can some1 help me out with this problem

Can Some1 Help Me Out With This Problem

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Compare the coordinates of corresponding vertices.

C(7, - 2 ) → C'(- 3, 7 )

x- direction 7 → - 3 , that is - 10 of a shift

y- direction - 2 → 7, that is + 9 of a shift

Thus the translation rule is

(x, y ) → (x - 10, y + 9 )


Related Questions

rationalise the following 1/√7

Answers

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         Hi my lil bunny!

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[tex]1\sqrt{7}[/tex]

[tex]= \frac{1}{7} \sqrt{7}[/tex] (Decimal: 0.377964)

OR

[tex]\frac{1}{\sqrt{7} }[/tex]

[tex]= \frac{1}{\sqrt{7} } X \frac{\sqrt{7} }{\sqrt{7} }[/tex]

[tex]= \frac{\sqrt{7} }{(\sqrt{7})^{2} }[/tex]

[tex]= \frac{\sqrt{7} }{\sqrt{7} }[/tex]

I don't really know because both of them seem right..

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If this helped you, could you maybe give brainliest..?

❀*May*❀

find the roots of the following equation X + 1 whole square minus x square equal to 2​

Answers

Answer:

x = 1/2

Step-by-step explanation:

Let's represent this in a mathematical way,

(x+1)^2 - x^2 = 2

Ok now we expand,

x^2 + 2x + 1 -x^2 = 2

rearrange,

x^2 - x^2 + 2x + 1 = 2

subtract,

2x + 1 = 2

subtract 1 from both sides,

2x + 1 - 1 = 2 - 1

2x = 1

Now divide 2 from both sides and get your answer,

x = 1/2

Answer:

[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]

[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]

[tex]2x + 1 = 2[/tex]

[tex]x = 1 \div 2[/tex]

Cheryl earns (p+3) dollars per hour. In 8 hour she earns ___ dollars.

Answers

Answer:

8p + 24 dollars

Step-by-step explanation:

1 hour = (p+3)

8 hours = 8 (p+3)

=> 8p + 24

In 8 hours, Cheryl earns 8p + 24 dollars.

Answer:

[tex]\boxed{8p + 24}[/tex]

Step-by-step explanation:

Hey there!

Well if Cheryl earns p + 3 per hour and it is asking us to find the amount made in 8 hours, we can make the following,

8(p + 3)

8*p = 8p

8*3 = 24

Together,

8p + 24

Hope this helps :)

can you make a triangle with 1. 2cm 3cm and 4cm 2. 2cm 3 cm 6 cm 3. 90 degrees 45 degrees 45 degrees 4. 90 degrees 60 degrees 60 degrees?

Answers

Answer:

1. 2cm 3cm and 4cm

yes, because 2+3>4

2. 2cm 3 cm 6 cm

no, 2+3<6

3. 90 degrees 45 degrees 45 degrees

yes, 90+45+45 = 180

4. 90 degrees 60 degrees 60 degrees?

no, 90+60+60=210!=180

True or false: f(x) is a function.
0
0
3
1
3
9
f(x)

Answers

Answer:

true

Step-by-step explanation:

it is true because there is one input for y output

Answer:

True

Step-by-step explanation:

This is a function.  Each value of x goes to only one value of y

The width of a rectangle measures (8.3c-8.4d)(8.3c−8.4d) centimeters, and its length measures (5.3c+4.8d)(5.3c+4.8d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answers

Answer:

P = 27.2c-7.2d

Step-by-step explanation:

It is given that,

The width of a rectangle is (8.3c-8.4d)

The length of a rectangle is (5.3c+4.8d)

The perimeter of a rectangle is equal to the sum of its all sides i.e.

P = 2(l+b)

P = 2(8.3c-8.4d+5.3c+4.8d)

P = 2[(8.3c+5.3c)+(4.8d-8.4d)]

P = 2(13.6c-3.6d)

P = 27.2c-7.2d

Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.

helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent​ "The product of 12 and a number y ​" mathematically.

Answers

Answer:

12y

Step-by-step explanation:

product means multiplycation so twelve times y is  12y

A plane is on its approach to land on the runway. The jet’s height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands. t (in seconds) h (in feet) 0 4000 5 3500 10 3000 15 2500 20 2000 25 1500. Determine where the graph crosses the h-axis. Then write the equation in slope-intercept form. a. (4000, 0); h = negative 100 t + 4000 b. (0, 4000); h = negative 100 t + 4000 c. (0, 4000); h = negative 4000 t + 100 d. (100, 0); h = 4000 t minus 100

Answers

Answer:

Step-by-step explanation:

This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line. If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept. If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.

Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:

h = -100t + 4000 which appears to be choice a.

Answer:

a

Step-by-step explanation:

i took the quiz and got it right :)

find six rational numbers between 3 and 4​

Answers

13/4, 10/3, 7/2, 11/3, 15/4, 35/9

Answer:

3.1

3.2

3.3

3.4

3.5

3.6

Hope this answer correct :)

to make a set for a stage, you bought a piece of lumber 9 feet long. How many 2 1/4 foot pieces can you cut from this piece of lumber? please answer ASAP

Answers

Answer:

4 pieces

Step-by-step explanation:

Total length of lumber = 9 feet

How many 2 1/4 foot pieces can you cut from this piece of lumber

To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber

9 ÷ 2 1/4

= 9 ÷ 9/4

= 9 × 4/9

= 36/9

= 4 pieces of lumber

Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber

A number “x” increased by 5 is 19?

Answers

Answer:

x+5=19

Step-by-step explanation:

i think that right let me know...:/

Answer:

x= 14

Step-by-step explanation:

a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes

x+5=19

19-5=x

14=x

There are 67 bikes in the bike rack outside a school. Out of all the bikes, 33 are silver. Half of the remaining
bikes are red.
Estimate how many bikes are red.

Answers

Answer:

17

Step-by-step explanation:

67 minus 33 leaves 34 red bikes but divided that by half gives you 17

There are approximately 17 red bikes in the bike rack outside the school.

What is Algebra?

Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.

We can solve this problem by setting up an equation to represent the relationship between the number of bikes in the bike rack, the number of silver bikes, and the number of red bikes.

Let's define a variable, r, to represent the number of red bikes. We know that 33 bikes are silver, so the number of bikes that are not silver is 67 - 33 = 34 bikes.

Half of the remaining bikes are red, so we can say that there are r = 34/2 = 17 red bikes.

Therefore, there are approximately 17 red bikes in the bike rack outside the school.

To learn more about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

If p-1 is a factor of p^4+p^2+p-k,the value of k is ?

Answers

[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]

Answer:

k=3

Step-by-step explanation:

Hello, if p-1 is a factor of

[tex]f(p)=p^4+p^2+p-k[/tex]

it means that f(1)=0, so

1+1+1-k=0

3-k=0

k=3

thank you

Which table represents a function?

Answers

Answer:

A

Step-by-step explanation:

it is A for every output y , there is only one input x

Answer:

A

Step-by-step explanation:

Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.

I need help with this question. PLZZ HELP!!!

Answers

Answer:

the 8 in the graph

Step-by-step explanation:

Tim owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.
He sells the shorts for $12 and the T-shirts for $8 each. Tim can work 18
hours a day, at most. It takes him 30 minutes to design a T-shirt and 45
minutes to design a pair of shorts. He must design at least 12 items each
day, but he cannot design more than 30 items in one day. Which set of
inequalities below represents this scenario?
A. s 2 12 + $ ss 30 + tiss 24-0.66t, s2; 0; t2 0
B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0
O c. s? 12-ts? 30-tss 24 -0.66t, s 2 0;t20
D. S 2 12-tss 30-ts 24 -0.66t, s 20; t 0​

Answers

Answer:

The correct option is;

B. s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t

Step-by-step explanation:

The given parameters are;

The number of T-shirts, t, and shorts, s, Tim must design a day = 12

The maximum number of T-shirts and shorts Tim can design a day = 30

The maximum number of hours Tim can work = 18 hours

Therefore, we have;

The number of shorts Tim designs in a day is ≥ The minimum number of T-shirts and shorts Tim must design a day less the number of T-shirts Tim designs

Which gives;

s ≥ 12 - t

Also the number of shorts Tim designs in a day is ≤ The maximum number of T-shirts, and shorts, Tim can design a day less the number of T-shirts Tim designs

Which gives;

s ≤ 30 - t

The number of 45 minute period for the design of shorts in 18 hours = 18×60/45 = 24

The fraction of 36 minutes in 45 minutes = 36/45 = 0.667

Therefore we have;

The number of shorts Tim designs in a day is ≤ The number of 45 minute periods in 18 hours less the number of 36 minutes periods used to design T-shirts

Which gives;

s ≤ 24 - 0.66·t

The correct option is s ≥ 12 - t, s ≤ 30 - t, s ≤ 24 - 0.66·t.

Answer:

B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0

Step-by-step explanation:

Hope this helps!!

The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1 . 108 kilometers. About how
many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun?
O 5.2. 107 kilometers
O 4.7. 108 kilometers
O 5.2. 108 kilometers
O 5.7. 109 kilometers

Answers

Answer: 1 is the answer

Raj correctly determined that ray LH is the bisector of AngleGLI. A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I. Which information could he have used to determine this? AngleGLH Is-congruent-to AngleILM mAngleKLM = 5mAngleILM mAngleGLI = 2mAngleGLH mAngleGLI = mAngleGLH + mAngleHLI

Answers

Answer: C.) mAngleGLI = 2mAngleGLH

Step-by-step explanation:

Hope it helps!!!

For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds

What is an angle?

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.

∠GLI is bisected by LH, hence:

∠GLH = ∠HLI (definition of bisection)

∠GLI = ∠GLH + ∠HLI (angle addition)

∠GLI = 2∠GLH

The information that can be used to determine this is ∠GLI = 2∠GLH

Find out more on angle at: https://brainly.com/question/25770607

which has greater cenetic energy a car traveling 30.0 km/hr or one twice as heavy traveling at 15 km/hr?​

Answers

Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

[tex]KE=\frac{1}{2} mv^2[/tex]

Assuming the mass m= 1 kg

 

For the 30 km/h

[tex]KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J[/tex]

   

For the 15 km/h

[tex]KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J[/tex]

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

Combine your expressions from part E (x+2) and part F (y+ (-4) to give the pair of coordinates of any point after a translation two yards East and four yards south.

Answers

Answer:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.

If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)

If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)

The location of the shape as shown in the diagram is:

A(3, 6), B(3, 3), C(4, 3), D(4, 6)

If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:

A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)

Answer:

ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).

Step-by-step explanation:

this is more simple

(Will give brainliest to the most explained answer!) Can someone explain how to factor Polynomials. Please explain it like you’re teaching this to a 5 year old. :)

Answers

Step-by-step explanation:

Find the Greatest Common Factor (GCF) of a polynomial.

Factor out the GCF of a polynomial.

Factor a polynomial with four terms by grouping.

Factor a trinomial of the form .

Factor a trinomial of the form .

Indicate if a polynomial is a prime polynomial.

Factor a perfect square trinomial.

Factor a difference of squares.

Factor a sum or difference of cubes.

Apply the factoring strategy to factor a polynomial completely

Answer:

See explanation

Step-by-step explanation:

We can factor polynomials by breaking down the expression.

For instance, let's say we have the polynomial [tex]x^2 - 9x + 14[/tex].

We can start solving this because this polynomial is in standard form, meaning that the highest exponents go first. ([tex]ax^2 + bx + c[/tex].)

To factor a polynomial, we are looking for two numbers that:

A. When multiplied, get us [tex]c[/tex] (in this case, 14)

B. When added, get us [tex]b[/tex] (in this case, -9).

If we play around with numbers, looking at the factors of 14, we see that the numbers 7 and 2 might be useful here. They add up to 9 and multiply to be 14.

However, these numbers ADD to be -9, meaning that they both need to be negative.

[tex]-7 + -2 = -9\\-7\cdot-2=14[/tex]

Now that we know our numbers, -7 and -2, we can make these our factors (which are represented by [tex](x + y)[/tex], y being our factor.

So our factors turn out to be [tex](x-7)[/tex] and [tex](x-2)[/tex].

Let me know if you need anything explained more, and I hope this helped!

i need help. Can u help me solve for x?

Answers

Answer:

[tex] x = \sqrt {40}[/tex]

Step-by-step explanation:

Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:

[tex] {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ [/tex]

Answer:

D. x = sqrt(52).

Step-by-step explanation:

Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.

a^2 + b^2 = x^2

4^2 + 6^2 = x^2

16 + 36 = x^2

52 = x^2

x = sqrt(52)

x = sqrt(2 * 2 * 13)

x = 2sqrt(13)

x = 7.211102551.

Hope this helps!

What is the value of b if -7 +b= -8?

Answers

Hope you got the answer.....this is correct

Answer:

-1

Step-by-step explanation:

-7 +b = -8

↦b = -8 + 7 [ Transition]

↦b = -1

.°. b = -1

Hope you understand it ✔

A student says that the function f (x) = –x² – 9 has the x-intercepts (-3,0) and (3,0). Is the student correct? If not, expl.
why. ​

Answers

Answer:

No

Step-by-step explanation:

The student is wrong because the function has no solutions.

You cannot factor it because the x² is negative.

If it was x² - 9 instead, you could factor it into (x-3)(x+3) which would get you the x-intercepts (-3,0) and (3,0).

But instead, -x² - 9 cannot be factored at all and has no x-intercepts/solutions.

what are the order of operations for integers ?​

Answers

Answer:

PEMDAS

Step-by-step explanation:

P - Parentheses (Brackets also!)

E - Exponents

M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).

A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.

A wooden jewelry box has the shape of a prism with a regular hexagonal base of 85.3 in2. The sides of the hexagonal base are all 5.73 inches. If the height of the box is 18.10 inches, what is the surface area of the wood used to make the jewelry box?

Answers

Answer:

792.9 in²

Step-by-step Explanation:

Given:

Area of the base of the regular hexagonal prism box (B) = 85.3 in²

Each side length of hexagonal base (s) = 5.73 in

Height of prism box (h) = 18.10 in

Required:

Surface area of the wood used in making the hexagonal prism box

SOLUTION:

Surface area for any given regular prism can be calculated using the following formula: (Perimeter of Base × height of prism) + 2(Base Area)

Perimeter of the hexagonal base of the prism box = 6(5.73) (Note: hexagon has 6 sides.)

Perimeter of base = 34.38 in

Height = 18.10 in

Base area is already given as 85.3 in²

Surface area of the hexagonal prism box [tex] = (34.38*18.10) + 2(85.3) [/tex]

[tex] = 622.278 + 170.6 = 792.878 in^2 [/tex]

Surface area of the wood used in making the jewelry box ≈ 792.9 in²

Plz ans ASAP! Tysm! Pzlllzzz!

Answers

Answer:

Step-by-step explanation:

Number of class intervals = 7

Class width = 5

Class intervals (heights)        Frequency (Number of boys)

130 - 135                                                     3                        

136 - 140                                                     5

141 - 145                                                      3

146 - 150                                                     5

151 - 155                                                      2

156 - 160                                                     1

161 - 165                                                      1

Therefore, frequency table given above will represent the distribution of the heights and number of students.

solve show all steps what is 7x-28≥-7

Answers

Answer:

x≥3

Step-by-step explanation:

7x-28≥-7

Add 28 to each side

7x-28+28≥-7+28

7x≥21

Divide by 7

7x/7≥21/7

x≥3

Answer:

7x-28≥-7

7x≥21

x≥3

help me plsssssssssssssssss

Answers

Answer:

Step-by-step explanation:

I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )

We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:

[tex]9sin^2(x)+3cos^2(x)=3[/tex]

From here we will factor out a 3 to get:

[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:

[tex]3sin^2x+cos^2x=1[/tex]

Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:

[tex]sin^2x+cos^2x=1[/tex], then

[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:

[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:

[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:

[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:

[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:

[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.

Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:

3sin(0) + √3cos(0) = -√3. We need to see if this is true.

The sin of 0 is 0; the cos of 0 is 1, so

0 + (√3)(1) = -√3?

The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?

3sin(180) + √3cos(180) = -√3. We need to see if this is true.

The sin of 180 is 0; the cos of 180 is -1, so

0 + (√3)(-1) = -√3?

The left side is -√3 and so is the right side, so

x = 180°

PLEASE help me with this question! No nonsense answers please. This is really urgent.

Answers

Answer:

The third option: x= [tex]\frac{8}{3} \pi[/tex]

Step-by-step explanation:

Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]

Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]

=[tex]\frac{8}{3}\pi[/tex]

Other Questions
What purpose do sentence startersserve?A)to introduce and to explain the textual evidenceB) to repeat the writer's ideaC) to explain the textual evidenceD)to introduce the textual evidence Stephanie is helping her band collect money to fund a field trip. The banddecided to sell boxes of chocolate bars. Each bar sells for $1.50 and eachbox contains 20 bars. Which equation represents the profit they will earnfor each box sold? *O p = 20 - $1.50O p= 20 + $1.50O p = 20 ($1.50)O p = 20/$1.505.How much profit will be made if they sell 100 boxes? ests de acuerdo con el utilitarismo? por qu? In the laboratory, a volume of 100 mL of sulfuric acid (H2SO4) is recorded. How many g are there of the liquid if its density is 1.83 g / cm3? A student ran the following reaction in the laboratory at 242 K: 2NOBr(g) 2NO(g) Br2(g) When she introduced 0.143 moles of NOBr(g) into a 1.00 liter container, she found the equilibrium concentration of NOBr(g) to be 0.108 M. Calculate the equilibrium constant, Kc, she obtained for this reaction. Kc Audrey is suffering from depression that was triggered by a breakup with her boyfriend. She tells her therapist that no man will ever love her. Her therapist challenges the validity of her belief by stating that just because one person broke up with her doesn't mean that all of her relationships will fail. The therapist then has Audrey make a list of all the guys she knows who would probably go out with her on a date. To her surprise, Audrey is able to name a handful and realizes that her belief that no one will love her probably is distorted by the emotional pain from her breakup. Audrey's therapist is using: a countrys population in 1995 was 206 million. In 1998 it was 210 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million Puns and Malapropisms are both examples of a play of words. Explain how they are different. What is the value of x in the equation 3x-4y =65, when y = 4? i will gift brainliest A coin is tossed 7 times. What is the probability that the number of heads obtained will be between 2 and 7 inclusive? Express your answer as a fraction or a decimal number rounded to four decimal places. You perform a test cross of the dihybrid AaBb and score the phenotypes of 1000 progeny. Assuming independent assortment, how many of the progeny do you expect to display the dominant phenotype for both the A and B genes? I need help on both answers. Theyre different from my other problems so Im kinda confused Finding operating and free cash flows Consider the following balance sheets and selected data from the income statement of Keith Corporation.Keith Corporation Balance Sheets December 31Assets 2015 2014Cash $ 1,500 $ 1,000Marketable securities 1,800 1,200Accounts receivable 2,000 1,800Inventories 2,900 2,800Total current assets $ 8,200 $ 6,800Gross fixed assets $ 29,500 $ 28,100Less: Accumulated depreciation 14,700 13,100Net fixed assets $ 14,800 $ 15,000Total assets $ 23,000 $ 21,800Liabilities and stockholders' equity Accounts payable $ 1,600 $ 1,500Notes payable 2,800 2,200Accruals 200 300Total current liabilities $ 4,600 $ 4,000Long-term debt 5,000 5,000Total liabilities $ 9,600 $ 9,000Common stock $ 10,000 $ 10,000Retained earnings 3,400 2,800Total stockholders' equity $ 13,400 $ 12,800Total liabilities and stockholders' equity $ 23,000 $ 21,800Keith Corporation Income Statement Data (2015)Depreciation expense $1,600Earnings before interest and taxes (EBIT) 2,700Interest expense 367Net profits after taxes 1,400Tax rate | 40%Requireda. Calculate the firm's net operating profit after taxes (NOPAT) for the year ended December 31, 2015b. Calculate the firm?s operating cash flow (OCF) for the year ended December 31, 2015c. Calculate the firm?s free cash flow (FCF) for the year ended December 31, 2015d. Interpret, compare, and contrast your cash flow estimates in parts b and c. A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below.Age (in years) Height (inches) 7 47.3 8 48.8 5 41.3 8 50.4 8 51 7 47.1 7 46.9 7 48 9 51.2 8 51.2 5 40.3 8 48.9 6 45.2 5 41.9 8 49.6 Requried:a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children? b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model? c. How much of the variation in the sample values of height does the model estimated in part (b) explain? Can integers be written as fractions? Evans dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work! 4.Aliyah, Brenda and Candy share a sum of money in the ratio of 3:5:6. AfterCandy gives $100 to Aliyah and $50 to Brenda, the ratio becomes 2 : 3:3.(a) Suppose Aliyah has $3x at the start, express Candy's initial sum of money interms of x.(b) Find the value of x.(c) Hence, how much money does Brenda have in the end? A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3. Suppose a 2.50 m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released? A restaurant hands out a scratch-off game ticket with prizes being worth purchases at the restaurant. The back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100. What are the odds that the ticket is worth at least $25? Many school districts have a summer vacation that is 72 days long. What percent of the entire year is summer vacation?