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3 years ago

11

Find the number of ways to partition the numbers 1, 2, . . . , 12 into four sets of three numbers, so that the sum of the number

s in each set is divisible by 3. (The order of the sets does not matter, and the order of the elements within each set does not matter. For example, the partition {1, 5, 12}, {2, 9, 10}, {3, 4, 8}, {6, 7, 11} is the same as the partition {8, 3, 4}, {9, 10, 2}, {7, 11, 6}, {12, 5, 1}.)

1 answer:

alukav5142 [94]3 years ago

6 0

Answer:

1 plus 1 equals a

Step-by-step explanation:

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PLEASE HELP ME!!!

VladimirAG [237]

Answer:

Part 1) $c=\sqrt{146}\ cm$

Part 2) $c=8\sqrt{2}\ in$

Part 3) The diagonal of rectangle is $d=3\sqrt{29}\ cm$

Part 4) The length of the diagonal of computer monitor is $d=15\ in$

Part 5) The ramp is $10.59\ ft$ long

Part 6) The distance between their houses is $=4\sqrt{2}\ mi$

Part 7) $234.31\ mi$

Part 8) 120 feet of wire is required

Step-by-step explanation:

Part 1) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

$a=11\ cm\\b=5\ cm$

substitute

$c^2=11^2+5^2$

$c^2=146$

$c=\sqrt{146}\ cm$

Part 2) we know that

To find the length of the hypotenuse in a right triangle apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (the greater side)

a and b are the legs

we have

$a=8\ in\\b=8\ in$

substitute

$c^2=8^2+8^2$

$c^2=128$

$c=\sqrt{128}\ in$

simplify

$c=8\sqrt{2}\ in$

Part 3) we know that

To find the length of the diagonal in a rectangle apply the Pythagorean Theorem

$d^2=b^2+h^2$

where

d is the diagonal of rectangle

b and h are the base and the height of rectangle

we have

$b=15\ cm\\hb=6\ cm$

substitute

$d^2=15^2+6^2$

$d^2=261$

$d=\sqrt{261}\ cm$

simplify

$d=3\sqrt{29}\ cm$

Part 4) we know that

To find the length of the diagonal of a computer monitor apply the Pythagorean Theorem

$d^2=w^2+h^2$

where

d is the diagonal of computer monitor

w and h are the wide and the high of computer monitor

we have

$w=12\ in\\h=9\ in$

substitute

$d^2=12^2+9^2$

$d^2=225$

$d=\sqrt{225}\ in$

simplify

$d=15\ in$

Part 5) we know that

To find out the length of the ramp apply the Pythagorean Theorem

$L^2=x^2+y^2$

where

L is the length of the ramp

x is the horizontal distance of the ramp

y is the vertical distance of the ramp

we have

$x=10\ ft\\y=3.5\ ft$

substitute

$L^2=10^2+3.5y^2$

$L^2=112.25$

$L=10.59\ ft$

Part 6) we know that

To find the distance between their houses apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (distance between their houses)

a and b are the legs

we have

$a=4\ mi\\b=4\ mi$

substitute

$c^2=4^2+4^2$

$c^2=32$

$c=4\sqrt{2}\ mi$

Part 7) we know that

The speed is equal to divide the distance by the time

$speed=distance/time$

so

the distance is equal to multiply the speed by the time

$distance=speed*time$

<em>First train</em>

speed=60 mph

time=3 hours

distance=60(3)=180 miles

<em>Second train</em>

speed=50 mph

time=3 hours

distance=50(3)=150 miles

To find out how far apart are the trains at the end of 3 hours apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (distance between the trains)

a and b are the legs

we have

$a=180\ mi\\b=150\ mi$

substitute

$c^2=180^2+150^2$

$c^2=54,900$

$c=234.31\ mi$

Part 8) we know that

For one tree is needed three wire

To find out the length of one wire apply the Pythagorean Theorem

$c^2=a^2+b^2$

where

c is the hypotenuse (length of one wire)

a and b are the distance above the ground and the distance from the base

we have

$a=3\ ft\\b=4\ ft$

substitute

$c^2=3^2+4^2$

$c^2=25$

$c=5\ ft$

so

For one tree is required ----> (5)3=15 ft

therefore

For 8 trees is required

Multiply by 8

15(8)=120 ft

6 0

3 years ago

If possible, give an example or if not possible, explain why<br>a whole number less than 0

aliya0001 [1]

Answer:

Not possible

Step-by-step explanation:

By definition, all whole numbers are non-negative.

4 0

2 years ago

For which independent value do the equations generate the same dependent value?

nalin [4]

Answer:

$x = - 3$

Step-by-step explanation:

The equations given are:

$y_1=6x+10$

$y_2=4x+4$

For the equations to generate the same independent value, then

$y_1=y_2$

This implies that:

$6x+10 = 4x + 4$

Group similar terms to get:

$6x - 4x = 4 - 10$

Simplify to get:

$2x = - 6$

$x = - 3$

5 0

3 years ago

a circle with radius of 2cm sits inside a 7cm x 11cm rectangle. what is the area of the shaded region ?

Agata [3.3K]

Answer:

The area of the shaded region is $(77-4\pi)\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the rectangle minus the area of the circle

step 1

Find the area of the rectangle

$A=(7)(11)=77\ cm^{2}$

step 2

Fin the area of the circle

$A=\pi (2)^{2}=4\pi \ cm^{2}$

step 3

Find the area of the shaded region

$77\ cm^{2}-4\pi \ cm^{2}=(77-4\pi)\ cm^{2}$ -----> exact value

To find the approximate value use $\pi=3.14$

$(77-4(3.14))=64.44\ cm^{2}$ -----> approximate value

7 0

3 years ago

What are the answers for 10-11...please show answer and need the answer asap..thank you

Mariana [72]

Dear Rosabella09: For 9- Two possible dimensions are 8x15 and 10x20.
For 10- 16(8+18)1/2=208 208-(16x8/2)=208-64= [144 squared feet]

4 0

3 years ago