14. Which points are on the graph by = 3x - 12? Select all that apply. (A) (B) (C) (D) (-2,0) (0,-2) (6,-3) (8,2) M 23 hp

14. Which Points Are On The Graph By = 3x - 12? Select All That Apply. (A) (B) (C) (D) (-2,0) (0,-2)

Answers

Answer 1

6y=3x-127

Replace the values of x , y in the equation by the coordinates values given on each option, and check if the equality remains.

A. (x,y) = (-2,0)

6y=3x-127

6(0) =3(-2)-127

0 = -6-127

0= -133

zero is not equal to -133.

A. is not

B. (0,-2)

6(-2) = 3(0)-127

-12 = -127

B is not

C, (6,-3)

6(-3) = 3(6)-127

-18 = 18-127

-18 = -109

C is not

D (8,2)

6(2) = 3(8)-127

12 = 24-127

12=-103

D is not

None of the points are in the graph


Related Questions

Find the percent of change and classify as a percent increase or decrease. Round to the nearest tenth of a percent when necessary. A $39 watch is now on clearance for $17.50.

Answers

The percent of increase or decrease = change/original x 100%

Since the original price of the watch is $39

Since its price now is $17.50, then

The change of the price = 39 - 17.50 = 21.50 dollars

The percentage of decrease = 21.50/39 x 100%

The percentage of decrease = 55.1282

Round it to the nearest tenth

The percentage of decrease is 55.1%

Which single transformation below would have the same effect as rotating the point (-3,4) by 180 degrees around the origin and then reflecting it in the y-axis?

Answers

First i will draw the original point in red

the rotation of 180° will give us the point (3,-4) the blue point

next, we reflect this point in the y-axis, the green point

if we see only the red point and the green point the transformation is equivalent to a reflection in the x-axis

the correct answer is 1

It takes Jenny 8.4 minutes to sweep a porch.Mofor can sweep the same porch in 13.3minutes. If they worked together how longwould it take them?

Answers

Rate of Jenny = 1/ 8.4 minutes

Rate of Mofor = 1/13.3 minutes

We know time and rate are inverses of each other.

So, if they work together, their rates would be:

[tex]\frac{1}{8.4}+\frac{1}{13.3}[/tex]

The time they will take will be the inverse of this, thus:

[tex](\frac{1}{8.4}+\frac{1}{13.3})^{-1}[/tex]

So, let's calculate it:

[tex]\begin{gathered} (\frac{1}{8.4}+\frac{1}{13.3})^{-1} \\ =5.1484 \end{gathered}[/tex]

That is around 5.15 minutes.

please help due in 5 minutes would mean a lot

Answers

Answer:

150 degrees

Explanation:

Given: m∠8=150 degrees

Angles 8 and 5 are vertically opposite angles.

Vertical angles are equal, therefore:

[tex]\begin{gathered} m\angle5=m\angle8 \\ m\angle5=150\degree \end{gathered}[/tex]

Next, angles 1 and 5 are corresponding angles.

Corresponding angles are equal, therefore:

[tex]\begin{gathered} m\angle1=m\angle5 \\ m\angle1=150\degree \end{gathered}[/tex]

The measure of angle 1 is 150 degrees.

how to find the center and scale factor of #5?

Answers

SOLUTION:

Case: Enlargement

Method:

Scale factor: The scale factor is the 3, because the image is three times the size of the object.

From the tracing, the center of dilation is at C(-2, -2).

Final answer:

Center = (-2, 2)

Scale factor = 3

Use the point-slope formula to write an equation of the line that passes through 4, 2 and 6,5.Write the answer in slope-intercept form (if possible).

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

point 01 (4 , 2)

point 02 (6 , 5)

Step 02:

equation of the line:

slope:

[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-2}{6-4}=\frac{3}{2}[/tex]

Point-slope form of the line

(y - y1) = m (x - x1)

[tex]\begin{gathered} (y-2)=\frac{3}{2}(x-4) \\ \\ (y-2)=\frac{3}{2}x\text{ -}\frac{12}{2} \\ \\ y-2=\frac{3}{2}x-6 \\ \\ y=\frac{3}{2}x-6+2 \\ \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]

The answer is:

y = 3/2 x - 4


1. Describe the shape of
distribution A:
Answer choices:

Symmetric

Negatively skewed

Positively skewed

Uniform

Answers

The shape of the distribution A is Negatively skewed.

What is a negatively skewed distribution?\

A negatively skewed distribution sometimes referred to as a left-skewed distribution, is a type of distribution where more values are concentrated on the right side (tail) of the distribution graph and the left tail of the distribution graph is longer.

The idea of skewness is used in finance to analyze the distribution of investment returns. An investor may anticipate frequent tiny wins and a few significant losses, according to the distribution's negative skewness. In fact, traders frequently use trading methods that are based on distributions that are negatively skewed.

To learn more about negatively skewed distribution, use the link given
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Cassius is purchasing flower baskets to be placed on each table at a volunteer appreciation lunch. Store Acharges $19.25 per flower basket plus a $15.00 delivery fee. Store B charges $17.50 per flower basket plusa $30.00 delivery fee. Which inequality can determine x, the maximum number of flower baskets that canbe ordered for the total cost at Store A to be cheaper the total cost from Store B?O 19.25 + 15x > 17.5 + 30xO 19.25 + 15x < 17.5 + 30x19.25x + 15 < 17.5x + 30O 19.25x + 15 > 17.5x + 30

Answers

We will have the following expressions for store A and B respectively:

[tex]19.25x+15[/tex][tex]17.50x+30[/tex]

From this, we can see that after certain ammount of flowers the price will be better if we arrage it as follows:

[tex]19.25x+15>17.50x+30[/tex]

find f^-1(f(x)) for f(x)=(x-3)/2

Answers

After solving the given equation for f(x) the resultant answer is f(x)=1.

What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, find f(x):

When f^-1(f(x)) in f(x)=(x-3)/2.

Now, calculate as follows:

f(x)=(x-3)/2f(x)=(f⁻¹-3)/2f(x)=(1/f - 3)/2f(x)=(1 -3f/f)/2f(x)=(1-3)/2f(x)=2/2f(x) = 1

Therefore, after solving the given equation for f(x) the resultant answer is f(x)=1.

Know more about equations here:

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50 POINTS!!!!!!
1. Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.

A) 250.4°
B) 63.2°
C) 70.4°
D) 19.6°

Answers

Answer:

C) 70.4°

Step-by-step explanation:

We know supplementary angles add up to 180°:

A + B = 180°

Find the missing one:

A + 109.6° = 180°A = 180° - 109.6°A = 70.4°

Correct choice is C.

C. 70.4
180-109.6=70.4

pol: Practice & Problem Solving 2.PS-22 Question Help Three sisters are saving for a special trip. The ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4. Together all 3 sisters have saved $60. How much has each girl saved? Answer questions 3–4. IS 4 squares long. Then, use the diagrams to show $60. (Type whole numbers.) 4. Complete the table. Helga's savings Maurice's savings Nora's savings $8 $ $24 $32 $ $6 $ $ 12 $4 $ $ $16 + Vi 1 1,0 More Enter your answer in the edit fields and then click Check Answer. 1 pant Clear All Check Answer remaining

Answers

Answer:

Explanation:

We know that the ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4.

It means that if Helga has $8, Maurice has $3 and Nora has $4

In the same way, we can multiply one quantity by 2, and all the quantities will be multiplied by 2, so if Helga has $16, Maurice has $6 and Nora has $8

Because:

$8 x 2 = $16

$3 x 2 = $6

$4 x 2 = $8

So, following the same logic, we can complete the table as:

Therefore, the complete table is:

What is the difference between a rectangle and a rhombus?

Answers

A rhombus is a two-dimensional shape and is also characterized as a special parallelogram. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.

A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.

Rhombuses and Rectangles have the following differences:

1) A rhombus has four equal sides while in a rectangle, the opposite sides are equal.

2) The diagonals of a rhombus bisect each other at 90° while the diagonals of a rectangle bisect each other at different angles.

2.A group of students in MATH 105 start a walking program. The chart below shows eachmember's self-reported walking time in minutes during May 2022.X-300A-325B-550C-400D - 900E-150F-60G-600H - 250By what percent did X exceed or fall below the mean? it’s number 2

Answers

Given: 300, 400, 60, 325, 900, 600, 550, 150, 250

1st we find the mean or avaerage of all the numbers.

Mean:

[tex]\frac{300+400+60+325+900+600+550+150+250}{9}=\frac{3525}{9}\approx392.778[/tex]

From here we can see that X=300 falls below the mean.

So we can use this formula:

[tex]\frac{mean-actual\text{ }value}{mean}*100\%\Rightarrow\frac{392.778-300}{392.778}*100\%\approx23.688\%[/tex]

Answer: X falls below the mean by 23.688%

-14x > -3 all I have to do is simplify it

Answers

The first step in simplifying the inequality is to divide both sides by -14:

[tex]\frac{1}{-14}\times-14x>-3\times\frac{1}{-14}[/tex]

Since we are dividing both sides by a negative number, the inequality reverses direction, and hence it becomes

[tex]\textcolor{#FF7968}{x<\frac{3}{14}}\text{\textcolor{#FF7968}{.}}[/tex]

This is the farthest we can go in simplifying the inequality; therefore, the above inequality is our answer

Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5

Answers

For the first equation:

y = (x + 5)(x + 1)

apply distribution property:

y = (x + 5)(x) + (x + 5)(1)

y = x·x + 5·x + x·1 + 5·1

y = x² + 5x + x + 5

y = x² + 6x + 5

For the second equation:

y = (x + 3)² - 4

use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:

y = x² + 2·x·3 + 3² - 4

y = x² + 6x + 9 - 4

y = x² + 6x + 5

The third equation is already in the convenient form.

Then, you can notice that all three equations are the same equations.

Question 5 of 9Translate the phrase into a variable expression. Use the letter m to name thevariable. If necessary, use the asterisk (*) for multiplication and the slash(/) for division.... the total number of minutes billed on the phone bill split between 3phones...Answer here

Answers

SOLUTION

From the question, let the total number of minutes billed on the phone bill be m

Splitting this into 3 phones, we have

[tex]\frac{m}{3}[/tex]

Hence the answer is m/3

solving compound qualities

Answers

S = {x ∈ R : 3≤x≤12}

1) To solve a compound inequality, we must do it one by one.

Let's start with

1.1) 0≤1/3x -1

1≤1/3x-1+1

1≤1/3x Multiplying both sides by 3

3≤x Flipping it

x≥3

1.2) 1/3x -1≤3

1/3x -1+1≤3+1

1/3x≤4

x≤12

2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:

So the Solution set is S = {x ∈ R : 3≤x≤12}

Please give me the correct answer.True or false.If a =b, then a +c = b+c.

Answers

Answer

a = b

a + c = b + c (Addition Property of Equality)

This operation is True.

Explanation

If we are told that

a = b

Adding the same number to both sides of an equation is called the Addition Property of Equality.

And it produces the same number on both sides after this operation.

a = b

Add c to both sides

a = b

a + c = b + c (Addition Property of Equality)

This operation is True.

Hope this Helps!!!

Y S 18. Graph triangle DEF with vertices D(-5,2), E(1.3), and F(-4,-3). Then graph the image of the triangle after it is translated 4 units right and 3 units down. What are the vertices of triangle D'E'F? 4 3 2 1 o 1 2 J 4 SX YTY

Answers

Graphing the triangle DEF, we have:

Now, translating the triangle 4 units right and 3 units down, we have the new vertices:

[tex]\begin{gathered} D(-5,2)\to D^{\prime}(-5+4,2-3)=D^{\prime}(-1,-1) \\ E(1,3)\to E^{\prime}(1+4,3-3)=E^{\prime}(5,0) \\ F(-4,-3)\to F^{\prime}(-4+4,-3-3)=F^{\prime}(0,-6) \end{gathered}[/tex]

Graphing the triangle D'E'F', we have:

A cosmetics company makes small, cylindrical bars of soap, and wraps them in plastic prior to packing them in boxes for shipping. Each bar of soap has a diameter of 5 cm and is 2 cm in height.a. How much soap material is used to make each bar of soap?b. How much plastic is required to wrap each bar of soap, assuming it is shrink-wrapped tightly around each bar?C.The company wants to be able to ship a minimum of 60 bars per box to save on shipping costs. What will be the dimensions of the box if the soap must be stacked no more than 5 bars high?d. Find the capacity of the box in litres.

Answers

a. In order to determine how much soap material is used for each bar of soap, consider that the shape of the bar is a cylinder, then, use the folowing formula for the volume of a cylinder:

V = π r² h

where r is the radius of the base and h is the height.

The diameter is 5 cm, then, the radius is r = d/2 = 5 cm/2 = 2.5 cm

The height is h = 2 cm

replace the previous values into the formula for V:

V = (3.14)(2.5 cm)²(2 cm)

V = 39.25 cm³

Hence, 39.25 cm³ of soap material is used to make each bar.

b. In this case it is necessary to calculate the suface area of the plastic used. As before, take into account that the bar has a cylindrical shape. Then, use the following formula for the surface area of a cylinder:

S = 2πr² + 2πrh

replace the values of the parameters to find S:

S = 2π(2.5 cm)² + 2π(2.5cm)(2cm)

S = 70.68 cm²

Hence, 70.68 cm² of plastic is required to wrap each bar

c. Take into account that the soap must be stacked no more than 5 bars high, and that the company wants to ship a minimum of 60 bars.

If there are 5 bars high x 3 bars length, in one face of the box you have 15 bars. Moreover, if there are 4 bars width, then, you have a total of 15x4 = 60 bars in one box, which is what the company wants.

The height of the box is given by 5 times the height of one bar (because there are 5 bars high). The length is given by 3 times the diameter of one bar and the width of the box is given by 4 times the diameter of one bar:

height of the box = 5(2 cm) = 10 cm

length of the box = 3(5 cm) = 15 cm

width of the box = 4(5 cm) = 20 cm

d. First, calculate the volume of the box, as follow:

V = h x l x w = (10 cm)(15 cm)(20 cm) = 3,000 cm³

take into account the conversion 1,000 cm³ = 1 L, then, the capacity of the box is:

V = 3,000 cm³ = 3L

Which symbol is used to represent Integer Numbers?1. Z2. W3. Q4. N

Answers

Answer: Letter Z.

The notation Z for the set of integers comes from the German word Zahlen, which means "numbers". Integers strictly larger than zero are positive integers and integers strictly less than zero are negative integers.

Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)

Answers

We have the following equation to solve

[tex]E=I\cdot Z[/tex]

Where E, I, and Z are complex numbers, therefore let's put it in numbers

[tex]E=(4+4i)(7+3i)[/tex]

We can solve it directly into the rectangular form by doing the distrutive

Then

[tex](4+4i)(7+3i)=28+12i+28i+12i^2[/tex]

Remember that

[tex]i^2=-1[/tex]

Then

[tex]\begin{gathered} (4+4\imaginaryI)(7+3\imaginaryI)=28+12i+28i-12 \\ \\ (4+4\imaginaryI)(7+3\imaginaryI)=16+40i \end{gathered}[/tex]

Now we have completely solved the problem!

[tex]E=16+40i[/tex]

______________________

The second solution (usual)

When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form

[tex]\begin{gathered} I=4+4i=4\sqrt{2}\angle45° \\ \\ Z=7+3i=\sqrt{58}\angle23.2° \end{gathered}[/tex]

Now to do the multiplication we multiple the magnitude and sum the phases (angles)

[tex]\begin{gathered} ZI=4\sqrt{2}\cdot\sqrt{58}\angle45°+23.2° \\ \\ ZI=4\sqrt{116}\operatorname{\angle}68.2° \end{gathered}[/tex]

We already have the result, now just put it in the rectangular form

[tex]\begin{gathered} ZI=4\sqrt{116}\cdot\cos(68.2)+i4\sqrt{116}\sin(68.2) \\ \\ E=16+40i \end{gathered}[/tex]

Question 3X1127INXRewrite in simplest rational exponent form VxVx. Show each step of your process.

Answers

Given

[tex]\sqrt[]{x}\cdot\sqrt[4]{x}[/tex]

So, we have that

[tex]\begin{gathered} \sqrt[]{x}=x^{\frac{1}{2}} \\ \sqrt[4]{x}=x^{\frac{1}{4}} \end{gathered}[/tex]

Therefore, the expression given is

[tex]x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}[/tex]

Apply the laws of exponents

[tex]x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex]

Answer:

[tex]x^{\frac{3}{4}}[/tex]

If x+4 is a factor of this polynomial, what is the value of a ?

Answers

Answer: -86

Given:

[tex]P(x)=2x^3-11x^2+ax-40[/tex]

If we consider x+4 as a factor of the given polynomial, this would mean that x=-4. For an x- value to be a factor of a polynomial, P(x) must be equal to 0. With that, we will have:

[tex]\begin{gathered} P(-4)=0 \\ P(-4)=2x^3-11x^2+ax-40 \\ 0=2(-4)^3-11(-4)^2+a(-4)-40 \\ 0=-128-176-4a-40 \\ 4a=-128-176-40 \\ 4a=-344 \\ a=-86 \end{gathered}[/tex]

Therefore, the answer is -86

Study the data given,Below are the weights of 6 randomly selectedblack bears and 6 randomly selected grizzly bearsliving on a wildlife refuge.Which type of bear had morevariation in weight?Black Bear Weights (lbs): 102, 151, 248, 342,453, 498A. Black BearsMean: 299MAD: 132B. Grizzly BearsC. Both showed the same amount ofvariation in weightHaven't learned this yet.Grizzly Bear Weights (lbs): 294, 302, 347, 422,553, 596Mean: 419MAD: 104 2/3

Answers

The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.

Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.

If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.

in a stable there are H horses 6 of them are taken into the the yard to exercise ⁰how many are left in the stable

Answers

Explanation:

If there are H horses and 6 are taken into the yard, then we have 6 horses less in the stable.

Answer:

There are (H - 6) horses left in the stable

1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x. The figure is not drawn to scale

Answers

1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x.

Remember that

the sum of complementary angles is 90 degrees

so

<1+<2=90

substitute given values

14+4x=90

solve for x

4x=90-14

4x=76

x=19

Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.45≥4x+5 and 53>4x+5

Answers

Expression given:

[tex]45\ge4x+5[/tex][tex]53>4x+5[/tex]

Procedure:

• Solving for ,x ,in first inequality

[tex]-4x\ge-45+5[/tex][tex]-4x\ge-40[/tex][tex]x\le\frac{-40}{-4}[/tex][tex]x\le10[/tex]

• Solving for ,x ,in second inequality

[tex]-4x>-53+5[/tex][tex]x<\frac{-48}{-4}[/tex][tex]x<12[/tex]

Thus, the graph would be:

If the solution is for both inequalities, then the answer is in which both are included:

[tex]x\le10[/tex]

what is the time it took to reach maximum height? round the answer to the nearest whole second.

Answers

3 seconds

Explanation

we have a graph where

x-axis: indicates the time

y-axis:indicates the height

to solve this we need to find the time, where the maximum heigth is reached

Step 1

check the coordinate where the maximum heigth is reached

and go down vertically to intersect the x-axis:

so, we have , it took around 3 seconds to reach the maximum heigth

I hope this helps you

Find each percent decrease. Rounf to thr nearest percent. The first one is done for you.From $60 to $40?

Answers

So the 100% percent is equal to $60 and is decreasing $40 so is:

[tex]60-40=20[/tex]

So is decreasing $20. now we can made a rule of 3 to finde the percentage so:

[tex]\begin{gathered} 60\to100 \\ 20\to x \end{gathered}[/tex]

and the ecuation will be:

[tex]\begin{gathered} x=\frac{100\cdot20}{60} \\ x=33.33\approx33 \end{gathered}[/tex]

So in total the decrese a 33%

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Write the place of the underlined digit then write its value. what is the value? From the Graph, find the constant of proportionality and write the direct variation equation In Texas v. Johnson Majority Opinion, Justice Brennan cites the Constitution as evidence to validate his argument.How will Brennan's document most likely be viewed in the future?A. It will also set a precedent for future legal matters.B. It will also be revised and updated by future historians.C. It will also be examined closely by future politicians.D. It will also address critical future events in history. Pam and Rachel buy books at the bookstore where Rachel works. As an employee, Rachel pays only 75% of the advertised price. How many books could each purchase and spend the same amount for the same number of books? who was involved in the Cherokee Uprising? Jeff picks a number with 2 tens 42 ones. victor picks a number with 3 tens 51 ones. what number does each child pick? Find the exact solutions to x2-3x+1-0 by using the Quadratic Formulal The area a of a circle is pi times the radius R squared as an equation I have to send the picCalculate the Area of the figure Help with explaining please! I have tried 4 tutors who could not answer this question. Someone, please help me. 1. The endpoints of line PQ on a real number line are -.5 and .72. What is the coordinate of the midpoint of line PQ? In 2018 it was estimated that approximately 41% of the American population watches the Super Bowl yearly. Suppose a sample of 118 Americans is randomly selected. After verifying theconditions for the Central Limit Theorem are met, find the probability that the majority (more than 50%) watched the Super Bow. Which option is an example of iteration in an algorithm?A. Instructing the computer to use a certain amount of its memory tosave the algorithm's dataB. Including a rigid sequence of events that the computer mustperform in an exact orderOC. Instructing the computer to repeat a step over and over while acertain condition is metD. Including an if-then statement to account for a specific condition What is the slope of the line shown?A. slope = 3B.slope = 12C. slope = 2D. slope = -3 Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.Year Mean SD n2009 11.4 3.6 502019 24.3 8.8 50Difference 12.9 5.52 50Round all calculated values to 4 decimal places as appropriate.1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:A. Large samples and no extreme outliers.B. There must be at least 3 levels of the categorical variable.C. np^10 and n(1p^)10D. Independently sampled pairs. Please help fast f(x) = 4x2 - 2x + 4 Find f(-9) What theme appears time and again in the epic, from the men opening the bag of winforgetting to sacrifice to the gods, to the suitors and the killing in the banquet hall, ancand his cattle? In your own words, explain what you know about a number that satisfies theequation x2 = -1. Sample Data48262191036984391035414135264238472947512227421220143514138142710482529331220229149943521413Computations(Round the mean and sample standard deviation to values to FIVE decimal places)Sample Mean = 25.42Sample Standard Deviation = 14.25724(Round the lower/upper limits and margin of error to THREE decimal places). #1. 80% Confidence Interval: 80% Confidence Interval Margin of Error:What does this confidence interval mean given the data?#2. 95% Confidence Interval:95% Confidence Interval Margin of Error: #3. 99% Confidence Interval:99% Confidence Interval Margin of Error:#4. Make up YOUR OWN Interval.50% Confidence Interval:50% Confidence Interval Margin of Error: