If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
NO
54
оо
96

Answer:

Step-by-step explanation:

The mean value theorem for integrals for the function f(c) over a given interval [a, b] is expressed as g prime(c) = g(b) - g(a)/b-a. The idea is that there is a value c in between the interval [a, b] for the function given.

Given the function g(x) = 5√x within the interval [4,9]

g prime (c) = g(9) - g(4)/9-4

g(9) = 5√9

g(9) = 5*3 = 15

g(4) = 5√4

g(4) = 5*2 = 10

g prime c) = 15-10/9-4

g prime (c) = 5/5

g prime(c) = 1

So we are to find the number for which g prime (x) = g prime(c)

If g(x) = 5√x = [tex]5x^{1/2}[/tex]

g prime (x) = [tex]5/2 \ x^{-1/2}[/tex]

g prime (x) = 5/2√x

Since g prime (c) = 1 then;

5/2√x = 1

5 = 2√x

√x = 5/2

x = (5/2)²

x = 25/4

The value of c guaranteed by the mid value theorem is 25/4

The possible value of c for [tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex] is 6.25

The function is given as:

[tex]\mathbf{f(x) = 5\sqrt x\ [4,9]}[/tex]

Calculate f(4) and f(9)

[tex]\mathbf{f(4) = 5\sqrt 4 = 10}[/tex]

[tex]\mathbf{f(9) = 5\sqrt 9 = 15}[/tex]

Substitute c for x in f(x)

[tex]\mathbf{f(c) = 5\sqrt c }[/tex]

Calculate f'(c)

[tex]\mathbf{f'(c) = \frac{f(b) - f(a)}{b - a}}[/tex]

So, we have:

[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{9 - 4}}[/tex]

[tex]\mathbf{f'(c) = \frac{f(9) - f(4)}{5}}[/tex]

This gives

[tex]\mathbf{f'(c) = \frac{15 -10 }{5}}[/tex]

[tex]\mathbf{f'(c) = \frac{5 }{5}}[/tex]

[tex]\mathbf{f'(c) = 1}[/tex]

Also, we have:

[tex]\mathbf{f'(x) = \frac 52x^{-1/2}}[/tex]

Substitute c for x

[tex]\mathbf{f'(c) = \frac 52c^{-1/2}}[/tex]

Substitute 1 for f'(c)

[tex]\mathbf{\frac 52c^{-1/2} = 1}[/tex]

Multiply through by 2/5

[tex]\mathbf{c^{-1/2} = \frac 25}[/tex]

This gives

[tex]\mathbf{c^{1/2} = \frac 52}[/tex]

Square both sides

[tex]\mathbf{c = \frac{25}4}[/tex]

[tex]\mathbf{c = 6.25}[/tex]

Hence, the possible value of c is 6.25

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Answer:

((23GM)

Step-by-step explanation:

it goes for this because 23gm = 40pm

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------             The frequency is ~7.5*1014 Hz

Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.

Step-by-step explanation:

Speed = wavelength × frequency

3×10⁸ m/s = (400×10⁻⁹ m) f

f = 7.5×10¹⁴

Answer:

8 classmates

Step-by-step explanation:

[tex]9/1\frac{1}{8}=\\9/\frac{9}{8}=\\9*\frac{8}{9}=\\\frac{72}{9}=\\8[/tex]

Answer: cross-sectional study

Step-by-step explanation:

Here, A research company uses a device to record the viewing habits of about 2500 ​households (that includes different persons such as adults , children and seniors )

The data collected today(at a single point in time).

If it is used to determine the proportion of households tuned to a particular children's children's program.

The type of observational study is described in the problem​ statement : "cross-sectional"

Answer:

the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

Step-by-step explanation:

From the information given :

Let a be the base if the rectangular box

b to be the height and c to be the  other side of the rectangular box.

Then ;

the area of the base is ac

area for the front of the box is ab

area for the remaining other sides   ab + 2cb

The base of the box is made from a material costing 8 ac

The front of the box must be decorated, and will cost 10 ab

The remainder of the sides will cost 4 (ab + 2cb)

Thus ; the total cost  C is:

C = 8 ac + 10 ab + 4(ab + 2cb)

C = 8 ac + 10 ab + 4ab + 8cb

C = 8 ac + 14 ab + 8cb   ---- (1)

However; the volume of the rectangular box is V = abc = 350 in³

If abc = 350

Then b = [tex]\dfrac{350}{ac}[/tex]

replacing the value for c in the above equation (1); we have :

[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]

[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

Differentiating C with respect to a and c; we have:

[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]

[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]

[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)

[tex]8a - \dfrac{4900}{c^2}=0[/tex]   ---(3)

From (2)

[tex]8c =\dfrac{2800}{a^2}[/tex]

[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)

From (3)

[tex]8a =\dfrac{4900}{c^2}[/tex]

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

Replacing the value of a in 5 into equation (4)

[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]

From (5)

[tex]a =\dfrac{4900}{8c^2}[/tex]   -----(5)

[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]

a = 5.8481

Recall that :

b = [tex]\dfrac{350}{ac}[/tex]

b = [tex]\dfrac{350}{5.8481*10.234}[/tex]

b =5.848

Therefore ; the dimensions that will minimize the cost of constructing the box is:

a = 5.8481  in ;   b = 5.848 in  ; c = 10.234 in

The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.

Given :

According to the given data the total cost is given by:

C = 8ac + 14ab + 8cb   --- (1)

The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:

[tex]\rm b = \dfrac{350}{ac}[/tex]

Now, substitute the value of 'b' in the equation (1).

[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]

First differentiating the above equation with respect to c.

[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex]   --- (2)

Now, differentiating the above equation with respect to a.

[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex]    --- (3)

Now, equate equation (2) and equation (3) to zero.

From equation (2):  

[tex]\rm a=\dfrac{4900}{8c^2}[/tex]    ----- (4)

From equation (3):

[tex]\rm c=\dfrac{2800}{8a^2}[/tex]   ----- (5)

Now, from equations (4) and (5).

[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]

Now, simplifying the above expression in order to get the value of c.

c = 10.234

Now, put the value of 'c' in equation (5) in order to get the value of 'a'.

a = 5.8481

The value of 'b' is given by:

[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]

b = 5.848

So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.

For more information, refer to the link given below:

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Answer:

The system has exactly one solution where x = 0 and y = -3.

Step-by-step explanation:

-6x + y = -3

7x - y = 3

(7x - 6x) + (y - y) = 3 - 3

x + 0 = 0

x = 0

7(0) - y = 3

0 - y = 3

-y = 3

y = -3

-6(0) + y = -3

0 + y = -3

y = -3

So, the system has exactly one solution where x = 0 and y = -3.

Hope this helps!

Answer:

108 degrees

Step-by-step explanation:

angle CDE is 108 degrees, which is supplementary to angle EDH, so EDH must be 72 degrees

then put it into an equation

90+90+72+x=360

solve

x=108

Answer:

The answer is 108

Answer:

the expected area of the resulting circular region is 616.38 m²

Step-by-step explanation:

Given that:

[tex]f(r) = \left \{ {{\dfrac{3}{4}(1-(14-r)^2)} \atop {0 }} \right. \ \ 13 \leq r \leq 15[/tex] otherwise

The expected area of the resulting circular region  is:

= [tex]E(\pi r^2)[/tex]

= [tex]\pi E (r^2)[/tex]

To calculate [tex]E(r^2)[/tex]

[tex]E(r^2) = \int\limits^{15}_{13} {r^2} \ f(r) \ dr[/tex]

[tex]E(r^2) = \int\limits^{15}_{13} \ \dfrac{3r^2}{4}(1-(14-r)^2)dr[/tex]

[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (1-196-r^2+28r) dr[/tex]

[tex]E(r^2) = \dfrac{3}{4} \int\limits^{15}_{13} \ r^2 (28r^3-r^4-195r^2)dr[/tex]

[tex]E(r^2) = \dfrac{3}{4}[\dfrac{28 r^4}{4}-\dfrac{r^5}{5}-\dfrac{195r^3}{3}]^{^{15}}}__{13}[/tex]

[tex]E(r^2) = \dfrac{3}{4} [ \dfrac{28 \times 50625}{4} - \dfrac{759375}{5} - \dfrac{195 \times 3375}{3} ]-[ \dfrac{28 \times 28561}{4} - \dfrac{371293}{5} - \dfrac{195 \times 2197}{3} ][/tex]

[tex]E(r^2) = \dfrac{3}{4} [ 354375-151875-219375-199927+74258.6+142805][/tex]

[tex]E(r^2) = \dfrac{3}{4} [261.6][/tex]

[tex]E(r^2) = 196.2[/tex]

Recall:

The expected area of the resulting circular region  is:

= [tex]E(\pi r^2)[/tex]

= [tex]\pi E (r^2)[/tex]

where;

[tex]E(r^2) = 196.2[/tex]

Then

The expected area of the resulting circular region  is:

= [tex]\pi \times 196.2[/tex]

= 616.38 m²

There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.

Now, sin51°/20=sinN/14

0.7771/20=sinN/14

0.038855=sinN/14

sinN=14×0.038855

sinN=0.54397

N=33°

Therefore, option B is the correct answer.

Learn more about the sine rule here:

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You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:

[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]

We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].

We also need to have

[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]

Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means

[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]

Then

[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]

So we end up with

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

Answer:

Step-by-step explanation:

In the form ...

  y(t) = Asin(ωt +φ)

you have ...

The translation from ...

  y(t) = 2sin(4πt) +5cos(4πt)

is ...

  A = √(2² +5²) = √29 . . . . the amplitude

  ω = 4π . . . . the angular frequency in radians per second

  φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift

Then, ...

  y(t) = √29·sin(4πt +1.1903)

_____

Comment on the conversion

You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)

If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.

Answer:

-1.946 ; C

Step-by-step explanation:

Here, we want to identify the value of the z-statistic

Mathematically;

z = (x -mean)/SD/√n

Thus we have ;

Z = (11.58-12)/1.93/√80

z = -1.946

Answer:

4.5 ×1000 =4500m

Step-by-step explanation:

450/1000=0.45km

Answer: 10 : 1

Step-by-step explanation: Now first let’s convert this to the same units, for instance, the SI unit for length meters. 4.5 x 1000 = 4500m. Then put the ratio 4500m : 450m. You can divide 4500 by 450 as it is divisible so you get 10 as the answer.

Even if you have converted them to kilometers before, nevermind, still 4.5 divide by 0.45 is 10 and there the answer is 10 : 1 or shortly the ratio is just 10.

Answer: 77 degrees

Step-by-step explanation:

interior angles on the same side of transversal are supplementary.  Thus,

103+x=180

x = 77

Hope it helps <3

Answer:

Hey there!

This is a parallelogram, and we have the angles next to each  other add to 180 degrees. Angle ABC+Angle BCD=180

103+x=180

x=77

BCD=77 degrees.

Let me know if this helps :)

Answer:

4/ 100000

hope it was useful for you

stay at home stay safe

pls mark me as brain.....m

keep rocking

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

The upper confidence bound for population mean escape time is: 379.27

The upper prediction bound for the escape time of a single additional worker  is 413.64

Step-by-step explanation:

Given that :

sample size n = 26

sample mean [tex]\bar x[/tex] =  371.08

standard deviation [tex]\sigma[/tex] = 24.45

The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%

We need to determine the standard error of these given data first;

So,

Standard Error S.E = [tex]\dfrac{\sigma }{\sqrt{n}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{\sqrt{26}}[/tex]

Standard Error S.E = [tex]\dfrac{24.45 }{4.898979486}[/tex]

Standard Error S.E = 4.7950

However;

Degree of freedom df= n - 1

Degree of freedom df= 26 - 1

Degree of freedom df= 25

At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

Similarly;

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 4.7950

The Margin of error = 8.18986

The upper confidence bound for population mean escape time is = Sample Mean + Margin   of  Error

The upper confidence bound for population mean escape time is =  371.08 +  8.18986

The upper confidence bound for population mean escape time is = 379.26986  [tex]\approx[/tex] 379.27

The upper confidence bound for population mean escape time is: 379.27

b.  Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.

The standard error of the mean = [tex]\sigma \times \sqrt{1+ \dfrac{1}{n}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+ \dfrac{1}{26}}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1+0.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times \sqrt{1.03846153846}[/tex]

The standard error of the mean = [tex]24.45 \times 1.019049331[/tex]

The standard error of the mean = 24.91575614

Recall that : At confidence level of 95% and Degree of freedom df of  25 ;

t-value = 1.7080

∴

The Margin of error = t-value × S.E

The Margin of error = 1.7080 × 24.91575614

The Margin of error = 42.55611149

The upper prediction bound for the escape time of a single additional worker  is calculate by the addition of

Sample Mean + Margin of Error

= 371.08 + 42.55611149

= 413.6361115

[tex]\approx[/tex] 413.64

The upper prediction bound for the escape time of a single additional worker  is 413.64

Answer:

Step-by-step explanation:

To find the value of x we use sine

sin ∅ = opposite / hypotenuse

From the question

29 is the hypotenuse

9 is the opposite

sin x = 9/29

x = sin-¹ 9/29

x = 18.08°

Hope this helps you

Answer:

Angle=71.9°

using the trig inverse formula sec(angle)= hypotenuse/adjacent

Answer:

23 dimes; 32 nickel

Step-by-step explanation:

Let n = number of nickels.

Let d = number of dimes.

A nickel is worth $0.05; n nickels are worth 0.05n.

A dime is worth $0.10; d dimes are worth 0.1d.

Number of coins:

d + n = 55

Value of the coins:

0.1d + 0.05n = 3.9

Solve d + n = 55 for d:

d = 55 - n

Substitute 55 - n for d in second equation.

0.1(55 - n) + 0.05n = 3.9

5.5 - 0.1n + 0.05n = 3.9

-0.05n = -1.6

n = 32

Substitute 32 for n in d + n = 55 and solve for d.

d + 32 = 55

d = 23

Answer: 23 dimes; 32 nickel

Answer:

168 mm²

Step-by-step explanation:

Let A be the area of this shape

the kite is made of two triangles

Let A' and A" be the areas of the triangles

let's calculate A' and A" :

The area of a triangle is the product of the base and the height over 2

Let's calculate A

Answer:  see below

Step-by-step explanation:

1) The equation of a circle is: (x - h)² + (y - k)² = r²    where

2) If you are given a point on the circle and the center (h, k)

you can input those points into the equation of a circle to find r².

Then input (h, k) and r² to identify the equation of that particular circle.

3) If you divide each term in the equation of a circle by r², you will get:

[tex]\dfrac{(x-h)^2}{r^2}+\dfrac{(y-k)^2}{r^2}=1[/tex]

The difference between a circle and an ellipse is that an ellipse is in the shape of an oval.  In other words, the x-radius and y-radius are different.

The equation of an ellipse is:

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

Answer:

0.078

Step-by-step explanation:

The probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question;

There are two events;

(i) Drawing a first card which is a king: Let the event be X. The probability is given by;

P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]

Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.

Also, the total number of sample space = 52, since there are 52 cards in total.

P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;

P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]

Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4

But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.

P(Y) = [tex]\frac{4}{51}[/tex]

Therefore, the probability of selecting a first card as king and a second card as queen is;

P(X and Y) = P(X) x P(Y)

= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078

Therefore the probability is 0.078

Answer:

I=0.24ampere

Step-by-step explanation:

Assuming that the voltage is the same:

I=V/R (V- voltage, I-current, R-resistance)

1/6ampere=V/3240ohms

V=1/6*3240

= 5400v

Voltage across =V=5400v

Since the voltage is the same when the resistance is 22500ohms

I=V/R

=5400/22500

=6/25

=0.24ampere

Answer:

24 ways.

Step-by-step explanation:

In this case, you just need a factorial.

For the first seat, you have 4 students you can place.

For the second seat, you have 3 students.

For the third, you have 2.

For the fourth, you have 1.

So, you can arrange the students by doing 4 * 3 * 2 * 1 = 12 * 2 = 24 ways.

Hope this helps!

Answer:

Explantation:

First seat: 4 seats

Second seat: 3 seats

Third: 2 seats

Fourth seat: 1 seat remaining

4 * 3 * 2 * 1 = 12 * 2 * 1 = 24 * 1 = 24

Answer:

twenty one balls.

Step-by-step explanation:

there would be three of each colour.

Answer:

the real answer is 15

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

We have to see the common things we have in both graphs and express them:

1. There is a value x=a≠0, where g(a)=f(a)=0

2. The slope of g(x) is of opposite sign of the slope of f(x). Then f(x)=m*g(cx) with m<0.

3. The slope of f(x) seems to be higher than the slope of g(x)

A. As the slopes are different, this is not adequate.

B. As the slopes are different, this is not adequate.

C. This can be adequate, as it applies to all the observations we have made.

D. This is not adequate because f(0)≠g(-2*0).

The only adequate option then is C.

Answer:

700

Step-by-step explanation:

500+10*20=700

it's f(n) = 500+10n

Answer:

68 degrees

Step-by-step explanation:

Y=56,

56+56=112

180-112=68

Hope this helps, if you have any other questions, feel free to ask me to explain more

Have a good day! :)

Hey there! I'm happy to help!

Let's set this up a proportion (two equal ratios) to find out how many miles Wina can drive on 12 gallons gas.

[tex]\frac{miles}{gallons} =\frac{282}{10} =\frac{m}{12}[/tex]

What do we multiply the bottom 10 by to get to 12? Well, to find out, we can divide 12 by 10 below.

12÷10=1.2

This means that we multiply the numbers in the first fraction by 1.2 to have the same numerator and denominator as the second fraction.

If we multiplied our 10 b y 1.2 to get the denominator in the second fraction, we should be able to multiply 282 by 1.2 to get the numerator in the second fraction!

282×1.2=338.4

If you use 338.4 in this proportion, the ratios will be equal.

Therefore, Wina could drive 338.4 miles on 12 miles of gas at this same rate.

Have a wonderful day!

Answer:

B

Step-by-step explanation:

Answer:

The answer for this Question is Elementary

It is B.