The mass of a an atom of helium is 6.65 x 10−24. Use scientific notation to express the mass of 250 helium atoms. A) 1.6625 x 10−21 B) 1.6625 x 10−22 C) 1.6625 x 10−24 D) 1.6625 x 10−26

Rewrite the innermost expressions with negative exponents:

[tex]\displaystyle \left[\left(\frac{a^6}{5b^{-1}}\right)^2 \cdot \left(\frac{b}{9a^{-11}}\right)^{-1}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac{ba^{11}}{9}\right)^{-1}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\left(\frac{a^6b^1}{5}\right)^2 \cdot \left(\frac9{ba^{11}}\right)^1\right]^{-3}[/tex]

Simplify the product:

[tex]\displaystyle \implies \left[\left(\frac{a^6b}{5}\right)^2 \cdot \frac9{ba^{11}}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\frac{\left(a^6b\right)^2}{5^2} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\frac{\left(a^6\right)^2b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\frac{a^{12}b^2}{25} \cdot \frac9{ba^{11}}\right]^{-3}[/tex]

[tex]\displaystyle \implies \left[\frac{9ab}{25}\right]^{-3}[/tex]

Rewrite the last negative exponent:

[tex]\implies \boxed{\left(\frac{25}{9ab}\right)^3}[/tex]

Answer:

Percent change = 600 - 30 |30| × 100% = 570 30 × 100 = 1900% (increase). Where: 30 is the old value and 600 is the new value.

Step-by-step explanation:

Answer: 4509

8,140-3,631

= 4509

[tex]\text{Area of circle} = \pi r^2\\\\\implies 2 = \pi r^2\\\\\implies r^2 = \dfrac 2{\pi}\\\\\\\implies r = \sqrt{ \dfrac 2{\pi}} = 0.798~ \text{m.}[/tex]

Answer:

r≈.8m

Step-by-step explanation:

Formula used

A=πr2

r=√a/π =√2/π ≈.79788

rounded it is .8m

Answer:

41

Step-by-step explanation:

In a direct proportion function, the constant of proportionality is the same as the slope of the graph.

Use points (0, 0) and (1, 41).

slope = (41 - 0)/(1 - 0) = 41/1 = 41

constant of proportionality = 41

Answer:

You know that 1 mile = 5280 feet and 1 foot = 12 inches, so using these conversion factors you can go from one to the other.

I hope this answered you question!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expected growth =  0.15*85 + 0.20 *20 + 0.45*10+0.20 * -20

= 17.25%.

Answer:

Given that they know the law I think 82.93% of drivers obey this law

Answer:

the answer is

Step-by-step explanation:

i took the test

The cost function of the rectangular yard is 114x + 57y = 1500

Let x represent the length of the rectangular yard and y represent the width of the rectangular yard.

Since you need to fence only 3 sides, hence:

2x + y = Perimeter

Each foot cost $57 per foot and there is $1500 to spend, hence:

2x(57) + y(57) = 1500

114x + 57y = 1500

y = (1500 - 114x) / 57

The area (A) of the rectangular yard is:

A = x * y

A = xy

A = x[(1500 - 114x) / 57)

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Problem 1

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

Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

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Problem 2

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

Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]

That equation represents the boundary of the circle, which is where the water can reach.

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Problem 3

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

Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

Explanation:

The drawings you made are constructions of the perpendicular bisector. The "perpendicular" refers to the fact the second line meets the first line at a right angle (aka 90 degree angle). The "bisector" portion indicates the segment has been bisected, which is mathematical way of saying "cut in half".

The key here is the "bisector" portion. Because we've cut a segment like AB in half, this means segment AC and CB are the same length. The point C is the midpoint of AB. Point C is formed by intersecting the perpendicular bisector and the original segment. I'm referring to drawing (a), but the same idea applies to drawing (b) as well. I recommend using another letter than C for the second drawing.

Answer:

4x+14 = 2(2x+7}

12x+6=6{2x+1}

Answer:

Step-by-step explanation:

Answer:

22. 30

23. 20

25. Thirty to twenty, or 30:20

Step-by-step explanation:

22.6*5

23.4*5

Answer:

Missing side = x+2

Step-by-step explanation:

The perimeter of the classroom, 6x+3, is equal to the 4 side lengths added up.

In their first line of work, the first plus sign should be an equal sign as follows:

6x+3 = 3x+1+x+x+?

simplify

6x+3 = 5x+1+?

subtract (5x+1) from both sides

x+2 = ?

There's the length of the missing side.

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

[tex](-4x^3-x^2+3)-(x^3-2x^2-7x+2)\\\\=-4x^3 -x^2 +3 - x^3 + 2x^2 + 7x -2 \\\\= -5x^3 +x^2 +7x +1 \\\\=-5x^3 -5x^2 +6x^2 +6x+ x+1\\\\=-5x^2(x+1) +6x(x+1) + (x+1)\\\\=(x+1)(-5x^2 +6x +1)\\\\=-(x+1)(5x^2 -6x -1)[/tex]

The expression of sinU as a fraction is 12/13

Find the diagram attached.

To get the fraction represented by sinU, we will use the SOH CA TOA identity.

From the diagram;

Since sin theta = opp/hyp

SinU = ST/SU

SinU = 12/13

Hence the expression of sinU as a fraction is 12/13

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[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x^2-9}{x^2+2x-3}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{(x+3)(x-3)}{x^2+3x-x-3}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{\cancel{(x+3)}(x-3)}{\cancel{(x+3)}(x-1)}[/tex]

[tex]\\ \sf{:}\Rrightarrow {\displaystyle{\lim_{x\to -3}}}\dfrac{x-3}{x-1}[/tex]

[tex]\\ \sf{:}\Rrightarrow \dfrac{-3-3}{-3-1}[/tex]

[tex]\\ \sf{:}\Rrightarrow \dfrac{-6}{-4}[/tex]

[tex]\\ \sf{:}\Rrightarrow \dfrac{3}{2}[/tex]

Hope you could understand.

If you have any query, feel free to ask.

[tex]\huge\bold{\purple{\bold{⚡133°⚡}}} [/tex]

Step-by-step explanation:

Co interior angles' sum is 180°

Answer: 12

Step-by-step explanation: there are 60 minutes in an hour. 60/5=12

Answer:

100%

Step-by-step explanation:

Numbers on a die are 1,2,3,4,5,6 which are all greater than zero, so the probability is 6/6 or 100%.

I’m not sure but I need points so please mark this as answer :)

Answer:

impossible

Step-by-step explanation:

a cube with faces labeled 1-6 does not have an odd number greater than 5

Answer:

Freeze thaw cycle

Step-by-step explanation:

The force which produce avalanches and landslides is gravity.

The process by which the Earth's surface is worn down is called erosion. Erosion and weathering are two distinct but related processes. The decomposition of materials through chemical or physical processes is known as weathering. When weathered materials like soil and rock fragments are carried away by wind, water, or ice, erosion occurs.

The Earth's three substances—air, water, and ice—continue to flow in large quantities from one location to another, making erosion an essential component of human life. The energy in their flow is extremely high. All of the small and large substances in their path break and move in the flow's direction.

The most dramatic, unexpected, and hazardous examples of earth elements being pushed by gravity are landslides and avalanches. Avalanches are abrupt snowfalls, whereas landslides are sudden rockfalls.

Massive chunks of rock move swiftly and violently when they abruptly break free from a cliff or hillside. The falling rocks are kept from slowing down by air that is trapped beneath them. Avalanches and landslides can travel at speeds of 200 to 300 km/h.

Prevention's,

Be mindful of your surroundings and keep an eye out for changes in the environment.

When it rains heavily, keep an eye out for deck or patio tilting, cracks or bulges in slopes, and drooping posts or fences. As soil steadily presses against a house and shifts windows and doors out of place, sticking windows and doors can be an indication of earth movement.

Because landslides are more likely to occur where they have already happened, look for landslide scars.

Hence,  Earth materials are transported by gravity from higher elevations to lower heights. Examples of hazardous gravity-driven erosion include mudflows, avalanches, and landslides.

Learn more about erosion;

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