The whole bar weighs 40 grams. If the whole bar is split into 100 equal parts, how much do
one of those parts weigh?

Answer:

3

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1  6  15  20  15  6  1

Decreasing powers of 1 from [tex]1^{6}[/tex] to [tex]1^{0}[/tex]

Increasing powers of 3x from [tex](3x)^{0}[/tex] to [tex](3x)^{6}[/tex]

[tex]1+3x)^{6}[/tex]

= 1.[tex]1^{6}[/tex][tex](3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](3x)^{3}[/tex] + 15.1²[tex](3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](3x)^{6}[/tex]

= 1 + 18x + 135x² + 540x³ + 1215[tex]x^{4}[/tex] + 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]

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

[tex](1-3x)^{6}[/tex]

= 1.[tex]1^{6}[/tex][tex](-3x)^{0}[/tex] + 6.[tex]1^{5}[/tex][tex](-3x)^{1}[/tex] + 15.[tex]1^{4}[/tex][tex](-3x)^{2}[/tex] + 20.[tex]1^{3}[/tex][tex](-3x)^{3}[/tex] + 15.1²[tex](-3x)^{4}[/tex] + 6.[tex]1^{1}[/tex][tex](-3x)^{5}[/tex] + 1.[tex]1^{0}[/tex][tex](-3x)^{6}[/tex]

= 1 - 18x + 135x² - 540x³ + 1215[tex]x^{4}[/tex] - 1458[tex]x^{5}[/tex] + 729[tex]x^{6}[/tex]

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

Collecting like terms from both expressions

[tex](1+3x)^{6}[/tex] + [tex](1-3x)^{6}[/tex]

= 2 + 270x² + 2430[tex]x^{4}[/tex] + 1458[tex]x^{6}[/tex]

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

(2)

Using Pascal's triangle with n = 5

1  5  10  10  5  1

Decreasing powers of 1 from [tex]1^{5}[/tex] to [tex]1^{0}[/tex]

Increasing powers of 2x from [tex](2x)^{0}[/tex] to [tex](2x)^{5}[/tex]

[tex](1+2x)^{5}[/tex]

= 1.[tex]1^{5}[/tex][tex](2x)^{0}[/tex] + 5.[tex]1^{4}[/tex][tex](2x)^{1}[/tex] + 10.[tex]1^{3}[/tex][tex](2x)^{2}[/tex] + 10.[tex]1^{2}[/tex][tex](2x)^{3}[/tex] + 5.[tex]1^{1}[/tex][tex](2x)^{4}[/tex]+ 1.[tex]1^{0}[/tex][tex](2x)^{5}[/tex]

= 1 + 10x + 40x² + 80x³ + 80[tex]x^{4}[/tex] + 32[tex]x^{5}[/tex]

Answer:

5 1/3

Step-by-step explanation:

2 times 8 is 16 and 16 over 3 is 5 with a remainder of one. So it's 5 1/3

Answer:

[tex] \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]

Step-by-step explanation:

Total distance ran

[tex] = \frac{2}{3} \times 8 \\ \\ = \frac{16}{3} \\ \\ = \boxed{ 5} \frac{ \boxed{1}}{ \boxed{3}}\: miles [/tex]

Answer:

B ?

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you picture this scene in your head, you will get a simple 3x4x5 right triangle. 4 times 2 is 8, 5 times 2 is 10, so Sarah should, by now, have traveled 3 times 2 miles.

Final answer: Sarah has traveled 6 miles after an hour.

Hope this helped! :)

Helping tip: The reason it is not 4 is because they are not traveling west and east away from each other. They are traveling north and east, so they are moving in two directions to form a right triangle, and the hypotenuse would be 10 (miles). The side, or distance, that Beth has traveled is 8. So as this is a typical variation of a 3x4x5 triangle, Sarah will have traveled  6 miles.

the answer will be thirty three cm.

Answer:

I think the equation would be 345 = 121 + p

Answer:

[tex]x = 9.9[/tex]

[tex]y= 7[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x and y

Considering  [tex]\theta = 45[/tex]

From the attached triangle, length x is the hypotenuse and length y is the adjacent

Solving for x

[tex]Sin\theta = \frac{Opp}{Hyp}[/tex]

[tex]Sin\theta = \frac{7}{x}[/tex]

So, we have:

[tex]Sin45 = \frac{7}{x}[/tex]

[tex]x= \frac{7}{Sin45 }[/tex]

[tex]x = \frac{7}{0.7071}[/tex]

[tex]x = 9.9[/tex]

Solving for y

Considering  [tex]\theta = 45[/tex]

[tex]Tin\theta = \frac{Opp}{Adj}[/tex]

So, we have:

[tex]Tin45= \frac{7}{y}[/tex]

[tex]y= \frac{7}{Tan45}[/tex]

[tex]y= \frac{7}{1}[/tex]

[tex]y= 7[/tex]

The value of x and y is 9.9 and 7.

Since theta is 45 degrees

So, we know that

Sin theta = opp/hyp

Sin theta = 7 /x

x = 7 / 0.7071

= 9.9

Now the value of Y should be

Tin theta = opp/hyp

y = 7 \tan 45

= 7 /1

= 7

Therefore, we can conclude that The value of x and y is 9.9 and 7.

Learn more about length here: https://brainly.com/question/19021872

Answer:

D. 11 feet 11 inches

1 foot= 12 inches

143/ 12 = 11 11/12

Answer:

D) 11 feet and 11 inches

Step-by-step explanation:

First we know that there is 12 inches in a foot. So let's start with a.

14 inches x 12 inches (one foot) is 168 inches (so it's not this one:)

13 inches x 12 inches is 156 inches (It's not this one either)

12 inches x 12 inches is 144 inches (not this one)

11 inches x 12 inches is 132 inches (so it could be this one, let's add the remaining inches).

132 + 11 inches = 143 inches.

(Notice I didn't add the remaining inches on A, B, or C because the number of inches was already too much. I did on D because the number of inches was below the given number of 143.

Hope this helps!!

Have a wonderful day!!

Answer:

3.5

Step-by-step explanation:

hope it helps

Answer:

x=9

Step-by-step explanation:

Since ABCD is a square, we know that AC bisects ∠BCD(=90), and therefore ∠ACB=45.

8x-27=45

8x=72

x=9

Answer:

x = 9°

Step-by-step explanation:

∠ACB = 45° because line AC bisects ∠BCD which is 90° (because square).

8x - 27° = 45°

add 27° to each side:

8x = 72°

divide both sides by 8:

x = 9°

Answer:

A

Step-by-step explanation:

Answer:

the awnser to your question is letter c

Answer:

x=5, y=2. (5, 2).

Step-by-step explanation:

3x-2y=11

x+2y=9

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

4x=20

x=20/4

x=5

5+2y=9

2y=9-5

2y=4

y=4/2

y=2

Answer:

y ≤ 1

Step-by-step explanation:

Answer:

[tex]V=502.5\ cm^3[/tex]

Step-by-step explanation:

The area of the pentagonal base, A = 33.5 cm²

The height of the prsim,h = 15 cm

We need to find the volume of the pentagonal base prism. The formula for the volume of the pentagonal base prism is given by :

[tex]V=A\times h\\\\V=33.5\times 15\\\\V=502.5\ cm^3[/tex]

So, the required volume is [tex]502.5\ cm^3[/tex].

Answer:

235.6

Step-by-step explanation:

A=πr2

=π·52

=78.53982x3=235.61946

235.6

Answer:

The slope is 1/2

Step-by-step explanation:

The equation is y= 1/2x +2

So the slope would be 1/2

Answer:

Tenía que hacerlo en menos de 2 minutos a más de 240 km/h

Step-by-step explanation:

La velocidad normal dada para completar el circuito de 6.000 metros = 240 km/h

El tiempo normal que se tarda en completar el circuito de 6000 metros = 2 minutos

Dado que Hamilton estableció el récord de vuelta, el tiempo que tuvo que hacer para recorrer el récord de vuelta es de 6000 metros en menos de 2 minutos

La velocidad media con la que lo hizo es de más de 240 km/h.

Answer:

See below, please!

Step-by-step explanation:

We can set up a system of equations to model this problem. Let's consider the student's ticket as x, and y for the adult ticket.

So since the student ticket is $1.50, and adult is $4, we can set up the following equation: [tex]1.5x+4y=5050[/tex], since they collected $5050 total.

We can set up another equation modeling the number of people who came to the game. This would be x+y=2200.

Solve this, and we get x= 1500 and y=700. So, they sold 1500 student tickets and 700 adult tickets.

Hope this helped!

Step-by-step explanation:

2+3=5

58+62=120

120÷5=24

so 24 carbohydrates are in one glass of milk

Answer:

10.6

Step-by-step explanation:

Answer:

x = 122°

Step-by-step explanation:

since it is a right triangle, the sum of the other 2 interior angles = 90°

the angle opposite x = 90° - 32° = 58°

58° and angle x are supplementary angles. Their sum is 180°.

180° - 58° = 122°

Answer:

5.50 per pond

3.5 pound

3.5 × 5.50

$19.25

Answer:

{-2, - 1, 0, 1}

Step-by-step explanation:

The integer solutions will be {-2, - 1, 0, 1}

Answer:

<3<3<3<3<3<3<3

{-2, - 1, 0, 1}

<3<3<3<3<3<3<3

Answer:

Grace's triangle is an obtuse triangle and a scalene triangle.

Step-by-step explanation:

Hope I helped!

Answer:

obtuse triangle and a scalene triangle

Step-by-step explanation:

:)

Answer:

5 pounds = 80 ounces

Hope it helps!!!

Answer:

5 15 10/3 7

3 12 12/3 5

Step-by-step explanation:

The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The ratio table is;

Pies         5       x      10/3   z

Cakes      3       12     y       5

Now,

Since, The ratios are equivalent to each other.

Thus, We can solve to find the value of x, y and z as;

⇒ 5 : 3 = x : 12

⇒ 5/3 = x/12

Multiply by 12;

⇒ 5 × 12 / 3 = x

⇒ 20 = x

And, 5 : 3 = 10/3 : y

⇒ 5/3 = 10/ (3× y)

⇒ 5/3 = 10/3y

Multiply by 3;

⇒ 5 = 10/y

⇒ y = 10/5

⇒ y = 2

And, 5 : 3 = z : 5

⇒ 5/3 = z/5

Multiply by 5;

⇒ 25/3 = z

⇒ z = 25/3

Therefore, The missing values in the ratio table will be;

Pies         5       20      10/3   25/3

Cakes      3       12        2      5

Learn more about the ratio visit:

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Answer:

2

Step-by-step explanation:

9x=8+5x

9x-5x=8

4x=8

x=8/4

x=2

Answer:

8.164

Step-by-step explanation:

The circumference of the ball is 8.164 inches.

Since the diameter of the tennis ball is 2.6 inches

So here the radius should be half i.e. 1.3 inches

Now we know that

Circumference = [tex]2\pi r\\\\[/tex]

= 2(3.14)(1.3)

= 8.164 inches

Therefore, we can conclude that The circumference of the ball is 8.164 inches.

Learn more about circumference here: https://brainly.com/question/15673093