How many different paths are there from the point (0, 0, 0) in three dimensional space to the point (7, 3, 4) if you are only allowed to move in steps of one unit in either the positive x direction, the positive y direction, or the positive z direction. (That is no backtracking is allowed and you can only move in a single direction on a given step)

Answers

Answer 1

Using the fundamental counting principle, it is found that there are 84 different paths.

-----------------------------

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

-----------------------------

The movements are independent, which means that the fundamental counting principle is used.

There are:

7 - 0 = 7 ways to move in the x-direction.3 - 0 = 3 ways to move in the y-direction.4 - 0 = 4 ways to move in the z-direction.

Thus, the number of different paths is:

[tex]T = 7 \times 3 \times 4 = 84[/tex]

A similar problem is given at https://brainly.com/question/24067651


Related Questions

4. what are two other ways to name plane v

Answers

Answer:

Plane ANM and Plane XNM.

Step-by-step explanation:

From the given figure, find the value of x and y:
pls pls pls answer my question​

Answers

Answer:

have a great day

god is great

A plant is already 12.00 meters tall and it will grow 20 cm every month.what is the plants height after 30 months

Answers

Answer:

18 m

Step-by-step explanation:

Hi there!

We're given:

⇒ The plant is already 12 m tall

⇒ It grows 20 cm every month

First, we must convert everything into the same unit. Divide 20 cm by 100 to convert it to meters:

20 ÷ 100 = 0.2

Now, we can form this equation:

Plant Height = 12 m + (0.2 m × number of months)

Let plant height be h and number of months be m:

[tex]H=12+0.2m[/tex]

To find the plant's height after 30 months, replace m with 30:

[tex]H=12+0.2(30)\\H=12+6\\H=18[/tex]

Therefore, the plant would be 18 m tall.

I hope this helps!

Simplify. (4x^2 - 2x) (-3x^2 - 4x^2 +1)
A) -12x^5 - 10x^4 + 8x^3 + 4x^2 -2x
B) -12x^5 -22x^4 - 8x^3 + 4x^2 - 2x
C) 12x^5 - 10x^4 +8x^3 + 4x^2 -2x
D) 12x^5 - 22x^4 - 8x^3 + 4x^2 - 2x

Answers

Answer:  Is the equation enered correctly?  

1.  The second term, (-3x^2-4x^2+1) is the same as (-7x^2 + 1)

2.  I don't see how the answer could contain an x^5 term.  The largest I see from the information is x^4

Step-by-step explanation:

1. a. How many times 45 be subtracted from 20835 to get 0?​

Answers

20835-45x = 0
Get the 45x to the other side
20835=45x
Divide both sides by 45
20835/45 =463
x=463

Answer:

463

Step-by-step explanation:

Division is repeated subtraction

So to get 0, we divide 20835 by 45

=> 20835/45

=> 463

6x10^-3 in standard notation

Answers

Answer:

0.006

Step-by-step explanation:

The number is currently in scientific notation. To change scientific notation into standard notation move the decimal place equal to the number of the exponent. In this case, the exponent is -3. So, move the decimal place 3 digits. Since the 3 is negative, move the decimal to the left. Therefore, 6.0x10^-3 becomes 0.006 because the decimal was moved 3 places to the left. When moving the decimal fill in any empty spaces with zeros.

charlie wants to order lunch for his friends he'll order 5 sandwiches and a $3 kids meal for his little brother. charlie has $28 . how much can he spend on each sandwich if they are all the same price?

Answers

Answer:

$5 for each sandwich.

Step-by-step explanation:

$28 - $3 = $25 (money left after purchasing meal for his little brother)

$25 / 5 sandwiches = $5

URGENT!!. Find the perimeter and area
9.85 m
15 m
11 m
9m

Answers

hope its helps

Step-by-step explanation:

total area = 99m² + 39.4m²

= 138.4m²

The lyric, "Historians research more than just the word of one/To learn all sides of history" most closely means that

Which?

Answers

Answer:

I would say C

Step-by-step explanation:

I said C because when people look for information they look at different sources instead of just one.

Please help me with A B and C

Answers

Answer:

b)A box from all 4 sides increases as the number increase

c)

Step-by-step explanation:

a+(n-1)d

a-first terms

d- difference

5+(n-1)4

5+4n-4

4n+1(the nth term)

so for 50th

its 4*50+1

Answer is 201 tiles

Hope this helps you :))

-7(8d+3z)+6 use z=-4 and d=7
Simplified is?

Answers

Answer:

-302

Step-by-step explanation:

z=-4

d=7

-7(8d + 3z) + 6

-7(8(7) + 3(-4)) + 6

-7(56 - 12) + 6

-302

“If I drink I die, if I eat I live. What am I?”

Answers

Answer:

fire ...............

Answer:

fire

Step-by-step explanation:

.....................

Nicole had the exact amount of money to buy 9 pens.
Instead she bought only 5 pens.
She used the rest of the money to buy 7 notebooks at $1.20 each.
How much money did Nicole have at first?​

Answers

Answer:

18.90$

Step-by-step explanation:

Pen = p

Notes = n

n = 1.20

5p + 7n = 9p

-9p + 5p + 7n = 0

-4p + 7n = 0

-4p + (7*1.2) = 0

-4p + 8.4 = 0

8.4/4 = p

2.1 = p

9p = 9*2.1

9p = 18.90$

Calculate the number of litres of water in the tank​

Answers

Answer:

SEE IMAGE FOR SOLUTION

HOPE IT HELPS

Step-by-step explanation:

900 litres

SOMEONE HELP ME PLEASE

Answers

Answer:

25.7

Step-by-step explanation:

PQ=PR-QR

PQ=38.3-12.6

PQ=25.7 cm

Answer: PQ = 25.7 cm

Concept:

Here, we need to know the idea of the segment addition postulate.

The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

Given information

PR = 38.3 cm

QR = 12.6 cm

Given expression deducted from the segment addition postulate

PQ = PR - QR

Substitute values into the expression

PQ = (38.3) - (12.6)

Simplify by subtraction

PQ = [tex]\boxed{25.7cm}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Which problem has a sum of 16.52 ?

1.42 + 3.1 + 12 = 16.52

Answers

Yh this is the answer

what is 3/4 x 3 + 2/4 + 1 = ????

as a whole number

Answers

Answer:

3/4×3 = 2.25

2/4×1= 0.5

Step-by-step explanation:

how it helps u

The cube of a whole number is 48 more
than the square of the same number.
What is the number?

Answers

Answer:

x  = 4

Step-by-step explanation:

Let the number = x

x^3 = x^2 + 48

x^3 - x^2 - 48 = 0

The answer is 4, but I have no method of doing this rigorously. I can just show that it is true.

x^3 = 4^3 = 64

x^2 = 4^2 = 16

64 - 48 = 16

Please Help! (Solve for x!)

Answers

Answer:

x=-8

Step-by-step explanation:

multiplying -5 * 2 to get rid of the 2 and the denominator which equals -10. Then, add two to the other side which equals negative eight.

James had “x” amount of jellybeans. Jordan had twice the amount of jellybeans than James. If they had a total of 72 jellybeans altogether, how many jelly beans did James have?​

Answers

Hope it helps! If it is, Brainliest please!

Write an algebraic expression for the following phrase: 3 more than twice a number O 3x + 2 O3+2+ x 02x3 2x+3​

Answers

Answer:

2x+3

Step-by-step explanation:

2x is twice a number and +3 is three more than that number.

for real values of x, the expression 2x-5 is negative

Answers

Answer:

(a+b) (a-b)

2x-5

x(-5+2)

x-3 x+3

Please help, ill give brainliest, only if its right

Answers

Answer:

it would be in the fourth quadrant, directly underneath where it is now. the base would be c and d

7 tens x 10 in standard form ​

Answers

Answer:

700

Step-by-step explanation:

7 tens is 70. 70*10=700.

is this right ,and if not respond quickly

Answers

Answer:

Q.3 It takes 490 seconds for light to get from the sun to the earth should light travel at the above-mentioned speed.

18. The cost of a television set recently increased from $160 to $200. What was the percent of increase in the price?
(A) 25
(B) 20
(C) 1/4
(D) 1/5
(E) 40

Answers

Answer:

25%

Step-by-step explanation:

Take the new price and subtract the original price

200-160

40

Divide by the original price

40/160

1/4

.25

Change to percent form

.25 *100%

25%

evaluate the expression (-2) - ( -5)

Answers

Answer:

The answer is 3

Step-by-step explanation:

(-2)+5=3

If (x + 4)^2 = 49 and x < 0. what is the value of x?

Answers

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

-11 + 4 = -7

(-7)^2 = 49

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

Write the equation y=-4x+7 passing through the point (-6,-8) in point slope intercept form?

Answers

Answer:

y + 8 = -4 (x + 6)

Step-by-step explanation:

y + 8 = -4 (x + 6)

I’m struggling.help please.

Answers

Answer:

21,23,25,27,29... and etc

Step-by-step explanation:

13,15,17,19, your going by 2, so.. 21,23,25,27,29. and counties. I don't know how long it goes but there you go hopefully this helps <3.

Answer:

2n + 11

Step-by-step explanation:

2(1) + 11 = 13

2(2) + 11 = 15

2(3) + 11 = 17

the 2 is the constant difference between the first 2 terms.

the numbers in brackets are the term number.

you have to multiply the difference with the term number.

then you will have to take that answer and subtract it from the first term number.

hope it helps xxx

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