If a recipe call for 1/4 cups oats per 1/2 cup flour, how much oats would
you need for 1 cup of flour? *
O 1/8 cup oats
O 1/4 cup oats
O 1/2 cup oats
O 3/4 cup oats

Answers

Answer 1

Answer:

1\2 oats that's easy it's 1\2 that's the answer


Related Questions

Can y'all please solve this.....will give brainliest ^_^​

Can y'all please solve this.....will give brainliest ^_^

Answers

x=6,004/5.019=1.196

x=1.2

y=3.999/9.241=0.432=0.43

Answer:

1.20.43

Step-by-step explanation:

\(x = \frac{\sqrt{36.05} }{5.019} \\ \\\sqrt{36.05}=6.00416\dots \\\\=\frac{6.00416\dots }{5.019}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{6.00416\dots }{5.019}=1.19628\dots \\\\=1.19628\dots \\\\= 1.2\)

\(y = \frac{\sqrt[3]{63.71}}{(3.04)^2} \\\\3.04^2=9.2416\\\\=\frac{\sqrt[3]{63.71}}{9.2416}\\\\\sqrt[3]{63.71}=3.99394\dots \\\\=\frac{3.99394\dots }{9.2416}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{3.99394\dots }{9.2416}\\=0.43217\dots \\\\= 0.43\)

Solve for the value of p.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER!!!!

Solve for the value of p.SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER!!!!

Answers

Answer:

The angles are supplementary meaning they equal 180 degrees so the angles have to equal 180.

p + 7 + 3p + 1 = 180

4p + 8 = 180

-8          -8(subtracting 8 from both sides)

4p = 172

/4     /4(dividing by 4 on both sides)

p = 43

Answer:

A straight angle measures 180°

(p + 7) + (3p + 1) = 180

p + 7 + 3p + 1 = 180

4p + 8 = 180

4p = 180 - 8

4p = 172

•°• p = 172/4 = 43

Assume f(x): x+2/3 find Find f-¹(4).


10
2
1/2
1


(the / represents fraction)

Answers

Answer:

Step-by-step explanation:

To find the inverse of a function, we need to switch the variables x and y and solve for the new variable.

Given f(x) = x + 2/3, we can write the inverse as f^-1(y) = x.

So we will replace y with 4 in the inverse function f^-1(y) = x and solve for x.

f^-1(4) = x

x + 2/3 = 4

x = 4 - 2/3

x = 8/3

Therefore, f^-1(4) = 8/3

Estimate σA and σB using the loan allocation deviation formula.
A. σ(A) = 12.25% ; σ(B) = 14.14%
B. σ(A) = 17.32% ; σ(B) = 20.0%
C. σ(A) = 16.33% ; σ(B) = 14.14%
D. σ(A) = 14.14% ; σ(B) = 16.33%

Answers

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

To know more about deviation visit:

https://brainly.com/question/31835352

#SPJ11

The midpoint of AB is at (-4, 3). If A = (0, -9), find B.

Answers

The coordinate of B is (15, -8) if the midpoint of AB is at (-4, 3) and A is (0,-9).

Given that, the midpoint of AB is at (-4, 3) and if A = (0, -9) then, we have to calculate the coordinates of point B.

Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves.

Let us suppose that the coordinates of B is (x,y)

⇒ -4 = 0+x/2

⇒ -4 = x/2

⇒ -4×2 = x

⇒ x = -8

Therefore, the x-coordinate of B is -8.

⇒ 3 = -9+x/2

⇒ 3 = x-9/2

⇒ 3×2 = x-9

⇒ 6 = x-9

⇒ 6+9 = x

⇒ 15 = x

Therefore, the y-coordinate of B is 15.

Hence, the coordinates of B is (15, -8) respectively.

Therefore, B = (15, -8) is the required answer.

Learn more in depth about midpoint at https://brainly.com/question/5566419

#SPJ1

i need help with this question pleasee​

i need help with this question pleasee

Answers

Answer:

A)

this is a corect answer for this question:)

A small amount of the trace element selenium, 50–200 micrograms (μg) per day, is considered essential to good health. Suppose that random samples of
n1 = n2 = 40 adults
were selected from two regions of Canada and that a day's intake of selenium, from both liquids and solids, was recorded for each person. The mean and standard deviation of the selenium daily intakes for the 40 adults from region 1 were
x1 = 167.8
and
s1 = 24.5 μg,
respectively. The corresponding statistics for the 40 adults from region 2 were
x2 = 140.9
and
s2 = 17.3 μg.
Find a 95% confidence interval for the difference
(μ1 − μ2)
in the mean selenium intakes for the two regions. (Round your answers to three decimal places.)
μg to μg
Interpret this interval.
In repeated sampling, 5% of all intervals constructed in this manner will enclose the difference in population means.There is a 95% chance that the difference between individual sample means will fall within the interval. 95% of all differences will fall within the interval.In repeated sampling, 95% of all intervals constructed in this manner will enclose the difference in population means.There is a 5% chance that the difference between individual sample means will fall within the interval.

Answers

We have come to find that confidence interval is (16.802, 37.998) μg

What is Micrograms?

Micrograms: This is a unit for measuring the weight of an object. It is equal to one millionth of a gram.

To find a 95% confidence interval for the difference in mean selenium intakes between the two regions, we can use the following formula:

Confidence interval = (x1 - x2) ± t * SE

where:

x1 and x2 are the sample means for region 1 and region 2, respectively.

t is the critical value from the t-distribution for a 95% confidence level.

SE is the standard error of the difference, calculated as follows:

\(\rm SE = \sqrt{((s_1^2 / n_1) + (s_2^2 / n2))\)

Let's calculate the confidence interval using the given values:

x₁ = 167.8

s₁ = 24.5 μg

n₁ = 40

x₂ = 140.9

s₂ = 17.3 μg

n₂ = 40

SE = √((24.5² / 40) + (17.3² / 40))

SE ≈ 4.982

Now, we need to determine the critical value from the t-distribution. Since both sample sizes are 40, we can assume that the degrees of freedom are approximately 40 - 1 = 39. Consulting a t-table or using a statistical software, the critical value for a 95% confidence level with 39 degrees of freedom is approximately 2.024.

Substituting the values into the confidence interval formula:

Confidence interval = (167.8 - 140.9) ± 2.024 * 4.982

Confidence interval = 26.9 ± 10.098

Rounded to three decimal places:

Confidence interval ≈ (16.802, 37.998) μg

Interpretation:

We are 95% confident that the true difference in mean selenium intakes between the two regions falls within the interval of 16.802 μg to 37.998 μg. This means that, on average, region 1 has a higher selenium intake than region 2 by at least 16.802 μg and up to 37.998 μg.

To learn more about confidence interval from the given link

https://brainly.com/question/32546207

#SPJ4

for a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what is the expected winnings per ticket? question options:

Answers

The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

Read more about equation on:

https://brainly.com/question/25976025

#SPJ4

Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

1/4 - 7/1 (pls i nee answer)

Answers

Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

compare using <,>, or = 4/9 5/10

Answers

Given data:

The first number is 4/9.

The second number is 5/10.

The first number can be written as,

\(\begin{gathered} \frac{4}{9}=\frac{4\times10}{9\times10} \\ =\frac{40}{90} \\ \end{gathered}\)

The second number can be written as,

\(\begin{gathered} \frac{5}{10}=\frac{5\times9}{10\times9} \\ =\frac{45}{90} \end{gathered}\)

Now compare both numbers as they have same denominator.

\(\begin{gathered} \frac{40}{90}<\frac{45}{90} \\ or \\ \frac{4}{9}<\frac{5}{10} \end{gathered}\)

Thus, the < symbol must be used between both n

Find an expression which represents the difference when (-2+9y) is subtracted
from (-6x + 4y) in simplest terms.

Answers

Answer:

-6x-5y+2

Step-by-step explanation:

The product of two numbers is 323 and the difference between them is 2. What are the two numbers?

Answers

Answer:

17 and 19

Step-by-step explanation:

17 * x = 323

x = 323 / 17

x = Second number = 19.

Step-by-step explanation:

323

2

=16×2=32

=3×1=3

=3

=16

=16,3

I hate math but plz help

I hate math but plz help

Answers

This answer may be for 7.75 dollars a week for two weeks

what is the least common denominator for 11/8 and 1/12

Answers

To find the least common denominator for 11/8 and 1/12, we need to determine smallest common multiple of denominators, which is the smallest number for both. Hence, LCD for 11/8 and 1/12 is 24.

The prime factors of 8 are 2 * 2 * 2, and the prime factors of 12 are 2 * 2 * 3. To find the LCD, we need to consider the highest power of each prime factor that appears in either number. In this case, the highest power of 2 is 2 * 2 * 2, and the highest power of 3 is 3.

Multiplying these together, we get 2 * 2 * 2 * 3 = 24. Therefore, the LCD for 11/8 and 1/12 is 24.Using the LCD, we can rewrite the fractions with a common denominator of 24 and perform operations such as addition, subtraction, or comparison more easily.

To learn more about denominators click here : brainly.com/question/32621096

#SPJ11

given:2y-1/-3=-5 prove:y=8

Answers

Answer:

2y + 1/3 = 5

2y = -5 -1/3

2y = -16/3

Y = -8/3

Step-by-step explanation:

im pretty sure thats the answer but good luck!

Help what is the solution to the system of equations graphed below

Help what is the solution to the system of equations graphed below

Answers

Answer:

(4, 2 )

Step-by-step explanation:

Given a graph of a system of equations, then the solution is at the point of intersection of the 2 lines.

The lines intersect at (4, 2 ) ← solution

solve 4 x 3/5. please help im giving 40 points

Answers

Answer:

12/5 is correct answer .

Step-by-step explanation:

\( \bf \implies4 \times \frac{3}{5} \\ \\ \bf \implies \frac{4 \times 3}{5} \\ \\ \bf \implies \frac{12}{5} \)

So, the required answer is 12/5 .

Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block

Answers

The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

To know more about parameter here

https://brainly.com/question/30757464

#SPJ4

Please help now! Simplify -4x - x.
A. -5x
B. -4x
C. -3x

Answers

Answer:

the answer is -5x

Step-by-step explanation:

plz give me 5star

Anwser is B hope this helps brainleist is appreciated

pls help :(
y= _x +_
Find the equation of the line

pls help :( y= _x +_Find the equation of the line

Answers

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

A={1,4,5,8) B = { 2, 8, 9) C = {3,5,8) Be (C-A) = { Ex: 3,6 }

Answers

The set (C-A) is {3, 6}.

To obtain this set, we first subtract the elements in A from the elements in C, which gives us {3, 0, 3}. Then, we remove any duplicates and sort the remaining elements in ascending order to get {3, 6}.

sam wishes to cross a circular lake with diameter 1 km. he can row across the water at a rate of 4 km/hour, or he can walk along the shore (carrying the rowboat) at a rate of 6 km/hour. what is the minimum amount of time necessary to cross the lake?

Answers

25 minutes. The time it would take to row across the lake is 15 minutes (1 km/4 km/hour = 0.25 hour), and the time it would take to walk around the lake is 10 minutes (1 km/6 km/hour = 0.1666 hour). Thus, the minimum amount of time necessary to cross the lake is 25 minutes (15 + 10).

1 km/4 km/hour = 0.25 hour (time to row across the lake)

1 km/6 km/hour = 0.1666 hour (time to walk around the lake)

Minimum amount of time necessary to cross the lake = 0.25 + 0.1666 = 0.4166 hour

0.4166 hour x 60 minutes/hour = 25 minutes

Sam can row across the lake in 15 minutes (1 km/4 km/hour = 0.25 hour) or walk around it in 10 minutes (1 km/6 km/hour = 0.1666 hour). The minimum amount of time necessary to cross the lake is 25 minutes (15 + 10), as this is the lowest total time to get from one side to the other.

Learn more about minutes here

https://brainly.com/question/15600126

#SPJ4

Help me please

Solve the inequality s:

5s+2>7

Answers

Answer:

s>1

Step-by-ste:p explanation:

the internet :)

3.1.PS-10
Question Help
The Stock Market Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,200 worth of
stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he
make in commission in 2011?
Last week, he made $ in commission.

Answers

The amount of commission made in the last week and in the year 2011 is $936 and $48,672, respectively.

The Stock Market Alexander is a stockbroker. It is given that he earns 13% commission each week. He sold $7,200 worth of stocks last week. We need to calculate the amount of commission he made in the last week.

Let the commission earned be represented by "C". The commission earned is the product of the rate of commission and the amount of stocks sold.

C = 13% of $7,200

C = 0.13*7200

C = $936

The commission made in the last week is $936. It is also given that he makes the same amount every week on an average. We need to calculate the commission earned in the whole year 2011.

We know that there are 52 weeks in a year. So, the total commission made in the year 2011 is the product of commission made in a week and the total number of weeks.

C = 52*936

C = $48,672

To learn more about average, visit :

https://brainly.com/question/24057012

#SPJ9

What’s the distance between the points! round to the nearest tenth i need to show work please help i’m failing!

Whats the distance between the points! round to the nearest tenth i need to show work please help im

Answers

Answer:

Distance=4.24

Step-by-step explanation:

By the Pythagorean Theorem:

3^2+3^2=distance^2

9+9=distance^2

Distance=4.24

The radius of a circle is 8 millimeters. What is the circle's area

Use 3.14 for PI

Answers

Answer:

200.96 millimeters²

Step-by-step explanation:

How do we find the area of a circle?

The area of a circle is πr², where r = radius. We're given the radius as 8 millimeters, and we're going to approximate pi as 3.14.

Solving

3.14 × 8²3.14 × 64200.96

Therefore, the area is 200.96 millimeters².

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Solution:

We know that:

Radius = 8 mmArea of circle = πr²

Finding the area of the circle.

Area of circle = πr²=> Area of circle = 3.14 x 8²=> Area of circle = 3.14 x 64=> Area of circle = 200.96 mm²

5. If v in R3 and v.v=0, then v is the zero vector. Is it true or false? Explain your answer. 6. Let [17] A= 25 Find the solution x of the equation Ax inverse matrix A! b for any b. From your solution read off the

Answers

The solution of the equation Ax inverse matrix A! b for any b is x = [1/25]b.From the given [17]A = 25, we can read off the inverse matrix A:inverse of A = [1/25]

If v in R3 and v.v=0, then v is the zero vector. Is it true or false? Explain your answer.

It is true that if v in R3 and v.v=0, then v is the zero vector. Because the dot product of a vector with itself is equal to the magnitude squared of the vector, which is non-negative for any non-zero vector, it follows that if v.v=0, then v must be the zero vector. Therefore, the statement is true.

Let [17] A= 25. Find the solution x of the equation Ax inverse matrix A! b for any b. From your solution read off the inverse matrix A!

Given, [17]A = 25.To solve the equation Ax inverse matrix A! b for any b, we need to find the inverse of matrix A, then we can use this inverse to find the solution x from Ax = b.First, let's find the inverse of matrix A. For a 1x1 matrix [a], its inverse is [1/a].Therefore, inverse of A = [1/25].

Now, we can find the solution x from Ax = b as follows:A.x = b Multiplying by inverse of A on both sides, we get:inverse of A . A . x = inverse of A . bx = inverse of A . b Substituting the values of x, b and inverse of A, we get:x = [1/25]bTherefore, the solution of the equation Ax inverse matrix A! b for any b is x = [1/25]b.From the given [17]A = 25, we can read off the inverse matrix A:inverse of A = [1/25]

Learn more about Inverse matrix

brainly.com/question/4017205

#SPJ11

Without using a calculator order these numbers from least to greatest

Without using a calculator order these numbers from least to greatest

Answers

Answer: 5, 6, √39

Step-by-step explanation:

√39 = 6.24

therefore, the order is 5, 6, √39

HELP URGENT
A 0.2 kg cue ball moving at 10 m/s hits a 0.15 kg 8 ball at rest. The cue ball continues rolling forward at 1 m/s. What is the velocity of the 8 ball?

Answers

Answer:

We can use the principle of conservation of momentum to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system.

Initially, only the cue ball is moving, and the 8 ball is at rest. Therefore, the initial momentum of the system is:

p_initial = m1 * v1 + m2 * v2

= 0.2 kg * 10 m/s + 0.15 kg * 0 m/s

= 2 kg m/s

After the collision, the cue ball is rolling forward at 1 m/s, and the 8 ball is moving in some direction with some velocity v_final. Therefore, the final momentum of the system is:

p_final = m1 * v1 + m2 * v_final

According to the conservation of momentum principle, p_initial = p_final. Therefore,

2 kg m/s = 0.2 kg * 1 m/s + 0.15 kg * v_final

Solving for v_final, we get:

v_final = (2 kg m/s - 0.02 kg m/s) / 0.15 kg

= 13.33 m/s

Therefore, the velocity of the 8 ball after the collision is 13.33 m/s.

josh’s favorite snack at a convenience store costs $3.47 before tax. if the tax rate is 8.3% how much would josh pay for his snack including taxes ?

Answers

Josh would pay $3.76 for his snack including taxes.

How much would josh pay for his snack including taxes?

Given that; josh’s favorite snack at a convenience store costs $3.47 before tax and tax rate is 8.3%.

To determine the cost of Josh's snack including taxes, we need to add the tax amount to the original price of the snack.

First, calculate the tax amount by multiplying the original price by the tax rate:

Tax amount = 3.47 × 8.3%

Tax amount = 3.47 × 0.083

Tax amount = $0.28801

Next, we add the tax amount to the original price to find the total cost of the snack including taxes:

Total cost = Original price + Tax amount

Total cost = $3.47 + $0.28801

Total cost = $3.76

Therefore, the total cost is $3.76.

Learn about selling price, markup price and cost here: https://brainly.com/question/29511226

#SPJ1

Other Questions
What emotion is being shown in thisWhat could love, the unsolved mystery, count for in the face of this possession of self-assertion which she suddenly recognized as the strongest impulse of her being! #19 Choose the correct code assignment for the following scenario: 51-year-old male with chronicpyelonephritis due to E. coli.A. B96.20B. N11.8C. N11.8, B96.20D. N11.9, B96.29 MARIGOLD SITUATIONAL IRONY QUESTIONWILL GIVE BRAINLISTHELP!!!!In the story Marigold by Eugenia Collier, there is situational irony. One of them is in the end where she plant the marigold years after she tore out Mrs. Lottie.CAN YOU FIND ANOTHER EXAMPLE OF SITUATION IRONY!?!PLEASE HELP 10Scientists need to test different abilities of the robots. While scientists performthese tests, they measure how much energy the robots require to function fora long period of time and how much space they take up.Why do the scientists run these tests and track these measurements to create a finalmodel? Use evidence from the text to support your answer. A firm that provides daycare for small children is considering expanding their business and opening a new daycare at a different location. They will use this new location for 30 years (t = 0, ..., 29).Use a 3% discount rate.If they do so, they will have to pay $51,000 immediately (t = 0) to get the location ready, and then $316,000 per year for rent, labour, and supplies (t = 1, ..., 29).They will earn revenue from the new location of $469,000 per year (t = 1, ..., 29).Calculate the net present value of opening the new location. A local talent is selling underground CD's to get his rap career off the ground. Each crate contains 40 blank CD's. Each crate cost $25. How much should he sell his CD's to make a profit of $135? aragraphsQuestion 3 of 10Who is most likely the target audience of the Bill of Rights?A. Citizens of Great BritainB. Citizens of the United StatesC. The king of EnglandD. The U.S. presidentSUBMIT PLEASE HELP ANSWER WHAT U CAN (you don't have to solve the whole page) HELP what should you do if you are not very good in something you love doing? Natural resources are the decisive ingredient in any country's prospects for economic growth. True False Which symbol represents enthalpy? qHelp ASAP :( A 30-N box is pulled 6.0 m up along a 37 inclined plane. What is the work done by the weight (gravitational force) of the box? -6x - 42= 10x + 62X = What is the circumference of this circle? 8 pi 9 pi 12 pi 16 pi How is peak-load pricing a form of price discrimination? Can itmake consumers better off? Give anexample. if agglutination occurs after a blood transfusion, it may indicate In a short story, a character decides to distance himselffrom his family by moving away. When he does, lifebecomes difficult. He realizes how often he had relied onhis family for support and encouragement. In order torespect his plea for independence, his family had refrainedfrom contacting him. In the end, the character moves backto his hometown and is happier because of it.Which common literary theme is best illustrated by the passage?O A. Parents can be a burden on personal freedom.OB. You don't know what you value until it's gone.O C. Love is the worthiest of pursuits.OD. Man struggles against man. 1. Succession is best defined at as a ______________ series of changes that occur in an ecosystem over time:a) randomb) predictable c) rapidd) beneficial Suppose that the series a_n (z z_0)^n has radius of convergence R_0 and that f(z) = a_n (z z_0)^n whenever |z z_0| < R_0. Prove that R_0 = inf{|z - z_0|: f(z) non-analytic or undefined at z} (R_0 is essentially the distance from z_0 to the nearest point at which f(z) is non-analytic) While studying in a noisy cafeteria, you get sleepy and doze off afew minutes. You awaken with a startle and realize that allcafeteria sounds have just "come back". While you were dozing thisaudito