What is the solution set for −4x−38<2

Answers

Answer 1

The solution set for the inequality is x < -10

What are inequalities?

The different signs for representing inequalities are;

< represents the sign for less than>  represents the sign for greater than≥ represents greater than or equal to≤ represents less than or equal to

From the information given, we have that;

−4x−38<2

To solve for the value of x, take the steps;

collect the like terms

-4x> 2 + 38

Add the values

-4x> 40

Divide both sides by the coefficient of x, we have;

x > -10

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Related Questions

Use the FOIL method to find the product. Express the product in descending powers of the variable.
(7+6x)(1-5x)

Answers

Answer down below!

To begin with, the FOIL method stands for First Outside Inside Last. This is the method we use to multiply numbers like this

So, how do we start?

First: 7 times 1
Outside: 7 times 5x
Inside: 6x times 1
Last: 6x times 5x

7 times 1 = 7
7 times 5x = 35x
6x times 1 = 6x
6x times 5x = 30x^2

Now, with all these numbers, we combine all like terms

Our final answer will be 30x^2 + 41x +7

After 2 hours, 36% of a certain element remains. If a sample has an initial amount of 100 grams, how many hours will it take until only 1 gram remains? Provide an answer supported by valid mathematical reasoning and/or calculations.

Answers

It will take approximately 12.85 hours until only 1 gram of the element remains.

If after 2 hours, 36% of the initial amount remains, then the remaining amount is 0.36 times 100 grams, which is 36 grams. Let's define the amount of the element remaining after time t in hours as R(t). Since the element is decaying exponentially, we can model it with the equation R(t) = 100[tex](0.36)^t[/tex].

We want to find how many hours it will take until only 1 gram remains. We can set R(t) equal to 1 gram and solve for t:

1 = 100[tex](0.36)^t[/tex]

Taking the logarithm of both sides, we get:

ln(1) = ln(100[tex](0.36)^t[/tex])

0 = ln(100) + t*ln(0.36)

t = -ln(100)/ln(0.36)

Using a calculator, we find that t ≈ 12.85 hours.

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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!

Answers

A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3

B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x

What is the Area of a Rectangle?

To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.

Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:

Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x

Length = 2x - 3

Part B: To prove this, we have:

length * width = 8x² - 12x

Substitute:

(2x - 3) * 4x = 8x² - 12x

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Need answers to this by 20 min please!

Dividing cubic polynomials by linear divisor

Answers

The solution to each of the given polynomials are:

1)  x² + 3x - 4

2) x² - 4x + 4

3) x² - 7x + 8

4) x² - 13 - (15/(x + 3)

How to carry out polynomial division?

1) We want to divide the polynomial. Thus:

          x² + 3x - 4

x + 2| x³ + 5x² + 2x - 8

     -   x³ + 2x²

                 3x² + 2x

               - 3x² + 6x

                        - 4x - 8

                      -  -4x - 8

                                0

2) We want to divide the polynomial. Thus:

        x² - 4x + 4

x - 2| x³ - 6x² + 12x - 8

     -  x³ - 2x²

              - 4x² + 12x

              - -4x² + 8x

                         4x - 8

                      -  4x - 8

                                0

3) We want to divide the polynomial. Thus:

         x² - 7x + 8

x + 3| x³ - 4x² - 13x + 24

      -  x³ + 3x²

              - 7x² - 13x

              - -7x² - 21x

                         8x + 24

                      -  8x + 24

                                0

4) We want to divide the polynomial. Thus:

        x² - 13

x + 3| x³ + 3x² - 13x - 15

      -  x³ + 3x²

              - 0x² - 13x

              - -7x² - 13x

                       0 - 15

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If cos⁡θ=-1/3 and θ is in quadrant III, find the exact values of sin⁡θ,tan⁡θ,sec⁡θ,csc⁡θ,and cot⁡θ. You can use the identities or x, y, r.

Answers

The exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

Given: cosθ = -1/3 and θ is in quadrant III.

This means that sinθ = ± √(1 - (cosθ)2).

We know that cosθ is negative, so sinθ will be negative.

Therefore, sinθ = -√(1 - (-1/3)2 )

sinθ = - √(1 - 1/9)

sinθ = -√8/9

tanθ = sinθ/cosθ

tanθ = (-√8/9)/-1/3

tanθ = √8/3

secθ = 1/cosθ

secθ = 1/-1/3

secθ = -3

cscθ = 1/sinθ

cscθ = 1/-√8/9

cscθ = -√9/8

cotθ = cosθ/sinθ

cotθ = -1/3/-√8/9

cotθ = √9/8

Therefore, the exact values of sinθ, tanθ, secθ, cscθ, and cotθ are -√8/9, √8/3, -3, -√9/8, and √9/8, respectively.

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What is the average of the two bases in the following trapezoid in feet? 22 ft 14.75 ft 11 ft 18 ft

Answers

Answer: 18 feet.

Step-by-step explanation:

Average of bases = (22 + 14.75) / 2

Average of bases = 18.375

18.375 to the nearest tenth is = 18ft

Therefore, the average of the two bases of the trapezoid is 18 feet.

Share your own multi-step combination problem

Answers

My own multi-step combination problem is given below:

Amanda  was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda  have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda  create?

How do you solve the multi-step combination?

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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I would be thankful if you help

Answers

To get a 1 in matrix row 1, column 1 all we have to do is divide the row by 7 which gives us:

[tex]\left[\begin{array}{ccc} 1\frac {-4}{7}&\frac{8}{7} \\-12&7&-13\end{array}\right][/tex]

Understanding Matrix

The solution provided above uses a method of matrix called Echelon.

Echelon matrix is a matrix that has been transformed using row operations into a specific form that makes it easier to solve systems of linear equations.

By applying these row operations, a matrix can be transformed into row echelon form, which is a weaker form of echelon form where the leading non-zero entry of each row is to the right of the leading non-zero entry of the row above it, but not necessarily strictly to the right.

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what principal will have majority value of $10,000 at 8.25% p.a in three months?

Answers

__________________________________

Simple Interest: A = P × i ÷ 100 × n = 10,000 × 8.25 ÷ 100 × 3= 247.5= 10,000 + 247.5= $10,247.5 Compound Interest: A = P (1 + i ÷ 100) n = 10,000 (1 + 8.25 ÷ 100) ³= $12,684.80The Compound Interest Principal Will Have Majority Value In 3 Months

__________________________________

Factor by grouping. Then supply the term that is missing below. 4mn+3m+8n+6=(m+2)(?+3)

Answers

Answer:

4mn + 3m + 8n + 6 = (m + 2)(4n + 3)

The missing term is 4n.

what is the quotient?

Answers

Answer:

a quotient is the result obtained by dividing one quantity by another.

Justin mowed 45% of her garden in 18 minutes.how many minutes will it take him to mow all of his garden at this rate? Explain

Answers

If Justin mowed 45% of her garden in 18 minutes, then we can set up a proportion to find how long it would take him to mow 100% of the garden:

45/100 = 18/x

where "x" is the unknown number of minutes it would take to mow 100% of the garden.

To solve for "x," we can use cross-multiplication:

45x = 100 * 18

Simplifying the right-hand side:

45x = 1800

Dividing both sides by 45:

x = 40

Therefore, it would take Justin 40 minutes to mow all of his garden at the same rate of 45% in 18 minutes.

To explain this, we used the fact that the amount of work done (mowing a certain percentage of the garden) is directly proportional to the time it takes to do that work. This means that if Justin mowed 45% of the garden in 18 minutes, he would take proportionally longer to mow the entire garden. The proportion we set up allows us to find the unknown amount of time it would take to mow the entire garden. Solving the proportion, we found that it would take Justin 40 minutes to mow all of his garden at the same rate he mowed the 45%.

Use the general form of the equation for an ellipse with center (0,0) with a vertex at (5,0) and a co-vertex at (2,0)​

Answers

The general form of the equation for an ellipse with center (0,0) and semi-axes lengths a and b is:

(x^2/a^2) + (y^2/b^2) = 1

Since the vertex is at (5,0), we know that a = 5. Since the co-vertex is at (2,0), we know that b = 2.

Plugging these values into the equation, we get:

(x^2/5^2) + (y^2/2^2) = 1

Simplifying, we get:

x^2/25 + y^2/4 = 1

Therefore, the equation of the ellipse with center (0,0), a vertex at (5,0), and a co-vertex at (2,0) is x^2/25 + y^2/4 = 1.

The area of the rectangle shown is 352 square inches. What are the dimensions of the rectangle? Write the dimensions from least to greatest.
Length= 4x Width= x+3 Area=352

Answers

Answer:

11 in and 32 in

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

Given a rectangle with dimensions of:

l = 4x in, w = x + 3 in,And area of A = 352 in²

Use area equation and find the value of x:

A = lw352 = 4x(x + 3)88 = x(x + 3)88 = x² + 3xx² + 3x - 88 = 0x² + 11x - 8x - 88 = 0x(x + 11) - 8(x + 11) = 0(x - 8)(x + 11) = 0x = 8 or x = - 11

The second root is ignored as being negative.

The dimensions of the rectangle are:

l = 4*8 = 32 inw = 8 + 3 = 11 in

For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose the best description of its solution. If the system has exactly one solution, give its solution. (see attached)

Answers

The systems of linear equations can be classified as "consistent dependent," "consistent independent," or "inconsistent" as follows:

A. System A = Inconsistent (No solution)

B. System B = Consistent dependent (Indefinitely many solutions)

C. System C = Consistent independent (A unique solution)

How to identify the systems of linear equations

To identify the systems of linear equations, you first need to note the meaning of the different systems of equations. First, the Consistent dependent has two equations that represent the same line, so they intersect at infinitely many points and any point on the line represents a solution to the system.

Next, the Consistent independent has the two equations represented by two distinct non-parallel lines, so they intersect at exactly one point, which is the unique solution to the system.

Finally, the Inconsistent has two equations that are represented by two distinct parallel lines, so they do not intersect, and there is no solution to the system.

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help with this word problem

Answers

The height of the school building is approximately 4.38 meters (rounded to the nearest hundredth).

How to calculate the height

JX / BX = JM / BT

Substituting the known values, we get:

(d1 + d2) / h = d1 / (h - 1.75)

(d1 + d2) * (h - 1.75) = d1 * h

d1 * h + d2 * h - 1.75 * d1 - 1.75 * d2 = d1 * h

d2 * h - 1.75 * d1 - 1.75 * d2 = 0

h = (1.75 * d1 + 1.75 * d2) / d2

h = (1.75 * 8.75) / 3.5

h = 4.375

The height of the school building is approximately 4.38 meters

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Please see the attached

Answers

the answer is feet ......

Adam works as an account manager for a local insurance company. He makes $3500 per month, after taxes. He sticks to a strict monthly budget to make sure that he is able to pay for all of his expenses each month. Look at the list below of the items Adam must budget for each month. He gives a specific percentage of his income to each item. Use his monthly income and the percentage of each item to determine how much Adam will need to budget for each expense. 30% for rent/mortgage $ 15% for Insurances $ 12% for food $ 8% for utilities $ 10% for savings $ 5% for fun $ 7% for clothing $ 3% for personal items $ 10% charitable giving $ How much money will Adam have left over after budgeting for each item on the list? $

Answers

Answer:

  see below

Step-by-step explanation:

Given a $3500 net income per month and a list of budget percentages, you want to know the budget amounts for each item, and the amount left over.

Amounts

Each budget amount is the product of the net income and the associated budget percentage. Those products are ...

rent: $1050insurance: $525food: $420utilities: $280savings: $350fun: $175clothing: $245personal: $105charity: $350

Left over

The sum of these amounts is $3500, so there will be $0 left over.

__

Additional comment

The list is stored in the variable 'b' by the first line in the calculator. Then these values are multiplied by the net income to get the budget amounts.

The simplest form of log5+log6-log2​

Answers

The simplest form of log5+log6-log2​ is:  log15.

What is the simplest form?

Let us simplify log5 + log6 - log2 by making use  logarithmic rules:

log a + log b = log (ab)

log a - log b = log (a/b)

So,

log5 + log6 - log2

= log (5 x 6) - log2

= log30 - log2

Now let make use of the  logarithmic rule:

log a - log b = log (a/b) = log a - log b

log30 - log2

= log (30/2)

= log15

Therefore the simplest form is log15.

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HELP FASTTTTT PLAZSSSS

Answers

Top right=1
Top left=2
Bottom left=3
Bottom right=4

Use the substitution u = 1/y and v = 1/y to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. -3/x + 4/y = 5 and 1/x - 2/y = -3

Answers

Starting with the given system of equations:

-3/x + 4/y = 5
1/x - 2/y = -3

We can use the substitutions u = 1/y and v = 1/x to rewrite the equations in terms of u and v:

-3v + 4u = 5 (multiply both sides by uv)
v - 2u = -3

Now we can solve this system of equations in terms of u and v. One way to do this is to multiply the second equation by 4 and add it to the first equation, eliminating the v variable:

-3v + 4u = 5
4v - 8u = -12
_____________
u = -1/2

Next, we can substitute this value for u into one of the equations to solve for v. Using the second equation, we get:

v - 2u = -3
v - 2(-1/2) = -3
v + 1 = -3
v = -4

Now we have the values of u and v:

u = -1/2
v = -4

To find the solution set in terms of x and y, we can back substitute these values into the original substitutions:

u = 1/y
-1/2 = 1/y
y = -2

v = 1/x
-4 = 1/x
x = -1/4

Therefore, the solution set to the original system of equations is:

x = -1/4
y = -2

What is the equation through the points: (6, 5), (8, -2)


ASAP please

Answers

The equation of the line passing through the points (6, 5) and (8, -2) is[tex]y = -\frac{7}{2} x + 26[/tex].

What is the equation of the line?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values:

m = (-2 - 5) / (8 - 6)

m = -7/2

Using the point-slope form, plug in one of the given points and slope m = -7/2 to find the equation of the line.

Let's use the point (6, 5):

y - y₁ = m(x - x₁)

[tex]y - 5 = -\frac{7}{2}( x - 6 )\\\\y - 5 = -\frac{7}{2} x + 21\\\\y = -\frac{7}{2} x + 21 + 5\\\\y = -\frac{7}{2} x + 26[/tex]

Therefore, the equarion of the line is [tex]y = -\frac{7}{2} x + 26[/tex].

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Please help solve graphs

Answers

The graphs are:

1) not one-to-one

2) one-to-one

3) not one-to-one

Are the graphs one-to-one?

A graph represents an one-to-one function only if.

We can't draw a vertical line that touches the graph twice or more.

We can't draw an horizontal line that touches the graph twice or more.

For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.

Similarly forthe third graph, the line y = 0 touches two points-

So these two are not one-to-one.,

For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.

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Vanessa purchased a used car on a payment plan. Four months after purchasing the car, the balance was $1,200. Seven months after purchasing the car, the balance was $975.

Write an equation that models the balance y after t months.

y =
t +

Answers

The equation that models the balance y after t months is y = -75t + 1,500

To write an equation that models the balance y after t months, we need to use the given information to determine the rate at which the balance is decreasing. We can use the formula for a straight line, y = mx + b, where m is the slope and b is the y-intercept.

We can start by finding the change in the balance over the three-month period from four to seven months after the purchase:

Change in balance = $1,200 - $975 = $225

The rate of change can be calculated by dividing the change in the balance by the number of months:

Rate of change = $225 / 3 months = $75 per month

We can use this rate of change as the slope of the equation:

y = -75t + b

To find the y-intercept b, we can use the fact that the balance was $1,200 four months after the purchase:

1,200 = -75(4) + b

b = 1,500

Therefore, the equation that models the balance y after t months is:

y = -75t + 1,500

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What is the answer?
A) Yes
B) No

Answers

Answer:

Step-by-step explanation:

No

no it is not proportional

A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder with a height of 5 in and a diameter of 6in . The paper label is wrapped around the can and covers only the side of the can (not the top or bottom). If the company has a total of 4521.6in^2 of paper available, how many labels can be made? Use 3.14 for n , and do not round your answer.

Answers

48 labels can be made if the company has a total of 4521.6in² of paper available.

We can calculate the number of labels by finding the surface area of the side of the can.

What is the surface area of the side of the can?

The surface area of the side of the can is the circumference of the base times the height:

C = πd

C = 3.14 x 6

C = 18.84 in

Area = C x h

Area = 18.84 x 5

Area = 94.2 in²

Therefore, each label requires 94.2 in² of paper.

To find the number of labels that can be made, we divide the total amount of paper by the amount needed per label:

Number of labels = Total area of paper / Area per label

Number of labels = 4521.6 / 94.2

Number of labels = 48

Therefore, 48 labels can be made using a total of 4521.6in² of paper.

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Please answer correctly and explain reasoning for brainliest (If correct) and thanks!
What are the coordinates of A’?

Answers

Check the picture below.

Graph the parabola.

y=x^2-2x+4
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.

Answers

A graph of the parabola with five points on the parabola is shown below.

What is the vertex form of a quadratic equation?

In Mathematics and Geometry, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

h and k represents the vertex of the graph.a represents the leading coefficient.

For the given quadratic function, we have;

y = x² - 2x + 4

When x = 0, we have:

y(0) = 0² - 2(0) + 4

y(0) = 4

When x = 2, we have:

y(2) = 2² - 2(2) + 4

y(2) = 4

When x = -2, we have:

y(-2) = -2² - 2(-2) + 4

y(-2) = 12

When x = 4, we have:

y(4) = 4² - 2(4) + 4

y(4) = 12

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Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.

Answers

The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100

What is an inequality?

The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.

The specified equations obtained from the constraints in slope intercept form are;

y = -0.5·x + 7; The region below the graph is shaded

y = -0.75·x + 9; The region below the graph is shaded

x = 0; The region to the right of the line x = 0 is shaded

y = 0; The region above the line y = 0 is shaded

The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9

Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3

The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)

The value of the function g for each of the feasible region are therefore;

g(0, 0) = 8 × 0 + 12 × 0 = 0

g(0, 7) = 8 × 0 + 12 × 7 = 84

g(8, 3) = 8 × 8 + 12 × 3 = 100

g(12, 0) = 8 × 12 + 12 × 0 = 96

The maximum possible value of g therefore is 100, which is the value at the point (8, 3)

Please find attached the graph of the inequalities showing the feasible region created with MS Excel

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if the area of the triangle is 8 15/16ths and the base is 5 1/2, what is the height

Answers

Answer:

h=.34

Step-by-step explanation:

1/2(bh)=A

1/2(5.5*h)=8.9375

5.5h=1.875

h=.34

Other Questions
In the year 2500, five male space colonists and five female space colonists (all unrelated to each other) settle on anuninhabited Earthlike planet in the Andromeda galaxy. The colonists and their offspring randomly mate for generations. Allten of the original colonists had free earlobes, and two were heterozygous for that trait. The allele for free earlobes isdominant to the allele for attached earlobes. Which of these is closest to the allele frequency in the founding population?A) 0. 4 a, 0. 6 AB) 0. 5 a, 0. 5 AC) 0. 2 a, 0. 8 AD) 0. 8 a, 0. 2 AE) 0. 1 a, 0. 9 A(please explain) What mass of methyl butanoate is produced from the reaction of 52.5g of butanoic acid answer 9.What is the solution set for this inequality?negative five D plus five and one over two symbol seventeen. Which statement best explains a reason the Mughal Empire declined and a reason the Ottoman Empire declined? the line is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) Assuming an approximately normal data set, find the 68% confidence interval for systolic blood pressure inwomen given a sample size of 1000 with a mean of 123.4 and a standard deviation of 19.9. an electrolytic cell is defined as: group of answer choices a cell in which a nonspontaneous reaction produces an electric current a cell in which an electric current drives a nonspontaneous reaction no correct answer a cell in which a spontaneous reaction produces an electric current a cell in which an electric current drives a spontaneous reaction According to the five forces model, _______ levels of competition for customers translate to _______ levels of profit in the industry. PROBLEM SOLVING1. An electron is traveling to the north with a speed of 3. 5 x 106 m/s when a magnetic field is turned on. The strength of the magnetic field is 0. 030 T, and it is directed to the left. What will be the direction and magnitude of the magnetic force?2. The Earth's magnetic field is approximately 5. 9 10-5 T. If an electron is travelling perpendicular to the field at 2. 0 105 m/s, what is the magnetic force on the electron?3. A charged particle of q=4C moves through a uniform magnetic field of B=100 F with velocity 2 x 103 m/s. The angle between 30o. Find the magnitude of the force acting on the charge. 4. A circular loop of area 5 x 10-2m2 rotates in a uniform magnetic field of 0. 2 T. If the loop rotates about its diameter which is perpendicular to the magnetic field, what will be the magnetic flux? Choisissez Complete each question with the correct form of quel Can you explain the chapter "feeling place in the city strange ontologies and location-based social media" by leighton evans. Share your own multi-step combination problem He clambered towards her and Curled her into his arms. Explain this figure of speech Part II: additional problems 1, 2, and 3 listed below.For each problem:a. Identify the given table as 1NF, 2NF, 3NF, or UNF (contains repeating group).b. Identify all partial and transitive dependencies by drawing a dependency diagram(for a UNF table, transform it to 1NF, then draw the dependency diagram).c. Transform all tables into 3NF by following the steps below. For c, you do NOT haveto draw dependency diagrams.1. STUDENT (STUDENT SSN, ST_NAME, MAJOR, ADVISOR NUM, ADV_NAME,ADV OFFICE. ADV PHONE ST CREDITHRS, CLASS STANDING)where:STUDENT SSN- All other attributesADVISOR NUM ADV_NAME, ADV OFFICE, ADV PHONEST CREDIT HRS > CLASS STANDINGNote: XYZ > ORS means that XYZ determines ORSYou can also find this notation in figure 6.3 and definition of determination on page62.2. MOVIE (MOVIE NUM, MOVIE TITLE, STAR NUM, STAR NAME)Sample data: (You can determine primary key based on the sample data.)MOVIE NUMMOVIE TITLESTAR NUMI STAR NAMEM001The MummyS001Brendan FraserS002Rachel WeiszM002CrashS001Brendan FraserS003Sandra Bullock(You may notice one movie can feature many stars and one star can act in many movies.)3. MOVIE (MOVIE NUM, MOVIE TITLE, DIRECTOR NUM, DIR NAME)where:MOVIE NUM> MOVIE TITLE, DIRECTOR NUM, DIR NAMEDIRECTOR_NUM >DIR NAME The heights of 14 plants, in inches, are listed.12, 14, 15, 15, 16, 16, 16, 17, 18, 18 ,19, 20, 22, 25If another plant with a height of 13 inches is added to the data, how would the mean be impacted? The mean would stay the same value of about 17.1 inches. The mean would decrease in value to about 17.1 inches. The mean would stay the same value of about 17.4 inches. The mean would increase in value to about 17.4 inches. In this excerpt from H. H. Munros "The Open Window," which line is an example of direct characterization? Small Birds InsectsInsectsOwlsPlantsThe removal of which of these would negatively affect the most populations in this ecosystem?SnakesFrogs HELP FASTTTTT PLAZSSSS The tin and zinc contents of a brass sample are analyzed with the following results:(a) Zn: 33. 27, 33. 37, and 33. 34%(b) Sn: 0. 022, 0. 025, and 0. 026%Calculate the standard deviation and the coefficient of variation (relative standard deviation) for the analysis. After 2 hours, 36% of a certain element remains. If a sample has an initial amount of 100 grams, how many hours will it take until only 1 gram remains? Provide an answer supported by valid mathematical reasoning and/or calculations.