I need help with this please

I Need Help With This Please

Answers

Answer 1

Answer: m<ABC = 45 degrees, m<DBC = 36 degrees

Step-by-step explanation:

set both equations equal to 81 because they add up to form one angle:

5x + 6 + 9x - 9 = 81

Combine like terms

14x - 3 = 81

Add three to both sides

14x = 84

Divide by 14 to find x

x = 6

To find the angles:

Measurement of angle ABC:

9(6) - 9 = 45 degrees

Take the original angle of 81 and subtract the angle you just found to find the remaining angle:

81 - 45 = 36

Therefore, the angle of DBC is 36 degrees


Related Questions

Find the measure of KNM

Answers

1 Kilonewton meter [kNm] = 1 000 Newton meter [Nm] - Measurement calculator that can be used to convert Kilonewton meter to Newton meter, among others.

To make barstools, Federico rents a shop for $1510 a month and calculates the materials for each stool are $45. Find the total cost for him to make 98 stools in a month.

Answers

Answer:

4410

Step-by-step explanation:

45 x 98 = 4410

You are lubricating several motors in the shop. One motor must be lubricated with of 3/16 an ounce of​ grease, and one larger motor must be lubricated with 3/8 of an ounce of grease. How many ounces of grease will you​ require? Your answer should be a fraction of an​ ounce, reduced to its lowest terms.

Answers

3/8 = 6/16

3/16 + 6/16 = 9/16 of an ounce

Suppose you are heading to the
beach with a friend. The beach is 80
miles from your house and the drive
takes about 1 hour and 30 minutes.
Your friend's house is 64 miles from
the beach. Use direct variation to
determine how long it will take to
drive to the beach if you leave from
your friend's house.

Answers

The time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes

Calculating time

From the question,  we are to calculate how long it would take to drive to the beach if you leave from your friend's house

From the given information,

The beach is 80 miles from your house and the drive takes about 1 hour 30 minutes

Distance, d, varies directly with time, t.

d ∝ t

d = vt

Where v is the proportionality constant.

Now, we will find v

d = 80 miles

t = 1.5 hours = 3/2 hours

Thus,

80 = (3/2)v

v = (2 × 80)/3

v = 160/3 miles/hour

Now, we will determine t when d is 64 miles

d = vt

64 = 160/3 × t

t = (64 × 3)/160

t = 192/160 hours

t = 6/5 hours

t = 1 hour 12 minutes

Hence, the time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes

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4x+3y=7 x+2y=-2


put both in slope-intercept form

Answers

Answer:

Second equation Answer: [tex]y=-\frac{1}{2}x-1[/tex]

First equation Answer: [tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]

Step-by-step explanation:

Concept:

The general equation of a line in slope-intercept form is given below as

[tex]y=mx+c[/tex]

where

[tex]m=slope[/tex]

[tex]c=intercept[/tex]

First equation

The first equation is given below as

[tex]4x+3y=7[/tex]

We will make y the subject of the formula to change the equation in slope-intercept form

[tex]4x+3y=7[/tex]

subtract 4x from both sides

[tex]4x-4x+3y=7=-4x[/tex]

[tex]3y=-4+7[/tex]

divide both sides by 3

[tex]\frac{3}{y} =\frac{-4x}{3} +\frac{7}{3}[/tex]

[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]

Hence,

The equation of 4x+3y=7 in slope intercept form is given below as

[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]Second Equation

The second equation is given below as

[tex]x+2y=-2[/tex]Subtract x from both sides[tex]x-x+2y=-2-x[/tex][tex]2y=-x-2[/tex]divide through by 2[tex]\frac{2y}{2} =-\frac{x}{2} =-\frac{2}{2}[/tex][tex]y=-\frac{1}{2}x-1[/tex]

Hence,

The equation of x+2y=-2 in slope-intercept form is

[tex]y=-\frac{1}{2}x-1[/tex]Hope this Helps! <3Answered by:

AshTheNeko

The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8

Answers

Answer:

y = - 8

Step-by-step explanation:

substitute x = 8 into the equation

y = 8 - 2(8) = 8 - 16 = - 8

1.Set up your equation too-
Y=8-2(8)
2. Multiply 8 and 2-
Y=8-16
3. Subtract 8 and 16-
Y=8

Write down two prime numbers that have a sum of 20​

Answers

3 and 17

7 and 13

Step-by-step explanation:

........

21 The average person at rest takes approximately 16 breaths per minute. Approxir many breaths do they take in 70 years of 365 days each? Use a calculator. Write in exponential notation using powers of 10.​

Answers

A person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.

Here, we are given that on average a person at rest takes approximately 16 breaths per minute.

1 hour = 60 minutes

Thus, in 1 hour a person will take-

60 × 16

= 960 breaths

Now, 1 day = 24 hours

Thus, in 1 day, a person will take-

24 × 960

= 23,040 breaths

Further, 1 year = 365 days

Thus, in 1 year, a person will take-

23,040 × 365

= 8,409,600 breaths

In 70 years, a person will take-

8,409,600 × 70

= 588,672,000 breaths

We can express this in exponential notation as-

5.88672 × [tex]10^{8}[/tex]

Thus, a person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.

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Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

Answers

The company's profit will start to decline if it only produces one bag.

Given f(x) = 2x⁴ ₋ 4x³ ₊ 7

Differentiate it with respect to x.

therefore, f'x) = 8x³ ₋ 12x²

= 4x²(2x ₋ 3)

For decreasing, f'(x) ≤ 0

⇒ 4x²(2x ₋ 3) ≤ 0

⇒ 2x ₋ 3  ≤  0

x  ≤ 3/2

Since the number of bags are represented by x.

Hence, x ∈ N

Therefore, x = 1 is only possibility.

Therefore, if the company only produces one bag, its profit begins to decline.

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Your question was incomplete. Please find the missing the content here.

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson's eventual profit function is given as: pi = 2x⁴ ₋ 4x³ ₊ 7 where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson's profit start decreasing?

At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.

Answers

The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x

The domain is x >= 0 and the range is c(x) >= 9.99

Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

The given parameters are:

One topping = 9.99

Additional topping = 1.25 each

We have x to represent the number of toppings

This means that

C(x) = One topping + Additional topping  * x

So, we have

C(x) = 9.99 + 1.25x

How to find the domain and range?

We have

C(x) = 9.99 + 1.25x

The smallest number of topping is 0

So, the domain is x >= 0

Substitute 0 for x in C(x) = 9.99 + 1.25x

C(0) = 9.99 + 1.25(0)

This gives

C(0) = 9.99

So, the range is c(x) >= 9.99

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Answer:
C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Step-by-step explanation:

a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.

So the equation is C(x) = 9.99 + 1.25x right?

Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!

So the new equation is:

    C(x) = 9.99 +1.25(x - 1)

or, C(x) = 9.99 + 1.25x - 1.25

or, C(x) = 1.25x + 8.74  

b) We need to find the Domain of C(x).

We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.

So we can choose up to 10 different toppings. And we need at least 1 topping.

∴ Domain is 1 ≤ x ≤ 10.

b) We need to find the Range of C(x).

We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.

Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.

    C(10) = 1.25(10) + 8.74

or, C(10) = 12.50 + 8.74

or, C(10) = 21.24

∴ Range of C(x) = [9.99, 21.24]

Answer:

C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]


Assume log x=0.27 and log by = 0.81. evaluate the following expression logb x/y

Answers

By evaluating following logarithm equation and we we get the value of required expression is -0.54.

What is logarithm?

The logarithm is the opposite of exponentiation as a function. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.

As per the question

we have to assume x

log x=0.27

log by=0.81

We have to calculate log bx/y by following expression

We know loge (a/b)= log_e a-log_e b

We know (x)= logb y

=0.27-0.81

= -0.54

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can someone help me with this

Answers

Distance varies directly as the square of the time it falls

s=kt^2
condition –> 64 feet in 1 second
s=kt^2
64=k(1)^2
64=k

s=64t^2

first part (how far will it fall in 5 seconds)

s=64(5)^2
s=1600


second part(how long will it take an object to fall 256 feet)

256=64t^2
256/64=t^2
4=t^2
√4=t
2=t

PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT

Answers

[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]

help me with this precal

Answers

Answer: Ok

Step-by-step explanation:

9-0-0

< Question 7, 1.5.25 >
The line graph to the right indicates that in 1960, 21% of taxes came from corporate income tax. For the period from 1960 through 2010,
this percentage decreased by approximately 0.32 each year. If this trend continues, by which year will corporations pay zero taxes?

Answers

The 21% of taxes and annual percentage decrease of 0.32, using arithmetic progression gives;

The year corporations will pay zero taxes as 2025

How can arithmetic progression be used to find the required year?

The percentage of tax that comes from corporate income tax = 21%

Amount by which the percentage decreased each year = 0.32

Period during which the tax reduced = Between 1960 and 2010

Required;

The year corporations pay zero taxes.

Solution;

The amount of tax paid each year can be given by the arithmetic progression formula,

[tex] a_{n} = a + (n - 1) \cdot d[/tex]

Where;

a = The first term = 21

[tex] a_{n} = value \: on \: the \: nth \: year[/tex]

d = The common difference = -0.32

When [tex] a_{n} = 0 [/tex], we have;

[tex] 0 = 21 + (n - 1) \times (-0.32) [/tex]

0.32•(n - 1) = 21

n - 1 = 21/0.32 = 65.625

n = 65.625 - 1 = 64.625 ≈ 65

The year the corporations will pay no taxes is 1960 + 65 = 2025

Corporations will pay no taxes in the year 2025

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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!

Answers

The proportion of users that park bike on the trail is 0.1728

How to determine the proportion of users that park bike on the trail?

The table represents the given parameters

From the table, we have the following parameters

Suburban total = 243

Users that park bike on the trail = 42

The proportion of users that park bike on the trail is then calculated as

P = Users that park bike on the trail/Suburban total

This gives

P = 42/243

Evaluate

P = 0.1728

Hence, the proportion of users that park bike on the trail is 0.1728

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High divers use the height of the diving platform to calculate the speed at which they enter the
water. The formula 58-34-12 models the diver's speed s (in miles per hour) and the height
h (in feet) of the platform.
a. Solve the formula for 3 and for h
b. At what speed does a diver enter the water when the platform is 82 feet tall?
c. A diver enters the water at 48 miles per hour. How tall is the platform?

Answers

a. 3h = -12 + 5s

b. Speed = 51. 6 miles per hour

c. Height = 76 feet

How to determine the value

Given the function;

5s - 3h = 12

Where;

s is the speed in miles per hourh is the height in feet

a. To solve for 3h

We have;

- 3h = 12 - 5s

3h = -12 + 5s

b. If the height is 82 feet , then

5s - 3(82) = 12

5s - 246 = 12

collect like terms

5s = 12 + 246

5s = 258

Make 's' the subject

s = 258/ 5

s = 51. 6 miles per hour

c. If the speed is 48 miles per hour, we have;

5(48) - 3h = 12

240 - 3h = 12

collect like terms

-3h = 12 - 240

-3h = -228

Make 'h' the subject

h = -228/ -3

h = 76 feet

Thus, the speed and height are 51. 6 miles per hour and 76 feet respectively.

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Triangle XYZ has translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?

Answers

The distance between any two point is 5 unit.

What is distance?

The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.

As per the question

Triangle xyz is translated = 4units

And triangle xyz left to yield=3 unit

The distance between the corresponding is hypotenuse of the triangle is-

Buy applying Pythagorus theorem we can get C^2=a^2+b^2

As we know a,b=legs

                       c=hypotenus

C^2=a^2+b^2C^2

      =3^2+4^2

     =9+16  

     =25C =√25 =5 unit

Therefore, the distance between any two point is 5 unit.

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a car rental company charges a daily rate of $26 plus $0.10 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $71. How many miles did you drive?

Answers

Answer: 450 miles

Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450

Given: p: x is a perfect square. q: x is even

What is a value of x that makes p and q true?

16
30
81
99

Answers

Answer:

16

Step-by-step explanation:

16: 16=4^2 and is even. 16/2=8

30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).

81: 81=9^2, but 81 is not even. 81/2=40.5.

99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.


Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment BC by 180 degrees. Describe the result.

Answers

Answer:

i don't known the question you are asking

Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.

How much does Mark owe?

ound your answer to the nearest cent.

Answers

The amount that he owes will be $6610.54.

How to compute the value?

From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.

Therefore the amount that will be paid will be:

= ($30.45 × 2) + (15.75 × 415.85 miles)

= $60.90 + $6549.64

= $6610.54

The cost is $6610.54.

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Which transformation would take Figure A to Figure B?

Answers

Answer:.......................

2.5 of what is 3?


Need help ASAP

Answers

Answer is 1.2

Step by step

2.5 of (multiply) x (unknown) is (=) 3

2.5 x = 3

Divide both sides by 2.5 to solve

2.5 / 2.5 x = 3/ 2.5

X = 1.2

Check your work, sub 1.2 in for x

(2.5) (1.2) = 3

3 = 3

Problem solved!!

Brock, age 50, and Erin, age 49, are married with three dependent children. They file a joint return for 2021. Their income from salaries totals $50,000, and they received $8,000 in taxable interest, $5,000 in royalties, and $3,000 in other ordinary income. Brock and Erin's deductions for adjusted gross income amount to $2,500, and they have itemized deductions totaling $19,250.

Answers

Based on the filing status of Brock and Erin, their itemized deductions, and their income from their salaries, their income tax liability is $4,250.

What is the income tax liability?

First, find the taxable income:

= Adjusted gross income - larger of Itemized deductions or standard deductions

= (50,000 + 8,000 + 5,000 + 3,000 - 2,500) - 24,800

= $38,700

The tax rate is 10 % for income between $0 and $19,750 and 12% for salaries between $19,751 and $80,250.

Brock and Erin therefore have a tax liability of:

= (10% x 19,750) + (12% x (38,700 - 19,750))

= $4,252

Rest of the question is:

Find the Income tax liability before any credits

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A certain plant grows 1 1/6 inches every week. How long will it take the plant to grow 6 1/6 inches?

Answers

It will take 6.14 weeks for the plant to grow the required length

The growth rate of the plant each week = 1 1/6 inches

Converting the mixed fraction into an improper fraction we multiply the whole number by the denominator and add the numerator to get the improper fraction, therefore

The growth rate of a plant in improper form = 7/6 inches

Required growth rate = 6 1/6 inches

The required growth rate in improper fraction = 43/6 inches

Number of weeks it will take the plant to grow the required length = Required length/Growth rate each week = (43/6)/(7/6)

= 43/7 weeks or 6.14 weeks

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denny is in the car repair business. Denny recently calculated his total cost conditions. He found that the total cost of repairing s cars is TC(s)=2s^2+10

If the market price is $20, how many cars will Denny be willing to repair?

Answers

When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.

How to calculate the value?

It should be noted that the total revenue will be:

= price × quantity

= 20 × s

= 20s

where s = number of cars

The marginal revenue will be 20.

The total cost is given as:

= 2s² + 10

The marginal cost will be 4s

We will equate the marginal. This will be:

4s = 20

Divide

s = 20/4

s = 5

Therefore, the number is 5.

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Use synthetic division to find the quotient and reminder when

X^3 - 7x^2 + 5x + 10 is divided by - 2

Answers

Hence , using synthetic division the quotient and remainder of given equation are x²- 9x + 23  and -36 respectively.

Synthetic division could be a methodology accustomed perform the division operation on polynomials once the divisor could be a linear issue. one in every of the benefits of mistreatment this methodology over the normal long methodology is that the artificial division permits one to calculate while not writing variables whereas performing arts the polynomial division, that additionally makes it a neater methodology compared to the division.

We have given an equation , x³ - 7x² + 5x + 10 which is divided by -2

Steps for using synthetic division are

Step 1 -  Write the coefficients of x within the dividend within associate inverted division image.

                   |  1    -7      5     10

                   |                                            

                   

Step 2 - As provides put = -2  place at the left.

             -  2 |  1    -7      5     10

                   |                                            

                       

Step 3 - Drop the primary constant of the dividend below the division image.

           -    2 |  1    -7      5     10

                   |                                            

                       1

Step 4 - Multiply the result by the constant, and place the merchandise within the next column.

           -   2 |  1    -7      5     10  

                   |        -2                                    

                      1    

Step 5 - Add down the column.

             -  2 |  1    -7      5     10  

                   |        -2                                    

                      1     -9

Step 6 - Repeat Steps Four and 5 till you'll go no further.

            -   2 |  1    -7      5     10  

                   |        -2    18   - 46                        

                      1     -9    23     -36

Hence the quotient is x²- 9x + 23 and remainder is -36

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Use properties of operations to add (−3) and (−17)

14

20

-20

-14

Answers

Answer:

Step-by-step explanation:

-20

Which of the following systems of equations has the same
solution as
-2x+2y=-2;3x-y=9
a.
A. 4x = 16;3x-y=9
B. [-2x+2y=-2;16x-2y = 9
C. -3x-7y=3;3x-y=9
D. [-2x+2y=-2;x+y=11

Answers

Answer:

Step-by-step explanation:

16/4

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How much more did bilingual medical secretaries make compared to monolingual medical secretaries?. *the puzzle* n 48 abcd w 117 efgh a) professor x traveled 1500 miles to see jean grey. he read one book every 450 miles he traveled. how many books had he finished by the time he arrived? b) storm had $74 and withdrew some more money from her bank account. she bought a pair of slacks at $34, two shirts at $16 each and a pair of shoes at $24. after shopping, storm had $15 left. how much money did she withdraw from the bank? c) there are 12 pacific northwest geocachers in wolverine's living room. six of them are wearing socks, four of them are wearing shoes, while four people are wearing both socks and shoes. how many geocachers have nothing on their feet for their upcoming geo-excursion together? d) cyclops will buy a new pair of shoes in 1200 seconds. how many minutes must he wait before he can buy them? (second digit in the answer!) e) quicksilver collected 700 nickels in a jar. he went to the bank to cash them in. how much money did the bank give him? f) for breakfast, mystique bought a bagel for $1.55 and a glass of orange juice for $2.25. at lunch, mystique spent $6.25 on a sandwich and $0.55 on a carton of milk. how much more money did she spend on lunch than on breakfast? g) mirage had three pizzas. each pizza had eight slices. if mirage at 75% of the pizza slices, how many were left? h) iceman has a highlighter obsession. in his desk drawer, there are 19 yellow highlighters. there are 15 more blue highlighters than yellow, and there are 37 green highlighters total. how many more green highlighters than blue does he have? What is the unspoken message the speaker is telling the reader about going after their own dreams? A television cost $1,275. It is marked down 35%. What is the new cost of the television? Please answer this!!! A young adult patient is admitted to the hospital for evaluation of severe weight loss. The patient demonstrates difficulty answering questions, and has trouble remembering simple details. The physical assessment reveals missing teeth and severe examples of tooth decay. Blood pressure is 160/98 mm hg. The provider suspects abuse of which substance? group of answer choices cocaine ecstasy marijuana methamphetamine who controls the government of burma (myanmar)?a.a monarchb.an elected presidentc.an elected prime ministerd.a military junta 5. The distance between two lighthouses is 137 miles. There are approximately 8 kilometersin 5 miles. Which measurement is closest to the number of kilometers between thesetwo lighthouses? find the LCM of 34,40,168 coinciding with the appearance of early hominins about 510 mya, the climate was a. increasingly hot and humid. b. less temperate. c. increasingly wet and rainy. d. increasingly dry and seasonal. irita k, kawashima y, morita k, et al. critical incidents during regional anesthesia in japanese society of anesthesiologists-certified training hospitals: an analysis of responses to the annual survey conducted between 1999 and 2002 by the japanese society of anesthesiologists. masui 2005;54:440-449 A well-written thesis statement for a research paper will do all of the following except which one?A. Define the topic of the paperB. Give details of all the supporting evidenceC. Outline the structure of the paper The graph of f(x) is increasing on(-, 0) and decreasing on (0, +).Which statement must be true?A f(x) has a maximum at x = 0.B f(x) has a minimum at x = 0.The domain of f(x) is (0, +).D The range of f(x) is (0, +). complete the following function, strcat list(l), which generalizes the previous function: given a list of strings, l[:], returns the concatenation of the strings in reverse order. for example: HELP.................................! ! 1.Kim wanted to determine how temperature affected the growth of E. coli, a common intestinal bacteria in humans. The normal body temperature for humans is 98.6oF. He took one culture of bacteria and grew them at 95oF, 98.6oF,100oF and 108oF. what is the control and experimental group? identify the necessary sociocultural skills for project managers. multiple select question. managing customer communication and expectations managing corporate politics motivating project team members using project software to plan, control, and schedule a project Given num_rows and num_cols, print a list of all seats in a theater. Rows are numbered, columns lettered, as in 1a or 3e. Print a space after each seat. List the 3 forms typically used in workers' compensation billing note use the information you gathered from the articles features to tell two central ideas of the article. The articles name is, how the news media works Enzymes act as_______________ in the body and help ______________ the metabolic processes within the cell. locks, slow down immune factors, protect chemical catalyst, speed up gatekeepers, monitor