1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pentagon [3]
3 years ago
15

How many different combinations are possible if each lock contains the numbers 0 to 39, and each combination contains three dist

inct numbers?(Combinations like 15-15-15 and 12-12-5 are not used.)
Mathematics
1 answer:
Georgia [21]3 years ago
8 0
(e) Each license has the formABcxyz;whereC6=A; Bandx; y; zare pair-wise distinct. There are 26-2=24 possibilities forcand 10;9 and 8 possibilitiesfor each digitx; yandz;respectively, so that there are 241098 dierentlicense plates satisfying the condition of the question.3:A combination lock requires three selections of numbers, each from 1 through39:Suppose that lock is constructed in such a way that no number can be usedtwice in a row, but the same number may occur both rst and third. How manydierent combinations are possible?Solution.We can choose a combination of the formabcwherea; b; carepair-wise distinct and we get 393837 = 54834 combinations or we can choosea combination of typeabawherea6=b:There are 3938 = 1482 combinations.As two types give two disjoint sets of combinations, by addition principle, thenumber of combinations is 54834 + 1482 = 56316:4:(a) How many integers from 1 to 100;000 contain the digit 6 exactly once?(b) How many integers from 1 to 100;000 contain the digit 6 at least once?(a) How many integers from 1 to 100;000 contain two or more occurrencesof the digit 6?Solutions.(a) We identify the integers from 1 through to 100;000 by astring of length 5:(100,000 is the only string of length 6 but it does not contain6:) Also not that the rst digit could be zero but all of the digit cannot be zeroat the same time. As 6 appear exactly once, one of the following cases hold:a= 6 andb; c; d; e6= 6 and so there are 194possibilities.b= 6 anda; c; d; e6= 6;there are 194possibilities. And so on.There are 5 such possibilities and hence there are 594= 32805 such integers.(b) LetU=f1;2;;100;000g:LetAUbe the integers that DO NOTcontain 6:Every number inShas the formabcdeor 100000;where each digitcan take any value in the setf0;1;2;3;4;5;7;8;9gbut all of the digits cannot bezero since 00000 is not allowed. SojAj= 9<span>5</span>
You might be interested in
Trong một thùng có chứa 3 bi đỏ 4 bi đen
borishaifa [10]

Answer:

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over.ep explanation:

7 0
2 years ago
A party planner is making gift bags for an event. He has 96 pencils,
Yuliya22 [10]

Considering the greatest common divisor, you obtain:

  • the greatest number of gift bags that the party planner can make is 12.
  • the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

<h3>Greatest common divisor </h3>

The greatest common divisor is the largest number that exactly divides two or more numbers at the same time. That is, it is the largest number by which two or more numbers can be divided, resulting in a whole number.

A method to calculate the greatest common factor must follow the following steps:

  • Decompose or separate each number into prime factors.
  • Common factors are noted.
  • In each of the commons, the factor with the smallest exponent is chosen.
  • Multiply the chosen factors.

<h3>This case</h3>

To find the greatest number of gift bags the party planner can make, you find the greatest common divisor.

To do this, decompose the numbers 96, 36 and 24:

  • 96= 2⁵×3
  • 36= 2²×3²
  • 24= 2³×3

The common factors with the smallest exponent are: 2² and 3

So, the greatest common divisor between 96, 26 and 24 is calculated as: 2²×3= 4×3= 12

This means that the greatest number of gift bags that the party planner can make is 12.

To calculate the number of each item present in each bag, you divide the quantity of each item by the quantity of gift bags:

  • 96 pencils÷ 12= 8 pencils
  • 36 erasers÷ 12= 3 erasers
  • 24 pencil toppers÷ 12= 2 pencil toppers

Finally, the number of each item present in each bag is 8 pencils, 3 erasers and 2 pencil toppers.

Learn more about greatest common divisor:

brainly.com/question/11993520

brainly.com/question/18635265

brainly.com/question/6032811

#SPJ1

5 0
11 months ago
What is the equation of the line through (4,5) and (0,-3)
Allisa [31]

Answer:

y = 2x - 3

Step-by-step explanation:

Slope intercept equation of a line:

y = mx + b

(0, -3) is the y-intercept, so b = -3

We have

y = mx - 3

Now we use the two points to find the slope.

slope = m = (-3 - 5)/(0 - 4) = -8/(-4) = 2

y = 2x - 3

8 0
2 years ago
Read 2 more answers
William just got hired for a new job and will make \$78,000$78,000 in his first year. William was told that he can expect to get
ASHA 777 [7]

Answer:

$162,000

Step-by-step explanation:

I hope this is help

7 0
2 years ago
Read 2 more answers
Simplify each expression then factor the expression 14-28t-5(7+10t)
ludmilkaskok [199]

Answer:

Simplified: -21-98t

Factored: -7(14t+3)

Step-by-step explanation:

The given expresion is:

14-28t-5(7+10t)

We expand the parenthesis to get:

14 - 28t -35 - 70t

We group like terms to get:

14 -35  - 28t- 70t

We combine similar terms to get:

- 21- 98t

We now factor to obtain:

- 21- 98t =  - 7(14t + 3)

5 0
3 years ago
Other questions:
  • A tent is in the shape of a triangular prism. The front and back are isosceles triangles with base 6 feet and height 4 feet. The
    11·2 answers
  • Select the table that represents the function f(x) = 3x + 5
    8·1 answer
  • A fish tank has 240 quarts of water. Levi adds another 120 quarts to the tank.
    7·2 answers
  • write a division equation to represent the repeated subtraction 32 take away 8 is 24 24 take away 8 is16 16 take away 8 is 8/8 t
    7·1 answer
  • Triangle D E F is shown. Angle D E F is a right angle. The length of hypotenuse DF is 13, the length of E F is 5, and the length
    13·1 answer
  • Please help asap!!!!
    10·2 answers
  • Help will give brainliest and don't put any links or I will report u and thx
    14·1 answer
  • A random sample of 5 paintings was studied in a museum. Please consult the data chart above to answer the following question. Wh
    5·1 answer
  • What is the volume of the right rectangular prism?
    15·2 answers
  • A manufacturing company finds that the daily cost associated with making tennis balls is
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!