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
Anna11 [10]
3 years ago
8

I WILL GIVE BRAINLIEST TO BEST EXPLANATION!! How many 6-digit numbers, formed using each digit from 1 to 6 exactly once, are div

isible by 6?
Mathematics
2 answers:
wolverine [178]3 years ago
4 0

Answer:

There are 360 such numbers.

Step-by-step explanation:

The number of 6-digit numbers, formed using each digit from 1 to 6 excactly once, means we can have numbers like

123456, 123465, 123546,123564,.... 654321

The number of such numbers is given by 6! because we have a choice of 6 numbers for the first digit, 5 left for the next, ... until the last digit has only one choice.

6! = 6*5*4*3*2*1 = 720

We know that 1+2+3+4+5+6 = 21 is divisible by three, so all 720 numbers are divisible by 3.

However, to be divisible by six, we need a number divisible by three AND divisible by two.

Thus, out of the 720 numbers, we need count only the even numbers, which are exact half of the 720, or 360.

Therefore there are 360 6-digit numbers, formed using each digit from 1 to 6 exactly once, are divisible by 6.

Anna35 [415]3 years ago
3 0

Answer:

360 numbers

Step-by-step explanation:

6-digit  numbers => the numbers have the form <u>abcdef</u>

f  3 values, <em>f = {2; 4; 6}</em>

<u>a</u>  <em>5 values</em>;   <u>b</u>  <em>4 values</em>, <u>c </u>  <em>3 values</em>,  <u>d</u>   <em>2 values</em>,   <u>e</u>  <em>one value,</em>

=> 5 * 4 * 3 * 2 * 1 * 3 = 360 numbers

You might be interested in
A coin is tossed 4 times. What is the probability if getting 2 heads, 2 tails?
gogolik [260]

Answer: 2:4

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Use the identity below to complete the tasks:
pashok25 [27]

Answer:

a = 5r² and b = r²s

Step-by-step explanation:

a3 - b3 = (a - b)(a + ab + b2)

Expressing 125q^6-r^6s^3 as a difference of 2 cubes

125q^6-r^6s^3  

= 5³(r²)³ - (r³)²s³

= (5r²)³ - (r²s)³

Comparing with a³ - b³

a = 5r² and b = r²s

Hence the value of a is 5r² and b is r²s

4 0
2 years ago
I need help with these two please :’)
tatiyna

Answer:

59)

Therefore the height of the pyramid is 14 meter.

60)

Therefore the Diameter of Cone is 17.32 cm.

Step-by-step explanation:

59 )

Given:

Shape is Rectangular Pyramid,

Length = 3 meter

Width = 8 meter

Volume of Rectangular Pyramid = 112 cubic meter

To Find:

Height:

Solution:

We Know,

\textrm{Volume of Rectangular Pyramid}=\frac{1}{3}(Length\times Width\times Height)

Substituting the given values we have

112=\frac{1}{3}(3\times 8\times Height)\\ \\\therefore Height=\frac{336}{24}\\\\\therefore Height=14\ meter\\

Therefore the height of the pyramid is 14 meter.

60 )

Thee shape is of Cone

Given:

Height= 5 cm

Volume of cone = 125 π cm³

To Find:

Diameter of a cone = d = ?

Solution:

We know,

\textrm{Volume of cone}=\frac{1}{12}\pi (Diameter) ^{2}\times Height

Substituting the given values we have

125\pi =\frac{1}{12}\pi  d^{2}\times 5\\ \\d^{2}=25\times 12\\  \\d^{2}=300\\\\d=17.32\\   \therefore Diameter = 17.32\ cm

Therefore the Diameter of Cone is 17.32 cm.

6 0
3 years ago
To gain a pass a student needs to achieve a mean of at least 60% in eight tests. In the first seven
Tanzania [10]

Step-by-step explanation:

the mean value is the sum of all data points divided by the number of data points.

first we have 7 tests and their mean value :

(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54

that means

(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378

in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480

because only then we have

(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60

and the student passes.

so,

(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480

378 + t8 = 480

t8 = 480 - 378 = 102%

the student would have to achieve 102% on the 8th test.

which would be normally impossible, but maybe the tests involve some bonus points.

6 0
2 years ago
What is 709032-249136?
alex41 [277]
709,032 - 239,136 = <span>469,896

Hope I Helped!!!</span>
7 0
3 years ago
Other questions:
  • as a puppy, kim's dog weighs 15 ounces. as an adult, kim's dog weighs 8 pounds. how many ounces did kim's dog gain
    9·2 answers
  • The graph shows the temperature of ice cream in an ice chest during an overnight trip. What is the domain of this function? Grap
    12·1 answer
  • What is the solution to the following equation? x+(-21)=8
    15·2 answers
  • 324 = a2<br>I need it for homework
    5·2 answers
  • The cube of the difference of 1 and a number
    11·1 answer
  • For what values of x and y must the figures below be a parallelogram?<br> SOMEONE HELP PLEASE!!!
    14·1 answer
  • Yesterday I sold 64 icecreams. This morning I sold 80 icecreams. With what percentage did my sales increase?
    11·1 answer
  • What is 29% of 135 kg?.<br><br><br><br><br>pls ans​
    11·1 answer
  • Find the percent of change for 25 is decreased to 10.
    7·1 answer
  • Which expression is equivalent to (2 cubed) Superscript negative 5?.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!