I need help question 3 and 4

I Need Help Question 3 And 4

Answers

Answer 1

Answer: k*6 and then you find the reciprocal of k*6 which is 1 over k*6

Step-by-step explanation:


Related Questions

f is a trigonometric function of the form f(x)=asin(bx+c)+d. The function intersects its midline at (π,−4) and has a minimum point at ( π/4 , − 5.5 ). Find a formula for f(x). Give an exact expression.

Answers

The given point on the midline of (π, -4), and the minimum point of (π/4, -5.5), give the exact expression for f(x) as; f(x) = 1.5•sin((2/3)•(x - π)) - 4.

Which method can be used to find the trigonometric function?

The amplitude, a = The difference between the y-values at the minimum point and the midline

Therefore;

a = -4 - (-5.5) = 1.5

d = The difference between the y-values of the midline and the x-axis

Therefore;

d = -4 - 0 = -4

The given function is presented as follows;

f(x) = a•sin(b•x + c) + d

Which gives;

-4 = 1.5•sin(b•π + c) - 4

sin(b•π + c) = 0

(b•π + c) = 0

-c/b = π

c = -b•π

Therefore;

-5.5 = 1.5•sin(b•π/4 + c) - 4

-1.5 = 1.5•sin(b•π/4 + c)

-1 = sin(b•π/4 - b•π) = sin(-3•b•π/4)

-3•b•π/4 = arcsine (-1) = -π/2

-3•b•π/4 = -π/2

3•b/4 = 1/2

b = 2/3

c = -(2/3)•π

Therefore, f(x) = a•sin(b•x + c) + d, gives;

f(x) = 1.5•sin((2/3)•x - (2/3)•π) - 4

By simplification, the exact expression for f(x) is therefore;

f(x) = 1.5•sin((2/3)•(x - π)) - 4

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Write an equivalent expression in simplest form for each given expression. Then, choose the answer that explains why the expressions are equivalent.
(A) 2y + 4(y + 1) = y +

First use the Property to simplify the expression in parentheses, then
combine like terms.

(B) 9y + 6 + 2(5 + y) = y +

After applying the Distributive Property, use the Properties to
combine like terms.

Answers

The equivalent expressions are 6y + 4 and 11y + 16

How to determine the equivalent expressions?

Expression (A)

We have:

2y + 4(y + 1)

Open the bracket

2y + 4y + 4

Evaluate the like terms

6y + 4

Expression (B)

We have:

9y + 6 + 2(5 + y)

Open the bracket

9y + 6 + 10 + 2y

Evaluate the like terms

11y + 16

Hence, the equivalent expressions are 6y + 4 and 11y + 16

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If a person rows to his favorite fishing spot 21 miles downstream in the same amount of time that he rows 7 miles
upstream and if the current is 7 mph, find how long it takes him to cover 28 miles.

Answers

28 miles upstream requires 28/7 = 4 hours.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

How long does it take him to cover 28 miles?

Apply the distance formula:

d = rt

where

d is distance

r is rate or speed

t is time

21 = t*(r+7)  = rt+ 7t

7 = t *(r-7)   = rt - 7t

            28 = 2rt

             14 = rt

             21 = rt + 7t

             21 = 14 + 7t

               7 = 7t

                 t=1

              21 = (r+7)*1 = r+7

                r = 14

The speed of the boat is 14 mph. With the current (downstream), the speed is 14+7 = 21 mph, so 21 miles are traveled in 1 hour. Against the current (upstream), the speed is 14-7 = 7 mph, which means 7 miles are traveled in the same 1-hour time frame.

28 miles downstream requires 28/21 = 4/3 hours, or 1 hour and 20 minutes.

28 miles upstream requires 28/7 = 4 hours.

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Kaitlin,Scott and bill served a total of 81 orders on Monday .Kaitlin served 9 fewest orders than Scott .bill served 3 times as many orders as Scott . How many orders did they each serve?

Answers

Answer: Scott - 18, Kaitlin - 9, Bill - 54

Step-by-step explanation:

Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:

Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.

Now if we view Scott's orders as one unit:

Scott - 1 unit

Kaitlin (after adding 9) - 1 unit

Bill - 3 units (he served 3 times as many orders as Scott)

In total there are 3 + 1 + 1 = 5 units.

90 / 5 = 18.

Therefore, Scott served 18 orders.

18 - 9 = 9.

Kaitlin served 9 orders.

18 x 3 = 54.

Bill served 54 orders.

And to check our answer, 54 + 18 + 9 is 81.

Find an equation for the plane that contains the line
v=(-3,4,5)+t(3,2,4)
and is perpendicular to the plane
2x+y-3z+4=0
(Use symbolic notation and fractions where needed.)

Answers

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

How to find the equation of a plane that contains a line and is perpendicular to another plane

From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:

(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3)     (1)

The normal vector of the plane is equal to the cross product of the direction vectors of (1):

[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]

[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]

[tex]\vec n = (-6-4,8+9, 3-4)[/tex]

[tex]\vec n = (-10, 17, -1)[/tex]

Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:

- 10 · x + 17 · y - z = k

- 10 · (- 3) + 17 · 4 - 5 = k

30 + 51 - 5 = k

k = 76

The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.

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Which equation is represented by the graph below?


A. Y= 1/8e^x
B. Y= 1/2e^x
c. Y=2e^x
D. Y= 8e^x

#49

Answers

Answer:

B

Step-by-step explanation:

When x = 1, it appears y is in between 1 and 2.

The only choice that satisfies this is B.

Answer:

The equation that represents the graph is y=2e^x

Step-by-step explanation:

plug in geogebra and confirm:D

Tim wants to build a rectangular fence around his yard. He has 42 feet of fencing. If he wants the length to be twice the width. What is the largest possible length

Answers

Answer: The largest he can possibly build is x = 14

Step-by-step explanation:

A bag contains 3 red balls, 4 green balls, and 2 yellow balls. Deborah reaches into the bag and pulls out the following 4 balls: red, red, green, yellow Deborah reaches into the bag to pick out another ball. What's the probability that the ball she picks is green?

Answers

The probability that the ball Deborah picks is green is; 3/5.

What is the probability that the ball picked last is green?

Since the bag initially contains; 3 red balls, 4 green balls, and 2 yellow balls, after Deborah pulls out the 4 balls: red, red, green, yellow.

The balls remaining are; 1 red ball, 3 green and 1 yellow.

Hence, the probability that the final ball she picks is green is; 3/(3+1+1) = 3/5.

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A dairy farmer wants to mix 75% protein supplement and 50% protein ration to make 1400 pounds of a high grade 70% protein ration. How many pounds of each should he use

Answers

The dairy farmer would mix 1120 pounds of 75% protein supplement and 280 pounds of 50% protein ration to make 1400 pounds of a high grade 70% protein ration.

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the amount of 75% protein supplement and y represent the amount of 50% protein, hence:

x + y = 1400     (1)

Also:

0.75x + 0.5y = 0.7(1400)     (2)

Hence:

x = 1120, y = 280

The dairy farmer would mix 1120 pounds of 75% protein supplement and 280 pounds of 50% protein ration to make 1400 pounds of a high grade 70% protein ration.

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find the maximum value of the function 7-2x-3x^2 and the equation of the axis of the curve ​

Answers

The maximum value of the function 7 - 2x - 3x² exists 22/3.

How to estimate the maximum value of the function 7 - 2x - 3x²?

Given: 7 - 2x - 3x²

We must begin by estimating the first derivative:

Differentiating the equation above, we have:

dy/dx = 0 - 2 - 6x = - 2 - 6x

We know that dy/dx = 0 at maxima and minima

Therefore, we contain, - 2 - 6x = 0

6x = - 2

x = - 1/3

Substituting x = - 3 back into the equation of the curve yields the following result:

y = 7 - 2(-1/3) - 3(-1/3)² = 22/3

y = 22/3

Therefore, 22/3 exists the maximum value of y.

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Which of the following equation(s) has/have slope zero?
a. x = 2
b.y = -3
c. y = 5x+2
d. x+ 5 = 0
O Both a and c
Only c
O Only b
O Both a and d

Answers

Answer:

b, only b

y = -3 has zero slope.

Step-by-step explanation:

Only a horizontal line has zero slope. A horizontal line's equation is given in the form: "y equals a number" So y=-3 is horizontal with zero slope.

Vertical lines have undefined slope. This is not the same as zero. Vertical lines have an equation in the form x= anumber. Above in the answer choices, choice a and d are both vertical with undefined slope and are not the correct answer. Choice c has slope 5, because that is the number beside the x in the form y=mx+b where m is the slope. So choice c is also not the answer.

Only choice b has zero slope.

the probability that an international flight leaving is delay in departing (event D) is .28. The probability that an international flight is a transpacific flight is (event P) is .55. The probability that an international flight leaving the U.S is a transpacific flight and delay is .13. What is the probability that an international flight leaving the United states is delay in departing given that the flight is a transpacific flight?

Answers

The probability that an international flight leaving the United states is delay in departing given that the flight is a transpacific flight is 0.7

What is probability?

Probability describes the likelihood of an event happening. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not.

The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The probability of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.

According to the question,

P(D)=0.28

P(P)=0.55

P(D∩P)=0.13

Thus, the required probability,

P(DUP)=P(D)+P(P)-P(D∩P)

            =0.28+0.55-0.13

            =0.70

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Would the horizontal translations shift the square root right or left? Sort each into the appropriate category.
f(x)=√x+0.8
f(x)=√x-4.7
f(x)=√x-25
f(x)=√x+6
f(x)=√x-11

Answers

Answer:

Step-by-step explanation:

Shift right

f(x)=√x-4.7

f(x)=√x-25

f(x)=√x-11

Shift left

f(x)=√x+0.8

f(x)=√x+6

Determine the equation (picture).

Answers

The line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

How to find equation of a line?

The equation of a line can be describe as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, lines that a perpendicular follows the rule below:

m₁m₂ = -1

Hence,

y + 6 = 3 / 4 (x - 2)

y + 6 = 3 / 4 x - 6 / 4

y =  3 / 4 x - 6 / 4 - 6

y = 3 / 4 x - 30 / 4

y = 3 / 4 x - 15 / 2

Hence,

3 / 4 m₂ = -1

m₂ = - 4 / 3

Therefore,

slope of the line is - 4 / 3

Let's find the y-intercept of the second line

4x + 5y -20 = 0

5y = -4x + 20

y = -4 / 5 x + 4

y-intercept  = 4

Therefore, the line perpendicular to the equation and has the same y-intercept with another is y = - 4 / 3 x + 4.

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Kite A B C D is shown. Lines are drawn from point A to point C and from point B to point D and intersect.
Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units.

What is the length of AC?

5 units
6 units
10 units
12 units

Answers

The length of AC is 12 units . Option D

How to determine the length

The formula for area of a kite is given thus;

Area = [tex]\frac{p * q}{2}[/tex]

Where p and q are the lengths

Area of kite = 48 square units

BD, q = 8 units

AC , p = unknown

Substitute the values

[tex]48 = \frac{AC * 8}{2}[/tex]

Cross multiply

[tex]AC * 8 = 48 * 2[/tex]

[tex]8AC = 96[/tex]

[tex]AC = \frac{96}{8}[/tex]

[tex]AC = 12[/tex] units

Thus, the length of AC is 12 units . Option D

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Answer:option 4

Step-by-step explanation:

Construct a 96% confidence interval if a sampling distribution has a mean of 20, a standard deviation of 5, and a size of 100.

Answers

Using the t-distribution, the 96% confidence interval is given as follows:

(18.96, 21.04).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.

The parameters are given as follows:

[tex]\overline{x} = 20, s = 5, n = 100[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]

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Given the graph of g(x), describes the transformation of the parent function f(x)=2^x

Answers

Answer:

The transformation being described is from g(x)=x2 g ( x ) = x 2 to f(x)=x2 f ( x ) = x 2 . The horizontal shift depends on the value of h . The horizontal shift is described as: f(x)=f(x+h) f ( x ) = f ( x + h ) - The graph is shifted to the left h units

Find the vertex, focus and diretrix of x^2+4x-12y=-64
It needs to be in (x-h)^2=4p(y-k) form

Answers

Vertex of the equation is (-2, 5)

Focus of the equation is (-2, 8)

Directrix of the equation is 2

What is a Quadratic curve?

A quadratic curve is a parabolic curve is a graph of the points which define a quadratic function. It shows how a function behaves in the cartesian plane.

Quadratic curve may bend upwards, or downwards depending on the gradient of the curve.

Analysis:

setting the equation in the form, [tex]x^{2}[/tex] +4x -12y = -64 in the form [tex](x-h)^{2}[/tex] = 4p(y-k)

Firstly we take -12y to the right hand side

[tex]x^{2}[/tex] +4x = 12y - 64

Making the left hand side a perfect square expression, we square both sides with -2

[tex]x^{2}[/tex] +4x + [tex](2)^{2}[/tex] = 12y -64 + [tex](2)^{2}[/tex]

[tex](x+2)^{2}[/tex] = 12y -60

[tex](x+2)^{2}[/tex]  = 12(y - 5)

comparing with the other equation

-h = , h = -2, -k = - 5 k = 5, 4p = 12, p = 3

Vertex is (h, k) = (-2, 5)

Focus is (h, k+p) = (-2, 5+3) = (-2, 8)

Directrix is y = k-p = 5 - 3 = 2

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Use properties of operations to find the quotient. -10.2/6
A. 1.7 B. -1.7 C. 4.2 D. -4.2

Answers

Answer:

B, -1.7

Step-by-step explanation:

-10.2 divided by 6 is -1.7.

I hope this helps!

average person burns approximately 221 calories per half-hour while bicycling. If a person does 2 hours of bicycling per day then how many calories will they burn in a week if they work out 5 days a week?

Answers

Answer: 4420 cals

Explaining:
221 every half hour
To find every hour you times it by 2 which equals to 442
1 hour = 442
2 hours = 442 times 2
2 hours= 884
To find how much a week you times it by 5
884 times 5
Equals to 4420 cals a week

Practice 3
Solving a Special Solution inequality
17<3h+2<2
h>______
h <______

Answers

Answer:

  h > 5

  h < 0

Step-by-step explanation:

We suppose that a "Special Solution" inequality is one that is technically incorrect, but is written using a compact "shorthand" form.

As written, the inequality claims that 17 < 2, which is false. There can be no value of the variable that will make this true. We presume the intended meaning is ...

  17 < 3h +2   or   3h +2 < 2

Special solution

Subtracting 2 from the inequality gives ...

  15 < 3h < 0

Dividing by 3 gives ...

  5 < h < 0

There is no value of h that is both greater than 5 and less than 0, so we presume this means the OR (union) of the solution sets ...

  h > 5

  h < 0

An issue of Taunton's Fine Woodworking included plans for a hall stand. The total height of the stand is 5912 59 1 2 inches. If the base is 25716 25 7 16 inches, how tall is the upper portion of the stand?

Answers

The length if the upper portion of the stand is 33. 56 inches

How to determine the length

The formula for the finding the length is given thus;

Total height = length of upper portion + length of base

Where

Length of base = 257/16

Total height = 591/2

Length of upper portion = total height - length of base

= 118/2 - 407/16

= 59 - 25. 44

= 33. 56 inches

Thus, the length if the upper portion of the stand is 33. 56 inches

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The princess of the Kingdom of Abundance accidentally drops her magic salamander's feeding bowl into a fire. She orders a new feeding bowl to be made out of Dragon Alloy #18, which is 86% magic steel and the rest titanium. The
dwarfs have a lot of Dragon Alloy #33, which is 28% titanium. How much of
that alloy and how much magic steel should they combine to make 700 grams of Dragon alloy #18?

Answers

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of magic steel and y represent the amount of alloy #33, hence:

(0 * x) + (y * 0.28) = 700(1 - 0.86)   (1)

Also:

x + (1 - 0.28)y = 0.86(700)    (2)

From both equations:

x = 350, y = 350

350 grams of magic steel and 350 grams of dragon alloy #33 is needed to make 700 grams of Dragon alloy #18.

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A carpenter built a square table with side length x. Next, he will build a rectangular table by tripling one side and halving the other. The area of the rectangular table is represented by the expression (3 x)(one-half x).

A square with sides x. A rectangle with side one-half x and side 3 x.

What is the simplified expression for the area of the rectangular table?

Three-halves x squared
Three-halves x
Five-halves x squared
Five-halves x

Answers

The area of a rectangle is given by its length multiplied by its width. So that the expression that represents the area of the rectangle in the given question is  [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex] squared unit.

A rectangle is a figure that has four straight sides, in which opposite sides are equal.

The area of a rectangle can be determined by the expression;

Area = length x width

Thus considering the given question, the length of the rectangle is tribble to that of the square. And the width of the rectangle is half of that of the square.

So that;

length = 3x

width = [tex]\frac{x}{2}[/tex]

Thus,

Area = length x width

        = 3x ([tex]\frac{x}{2}[/tex])

        = [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex]

Therefore, the area of the rectangle is  [tex]\frac{3}{2}[/tex] [tex]x^{2}[/tex] squared unit.

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Determine the area under the standard normal curve that lies to the left of (a) Z=081. (b) Z=0.43. (c) Z= -0.33. and (d) Z= 1.04.

Answers

Using the normal distribution, the areas to the left are given as follows:

a) 0.7910.

b) 0.6664.

c) 0.3707.

d) 0.8508.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X, and is also the area to the left of Z.

Hence:

The area to the left of Z = 0.81 is of 0.7910.The area to the left of Z = 0.43 is of 0.6664.The area to the left of Z = -0.33 is of 0.3707.The area to the left of Z = 1.04 is of 0.8508.

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I need this answered please and thank you! ASAP

Answers

Answer:

Greetings!

The answer for the first figure is attached but the second diagram is not clear.

Also use the image i attached horizontally.

and also it TD subject not Mathematics.

Find the sum of the arithmetic series given a1=45, an=85, and n=. 5

Answers

The sum of the arithmetic series is 325

How to determine the sum?

The given parameters are

a1 = 45

an = 85

n = 5

The formula for the sum of arithmetic series is:

[tex]S_n = \frac n2 * (a_1 + a_n)[/tex]

Substitute the values of a1, an and n in the above equation

[tex]S_5 = \frac 52 * (45 + 85)[/tex]

Add 45 and 85

[tex]S_5 = \frac 52 * 130[/tex]

Divide 130 by 2

[tex]S_5 = 5 * 65[/tex]

Multiply

[tex]S_5 = 325[/tex]

Hence, the sum of the arithmetic series is 325

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Claire has 18 nail polish bottles while Becky has 2/3 of that amount. How many bottles of nail polish does Becky have?​

Answers

Answer:

15/16

Step-by-step explanation:

because 2/3have Becky

A​ cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-third its​ height, what portion of the volume of the cup is filled with​ water?

Answers

Answer is 150.72 cu.cm.
Let’s find the total cone volume first
Cone volume formula is 1/3 pi r^2 height
We know r = 6
We know height is 12
We will use 3.24 for pi
So
(1/3) (3.14) (6^2) (12) = 452.16
Now we want to find 1/3 of the volume so divide that by 3
Amount of water is 150.72 cu.cm.
Problem solved

`H_0: p = 0.63`
`H_1: p > 0.63`

Your sample consists of 150 subjects, with 96 successes. Calculate the test statistic, rounded to 2 decimal places
`z=`

Answers

The test statistic, rounded to 2 decimal places is equal to

How to calculate value of the test statistic?

For this sample, the hypothesis is given by:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

Assuming this sample has a normal distribution, we would use a pooled z-test to determine the value of the test statistic:

Substituting the given parameters into the formula, we have;

[tex]z = \frac{\frac{96}{150} \;-\;0.63}{\sqrt{0.63\; +\; \frac{1\;-\;0.63}{150}} }\\\\z = \frac{0.64 \;-\;0.63}{\sqrt{0.63\; +\; \frac{0.37}{150}}}\\\\z = \frac{0.01}{\sqrt{0.63\; +\; 0.0025}}\\\\z = \frac{0.01}{\sqrt{0.6325}}\\\\[/tex]

z = 0.01/0.7953

z = 0.013.

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Briana estimates the length of a living room to be 24 feet. Ariane estimates it to be 9 yards. If the actual length is 26 feet, which is the better estimate explain What rhyme scheme does the poet use and how does it contribute to the poem I felt a funeral in my brain? How did the arrival of the Spanih in the 1500 impact indigenou people in the America? Kesia a senveth grader girl studied for three hours today Which statement best describes Grendel's perspective?Then they would fight. Spears flying, swords whonking, arrows raining from the windows and doors of the meadhall and the edge of the woods. Horses reared and fell over screaming, ravens flew, crazy as bats in a fire, men staggered, gesturing wildly, making speeches, dying or sometimes pretending to be dying, sneaking off. Sometimes the attackers would be driven back, sometimes they'd win and burn the meadhall down, sometimes they'd capture the king of the meadhall and make his people give weapons and gold rings and cows.It was confusing and frightening, not in a way I could untangle. I was safe in my tree, and the men who fought were nothing to me, except of course that they talked in something akin to my language, which meant that we were, incredibly, related. I was sickened, if only at the waste of it: all they killedcows, horses, menthey left to rot or burn. How does the author develop the central idea over the course of the article.Organized labor and the great upheaval commonlit Select the correct answer. what is the root of the word visibility? a. vis b. sib c. bil d. lity List the point coordinates for all atoms that are associated with the FCC unit cell. Define all symbols that you use. Both of these historical objects were intended to educate students. Protest inequality. Be circulated in society. Satisfy political leaders. write a bulleted list of the positive impacts of genetically modified foods on society and the environment. Fair youth, beneath the trees, thou canst not leave Thy song, nor ever can those trees be bare; Bold Lover, never, never canst thou kiss, Though winning near the goalyet, do not grieve; She cannot fade, though thou hast not thy bliss, For ever wilt thou love, and she be fair! "Ode on a Grecian Urn," John KeatsWhat is the topic of the passage?1. the beauty of nature2. the images on a work of art3. the achievement of goalsWhat does the passage say about this topic?1. the images on the urn never change2. trees are most beautiful in the spring3. some people do not achieve their goalsWhat theme does the passage express?1. nothing is more beautiful then the natural world2. art is eternal and a unchanging source of truth3. trying hard is more important than winning Does homework help to improve the students? During the Reformation, Lutheranism took a firm hold in Germany (the Holy Roman Empire), especially in the northern and eastern areas. Referring to the map, in which other countries did Lutheranism become the main religion? A rocket blasts away from the earth with a cargo for the international space station. Sketch the graph of the force of gravity the rocket experiences from the earth as a function of time. What are the three major tools of foreign policy? The diagram shows part of a regular polygon.The sides of this polygon subtend angles of 15 at the centre of the polygon.How many sides does the polygon have? What is 50% dilated? HELP pls will mark you the brainliest Need help pleaseThe solution to:x^3 + 12 = -52x = there are ________ molecules of methane in 0.123 mol of methane (ch4).