A lock has a 3-number code made up of 15 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
Answers
Answer:2730
Step-by-step explanation:
The number of ways we can choose three different numbers in order for a unique code for this case is 2730
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number codeThere are 15 numbers available.None of the number can repeat.In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = [tex]^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730[/tex]
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
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Related Questions
The Clothes Barn is having a 65% off sale on all the dresses. Jennifer paid $43.75 for a dress that was on
sale. What was the original price of the dress?
1. $125.00
2. $28.44
3. $15.31
4. $105.00
Answers
Answer:A
Step-by-step explanation:
I used the process of elimination. I did, 125 x .65 to get 81.25. Then, I subtracted 81.25 to 125. To get 43.75.
The original price of the dress was $125.00.
What is the percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.
How to solve this problem?Given that the discount = 65%
Sale price = $43.75
Let the original price of the dress is $x.
Now, sale price = x - x * 65% = x - x * 65/100 = (100 - 65)x/100 = 35x/100
We can write
35x/100 = 43.75
i.e. x = (43.75 * 100)/35 = 4375/35 = 125
Therefore, the original price of the dress was $125.00. So, option 1 is correct.
Learn more about percentages here -
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A sample of restaurants in a city shows that the average cost of an appetizer is $6.32 with a standard deviation of
$0.47. A brand new restaurant wants to get noticed by offering appetizers for a much lower price. To determine the
lower price, should the formula use a z-value that is greater than or less than-1?
a. Greater than -1
C. Greater than 1
b. Less than -1
d. Either way, it doesn't matter
Please select the best answer from the choices provided
A
B
Answers
Which of the below is the correct name for a plane that contains points A, B, C, and D?
plane CDE
plane CD
⭐️plane ACD
plane A
Answers
Answer:
Step-by-step explanation:
Determine the volume!
Answers
I can’t see the picture
Explanation:
What do you need help with?
Here is the problem for you :)
Answers
Answer:
Angle Y:
Sin(Y) = 36/39, if simplified: 12/13, in decimal it would be: 0.92Cos(Y) = 15/39, if simplified: 5/13, in decimal it would be: 0.38Tan(Y) = 36/15, if simplified: 12/5, in decimal it would be: 2.4Angle X:
Sin(X) = 15/39, if simplified: 5/13, in decimal it would be: 0.38Cos(X) = 36/39, if simplified: 12/13, in decimal it would be: 0.92Tan(X) = 15/36, if simplified: 5/12, in decimal it would be: 0.42Hope this helps!
A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with s = 17.6 milligrams. A confidence interval of 173.8 mg < μ < 196.2 mg is constructed for the true mean cholesterol content of all such eggs. It was assumed that the population has a normal distribution. What confidence level does this interval represent?
Answers
Answer:
The appropriate solution is "95%".
Step-by-step explanation:
The given values are:
Lower bound,
= 173.8
Upper bound,
= 196.2
Mean of cholesterol,
= 138 milligrams
S = 17.6 mg
Now,
The margin of error (E) will be:
= [tex]\frac{Upper \ bound-Lower \ bound}{2}[/tex]
= [tex]\frac{196.2-173.8}{2}[/tex]
= [tex]\frac{22.4}{2}[/tex]
= [tex]11.2[/tex]
As we know,
⇒ [tex]E=t_{\alpha 12}\times \frac{S}{\sqrt{n} }[/tex]
On putting the values, we get
⇒ [tex]11.2=t_{\alpha 12}\times \frac{17.6}{\sqrt{12} }[/tex]
On applying cross-multiplication, we get
⇒ [tex]t_{\alpha 12}=2.2044[/tex]
∴ [tex]\frac{\alpha}{2} =0.025[/tex]
[tex]\alpha = 0.025\times 2[/tex]
[tex]=0.05[/tex]
hence,
The confidence level will be:
⇒ [tex]CI=1-\alpha[/tex]
⇒ [tex]=1-0.05[/tex]
⇒ [tex]=0.95[/tex]
⇒ [tex]=95[/tex]%
what is 1/3 plus 4/5
Answers
You can round it and then it will be 1.13
The rounding will be that as the number after the point is not 5 or above
Answer:
1.13333333333
Step-by-step explanation:
sorry if it’s wrong!
-3.5 + 7.75 + 6.9 (4.3)
Answers
Answer:
33.92
Step-by-step explanation:
A school has 510 male students and 850 female students. If a student from the school is selected at random, what is the probability that the student would be a male?
- 0.5
- 1
- 0.375
- 0.625
Answers
Answer:
0.375
Step-by-step explanation:
510 male out of a total of 1360
510/1360 = 0.375
Select the correct answer.
What does an individual's effective tax rate indicate?
Α.
the average Income earned
B.
the average tax rate
C.
the minimum tax rate
D.
the next year's tax rate
Answers
Answer: B
Step-by-step explanation:
An individual's effective tax rate is the average tax rate.
Please help me :( I feel worthless because of math
Answers
Answer:
I think 262 is the right answer.
Step-by-step explanation:
Don't feel worthless because of math! Math is a diffcult to understand subject, and a real pain in the butt.
Some help please! :) Branliest
Answers
Answer:
Households without a vehicle were not surveyed. D
Step-by-step explanation:
I just finished with Maps testing like 10 minutes ago XD good luck!!
What is the probability of drawing 2 aces (at once) from a standard deck of cards? Leave your answer as a simplified fraction
Answers
Anwner : 4/52
Explanation : The chance of drawing one of the four aces from a standard deck of 52 cards is 4/52; but the chance of drawing a second ace is only 3/51, because after we drew the first ace, there were only three aces among the remaining 51 cards. Thus, the chance of drawing an ace on each of two draws is 4/52 × 3/51, or 1/221.
Please help will give brainliest
Small
Large
Blue 17
Red
8
3
12
?
Find: P(Red and Small)
Remember to reduce your answer.
Answers
Answer:
3/10
Step-by-step explanation:
Remark
The denominator of the probability is the entire amount present. Just add
Denominator
Blue/Large 17
Red/Large 8
Small 3
Red Small 12
Total 40
Red / Small
P(red/small) = 12 / 40
P(red/Small) = 3 / 10
a(-6) = -42 what is a?
Answers
Answer:
it is 7
Step-by-step explanation:
What is product of 3x-4 an 5x^2-2x+6
help me please, please, please
Answers
15x^3-6x^2+18x-20x^2+8x-24
15x^3-26x^2+26x-24
Step-by-step explanation:
[tex]thank \: you[/tex]
Write the fraction as a decimal and as a percent.
1
4
1
3
Answers
Answer:
1/4 as decimal =0.25
and as percentage 25%
1/ 3 as decimal = 0.33
and as percentage = 33.33%
4log(2) x + log(2)5 = log(2)405
Answers
Answer:
3/2
Step-by-step explanation:
Similar Triangles
When are triangles considered similar?
a. corresponding angles are equal AND corresponding sides are proportional
b. corresponding angles are proportional AND corresponding sides are equal
c. corresponding angles are equal OR corresponding sides are proportional
d. corresponding angles are proportional OR corresponding sides are equal
Please select the best answer from the choices provided
Answers
Answer:
A. Corresponding angles are equal AND corresponding sides are proportional
Step-by-step explanation:
I calculated it logically
Answer:
A. Corresponding angles are equal AND corresponding sides are proportional
At one point during the hike, Noe is at an elevation of 453 feet. After descending at a rate of 50 feet per
minute, she reaches an elevation of 146 feet.
How long does the descent take?
Answers
Answer:
6.14 minutes or 6 minutes & 8.4 seconds
Step-by-step explanation:
Initial elevation: 453 ft
Final elevation: 146 ft
Difference in elevation: 453 ft - 146 ft = 307 ft
speed = 50 ft/min
speed = distance/time
time * speed = distance
time = distance/speed
time = (307 ft)/(50 ft/min)
time = 6.14 minutes = 6 minutes + 0.14 * 60 seconds
time = 6.14 minutes = 6 minutes + 8.4 seconds
25, 41, 49, 64Multiple ChoiceThe integers are not pairwise relatively prime since two of them have a common factor 3.The integers are pairwise relatively prime because there is no prime that divides all of them.The integers are pairwise relatively prime since two of them are prime.The integers are pairwise relatively prime because no two of them have a common prime factor.
Answers
Answer:
The integers are pairwise relatively prime since two of them are prime
Step-by-step explanation:
Given
[tex]25, 41, 49, 64[/tex]
Required
Determine if they are prime factors
First, we determine the gcd of the 4 numbers
[tex]25 = 1 * 5 * 5[/tex]
[tex]41 =1 * 41[/tex]
[tex]49 = 1 * 7 * 7[/tex]
[tex]64 = 1 * 2 * 2 * 2 * 2 * 2 * 2[/tex]
The common factor in the above computation is: 1
So:
[tex]gcd = 1[/tex]
Because the gcd is 1, this implies that no prime divides all the given numbers.
Hence, they are pairwise relatively prime
radio y diametro de
55.292cm
Answers
Answer:
Radio es 8.799974535 cm
Diametro es 17.59994907 cm
Explicación paso a paso:
Como tienes la medida en cm, me indica que es el perimetro del circulo
C=πd
55.292=3.1416 d
\frac{55.292}{3.1416} =d
3.1416
55.292
=d
17.59994907=d
Para sacar radio hay que dividir entre 2
r=8.799974535
1. Sandra is trying to determine the height of a light pole at the corner of the block on
which she lives. The shadow cast by the light pole is 5 feet.
If the angle of elevation from the sidewalk to the top of the light pole is represented
as e, which equation could be used to find the height of the light pole?
Answers
Answer:
h = 5(tane)
Step-by-step explanation:
The diagrammatic representation of the question given is attached below ;
The height of the light pole, h = opposite side
Adjacent side = 5 feets
Angle of elevation = e
Using trigonometry ;
Tan e = opposite / Adjacent
Tan e = h / 5
Making h the subject ;
h = 5(tane)
Find the missing angle x
Then BAC
Answers
Answer:
Step-by-step explanation:
since arc BC is 2 time the angle of A , then
2(9x +12) = 21x +3
18x +24 = 21x + 3
21 = 3x
7 = x
x = 7
∠BAC = 9(7) +12
∠BAC = 63 +12
∠BAC = 75°
plzzzzz help me is for mathhhh
Answers
HELP ASAP DUE TOMORROW
Answers
Answer:
5) P (arrive) + P (not arrive) = 100% Complements
80% + P( not arrive) = 100% Substitute thr ralees
P ( not arraive) = 100% - 80% Isolate the needed
P ( not arrive) = 20%
therefor, the probability of not arriving on time is:-
20%, or 0.20, or 1/5
The complements of arriving on time is not arriving on time.
The probability is equal to 100%
--------------------------------
hope it helps..
have a great day!
40% is NOT equivalent to....?
A. 0.4
B.2/5
C.40/100
D. 0.04
E. None correct
Answers
Answer:
d
Step-by-step explanation:
d is .04 percent plz mark branliest
NEED HELP PLZ
Consider the following set of equations:
Equation A: y = -x + 5
Equation B: y = 6x − 4
Which of the following is a step that can be used to find the solution to the set of equations? (4 points)
a
−x = 6x + 4
b
−x − 2 = 6x + 4
c
−x + 5 = 6x − 4
d
−x + 5 = 5x
Answers
Answer:
look at the picture i sent......
Answer:
for other guy brains
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ
Answers
Answer:
c) [tex]\frac{x-2}{x+6}[/tex]
Step-by-step explanation:
When given that function (f) is the following,
[tex]f(x)=\frac{x+2}{x^2+4x-12}[/tex]
The wisest move to first make is to factor the expression, factoring is the process by which one rewrites a quadratic expression as the product of two linear expressions,
[tex]f(x)=\frac{x+12}{(x+6)(x-2)}[/tex]
If is given that function (g) is the following,
[tex]g(x)=\frac{4x^2-16x+16}{4x+48}[/tex]
Then one should also factor the expression,
[tex]g(x)=\frac{4(x-2)^2}{4(x+12)}[/tex]
One is asked to find the following,
[tex]f(x)*g(x)[/tex]
To do this operation, one must multiply the two functions together. It is easiest to do so when the functions are in factored form,
[tex]f(x)*g(x)[/tex]
Substitute,
[tex](\frac{x+12}{(x+6)(x-2)})(\frac{4(x-2)^2}{4(x+12)})[/tex]
Simplify, cross out like terms in the numerator and denominator,
[tex]\frac{x-2}{x+6}[/tex]
Help !!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
6
1+6
2+5
3+4
4+3
5+2
6+1
hope it helps