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
What is the greatest to least -1, 3/2, 2.5, 0, -1/2, 2, 0.2
zlopas [31]

Answer: 2.5, 2, 3/2, 0.2, 0, -1/2, -1

Step-by-step explanation:

From left to right biggest number

5 0
3 years ago
If the volume of a cube is 729cm^3, what is the surfface area.<br><br> Thanks!!
bezimeni [28]

Answer:

486cm^2

Step-by-step explanation:

cube volume: 729cm^3

cube faces count: 6

How you calculate square area:

s(cm) * s(cm) or just s^2(cm^2)

s = side length

If you want to find out the side length of a cube by its volume. Then simply just remove the ^3 by taking the cubic root (also written ^(1/3))

729^(1/3) = 9

then just calculate the area like i showed earlier:

(9cm)^2 = 81cm^2

But that is only one side of a cube's 6 sides, so multiply by 6:

81cm^2 * 6 = 486cm^2

Hope i could help :D

Dont be scared to ask me questions..

4 0
2 years ago
You drive 8 miles from your house to your friend's house. Your house is at an elevation of 240 feet. Your friend's house is at a
dedylja [7]
(680 - 240) / 8 = 440/8 = 55 ft per mile
7 0
3 years ago
Find the midpoint of the line segment with the given endpoints: (-1, -6) and (-6, 5).
Vikentia [17]

Answer:

Step-by-step explanation:

First, we will find the midpoint for the x - coordinate first.

Midpoint (x) = \frac{-1+(-6)}{2} \\=\frac{-1-6}{2} \\=\frac{-7}{2} \\=-3.5

Now we will find the midpoint for the y - coordinate.

Midpoint (y) = \frac{-6+5}{2} \\=\frac{-1}{2} \\=-0.5

Therefore from these 2 values we know that the midpoint of this 2 points is (-3.5,-0.5)

8 0
1 year ago
The value of a car depreciates by 35% per year. Work out the current value of a car bought 2 years ago for £20000
Rzqust [24]

First year: the depreciation is (35/100) x 20000 = £7000; now the value of the car is £20000 - £7000 = £13000;

Second year: the depreciation is (35/100) x 13000 = £4550; the current value of the car is £13000 - £4550 = £8450.

6 0
3 years ago
Other questions:
  • Machines a and t were both cleaned this week machine a is cleaned every 12 weeks and machine t is cleaned every 8 weeks what is
    9·2 answers
  • Which equation is in standard form and represents a line with the slope -1 through the point (-3,5)
    8·1 answer
  • What Is The Answer To: 2x3x21x92
    14·2 answers
  • The larger of two numbers is 12 times the smaller number. if the sum of two numbers is 15,600, find the two numbers.​
    9·1 answer
  • Consider ΔDEF with centroid at point G and median EH. What is GH, if EG=3x+4 and GH=x+10?
    8·1 answer
  • Solve 7w – 3r = 15 for r. Show your work.
    12·2 answers
  • Someone please help! <br> Find the value of x. Then find the angle measures of the triangle.
    9·1 answer
  • 8x1 = 8
    11·2 answers
  • Graph the solution c-12&gt;-16
    10·1 answer
  • If f(x) =1/9x-2 what is f^1(x)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!