rainfall last year was X = 63 inches.
The difference between X and the mean x is d = X - x
= 63 - 51.84 in
= 11.16 in
To find the number of standard devaitions X is from the mean, n, we divide d by the standard deviation,σ.
So, n = d/σ
= 11.16 in/8.05 in
= 1.39
So, it is 1.39 standard devaitions away from the mean.
Learn more about number of standard deviations here:
https://brainly.com/question/24254824
1/5 divided by 2/3 input the answer as a fraction
Answer:
Three tenths/ 3/10
Step-by-step explanation:
1/5 divided by 2/3 is 0.3 which is equal to 3/10
solve for x and y then find the measure of each angle
Step-by-step explanation:
∵ MP is a straight line.
∴ ∠MNQ + ∠PNQ = 180°
[tex](3y + 8)° + (3y + 22)° = 180° \\ 3y + 8 + 3y + 22 = 180 \\ 6y + 30 = 180 \\ 6y = 150 \\ y = 25[/tex]
∵ MP is a straight line.
∴ ∠MNR + ∠PNR = 180°
[tex](2x + 5)° + (3x - 55)° = 180° \\ 2x + 5 + 3x - 55 = 180 \\ 5x - 50 = 180 \\ 5x = 230 \\ x = 46[/tex]
True / False: ANOVA, Part I. Determine if the following statements are true or false in ANOVA, and explain your reasoning for statements you identify as false.
(a) As the number of groups increases, the modified significance level for pairwise tests increases as well.
(b) As the total sample size increases, the degrees of freedom for the residuals increases as well.
(c) The constant variance condition can be somewhat relaxed when the sample sizes are relatively consistent across groups.
(d) The independence assumption can be relaxed when the total sample size is large.
PLEASE SHOW YOUR WORK!!!
Solve for y: 3^3 + 14 y- (25y - 13) = y + 7y - 9y
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3^3+14*y-(25*y-13)-(y+7*y-9*y)=0
Equation at the end of step 1
((3³ + 14y) - (25y - 13)) - -y = 0
Pull out like factors :
40 - 10y = -10 • (y - 4)
Equation at the end of step3:
-10 • (y - 4) = 0
STEP4:
Equations which are never true:
Solve : -10 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4
[tex]y = 4[/tex]Find the square of the given algebraic expression (p+9).
I mark u brainliest answer
Help help help help help help help help help help help
Answer:
A' 2,2
B' 3, -1
C' -1,0
Step-by-step explanation:
Because you're translating it by -2, 3, you're basically subtracting 2 from the x value and adding 3 to the y value.
A = 4, -1
A' = 2, 2
B = 5, -4
B' = 3, -1
C = 1, -3
C' = -1, 0
DeAnna Worley is the office manager at Central
BioEnergy. She is married with one dependent. Her annual
graduated state income tax is $3,520. What is her semimonthly
salary
Answer:
67 i thing so if it wrong sorry and ill answer it again ight
Step-by-step explanation:
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of $15. a) What assumptions must you make in order to use these statistics for inference
The assumptions required for making inference about a population using sample data include ;
The 10% condition, sample size must not be more than 10% of the population size Data should be approximately normal with sample size, n being greater than 30 (n ≥ 30).The sample selection must be independent, as the outcome of a certain trial must not depend on the outcome of another.Learn more : https://brainly.com/question/25609474
Plz help me well mark brainliest!!
Answer:
x=-52
1/3x-2/3=-18
multiply both sides by 3
x-2=-54
x=-54+2
x=-52
Use the ALEKS calculator to write 2/63 as a percentage.
Round your answer to the nearest tenth of a percent.
Answer:
3.2%
Step-by-step explanation:
2 / 63 = 0.031746031746
0.031746031746 x 100 = 3.1746031746 and round
Please help! Answer if correctly only.
Answer:
f(X)= 4 and g(X)= 49 are the answers!
Answer:
f(6) = -8
g(-3) = 49
Step-by-step explanation:
So when observing a function we have to remember that the desired input value is correspondent to the function. So when looking at the first function of:
f(x) = -2x+4
we can see that we are trying to find f(6) meaning all of the values of x are 6 in the equation. When plugging in the value of x into the equation then we have:
f(6) = -2(6)+4
the next step would be to simplify. -2*6 = -12 and -12+4=-8 and thus:
f(6) = -8
Now the steps are the same with g(-3) except with the other function:
g(x) = -2x^3-5
g(-3) = -2(-3)^3-5
g(-3) = 49