The speed of light is a constant and approximately equal to 300,000,000 meters per second.

Green lasers emit light at a wavelength of 532 nm. However, the material that is used to make most green lasers does not emit light at 532 nm. Instead, it emits light at a different wavelength, and the laser then uses a “frequency doubler.” This doubles the frequency of the emitted light, and the resultant light is the green 532 nm that we observe.

1 meter is equal to 1,000,000,000 nanometers.

What is the output light frequency of the material used before doubling?

This is a geometric progression

So

The general formUla is

[tex]\\ \rm\Rrightarrow a(n)=ar^{n-1}[/tex]

[tex]\\ \rm\Rrightarrow a(n)=\dfrac{1}{4}\left(\dfrac{1}{4}\right)^{n-1}[/tex]

Answer:

[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Step-by-step explanation:

Series: the sum of the elements of a sequence.

Therefore, as the numbers have been defined as a series and we need to find [tex]S_n[/tex]:

[tex]\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{1}{64}+\dfrac{1}{256}+...[/tex]

First determine if the sequence is arithmetic or geometric.

If it is an arithmetic sequence, there will be a common difference between consecutive terms.

if it is a geometric sequence, there will be a common ratio between consecutive terms.

From inspection of the terms, we can see that there is a common ratio of 1/4, as each term is the previous term multiplied by 1/4, so it is a geometric series.

Sum of the first n terms of a geometric series:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

Given:

[tex]a=\dfrac{1}{4}[/tex]

[tex]r=\dfrac{1}{4}[/tex]

Substitute the values of a and r into the formula:

[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{1-\frac{1}{4}}[/tex]

[tex]\implies S_n=\dfrac{\frac{1}{4}\left(1-\left(\frac{1}{4}\right)^n\right)}{\frac{3}{4}}[/tex]

[tex]\implies S_n=\dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Therefore:

[tex]\displaystyle \lim_{n \to \infty} \dfrac{1}{3}\left(1-\left(\dfrac{1}{4}\right)^n\right)[/tex]

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

34.3 square unit.

Step-by-step explanation:

[tex]calculate \: df \: using \: pythagoras \\ theorem \\ df {}^{2} = 8 {}^{2} + 6 {}^{2} \\ df {}^{2} = 64 + 36 \\ df {}^{2} = 100 \\ df = \sqrt{100} \\ df = 10 \\ calculating \: for \: the \: area \: of \: \\ angle \: \: dfg \\ using \: heros \: formular \\ \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{10 + 11 + 7}{2} = \frac{28}{2} = 14 \\ area = \sqrt{14(14 - 10)(14 - 11)14(14 - 7)} \\ area = \sqrt{14(4)(3)(7)} = \sqrt{14 \times 84} \\ area = \sqrt{1176} = 34.2928564 \\ to \: the \: nearest \: tenth \: = 34.3[/tex]

Here it is stated that, side DE = 8 units, side EF = 6 units, side FG = 7 units and side GD = 11 units. We have to find area of ∆DFG, here we will use heron's formula which is given by:

Area of ∆ = √[s(s – a) (s – b) (s – c)]

Here a, b, and c are sides of ∆. We have;

So firstly lets calculate a i.e DF by using Pythagoras theorem on ∆DEF:

➸ DF² = 8² + 6²

➸ DF² = (8 × 8) + (6 × 6)

➸ DF² = 64 + 36

➸ DF² = 100

➸ DF = √(100)

➸ DF = √(10 × 10)

➸ DF = 10 units

Now, lets calculate s i.e semi - perimeter:

Now, using heron's formula on ∆DFG to calculate its area:

➸ Area(∆DFG) = √[14(14 – 10) (14 – 7) (14 – 11)]

➸ Area(∆DFG) = √[14(4) (7) (3)

➸ Area(∆DFG) = √(14 × 4 × 7 × 3)

We can write it as;

➸ Area(∆DFG) = √(2 × 2 × 2 × 7 × 7 × 3)

➸ Area(∆DFG) = 2 × 7√(2 × 3)

➸ Area(∆DFG) = 14√(6)

➸ Area(∆DFG) = 14 × 2.449

➸ Area(∆DFG) = 34.28

➸ Area(∆DFG) = 34.3 square units (approx)

Answer:

The only methods allowed are

-  "Subtract equation 2 from equation 1,"  and "Multiply equation 1 by 2. Then add the new equation to equation 2"

-

Step-by-step explanation:

Subtract Eq 2 from Eq 1:

3x-2y=7

-3x-4y=-17

-6y = -10

y = (5/3)

Use y =(5/3) to solve for x in both equations.

x=(31/9)

Subtract the left side of equation 2 from the left side of equation  No, this is not a legal operation.  

Multiply equation 1 by 2. Then add the new equation to equation 2  Yes, this works.  Instead of solving for y first, this method solves for x, which can then be used to find y:

2(3x-2y=7)

  6x-4y=14

  3x+4y=17    

   9x = 31    (y is eliminated)

x = (31/9)

Now use this to find y in either equation:

3x-2y=7

3x-2(31/9)=7

y = (5/3)

Answer:

1/6

Step-by-step explanation:

Rational numbers between two rational numbers:

LCD of 2 and 3 = 6

[tex]\sf \dfrac{-1}{3}=\dfrac{-1*2}{3*2}=\dfrac{-2}{6}\\\\\dfrac{1}{2}=\dfrac{1*3}{2*3}=\dfrac{3}{6}[/tex]

[tex]\sf Rational \ number \ between \ \dfrac{-2}{6} \ and \ \dfrac{3}{6} \ is \ \bf \dfrac{1}{6}[/tex]

By looking at the graph of the piecewise function, we can see that:

On the graph, we have a piecewise function, which we want to evaluate in some different values.

First we have x  = -0.0001

This value belongs to the interval (-5, 0), and by looking at the graph, you can see that the function on that interval is equal to -9, then:

G(-0.0001) = -9

x = 0

x = 0 belongs to the interval [0, 9). On that interval the function values -1. (x = 0 belongs to that interval because we have a closed dot). Then we conclude

G(0) = -1

x = 0.0001

This value also belongs to the interval  [0, 9)

Then G(0.0001) = -1

Finally, x = 9.

If you look at the domain of the function, you can see that there is an open dot at x = 9.

This means that x = 9 does not belong to that domain, so:

G(9) is not defined.

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Answer:

the LCM of 18 25 40 80 81 and 72 is 226800

i hope this helps you

Step-by-step explanation:

by which method

prime factorization , division or defination method

Answer:

1 (2/3) or 1.66666667

Step-by-step explanation:

The slope of a line is found by using the equation :

y2 - y 1 / x2 - x1

So all we have to do is plug in our values given.

To find which belongs with which variable (such as x2 or y1), we do the following:

We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.

(2, 8) will be x1 and y1.

(5, 13) will be x2 and y2

Plug in the values :

13 - 8 = 5

5 - 2 = 3

5 / 3 = 1 (2/3)

So, the slope of the line is 1.66666667 or 1 and (2/3)s

Answer:

65.4

Step-by-step explanation:

5 × 6 = 30 square meter

30 × 2.18 = 65.4

Answer:

It's the third one

Step-by-step explanation:

The cube root of 1/1000 is 1/10.

The cube root of c^9 is c^3.

The cube root of d^12 id d^4.

When you are doing to roots of variables, just divide :)

9/3 = 3

12/3 = 4

Answer:

D. 41

Step-by-step explanation:

To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:

The only solution for 22x=901 is 41

Answer: x=41

Step-by-step explanation:

Hii!

Do you need to know the solution set of 22x=902? No problem! (:

We just need to divide both sides by 22 to solve for "x".

x=41; this equation has one solution only

--

Hope that this helped! Best wishes.

--

Answer:

3.2

The value of C when B is 5 is 3.2

Step-by-step explanation:

Answer:

Graph C

Step-by-step explanation:

Rearrange the terms so the equation is in slope-intercept form:
4x + y = 7
y = -4x + 7
The slope is -4, and the only graph that has a slope of -4 is graph C.

Answer:

Area = 168 cm²

Step-by-step explanation:

**Please note that there is an error in the drawing of the given parallelogram.  In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations.  However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**

To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height.  As the perpendicular height is unknown in the given parallelogram, use the following formula:

[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]

where:

As the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.

Cosine Rule (for finding angles)

  [tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

From inspection of the given diagram:

Substitute the given values into the cosine rule formula and solve for ∠ABC:

[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]

[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]

Substitute the found angle and the length of the parallel sides into the area formula:

[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]

Therefore, the area of the given parallelogram is 168 cm².

Answer:

a) The mass of a box of bolts is greater.

b) 3/20 kg

Step-by-step explanation:

a) Firstly, you have to make the denominators of the two fractions the same (by finding the LCM of the denominators).

The LCM of 4 and 5 is 20.

Converting 3/4 into denominator 20:

[tex]\frac{3 * 5}{4 * 5}[/tex]

= 15/20

Converting 3/5 into denominator 20:

[tex]\frac{3 * 4}{5 * 4}[/tex]

= 12/20

Now comparing the numerators:

15 > 12

Hence,

3/4 > 3/5

b) Difference of the boxes can be done by subtracting the numbers with the same denominator:

15/20 - 12/20

= 3/20 kg

Hope this helps and feel free to give me brainliest! :)

Answer: 8

Step-by-step explanation:

We know that:

[tex]\frac{10^{12}}{10^{4}}=10^{12-4}=10^{\boxed{8}}[/tex]

LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)

The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.

It is given that

lim x->2 for f(x)

[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]

f(x) = 2x+1 x ≤2

f(x)= x² , x >2

When both the function tends to 2

Left Hand Limit

f(x) = 2 *2 +1

f(x) = 5

Right Hand Limit

f(x) = x² ,

f(x) = 4

LHL in not equal to RHL , Therefore the limit does not exists.

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Answer:

A. (6x + 7)(6x - 7)

Step-by-step explanation:

use difference of squares, which says a^2 - b^2 =(a+b)(a-b)

take the square roots of the two numbers, 6x and 7, and use them as a and b

Answer:

28 portraits

Step-by-step explanation:

Let's first figure out how many portraits Lamy can paint in 1 week, which is his unit rate. To calculate this, we just have to divide the number of portraits he paints by the amount of time it takes him to paint them.

In this case, the former quantity is 84 portraits, and the latter quantity is 6 weeks, so his unit rate is [tex]\frac{84 \text \: portraits}{6 \text \: weeks}[/tex] = 14 paintings per week.

Now, we know that in 1 week, Lamy can paint 14 portraits. Therefore, since this is a directly proportional relationship, all we have to do to find how many portraits he can paint is 2 weeks is double the unit rate. This is because in a directly proportional relationship, if you multiply one variable by a number, you have to multiply the other by the same number to maintain equality, and here we are multiplying weeks by 2 so we need to multiply paintings by 2 as well.

Thus, Lamy can paint 14 · 2 = 28 paintings in 2 weeks.

Hope this helps!

The Range of the function is  {y|y is a real number} , Option D is the correct answer

Range of a function is all the value a function can obtain.

From the figure it can be seen that the graph is moving slowly in either direction.

It extends from -∞ to +∞ ,

Therefore ,  {y|y is a real number} , Option D is the correct answer.

The complete question is

The graph shows a vertical translation of y = ³√x

What is the range of the translated function?

{y|y < 0}

{y|y ≥ 0}

{y|y is a natural number}

{y|y is a real number}

The image of the translated function is attached.

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The number of possible combinations of 7 objects taken 4 at a time is 35. Then the correct option is D.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.

The number of possible combinations of 7 objects taken 4 at a time.

so, the number of the combination is given as

[tex]^7C_4 = \dfrac{7!}{4!(7-4)!} \\\\\\^7C_4 = \dfrac{7!}{4!(3)!} \\\\\\^7C_4 = \dfrac{7 \times 6\times 5\times 4!}{4!(3\times 2)} \\\\\\^7C_4 = 35[/tex]

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Answer:

D. 35

Hope this helps!

Step-by-step explanation:

The complete question is

"What is the component form of the vector represented by 2a when a =⟨−2,3⟩?"

The Component form of the vector represented by 2a is (-4,6)

The component form of a vector is represented by (x, y) that has gone x units left to the origin and y units up from the origin.

Given, a=(-2,3)

By using scalar multiplication,

2a = (2(-2), 2(3))

2a = (-4,6).

Therefore the component form of 2a=(-4,6)

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Step-by-step explanation:

4.500 mm³ → cm³

1 cm³ = 1.000 mm³

= 4.500 ÷ 1.000

= 4,5 cm³ IS THE ANSWER

Answer:

The answer is figure A, B, C, D.

Step-by-step explanation:

Because, polygon means a shape with more then 1 side, and in your pic all of the figures have more than one side, so that's the answer.

The value of pi determined is same when used the circumference formula and the formula of area.

A circle is a round shaped figure , whose all the point lie on same plane.

It is given that

The value of pi is about 3.14, and it is the same when using both the area and circumference.

The circumference is found by

Circumference = π * diameter

For circle A:

25.12 = π * 8

π = 3.14

For circle B:

9.42 = π * 3

π = 3.14

The area is given by

Area = π * diameter² / 4

For circle A:

50.24 = π * (8²)/4

π = 3.14

For circle B:

7.065 = π * (3²)/4

π = 3.14

The value of pi is about 3.14,

The value of pi determined is same when used the circumference formula and the formula of area.

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The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

[tex]\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\[/tex]

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

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Triangles FGH and ABC are congruent because of the: AAS congruence theorem.

The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.

In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.

Therefore, both triangles are congruent because of the AAS congruence theorem.

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Answer:

24

Step-by-step explanation:

7 hours = 420 mins (7×60)

420-60=360 (time taken for lunch)

15mins=one ride

360÷15=24 rides