Plz answer the questions

How many different 4 digit even numbers can be written using 0,5,6,3,8,7?<br><br> help asap please!!

fiasKO [112]

Step-by-step explanation:

I guess that means the digits can not be repeated in such a number.

let's start with how many numbers in general can be created :

we have 6 basic digits, and we are pulling 4 of them for a number.

if the sequence of the pulled digits would not matter, it would be combinations C (6, 4).

but we are creating different numbers, so the sequence of the digits does matter. so, it is permutations P (6, 4).

P(6, 4) = 6!/(6-4)! = 6!/2! = 6×5×4×3 = 360

so. bauxite, we can create 360 different 4 digit numbers out of these 6 digits.

but not all of them are wanted.

for example, I assume we don't want the numbers that start with a 0, because they would normally count as 3-digit numbers.

if that assumption is correct, we need to find how many would start with a 0, and subtract those from the total number.

since we are handling all 6 digits in the same way, an equal number must start with 0, with 5, with 6, with 3, with 8 and with 7.

so, 1/6 of the total number start with 0 : 360×1/6 = 60.

that means the total number of 4-digit numbers out of these 6 digits that do not start with 0 is 360-60 = 300.

but we are still not finished : we only want even numbers. that means they end with 0, 6 or 8.

in the same way we considered the first position, we consider also the last position. we have an equal amount of numbers that end with the different digits.

and so, we have 1/6 of 300 for each ending digit.

we want the specified 3 digits as end digits, so we get

3×1/6 of the 300 = 1/2 × 300 = 150

so, we can write 150 different 4-digit even numbers out of these 6 digits.

3 0

3 years ago

Can anyone help me convert these??

KIM [24]

Answer:

0.321233-cups, 0.321233-tablespoon, 0.321233-teaspoon

Step-by-step explanation:

the next 2 questions I can't convert because I don't have grams

4 0

3 years ago

Read 2 more answers

Moya picked 3 dozen apples she wents to share her apes in equal groups. show how many different way can she do this

lys-0071 [83]

Answer:

Groups of 12, Groups of 4, Groups of 6, Groups of 18

Step-by-step explanation:

12 x 3 = 36

36 splits evenly into 12, 4, 6, and 18 therefore that is your answer.

5 0

3 years ago

HELP PLEASE!!!

VMariaS [17]

Answer:

Neither

Step-by-step explanation:

First, you need to put your equations in y=mx+b form

Your first equation...

5x + 4y = 3

4y = 3-5x

y = -5/4x + 3/4

Your second equation...

5x-4y = -3

-4y = -5x -3

y = 5/4x + 3/4

The slopes aren't the same and are not reciprocals, so the answer would be neither.

7 0

3 years ago

Suppose that a tunnel is dug through the center of the earth. You stand on a tower 100 m tall and drop a 3-kg rock into the tunn

Mashutka [201]

Answer:

The frequency of the resulting harmonic motion is 0.000219 Hz

Step-by-step explanation:

We are going to calculate the time it takes for one single wave ocillation.

Frequency and the time taken to finish a single wave oscillation are inversely proportional. The formula for calculating frequency when given the time taken to complete a wave cycle is written as: f = 1 / T

In this formula, f represents frequency and T represents the time period or amount of time required to complete a single wave oscillation.

I consider the initial speed to be zero, because it is of no significance compared with the free fall into the earth, through the earth and back again.

Given from Wikipedia:

The diameter of the earth is 1.2742 * 10⁴ km which is 1.27 * 10⁷ m

2 times the radius = diameter, so the radius of the earth = (1.27 * 10⁷ m) /2 = 6.4 * 10⁶ m

radius earth = r

r = 6.4 * 10⁶ m

Now imagine the tunnel and the free fall.

1. Initially the rock has no speed.

2. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

3. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed and it has travelled the distance r !

4. After this moment, the Rock will be slowed down because of the negative accelleration...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely, and again passing the distance r.

5. Now at the other end of the earth there is the same initial situation as described at point 1, only the Rock has travelled the distance equal to the diameter of the earth, (exactly 2 times r).

So basically, the samething happens once more, only this time it starts exactly from the other end of the earth...

6. Initially the rock has no speed.

7. Due to the gravitational accelleration, the rock will increase it's speed every second by a factor of 9.8.

8. The Rock gains speed untill it reached the centre of the earth. By then it will have reached it's maximum speed.

9. By now the Rock will be slowed down because of the negative accelleration... It is moving towards the initial starting point...

After it has travelled from the centre of the earth to the other end of the earth, it will have stopped completely.

10. Now finally the Rock is exactly at the starting position.

In reality there will have been some loss of speed due to friction, so the Rock will be slightly lower then the 100 m above the ground.

let's calculate the time it takes to free fall for the distance r.

initial speed =0 and after 6.4 * 10⁶ m it's speed will be maximum. We need to find out how much time passes before that distance is passed.

r = v*t + 0.5*a*t²

r = 0 + 0.5*a*t²

0.5*a*t² = r

t² = r / ( 0.5 * a )

t² = 6.4 *10⁶ / ( 0.5 * 9.8 )

t² = 1.306 * 10 ⁶

t = 1142.86 s

Now please confirm that in order for the Rock to move back to the initial starting point it has to travel 4 times as much time. It has to travel r to centre of the earth then another r to travel to to the other side of the earth, and back again. So indeed 4 times r.

The time it will take must be the same as 4 * 1142.86 s

now this is the time of one single wave ocillation.

Since T = 4571.43 s

f = 1 / 4571.43

f = 0.00021874993164 Hz

The frequency of the resulting harmonic motion is 2.19 *10-4

The frequency of the resulting harmonic motion is 0.000219 Hz

6 0

3 years ago