Ask question

Ask question

All categories

oksano4ka [1.4K]

2 years ago

5

The faces of a cube are to be numbered with integers 1 through 6 in such a way that consecutive numbers are always on adjacent f

aces (not opposite ones). The face numbered 1 is on top and the face numbered 2 is toward the front. In how many different ways can the remaining faces be numbered?

1 answer:

Blizzard [7]2 years ago

7 0

Answer:

Total different ways to number the remaining faces is 10.

Step-by-step explanation:

It is given that consecutive numbers are always on adjacent faces (not opposite ones).

The face numbered 1 is on top and the face numbered 2 is toward the front.

Top = 1

Front = 2

The remaining faces are left right bottom back. Total possibilities are shown below.

S.no. 3 4 5 6

(1) Right Back Bottom Left

(2) Right Back Left Bottom

(3) Right Bottom Left Back

(4) Right Bottom Back Left

(5) Bottom Right Back Left

(6) Bottom Left Back Right

(7) Left Back Bottom Right

(8) Left Back Right Bottom

(9) Left Bottom Right Back

(10) Left Bottom Back Right

When Bottom=3, then we can not place 4 on back because doing this 5 and 6 are opposite ones.

Therefore, total different ways to number the remaining faces is 10.

You might be interested in

If x > y, then |x| > |y|. This conditional statement is (true or false) . Counterexample:

Mademuasel [1]

$x=1$
$y=-2$

$x>y$ is true, but $|x|=1$ and $|y|=2$ , but $1>2$ is false.

3 0

2 years ago

Which is the value of the expression (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed?

Flura [38]

Answer:

The value to the given expression is 8

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Step-by-step explanation:

Given expression is (StartFraction (10 Superscript 4 Baseline) (5 squared) Over (10 cubed) (5 cubed)) cubed

Given expression can be written as below

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3$

To find the value of the given expression:

$\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=\frac{((10^4)(5^2))^3}{((10^3)(5^3))^3}$

( By using the property ( $(\frac{a}{b})^m=\frac{a^m}{b^m}$ )

$=\frac{(10^4)^3(5^2)^3}{(10^3)^3(5^3)^3}$

( By using the property $(ab)^m=a^mb^m$ )

$=\frac{(10^{12})(5^6)}{(10^9)(5^9)}$

( By using the property $(a^m)^n=a^{mn}$ )

$=(10^{12})(5^6)(10^{-9})(5^{-9})$

( By using the property $\frac{1}{a^m}=a^{-m}$ )

$=(10^{12-9})(5^{6-9})$ (By using the property $a^m.b^n=a^{m+n}$ )

$=(10^3)(5^{-3})$

$=\frac{10^3}{5^3}$ ( By using the property $a^{-m}=\frac{1}{a^m}$ )

$=\frac{1000}{125}$

$=8$

Therefore $\left[\frac{(10^4)(5^2)}{(10^3)(5^3)}\right]^3=8$

Therefore the value to the given expression is 8

3 0

2 years ago

Read 2 more answers

Which equation below represents a rate of change of -3?

Amanda [17]

The answer is C

Is shows a change of rate for the integer

Hope this helps

6 0

2 years ago

Find the volume of a pyramid with a square base, where the perimeter of the base is

NikAS [45]

Answer:

132 cm. 3. 3. a rectangular pyramid with a height of 5.2 meters and a base 8 ... 7. an oblique cone with a height of 10.5 millimeters and a radius of 1.6 ... base is about 15,400 square feet, find the volume of air that the ... ANSWER: 32.2 ft. 3. Find the volume of each solid. Round to the nearest tenth. eSolutions ...

Step-by-step explanation:

8 0

2 years ago

For the graph shown to the right, find (a) AB to the nearest tenth and (b) the coordinates of the midpoint of AB.

Shkiper50 [21]

AB =

$\sqrt{( {4 - (- 2))}^{2} + {( - 5 + 3)}^{2} } = \sqrt{40} = 6.3$
The midpoint os segment AB =

$(( \frac{ - 2 + 4}{2} ) = the \: x \: coordinate \: of \: the \: midpoint \\ \\ ( \frac{ - 3 - 5}{2})) = the \: y \: coordinate \: of \: the \: midpoint$
The midpoint is:

(1,-4)

8 0

2 years ago