What is the sum of the complex numbers −9−i−9−i and −5−i−5−i?

Answers

Answer 1

Answer:

The sum of the complex numbers will be - 28 - 4i

Step-by-step explanation:

We have the sum  −9−i−9−i + −5−i−5−i. Let's group like elements and simplify this expression,

−9−i−9−i + −5−i−5−i ( Group like terms )

- i - i - i - i - 9 - 9 - 5 - 5 ( Add like terms )

- i - i - i - i = - 4i, - 9 - 9 = - 18, and - 5 - 5 = - 10

- 18 - 10 = - 28 ( Substitute )

Solution : - 28 - 4i


Related Questions

A group of pirates captures Kevin, Lisa, Matt and Neal, and forces them to play a game. They each roll a fair 6-sided-die once. If the product of their roll is a multiple of 3, they all have to walk the plank, but otherwise they are safe. What is the probability that they survive? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 PLZ answer been waiting. I'll give 30 points

Answers

Answer: Option B, 16/81

Step-by-step explanation:

So we have 4 prisoners, they will roll a fair six side die and the product of the four rolls must NOT be a multiple of 3.

We know that every integer number can be "decomposed" into a product of prime numbers.

Then a number N,  that is divisible by 3, can be written as:

N = 3*k

Where k is another integer.

Here we will have a product of 4 numbers, each of them are in between 1 and 6.

Now, if only one of the prisoners rolls a 3, then the product of the rolls will always be a multiple of 3. And if one of the rolls is 6 the same will happen, because 6 = 3.2

Then the probability of surviving is when in none of the four rolls we have a 3 or a 6.

Then we must have a 1, 2, 4 or 5.

The probability of 4 outcomes out of 6, is:

P = 4/6.

But we have 4 rolls, so we have that probability four times, and the joint probability will be equal to the product of the probabiliities for each roll, then the probability of surviving is:

P = (4/6)^4 = (2/3)^4 = 16/81

Answer:

16

Step-by-step explanation:

if pentagon OPQRS is dilated by a scale factor or ?
from the origin to create O'P'Q'R'S: what is the ordered pair of point S'?

Answers

Answer:

Option (D) : (3.5, 8.75)

Let f (x)
sinx cosx, then f'(x) =
A. Cos2x
B. sin2x
C. tan 2x
D. cos2x - sin2x

Answers

Answer:

A. Cos2x

Step-by-step explanation:

f(x) = sin(x)cos(x) = (1/2) sin(2x)   using double angle formula.

f'(x) = ( (1/2)sin(2x) )' = 2(1/2)cos(2x) = cos(2x)

Solve for x: −3|2x + 6| = −12.

Answers

Answer:

x = -1 or x = -5

Step-by-step explanation:

−3 * |2x + 6| = −12 / -3

|2x + 6| = 4

because this is an absolute value equation there are 2 solutions:

2x + 6 = 4 or 2x + 6 = -4

2x = -2 or 2x = -10

x = -1 or x = -5

Answer:

x = -1 or x = -5

Step-by-step explanation:

cuz it is

A number plus its fifth add up to 17 What is the number

Answers

Answer:

Step-by-step explanation:

we call the number X

x/5 is the fifth part of that number

I propose equality:

x + x/5 = 17

we add the fractions on the left side:

6x/5 = 17

We pass 5 to multiply to the other side:

6x = 5 * 17

6x = 85

we clear x

x = 85/6

x = 14.17

test

14.17 + 2.83 = 17

okay

Answer:

14.1666666667

Step-by-step explanation:

We can write the equation as:

x + x/5 = 17

=> 5/5x + 1/5x = 17

=> 6/5x = 17

=> 6x = 17 * 5

=> 6x = 85

=> x = 85/6

=> x = 14.1666666667

Let's check whether our answer is correct

=> 14.1666666667 + 14.1666666667 / 5 = 17

=> 14.1666666667 +  2.83333333333 = 17

=> 17 = 17

So, the answer is 14.1666666667

Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

Answers

Find the powers [tex]a=\sqrt{2}+\sqrt{3}[/tex]

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

Answer:

[tex]y^3 -6y-6[/tex]

PLEASE HELP WILL GIVE BRAINLIEST AND THX Which ratios have a unit rate of 3? Choose all that apply. 15/2 cups: 2 1/2 cups 1 cup: 1/4 cups 2/3 cups: 1 cup 3 3/4 cups: 2 cups 2 cups: 2/3 cups 2 1/2 cups: 5/6 cups

Answers

Answer:

15/2 cups: 2 1/2 cups

2 cups: 2/3 cups

2 1/2 cups: 5/6 cups

Step-by-step explanation:

Take and divide each by the smaller number

15/2 cups: 2 1/2 cups

First put in improper fraction form

15/2 : 5/2

Divide each by 5/2

15/2 ÷ 5/2  : 5/2 ÷5/2

15/2 * 2/5  : 1

3 :1   yes

1 cup: 1/4 cups

Divide each by 1/4 ( which is the same as multiplying by 4)

1*4  : 1/4 *1

4 : 1    no

2/3 cups: 1 cup

Divide each by 2/3  ( which is the same as multiplying by 3/2)

2/3 * 3/2  : 1 * 3/2

1 : 3/2   no

3 3/4 cups: 2 cups

Change to improper fraction

( 4*3+3)/4  : 2

15/4    : 2

Divide each side by 2

15/8  : 2/2

15/8   : 1    no

2 cups: 2/3 cups

Divide each side by 2/3 ( which is the same as multiplying by 3/2)

2 * 3/2 : 2/3 *3/2

3  : 1   yes

2 1/2 cups: 5/6 cups

Change to an improper fraction

( 2*2+1)/2 : 5/6

5/2  : 5/6

Divide each side by 5/6( which is the same as multiplying by 6/5)

5/2 * 6/5  : 5/6 * 6/5

3  : 1   yes

The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

What is the ratio?

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

For checking: 15/2 cups: 2 1/2 cups

= (15/2)/(5/2)       [2(1/2) = 5/2]

= 3

For checking:  1 cup: 1/4 cups

= 1/(1/4)

= 4

For checking: 2/3 cups: 1 cup

=(2/3)/1

= 2/3

For checking: 3 3/4 cups: 2 cups

= (15/4)(2)

= 15/8

For checking: 2 cups: 2/3 cups

= (2)/(2/3)

= 3

For checking: 2 1/2 cups: 5/6 cups

= (5/2)/(5/6)

= 3

Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3

Learn more about the ratio here:

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Consider exponential function h.
h(x) = 3x + 4

Answers

The function is always positive.

(0,5) is the y-intercept, since the graphed line never crosses the x axis, there is no x-intercept.

The function is positive and  greater than 4 for all values of x

Not sure what the actual choices are on a couple of the questions. The choices would help answering.

PLEASE ANSWER ASAP!!!!


Divide. Equation and answer choices in picture



any unrelated answer will be reported​

Answers

Answer:

B =

[tex]4x - 1 - \frac{4}{2x - 3} [/tex]

Step-by-step explanation:

In this type of questions the answers are required in the

[tex]quotient \: + \frac{remainder}{divisor} [/tex]

form.

First of all, the equations in question must be arranged properly

[tex](8 {x}^{2} - 14x - 1) \div 2x - 3[/tex]

Then you divide.

[tex]2x - 3 \sqrt{8 {x}^{2} - 14x - 1 } [/tex]

Answer

[tex]4x - 1 - \frac{4}{2x - 3} [/tex]

You buy butter for $5.60 a pound. One portion of onion compote requires 1.7 oz of butter. How much does the butter for one portion cost? Round to the nearest cent.

Answers

Answer:

Butter per portion equals 60 cents .

Step-by-step explanation:

A pound of butter is worth $ 5.60.

5.60 dollars are converted to cents, 1 dollar equals 100 cents, then:

- One pound of butter equals 560 cents.

A portion of onion compote requires 1.7 oz of butter.

Convert 1.7 oz to pounds, so:

- 1.7 oz of butter equals 0.10625 pounds.

If a pound of butter is worth 560 cents, how much will 0.10625 pounds of butter be worth.

- Rule of 3 is used:

- 560 cents        1 pound butter

  X cents            0.10625 pounds of butters

X = 560 * 0.10625

X = 59.5 cents

X = 60 cents per portion

Does anyone have the solution to this

Answers

Step-by-step explanation:

There is 1 root at x = 1, where the function crosses the x-axis.

There are 2 roots at x = -2, where the function touches the x-axis but does not cross.

So there are 3 real roots total.

The function is:

y = (x − 1) (x − (-2))²

y = (x − 1) (x + 2)²

jeff buys 44 watermelons, he gets into a car accident and loses 31, how many does jeff have left

Answers

Answer:

Jeff has 3 watermelons left

Step-by-step explanation:

44-31=13 watermelons

Answer:

13

Step-by-step explanation:

44

-31

13

Tickets to a school production cost $5 for a student ticket and $10 for an adult ticket. A total of 67 tickets were purchased at a cost of $440. Which value or expression could replace c in the table? 67 440 67 – a 440 – a

Answers

Answer:

Step-by-step explanation:

Keywords:

System of equations, variables, cost, tickets, adults, children.

For this case we must solve a system of equations with two variables represented by the tickets of students and adults of a school production.

We define the variables according to the given table:

a: Number of tickets sold to adults

c: Amount of tickets sold to children.

We then have the following system of equations:

A + c = 67

10a + 5c =440

From the first equation, we clear the value of the variable c:

C = 67 - a

Answer:

The value that could replace c in the table is:

C = 67 - a

Option C is the answer!

Hope it helped u if yes mark me BRAINLIEST!

Tysm! Plz

The answer is c hope it helps

RATIO AND PROPORTION PROGRAM ENHANCEMENT UNIT PAUL IS PAID 473.88 FOR 38 1/4 HOURS OF WORK WHAT AMOUNT SHOULD HE BE PAID FO 40 HOURS

Answers

Answer:

495.56 should be p[aid for 40 hours.

Step-by-step explanation:

concept used

In ratio

a:b = c:d

__________________________________________

Given

IS PAID 473.88 FOR 38 1/4 HOURS OF WORK

38 1/4 hour = 38.25 hours

if we get ratio for payment per hour

we have

473.88 / 38.25 or  473.88 : 38.25

___________________________________

now we have to find payment for 40 hours

let that payment be x

thus,  ratio for payment per hour in this case will be

x/40 or x:40

since

x:40 and  473.88 : 38.25 is representative of same program enhancement unit both ratio will be equal

thus

x:40 =  473.88 : 38.25

x/40 =  473.88 / 38.25

=> x = 40*(473.88 / 38.25 ) = 495.56

Thus,  495.56 should be p[aid for 40 hours.

There are four main steps in building a Monte Carlo simulation: select probability distribution(s); run the simulation model through a large number of trials; analyze results of multiple trials to assess risks and opportunities; and generate ______ variables.

Answers

Answer:

random

Step-by-step explanation:

Monte Carlo simulation is a technique which is used to analyze the impact of risk and uncertainty in financial projects and forecasting models. It helps to understand the potential outcomes to better understand the decision based on risk level. It analyzes the probability of different outcomes by intervention of random variables.

Assume that thermometer readings are normally distributed with a mean of 0C and a standard deviation of 1.00C. A thermometer is randomly selected and tested. For the case​ below, draw a​ sketch, and find the probability of the reading.​ (The given values are in Celsius​ degrees.) Between and

Answers

Answer: 0.0546 and 0.9829

Step-by-step explanation:

solution:

= P( 1.50< Z <2.25 )

= P(Z <2.25 ) - P(Z <1.50 )

Using z table,

= 0.9878-0.9332

=0.0546

b.

= P( -2.12< Z <3.73 )

= P(Z <3.73) - P(Z <-2.12 )

Using z table,

= 0.9999-0.0170

=0.9829

The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if rho is a density function, then rhoave is the average density of E. Find the average value of the function f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the plane z = 0.

Answers

Answer:

An aluminum bar 4 feet long weighs 24 pounds

Step-by-step explanation:

For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 60 N acts on a certain object, the acceleration of the object is 10 m/s^2 . If the force is changed to 54 N, what will be the acceleration of the object

Answers

Step-by-step explanation:

Hey, there!!!

According to your question,

case i

force (f) = 60 n

acceleration due to gravity (a)= 10m/s^2

now,

force = mass × acceleration due to gravity

or, 60 = m × 10

or, 10m= 60

or, m= 60/10

Therefore, the mass is 6 kg.

now,

In case ii

mass= 6kg {Because there was no change in mass only change in force}

force= 54 n

now, acceleration due to gravity = ?

we have,

f=m×a

or, 54= 9×a

or, 9a= 54

or, a= 54/9

Therefore, the acceleration due to gravity is 6m/ s^2.

Hope it helps....

A truck carries 360 crates of avocados to a grocery distribution center. If there are 8640 avocados total, how many avocados are in each crate?

Answers

Answer:

There are 24 avocados in each crate.

Step-by-step explanation:

This is a division problem.

8640/360 = 24

There are 24 avocados in each crate.

24 Avocados in each crate, 8640/360 = 24

A researcher wishes to see if the average weights of newborn male infants are higher than the
average weights of newborn female infants. She selects a random sample of 12 male infants and
finds the mean weight is 7.70 pounds. She selects a random sample of 9 female infants and finds
that the mean Leight is 7.80 pounds. Assume that the variables are normally distributed and the
population standard deviation is 0.5 for each group.
Using alpha=0.05 to test if the mean weight of the males is higher than the mean weight of the
females, the pvalue of the test is:​

Answers

Answer:

The  p-value is  [tex]p-value = 0.62578[/tex]

Step-by-step explanation:

From the question we are told that    

    The  sample size of male infant is  [tex]n_1 = 12[/tex]

     The  sample size of female infant is [tex]n_2= 9[/tex]

     The sample mean of male infant is  [tex]\= x_1 = 7.70 \ lb[/tex]

      The sample mean of female infant is  [tex]\= x_2 = 7.80 \ lb[/tex]

     The population standard deviation is  [tex]\sigma = 0.5[/tex]

       The significance level is  [tex]\alpha = 0.05[/tex]

The null hypothesis is  [tex]H_o : \mu_ 1 = \mu_2[/tex]

The  alternative hypothesis is  [tex]H_1 : \mu_1 > \mu_2[/tex]

The  test statistics is mathematically represented as

            [tex]t =\frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma }{n_1} } + \frac{\sigma }{n_2} } }[/tex]

=>          [tex]t = \frac{7.70 -7.80}{\sqrt{\frac{0.5 }{12} } + \frac{0.5 }{9} } }[/tex]

=>        [tex]t = -0.3207[/tex]

From the z-table  the p-value is  obtained, the value is  

     [tex]p-value = P(Z > -0.3207) = 0.62578[/tex]

     [tex]p-value = 0.62578[/tex]

Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)

Answers

The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)

The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80

This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%

We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.

The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)

=========================================

In summary, we have these answers

confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80

The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.

Answers

Answer:

36

Step-by-step explanation:

formula of area for square:

A=s^2

s=6

A=6^2

A=36

Answer:

36

Step-by-step explanation:

I got it right

Which of the following uses parallel construction? Select one: a. Jim likes to hunt, bike, and throwing darts. b. Mimie has to study, drive her sister to the store, and enjoy herself in the garden. c. Joe will go running, biking, and hunting. d. Jane will throw a ball, then she will mow the lawn.

Answers

Answer:

The correct answer is:

c. Joe will go running, biking and hunting

Step-by-step explanation:

Parallel construction or parallelism or parallel structure is a style used in writing a sentence, where there is a balance in phrases or clauses within one or more sentences by them having the same grammatical structure. parallelism adds elegance, clarity and symmetry to sentences. It essentially has to so with a repetition of a chosen grammatical form within a sentence.

In our example:

a.  Jim likes to hunt, bike, and throwing darts. (not parallel)

    Jim likes to hunt, bike, and throw darts (parallel)

The verbs, hunt, bike and throw must be in the same form (present continuous) to be parallel

b. Mimie has to study, drive her sister to the store, and enjoy herself in the garden. (not parallel).

The sentence in option b is not parallel because the other actions apart from "study" have a place where they took place; drive her sister to the store, enjoy herself in the garden, however, "study" doesn't have a place where the action occurs.

c. Jane will throw a ball, then she will mow the lawn. (not parallel)

the sentence is not parallel because there is an inconsistency in the pattern of the construct. a parallel version is:

Jane will first throw a ball, then she will mow the lawn, or

jane will throw a ball and mow the lawn.

d. Joe will go running, biking, and hunting. (parallel)

all the verbs are in the present continuous form.

The following data set represents the number of new computer accounts registered during ten consecutivedays:43,37,50,51,58,52,45,45,58,130(a) Compute the mean, median, IQR, and standard deviation(b) Check for outliers using the 1.5(IQR) rule, and indicate which data points are outliers.(c) Remove the detected outliers and compute the new mean, median, IQR, and standard deviation.(d) Make a conclusion about the effect of outliers on the basic descriptive sta

Answers

Answer:

Outliers have great effect on the mean and standard deviation of the data set

Step-by-step explanation:

Mean =(43+37+50+51+58+52+45+45+58+130)/10

Mean= 579/10

Mean = 57.9

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58,130

Median= (50+51)/2

Median= 101/2

Median= 50.5

IQR= (130-37)/2

IQR= 93/2

IQR= 46.5

Standard deviation

=√(((37-57.9)²+(43-57.9)²+(45-57.9)²+(45-57.9)²+(50-57.9)²+(51-57.9)²+(52-57.9)²+(58-57.9)²+(58-57.9)²+(130-57.9)²)/10)

Standard deviation= 25.1

1.5*(46.5)= 69.75

The number more than 69.75 is 130 and it's the outlier

Without outlier

Mean= (43+37+50+51+58+52+45+45+58)/9

Mean = 449/9

Mean = 49.88

Arranging in ascending order

= 37,43,45,45,50,51,52,58,58

Median= 50

IQR= (58-37)/2

IQR=21/2

IQR=10.5

Standard deviation

I don't understand word problems can someone please answer it for me and I need it ASAP.

Answers

Answer:

Inequality: 3 + 1.2c

What you'd put on graph: 1 ≥ 13.50

CD is the perpendicular bisector of XY Determine the value of x. Question 8 options: A) –2 B) –1∕2 C) 4 D) 1.25

Answers

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

What is perpendicular bisector?

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

To learn more about perpendicular bisectors click :

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Find the reciprocal of the equation in standard form. The selected answer is incorrect.

Answers

Answer:

C

Step-by-step explanation:

reciprocal of z=1/z

[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]

helppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

Brainliest!

Step-by-step explanation:

36x^-4y^2/5x^2y^-3z^-2

36y^5z^2/5x^6

make everything positive

There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?

Answers

Answer:

97290

Step-by-step explanation:

47 different people can win first

47

Now there are only 46 people left

46 different people can win second

46

45 different people can win third

47*46*45

97290

_Thirty-two holes are drilled in rows on a metal block. The number of rows is more than the number of holes in each

row. Find the number of row. (a)7 (b)25(c)67

(d)4 (e) 12
_​

Answers

Answer:

D

Step-by-step explanation:

Let the number of rows be x

And the numbers of holes in each be y

xy = 32

x and y must be factors of 32

From options stated

4 is the only factor of 32

Hence option D is correct

Other Questions
An asset has an average return of 11.57 percent and a standard deviation of 24.54 percent. What is the most you should expect to lose in any given year with a probability of 2.5 percent? A 17.0 g bullet traveling horizontally at 785 m/s passes through a tank containing 13.5 kg of water and emerges with a speed of 534 m/s.What is the maximum temperature increase that the water could have as a result of this event? (in degrees) (10 PTS) How do I solve for this? Please show work Tuition for one year at the University of Atlantis costs $12,000 per year. Rachel would like to attend this university and will save money each month for the next 3 years. Her parents will contribute $3,000 for her first year's tuition. How much money will Rachel need to save each month to have enough money for the first year of college at the University of Atlantis? Break-Even Sales Under Present and Proposed Conditions Portmann Company, operating at full capacity, sold 1,000,000 units at a price of $188 per unit during the current year. Its income statement is as follows: Sales $188,000,000 Cost of goods sold (100,000,000) Gross profit $88,000,000 Expenses: Selling expenses $16,000,000 Administrative expenses 12,000,000 Total expenses (28,000,000) Operating income $60,000,000 The division of costs between variable and fixed is as follows:Variable Fixed Cost of goods sold 70% 30% Selling expenses 75% 25% Administrative expenses 50% 50% Management is considering a plant expansion program for the following year that will permit an increase of $11,280,000 in yearly sales. The expansion will increase fixed costs by $5,000,000 but will not affect the relationship between sales and variable costs.Required:1. Determine the total variable costs and the total fixed costs for the current year.2. Determine (a) the unit variable cost and (b) the unit contribution margin for the current year.3. Compute the break-even sales (units) for the current year.4. Compute the break-even sales (units) under the proposed program for the following year.5. Determine the amount of sales (units) that would be necessary under the proposed program to realize the $60,000,000 of operating income that was earned in the current year.6. Determine the maximum operating income possible with the expanded plant.7. If the proposal is accepted and sales remain at the current level, what will the operating income or loss be for the following year?8. Based on the data given, would you recommend accepting the proposal?A. In favor of the proposal because of the reduction in break-even point.B. In favor of the proposal because of the possibility of increasing income from operations.C. In favor of the proposal because of the increase in break-even point.D. Reject the proposal because if future sales remain at the current level, the income from operations will increase.E. Reject the proposal because the sales necessary to maintain the current income from operations would be below the current year sales. Which of the following is NOT a property of a paralleogram? * The opposite sides are equal. The opposite angles are equal. Each diagonal bisects the parallogram. The diagonals of all parallograms bisect each other at 90 degree angles. I will give brainliest when you tell the most important part of text you are identifying The sum of 4 consecutive integers is 130 what is the third number in the sequencePLZ HELP!!! Find the odd one out a)Planets moving on it's axis,Strings of guitar (being played),Motion of a ferry wheel,The vehicles moving on a straight road. b)Motion of the moon around the earth,Motion of the earth around the sun,Motion of a merry-go-round,Heart-beat in a healthy person. c)Motion of a bullet fired from gun,Motion of a football player in the ground,Motion of a vehicle on a straight road,Motion of an apple falling from a tree Find the solution set of the inequality and what is the number? 16x 7 71 A. C. D. E. = in need of assistance answers are greatly appreciated thank you for your time and effort Two angles form alinear pair. Themeasure of oneangle is three timesthe measure of theother. Find themeasure of each Which pair has examples of a balanced budget at the personal and national levels? Arthur budgeted $100 for expenses and spent $75. A government agency budgets $8,000 for the year and spends $9,000. Elise spent $300 on a new phone after earning $200. A government agency has to let go staff after a budget shortfall. Jessica spends exactly as much as she makes. A government agency budgets $20,000 for the year and spends $20,000. Harvey saves some money each month to buy a car. The government sets money aside to fund a future project. Help Please. I will Give Brainliest. What the correct answer now What was the first conflict theory in sociology? A corporation has 12,000 shares of $20 par stock outstanding that has a current market value of $150. If the corporation issues a 4-for-1 stock split, the market value of the stock will fall to approximately $50.a. Trueb. False What is the image below? The inside of a basilica by Filippo Brunelleschi in Florence, Italy. The church has free-standing columns and a long hall. What is the correct order of organization in animals?A. Organ, organ system, cell, tissue, organismB. Cell, tissue, organism, organ, organ systemC. Tissue, cell, organ, organ system, organismD. Cell, tissue, organ, organ system, organism Beyond changes in relationships described above, explain what other characteristics of man changed after the Fall.