help me pls kinda stuck lol

Help Me Pls Kinda Stuck Lol

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

To find the x- intercepts , let y = 0 , that is

6x - x² = 0 ← factor out x from each term

x(6 - x) = 0

Equate each factor to zero and solve for x

x = 0

6 - x = 0 ⇒ x = 6

Coordinates of P (6, 0 )

(b)

The axis of symmetry is a vertical line, positioned at the midpoint of the zeros

x = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Equation of axis of symmetry is x = 3

(c)

Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 )

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = 6x - x² = - x² + 6x ← is in standard form

with a = - 1, b = 6 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{6}{-2}[/tex] = 3

Substitute x = 3 into y = 6x - x² for y- coordinate

y = 6(3) - 3² = 18 - 9 = 9

coordinates of maximum point = (3, 9 )


Related Questions

-9 + (-27x) please help

Answers

Answer:−

-9−27x

Step-by-step explanation:

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The function a(g)=10-log base 3(g+1) represents the home attendance of a football team in hundreds depending on the number of home games, g.


How many people will attend the second home game?


How many people will attend the eighth home game?


At which game were there 500 attendees? Does this answer seem reasonable based on context of the problem?

Answers

The number of people that will attend each game is given as follows:

Second game: 9,000.Either game: 8,000.

The number of attendees will be of 500 on the 857th game, which does not make sense in the context of this problem, as a football team plays at most nine home games during a season. (taking the NFL in context).

What is the logarithmic function?

The logarithmic function for this problem is defined as follows:

[tex]a(g) = 10 - \log_3{(g + 1)}[/tex]

Hence the number of people that will attend the second home game, when g = 2, is given as follows:

[tex]a(2) = 10 - \log_3{(2 + 1)}[/tex]

a(2) = 10 - 1

a(2) = 9.

Hence 9,000 people, as a(g) is measured in thousands.

The number of people that will attend the eight home game is given as follows:

[tex]a(8) = 10 - \log_3{(8 + 1)}[/tex]

a(8) = 10 - 2

a(8) = 8. (8,000, considering the unit of a(g)).

The game in which 500 people will attend is obtained as follows:

[tex]0.5 = 10 - \log_3{(g + 1)}[/tex]

[tex]\log_3{(g + 1)} = 9.5[/tex]

Applying the cube to both sides, we have that:

g + 1 = 9.5³

g = 857.

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a store pays $68 for a portable dvd player. the markup is 35% what is the sellng price?

Answers

Answer:

$91.80 selling price

Step-by-step explanation:

A store pays $68 for a portable DVD player. the markup is 35% what is the selling price?

35% = 0.35

The multiplier for  markup of 35% = 1 + 0.35 = 1.35

68 * 1.35 = $91.80 selling price

Is it possible to have a triangle with the following sides 6cm 7cm 2cm?

Answers

We can form a triangle with sides 6cm, 7cm, and 2cm.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

6cm, 7cm, 2cm

Here,

6 + 7 > 2

Hence, we can form a triangle with sides 6cm, 7cm, and 2cm.

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The measures of the interior angles of a convex octagon are 45x,40x, 155, 120, 155, 38x, 158x, and 41x. What is the measure of the smallest interior angle

Answers

The sum of the interior angles of an octagon is 1080 degrees.
You were given:
45x, 40x, 155, 120, 155, 38x, 158, and 41x. You were told to find the smallest angle. The smallest angle is 38x but we need to find x first.
We add what has been given, equate to 1080 and solve for x.
45x + 40x + 155 + 120 + 155 + 38x + 158 + 41x = 1080

164x + 588 = 1080
Subtract 588 from 1080.
164x = 1080 - 588
164x = 492
Divide both sides by 164.
x = 492/164
x = 3
We now multiply 3 times 38 to find the smallest angle.
Smallest angle = 3 times 38
Smallest angle = 114

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Simon's photo album has 8 photos of his car and some photos of his motorbike
He replaced some of the photos of his motorbike with some more photos of his car.
The number of photos of his car became 12. The ratio of the number of photos of his car to his motorbike became 3:5. How many photos of Simon's bike was there in the album ORGINALLY?

Answers

There were 24 photos of Simon's motorbike in the album originally.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x be the number of photos of Simon's motorbike in the album originally.

We know that the number of photos of his car became 12, so the number of photos of his car originally was 8.

We also know that the ratio of the number of photos of his car to his motorbike became 3:5.

So the number of photos of his car and his motorbike originally was x-4.

We can set up the following equation:

12/(x-4) = 3:5

We can cross-multiply and simplify to get:

3x - 12 = 60

3x = 60 + 12

3x = 72

x = 72/3

x = 24

Hence, originally there were 24 photos.

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What are the 3 types of triangles according to sides describe each?

Answers

Three types of triangles according to scalene, isosceles and equilateral triangle.

What is meant by scalene?

Every triangle side in a scalene triangle has a different length.Two triangle sides that are of the same length are called isosceles triangles.All of the sides of a triangle are the same length in an equilateral triangle.An equilateral triangle naturally has three equal internal angles and three equal length sides because, as the triangles above demonstrate, the length and internal angles of a triangle are closely connected.A scalene triangle is a triangle whose three sides are all of various lengths and whose three angles are all of different sizes. Scalene triangle angles always add up to 180 degrees and adhere to the angle sum property.

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A store owner gathered data for several days about the methods customers used to pay for their purchases. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0. 755x + 11. 339. Based on the line of best fit, approximately how many customers are predicted to use a card to pay on a day when 90 customers pay by cash? a. 68 b. 79 c. 92 d. 104.

Answers

According to the line of best fit, 79 consumers are predicted to use their card to pay during a day when 90 customers pay in cash. The correct answer is C.

The answer is 79. This is because the equation of the line of best fit is:

y = 0.755x + 11.339

Which is a linear equation that represents the relationship between the number of customers who pay by cash (x) and the number of customers who pay by card (y).

To use this equation to predict the number of customers who pay by card on a day when 90 customers pay by cash, we can substitute x = 90 into the equation:

y = 0.755x + 11.339y = 0.755(90) + 11.339y = 67.95 + 11.339y = 80.284Y = 79.28

79.28 ≈ 79, hence the correct answer is C.

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After allowing a discount of 20% on the marked price then
levying 10% VAT, a radio was sold. If buyer had paid Rs.320 for VAT how much had he got the discount?

Answers

Amount of discount allowed = 640 Rs.

What is VAT?

VAT meaning value added tax that is attached to an item of product while bought by the buyer and also in each stage of production, distribution level. It is almost similar to a sales tax that is paid within the item price.

What is the value of discount?

given, discount allowed = 20% on the market price.

VAT = 10% on the market price.

Buyer paid as VAT = 320 Rs

Assume, market price of radio = X Rs

now amount of discount = 20/100× X = 0.2X

amount of VAT = 10/100×X = 0.1X

it is said that VAT paid by buyer = 320 Rs

now 320 = 0.1X

X = 320 / 0.1 = 3200 Rs

market price of radio = 3200 Rs

amount of discount = 20/100× 3200 = 640 Rs

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How do you dilate by a scale factor of 3 4?

Answers

16 is a scale factor of 3 4

What is scale factor ?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.Scale factor is a number that is used to draw the enlarged or reduced shape of any given figure. It is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It helps in changing the size of the figure but not its shape.

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What is the area of the trapezoid?
19 cm
30 cm;
31 cm
32 cm
square centimeters

Answers

The answer for this is 32

A girl answered 38 questions on a reading app named lightsail.
The system indicated that she was 60% complete
How many questions are there in total?

Answers

Answer:

its either 63 or 64, im not really sure

yann just started a new job. for every 5 hours he works yama earns $90. the graph represents yamas earnings for diffrent numbers of hours

Answers

Answer:

12

Step-by-step explanation:

2x3 4+5

One Kung Pao chicken and two Big Macs provide 2620 calories. Two Kung Pao chickens and one Big Mac provide 3740 calories. Find the caloric content of each item.

Answers

One Kung Pao chicken contains 1620 calories. One Big Mac contains 500 calories.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Assume that one Kung Pao chicken content x calories and one Big Mac content y calories.

Given that one Kung Pao chicken and two Big Macs provide 2620 calories.

Two Kung Pao chickens and one Big Mac provide 3740 calories.

Now using the variable finding calories:

One Kung Pao chicken and two Big Macs provide x + 2y calories.

Two Kung Pao chickens and one Big Mac provide 2x + y calories.

The system of equations is:

x + 2y = 2620  ......(i)

2x + y = 3740  .....(ii)

Using the elimination method to solve the given equations.

Multiply equation (i) by 2 and subtract it from equation (ii)

2x + y = 3740

2x + 4y = 5240

(-)  (-)      (-)

_____________

      -3y = -1500

Divide both sides by -3:

y = 500.

Putting y = 500 in equation (i)

x + 2(500) = 2620

x + 1000 = 2620

x = 1620

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A vertical number line is given.


A vertical number line starting at negative 2 with tick marks every one half unit up to positive 4. The value 1.25 is labeled.


When scuba diving, a student recorded the value plotted in the image. If 0 represents sea level, which of the following is true about the value?


The student is −1.25 ft above sea level, and the absolute value is 1.25 ft.

The student is −1.25 ft below sea level, and the absolute value is 1.25 ft.

The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.

The student is 1.25 ft below sea level, and the absolute value is 1.25ft.

Answers

The true statement regarding the number line and the absolute value is given as follows:

The student is 1.25 ft above sea level, and the absolute value is 1.25 ft.

How to interpret the number line and the absolute value?

The number line gives the heights relative to the sea level, and thus their signal are interpreted as follows:

Positive numbers: heights that are above sea level.Negative numbers: heights that are below sea level.

The absolute value of a number represents the distance that the number is from the origin. In the context of this problem, it will give the distance of the measure from the sea level of 0 ft.

The height is given as follows:

1.25 ft.

Which is a positive measure, hence the correct option is given by the third option.

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The radius of a circle is increasing at a constant rate of 0. 5 meter per second. What is the rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters?.

Answers

The rate of increase in the circumference of the circle at the instant when the radius of the circle is 3 meters is 3 phi m/s

From the question, we have the following information :

1. Constant rate of increasing radius with respect of time (t)

  = [tex]\frac{dR}{dt}[/tex] = 0.5 m / s

2. Radius of circle is 3 meters ( 3m )

To find constant rate of increasing circumference, we have to know formula of circumference.  

We know that circumference = 2 π R

Constant rate of increasing circumference with respect of time (t) can be formulated from contant rate of increasing radius multiply with formula to find circumference

[tex]\frac{dC}{dt}[/tex] = 2πR [tex]\frac{dR}{dt}[/tex]

[tex]\frac{dC}{dt}[/tex] = 2πR ( 0.5 )

    = πR

From above equation, we know that the rate of increasing circumference is πR

When R = 3 m, we just simply subtitute πR with R=3

The constant rate will be :

Rate of increasing circumference = πR m/s

                                                        = π (3) m/s

                                                        = 3π m/s

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which word does not belong with the other guitar,flute,violin,cello​

Answers

The flute does not belong in the group.

I need help … please

Answers

Check to see if there is a constant rate of change to determine if a table of values represents a linear function. You're looking at a linear function if there is! You can learn how to determine whether a table of values represents a linear function in this tutorial.

Two linear equations are what?

If an equation is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Which two types of equations are there?

Identities and conditional equations are the two types of equations.

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Find and graph the image of quadrilateral PQRS after a dilation centered at the origin with a scale factor of 1/4. What are the coordinates of Q'?

Answers

The coordinates of point Q after dilation will be (2,-1). The correct option is B.

What is coordinate geometry?

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the coordinate is Q(8,-4). The point is dilated by a factor of 1/4.

The dilation of the point will be calculated as,

Q(8,-4) = Q'(8/4, -4 / 4)

Q(8,-4) = Q'(2, -1)

Hence the dilated point is Q'(2,-1).

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In circle O shown below, diameter DB is perpendicular to chord AC at E.

If DB = 34, AC = 30, and DE > BE, what is the length of
BE?

Answers

The length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.

What is the length of EH ?

Length of each segment

16. Length of segment DF

DF=-1-(-4)

DF=3

19. Length of segment FR

FR=-1 1/3-(-4)

FR= 2 2/3

17. Length of segment DE

DE=2 -(-1)

DE=3

20. Length of segment GH

GH= 3 1/2 -(-1)

GH=4 1/2

18. Length of segment FG

FG=3 1/2 -2

FG=1 1/2

21. Length of segment EH

EH=3 1/2-(-1 1/3)

EH= 4 5/6

Therefore the length of each segment is: DF=3, FR= 2 2/3, DE=3, GH=4 1/2, EH= 4 5/6.

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Find the vale of :

sin 1230°

Answers

Answer:

1/2

Step-by-step explanation:

I think it is 1/2 Sorry If i am Wrong

Is root 3x² 2x a polynomial?

Answers

The given expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial as the power of x are 2 and 1 which are whole numbers .

What are Polynomials ?

The Polynomials are defined as an expression that are composed of variables, constants and exponents, which are combined using mathematical operators .
For Example : [tex]x^{2} +4x[/tex] .

The Expression can be called as a polynomial if the power of variable present in the expression is a whole number .

The expression is given as : [tex]\sqrt{3}x^{2} -2x[/tex] ,

we can see that , in the first term the power of x is 2 , which is a whole number , and

in the second term the power of x is 1 , which is also a whole number .

Therefore , the expression [tex]\sqrt{3}x^{2} -2x[/tex] is a polynomial .

The given question is incomplete , the complete question is

Is [tex]\sqrt{3}x^{2} -2x[/tex] a polynomial ?

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the first term in this number pattern is 5. 5,10,15,20,25,30...

Answers

The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1 so options (A), (B), and (E) will be correct.

What is the pattern?

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint. The hint which is present in a given pattern hides in the pattern only.

Given the two patterns.

In the first pattern, each term become by adding 5 so option (A) is correct.

In the second pattern, each term become by adding 10 so option (B) is correct.

The term in the second pattern becomes by multiplying 2 in pattern 1

For example 5× 2 = 10 and 10 × 2 = 20 so option (E) will be correct.

Hence, "The first pattern has a difference of 5 while the second is 10 and become by multiplying 2 in pattern 1".

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What is the length of the long leg of a 30 60 90 triangle?

Answers

The longer leg is the one that faces the 60-degree angle.

Any triangle with a 90-degree angle is considered a right triangle. A unique variety of right triangle with a 30-degree angle and a 60-degree angle in addition to the right angle is known as a 30-60-90 triangle.

Triangle Properties 30-60-90

A triangle with sides of 30-60-90 can be recognized by how they relate to the angles.

The shorter leg is the one that faces the 30-degree angle.

The longer leg is the one that faces the 60-degree angle.

The hypotenuse is the side that faces the right angle of 90 degrees.

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HELP ME On the planet vreel, there are 8 alabers to ever 5 totts. if farmer joogh has 30 totts on his gepsil farm, how many alabers are on the farm? your answer may be exact or accurate to the nearest tenth

Answers

Answer:

48

Step-by-step explanation:

[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{30}[/tex]

In the ratio there are 5 totts.  The farmer has 30 totts.

5 x 6 = 30, so 8 x 6 = 48

Answer:

Step-by-step explanation: i pretty sure it 240 because there is 8 on every 5 so 8x5 and there is 8 on every 30 8x30=240

Please help solve this, my last two brain cells aren't working rn

Answers

Answer:

dude my brain cells are perishing

-2/3 is your answer my guy

have fun

Step-by-step explanation:

A alone can do piece of work in 6 day and B alone in 8 day. A and B undertook to do it for $3200. With the help of C, they completed the work in 3 day. How much i to be paid to C?

Answers

If A alone can do a piece of work in 6 days and B alone in 8 days, then A and B undertook to do it for $3200 and complete the work in 3 days with the help of C, then C would be paid 400 dollars.

Therefore the answer is $400.

This is a work and time problem that can be solved using the concept of rate of work. Let's call the amount to be paid to C as "x".

A can do 1 piece of work in 6 days. Therefore, his rate of work is 1/6.

B can do 1 piece of work in 8 days. Therefore, his rate of work is 1/8.

Amount of work A and B can do in 3 days is

= 3×(1/6) + 3×(1/8)

= 3×(1/6)×(4/4) + 3×(1/8)×(3/3)

= 12/24 + 9/24

= 21/24

= 7/8

So amount of work C doing is

= 1 - 7/8

= 1/8

As C do 1/8 amount of work, the amount C would receive is

= 3200 × (1/8)

= 400

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you are standing 10 feet from the base of a tree. the angle of elevation to the top of the tree is 70 degrees. what is the height of the tree

Answers

The height of the tree is 17.32 feet.

What is height?

Height is the measurement of a person's or object's vertical distance from the ground. It is usually expressed in units of meters or feet. Height is an important factor in determining physical characteristics, such as BMI, or Body Mass Index. Height can also be used to estimate the age of a person, and to measure the effects of a growth-promoting treatment. Height is also used in many sports, as it is often an advantage for athletes.

Using the tangent formula, the height of the tree is approximately 17.32 feet. To calculate this, take the tangent of 70 degrees (which is 1.19175) and multiply it by the 10 feet of distance.

The result is 11.9175 feet, which when rounded to the nearest hundredth is 17.32 feet.

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what is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning
HHH
0
8. 2x
C. 4x
D. 2x
E. 4x

Answers

Answer: i believe is c or d i not 100% sure

You will be writing a short essay on how you can apply the processes you have learned in this unit to solve one of those questions

Calculating Unit Price for Business Owner
A restuarant owner is trying to choose a vendor for their supplies needed for their to-go operation. Since COVID their to-go orders have sky rocketed. Below he has listed how many of each item he has used in the past 6 month. Choose between the two vendors pricing sheets to decide who would be the best option. Give a detailed breakdown of unit prices and amount needed by the particular business to choose between the vendor.

6-month inventory break down:
large to-go boxes: 2,575
small to-go boxes: 1,890
to-go cups w/ lid: 3,010


Vendor 1 pricing:
large to-go boxes: $45.49/case (200 boxes per case)
small to-go boxes: $45.51/case (400 per case)
to-go cups w/ lid: $59.49/case (600/case)

Vendor 2 pricing:
large to-go boxes: $25.49/case (150 boxes per case)
small to-go boxes: $40.51/case (500 per case)
to-go cups w/ lid: $37.50/case (500/case)

Answers

Answer:

large to-go boxes: $45.49/case (200 boxes per case)

small to-go boxes: $45.51/case (400 per case)

Step-by-step explanation:

large to-go boxes: $25.49/case (150 boxes per case)

small to-go boxes: $40.51/case (500 per case)

to-go cups w/ lid: $37.50/case (500/case)

Other Questions
today, primary media usage is from select one: a. tv and computer. b. video games and tv. c. dvds and computer. d. video games and computer. What is the energy associated with the formation of 2.55 g of 4He by the fusion of 3H and 1H?Substance Mass (u)4He 4.002603H 3.016051H 1.00783 umbilical herniation is the most common congenital defect in cattleT/F Andrew plays football. On one play, he ran the ball 24 1/3 yards. The following play, he was tackled and lost 3 2/3 yards. The next play, he ran 5 1/4 yards. The team needs to be about 30 yards down the field after these three plays. Did the team make their 30 yard goal? Explain To minimize exposure to political risk, a multinational firm may establish a joint venture with a local entrepreneur, establish a joint venture with a group of multinationals, orpurchase an insurance policy from the Foreign Credit Insurance Association (FCIA).hedge in the Eurodollar market.purchase an insurance policy from the Overseas Private Investment Corporation (OPIC).any combination of the above. The acceleration of a model car along an incline is given by att)-1cm/sec', for ost The density of a 3.539 M HNO3 aqueous solution is 1.150 g/ml. at 20C. Calculate the molality of the solution. The molar mass of HNO3 is 63.02 g/mol. a. 3.946 m b. 3.818 m O c. 5.252 m O d. 3.077 m Moving to another question will save this response. what is the distance of the hyperplane (5 3x1 4x2 = 0) to the origin? How many six-digit strings have a digit sum of 35? elana sells 3a adult tickets if elana sells 15 adult tickets does she sell at least 100 total tickets Which list is in order from least to greatest? 1. 94 times 10 Superscript negative 5, 1. 25 times 10 Superscript negative 2, 6 times 10 Superscript 4, 8. 1 times 10 Superscript 4 1. 25 times 10 Superscript negative 2, 1. 94 times 10 Superscript negative 5, 6 times 10 Superscript 4, 8. 1 times 10 Superscript 4 1. 25 times 10 Superscript negative 2, 1. 94 times 10 Superscript negative 5, 8. 1 times 10 Superscript 4, 6 times 10 Superscript 4 1. 94 times 10 Superscript negative 5, 1. 25 times 10 Superscript negative 2, 8. 1 times 10 Superscript 4, 6 times 10 Superscript 4. To Kill A Mocking Bird: Chapters 1 - 5: Put the following events in order as they appeared in the novel:Burris Ewell was told to leave school so he could go home and wash the "cooties" out of his hair.Scout beat up Walter Cunningham, Jr.Scout, Jem, and Walter went to the Finch's house for lunch.Miss Caroline unintentionally humiliated Walter Cunningham, Jr.Little Chuck Little offered Miss Caroline a cup of water. ___ what was the first step in the treatment processses that removes particles from river water(a) Sand filtration(b) Carbon filters(c) A coagulant (usually chlorides or sulfate salts) If, for a given policy option, PVB equals $250,000, and PVC equals $500,000, thenA) the benefit-cost ratio equals 0.5B) the benefit-cost ratio equals 2.0C) the benefit-cost ratio equals 1.5D) there is insufficient information to determine the benefit-cost ratio What types of measurements are typically made by surveyors in performing work for condominium developments? O deformation surveys O as built surveys O mortgage surveys hydrographic surveys What are the primary components of a land tenure system? Check all that apply. erify that the vector X is a solution of the given system. X'= 10 1 1 ox; X = -2 0-1 sin(t) 1 sin(t) cos(t) 2 -sin(t) + cos(t) For X = sin(t) 1 sin(t) cos(t) 2 -sin(t) + cos(t) one has X' 1 0 1 1 1 0 X- 1-2 0-1 Since the above expressions -Select- sin(t) sin(t) cos(t) is a solution of the given system. -sin(t) + cos(t) If the cost of an item of inventory is $59 and the current replacement cost is $69, the amount included in inventory according to the lower of cost or market is:________ The frequency response of a system is given as Vout/Vin= jL / (( j)2+ jR+L). If L=2 H and R=1 , then what is the magnitude of the response at 70Hz?A. 14.310-B. 10C. 0.5D. 4.5510- Imagine the owner of a movie theater who has complete freedom in setting ticket prices. The more he charges, the fewer the people who can afford tickets. In a recent experiment the owner determined a precise relationship between the price of a ticket and average attendance. At a price of Rs 500 per ticket, 120 people attend a performance. Decreasing the price by Rs. 10 increases attendance by 15. Unfortunately, the increased attendance also comes at an increased cost. Every performance costs the owner Rs18000. Each attendee costs another Rs. 4. The owner would like to know the price at which he can make the highest profit. (Assume the answer is less than Rs. 500) [Adapted from "How to Design Programs". Currency changed from $ to Rs) write the following using sigma notation and then evaluate. the sum of the terms 2k for k=2,3,5. provide your answer below: