If n lines are drawn on a plane, no two lines are parallel, and all lines intersect at different points, how many sections do they separate the plane into? assume that no more than two lines intersect at any one point and prove your result using weak induction. Don’t include unneeded base cases.

Answers

Answer 1

Proved our result using weak induction.

Given:

If n lines are drawn on a plane, no two lines are parallel, and all lines intersect at different points, how many sections do they separate the plane into, assume that no more than two lines intersect at any one point.

Suppose it is true for n .Now add a new line , the number of  vertices increases by n one with each of the old line and the number of line segments increases by 2n+1 ( Each of the n old lines is broken into one more piece and the new line has n+1 segments , hence by euler's theorem on planar graphs the number of regions (F) increases by n+1 since V - E + F is constant and V - E is reduced by n+1.

so we now have

[tex]n^{2}[/tex]+n+2/2 + n + 1 = [tex](n+1)^{2}[/tex]+ n+1+2/2  vertices are desired

Therefore proved our result using weak induction.

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Related Questions

for any two real numbers a and b where b ≠0 and for all integers is this true

Answers

Given:-

[tex]64^{\frac{1}{4}},256^{\frac{1}{8}},125^{\frac{1}{3}}[/tex]

To find:-

The simplified value.

So now we have,

[tex]\begin{gathered} 64=2\times2\times2\times2\times2\times2 \\ 256=2\times2\times2\times2\times2\times2\times2\times2 \\ 125=5\times5\times5 \end{gathered}[/tex]

So we have,

[tex]64=2^6,256=2^8,125=5^3[/tex]

So now,

[tex]\begin{gathered} 64^{\frac{1}{4}}=(2^6)^{\frac{1}{4}},256=(2^8)^{\frac{1}{8}},125=(5^3)^{\frac{1}{3}} \\ 64=4,256=2,125=5 \end{gathered}[/tex]

So the value is,

[tex]4,6,5[/tex]

what is the justification for step 3 in the solution process?
0.8a-0.1a=a-2.5
Step 1: 0.7a=a-2.5
Step 2: -0.3a=-2.5
Step 3: a=8.3

Answers

In step 3 each side of the equation is divided by - 0.3 to obtain the value of a = 8.3.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Consider the expression,

0.8a - 0.1a = a - 2.5

Step 1,

Subtracting similar terms,

a( 0.8 - 0.1 ) = a - 2.5

0.7a = a - 2.5

Step 2: Subtracting the term a from each side of the equation.

0.7a - a = a - 2.5 - a

- 0.3a = - 2.5

Step 3: Multiplying each side of the equation by - 1.

- 0.3a × - 1 = - 2.5 × - 1

0.3a = 2.5

Dividing each side of the equation by 0.3.

a = 2.5/0.3

a = 8.3

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Question 3(Multiple Choice Worth 5 points)(05.01)A picture is 5 inches wide and 8 inches tall: A photographer wants to use a scale factor of 2.5 to enlarge a picture. What will the area of the picture be after it is enlarged?40 in2250 in2100 in281.9 in2

Answers

Find the new dimentions of the enlarged picture multiplying the length of each side by the scale factor of 2.5:

[tex]\begin{gathered} 5in\times2.5=12.5in \\ 8in\times2.5=20in \end{gathered}[/tex]

Now, multiply width times height to find the area of the picture (assuming that it has a rectangular shape):

[tex]12.5in\times20in=250in^2[/tex]

Therefore, the area of the enlarged picture will be 250 squared inches.

Name a principal and interest rate where the amount of simple interest earned in 10 years would be $200. Justify your answer.

Answers

The relation between a principal and interest rate is;

⇒ P = $20 / r

Where, P is the principal amount and r is the interest rate.

What is Simple interest?

The simple interest is defined as;

Simple interest = P r t

Where, P is principal amount.

r is rate and t is time period.

Given that;

Simple interest = $200

Time period = 10 years.

Let principal amount = P

And, The interest rate = r

So, We get;

Simple interest = P r t

Substitute all the values, we get;

Simple interest = P r t

$200 = P × r × 10

Pr = $20

P = $20 / r

Thus, We get the relation between a principal and interest rate is;

⇒ P = $20 / r

Where, P is the principal amount and r is the interest rate.

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Estimate a 10% tip on a bill of $159.63 by first rounding the bill amount to the nearest ten dollars.​

Answers

Answer: Tip Total: $ 16.00Total (Bill + Tip): $ 176.00

Which rounding to the dearest ten dollars will be 186.00

how much more is 6.302 than 6.002 ?

Answers

Answer:

Step-by-step explanation:

0.3

Answer:

It is 0.3 more or 0.300 more

Step-by-step explanation:

6.002 + 0.3 or 0.300 = 6.302

6.302- 0.300 or 0.3 = 6.002

Hope I helped

which expression is equivalent to 4/5-1/2
4/10-1/10
6/5-5/7
4/7-1/7
8/10-5/10​

Answers

the last one is correct

Theatre tickets cost either $30 or $42. One evening twice as many $30 tickets are sold as $42 tickets and the total money taken is $18564. Find the total number of tickets that are sold.​

Answers

Ratio = 1:2
1 + 2 = 3
18564 / 3 = 6188
6188 x 2 = 12376
Ratio = 6188:12376
6188 / 42 = 148 tickets
12376 / 30 = 413 tickets
413 + 148 = 561 tickets

NEED ANSWER ASAP. please help

what is the value of x?

- 20
- 40
- 8
- 12​

Answers

Answer:

8

Step-by-step explanation:

8x-4=60

8x=64

x=64/8

x=8

Answer:

x = 8

Step-by-step explanation:

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Therefore, equate the two angles and solve for x:

⇒ (8x - 4)° = 60°

⇒ 8x - 4 = 60

⇒ 8x - 4 + 4 = 60 + 4

⇒ 8x = 64

⇒ 8x ÷ 8 = 64 ÷ 8

⇒ x = 8

Which expressions represent the volume of the cube? Select all that apply.

A cube with side length 3-fourths foot.
3343ft3
(34)3ft3
2716ft3
2764ft3
916ft2
(34)2ft2

Answers

The volume of cube with side length 3/4 of a foot is  (27/64) square feet which is the fourth option.

We know that the formula for the volume of a cube is given by:-

Volume of cube = (side)*(side)*(side) = [tex]side^3[/tex]

Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

We have,

side = (3/4) foot

Hence, we can write,

Volume of cube = (3/4)*(3/4)*(3/4) = (27/64)  square feet.

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Next questionA man uses a loan program for small businesses to obtain a loan to help expand his vending machine business. The man borrows $27,000 for 3 years with a sirinterest rate of 1.5%. Determine the amount of money the man must repay after 3 years.The man must repay

Answers

Simple interest formula (not compound interest formula) is used here, as much as i know.

the formula is:

f = p * (1 + r * n).

f is the future value

p is the present value

r is the interest rate per time period

n is the number of time periods

Given

[tex]\begin{gathered} P=27000 \\ r=1.5\%=\frac{1.5}{100}=0.015 \\ n=3years \end{gathered}[/tex]

Therefore, we have

[tex]f=27000(1+0.015\times3)=\text{ \$}28215[/tex]

Hence, the answer is

[tex]\begin{equation*} \text{\$}28215 \end{equation*}[/tex]

16. The greatest distance between the Sun and
greatest distance between the Sun and Saturn
Jupiter is about 8.166 x 10^8 kilometers. The
is about 1.515 x 10⁹ kilometers. What is the
difference of these two distances?

Answers

The difference of the distance given for Sun, Saturn and Jupiter is   6.984 x 10⁸ kilometers.

What is termed as the scientific notations?Every day, we use numbers in our lives. Scientific notation is a method of writing extremely large and extremely small numbers. Scientific notation consists of two parts: a coefficient between 1 and 10 and a power of ten. The mantissa is the difference between the whole part (left of a decimal point) and also the decimal part (right of a decimal point) of the coefficient. The exponent would be positive or negative depending on which way the decimal point is moved.

For the given question;

The greatest distance between the Sun and Jupiter is about 8.166 x 10⁸ kilometers.

The greatest distance between the Sun and Saturn is about 1.515 x 10⁹ kilometers.

Write this distance in the form of 10⁸ , the point will shift towards right one decimal.

Sun and Saturn distance =  15.15 x 10⁸ kilometers.

Difference =   Sun and Saturn distance - Sun and Jupiter distance

Put the values,

Difference =   15.15 x 10⁸ -  8.166 x 10⁸

Difference =  6.984 x 10⁸ kilometers.

Thus, the difference of the distances is found as   6.984 x 10⁸ kilometers.

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simplify:

4(6+7)
O 13
O 17
O 24
O 52

Answers

Answer:

52

Step-by-step explanation:

[tex](4 \times 6) + (4 \times 7) \\ 24 + 28 = 52[/tex]

Answer:

4th answer is correct

Step-by-step explanation:

We have to solve this sum according to the BODMAS theorem.

That is:

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Let us solve it now.

4 ( 6 + 7 )

4 × 13

52

please help and show steps am failing class

Answers

answer:

D. y = 3x + 9

perpendicular means negative reciprocal of the number next to x

so if its 5x perpendicular would be -1/5x

make the equation look like y = ...

2x + 6y = 6

6y = -2x + 6

y = (-2x + 6)/6

y = -2x/6 + 6/6

y = -1/3x + 1

perpendicular line would be a negative reciprocal so

-1/3x would have a perpendicular that would be 3x

D. is the only one that has 3x

The northern hemisphere of planet earth has an inner core that is made up of iron and nickel. This iron nickel core is 30% of the volume of the northern hemisphere. If the diameter of the earth is 8,000 miles, what is the volume of iron-nickel core?

Answers

It turns out that the dynamo effect depends on the presence of up to 20% nickel in the Earth's core, a metal that behaves very differently from iron under extreme temperatures.  Unlike the northern hemisphere mineral-rich crust and mantle, the core is made almost entirely of metal—specifically, iron and nickel. The shorthand used for the core's iron-nickel alloys is simply the elements' chemical symbols—NiFe. Elements that dissolve in iron, called siderophiles, are also found in the core.

Explain about the volume of iron nickel core?The core is almost entirely comprised of metal, notably iron and nickel, in contrast to the crust and mantle, which are rich in minerals. Iron-nickel alloys found in the core are denoted by their chemical symbols, NiFe. The core also contains siderophiles, or substances that dissolve in iron.volume calculation for the earth. Since the Earth is nearly spherical, its volume (V) may be determined using the formula V = 4/3 pi x r3, where r is its radius.The core of the earth is made up of iron, nickel, and other heavy metals like gold since they are the heaviest of all the metals and gravitated into the center of the planet.

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What is the horizontal distance in inches covered by 12 stair steps if each is 11 in. wide?

Answers

The total horizontal distance covered by 12 stair steps is 132 inches.

What is an equation?

An equation is an expression that can be used to show the relationship between numbers and variables.

Given that:

Each stair step is 11 inches wideThere are 12 stair steps

Total horizontal distance = 12 stairs * 11 in/stair = 132 inches

Total horizontal distance is 132 inches

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Andre is setting up rectangular tables for a party. He can fit 6 chairs around a single table. Andre lines up 10 tables end-to-end and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. IS THE RELATIONSHIP PROPORTIONAL

THIS IS DUE TODAY ​

Answers

He can’t fit them all because he can only put 4 chairs per table because it is an rectangle



Reason is because a rectangle has 4 sides at here for he can only put 4 chairs per table

a quarter of which is 15

Answers

a quarter of 15 is 3.75

Is the function y=x^2-x linear or not?

Answers

Answer:

NOT linear

Step-by-step explanation:

Your equation is:

y = x^2 - x

Since the y has no exponent, (which is a power of 1) and the x has an exponent of 2, this function is a parabola. It is not linear. (Linear functions have a graph that is a line)

Functions that are NOT linear have exponents greater than 1, or variables in the denominator, or, variables inside a radical.

URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS

Answers

your answer would be C.

Guys i need helps is this right?​

Answers

you are correct!!! the answer is F.

What’s the answer plss I need help asp

Answers

Answer:

I am 80% positive that it is DE but there is still that other 20% so keep in mind I am not entirely sure

Jason is testing two fertilizers, grow well and green grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants In an identical environment. He then administered grow well to 25 of the tomato plants and green grow to the remaining 25 tomato plants

Answers

The true statements is:

(A) The number of tomato plants treated with Green Grow that are over 18 inches tall is more than the number of tomato plants treated with Grow Well that are over 18 inches tall.

Jason is testing with two fertilizers namely, grow well and green grow.

Jason brought 50 tomato plants of the same variety and planted them in an identical environment.

Jason administered grow well to 25 and green grow to the remaining 25.

The values and recorded data from the  above histograms are:

Grow Well

height numbers of plants

12 - 14        14

15 - 17         6

18 - 20         3

21 - 23         2

Green Grow

height numbers of plants

12 - 14      4

15 - 17      3

18 - 20      6

21 - 23     12

From the table,

(A) The number of tomato plants over the height of 18 inches, when treated with green grow is, GG = 6 + 12 = 18

The number of tomato plants over the height of 18 inches, when treated with grow well is, GW = 3 + 2 = 5

Therefore, GG > GW

Hence, the statement is true.

(B) As statement A is true, this statement is false.

(C) The tomato plants over 18 inches when administered with green grow, GG = 6 + 12 = 18

The tomato plants over 18 inches when administered with grow well, GW = 3 + 2 = 5.

As GG ≠ GW, the statement is false.

(D) As the number of tomato plants over 18 inches when treated with green grow is greater than when treated with grow well. Hence, the statement is false.

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The complete question is mentioned below:

Jason is testing two fertilizers, Grow Well and Green Grow, so he went to a nursery and bought 50 tomato plants of the same variety. He planted all 50 plants in an identical environment. He then administered Grow Well to 25 of the tomato plants and Green Grow to the remaining 25 tomato plants. After four weeks, Jason measured the heights of the tomato plants to the nearest inch and recorded their heights in the following histograms.      

Grow Well

height numbers of plants

12 - 14        14

15 - 17         6

18 - 20         3

21 - 23         2

Green Grow

height numbers of plants

12 - 14      4

15 - 17      3

18 - 20      6

21 - 23     12

Which of the following statements is true for the data sets above?

A.  The number of tomato plants treated with Green Grow over the height of 18 inches is more than the number of tomato plants treated with Grow Well over the height of 18 inches.  

B.  All of the statements are false for the given data sets.  

C.  The number of tomato plants treated with Green Grow over 18 inches equals the number of plants treated with Grow Well over 18 inches.  

D.  The number of tomato plants treated with Green Grow over the height of 18 inches is to the number of tomato plants treated with Grow Well over the height of 18 inches.  

NuHome Movers charges $95 per hour for loading/unloading services and $80 per hour for packing/unpacking services. Their charge is $2.50 per mile for truck rental. Jay is moving a distance of 200 miles and needs 9 hours of loading/unloading and 7 hours of packing/ unpacking. What will his moving cost be if the service also charges 7.25% tax on the total?​

Answers

Answer:

Total moving cost = $2,053.84

Step-by-step explanation:

Let's write down Jay's requirements and costs associated

9 hours of loading/unloading at $95 per hour = 95 x 9 = $855

7 hours of packing/unpacking at $80 per hour = 80 x 7 = $560

200 miles of transportation at $2.50 per mile = 2.50 x 200 = $500

Total before-tax cost of moving = $855 +  $560 + $500 = $1, 915

Sales Tax is additional at 7.25%

Sales Tax amount = 1915 x 7.25%

= 1915 x 7.25/100 = 138.8375 = $138.84

Total cost including sales tax = 1915.00 + 138.84 = $2,053.84

Can you please help me find the limit and identify any vertical asymptotes? Thanks

Answers

Given: The limit below

[tex]\lim_{x\to7^-}(\frac{1}{x-7})[/tex]

To Determine: The limit and the vertical asymptotes

Solution

[tex]\begin{gathered} \lim_{x\to7^-}(\frac{1}{x-7}) \\ \mathrm{For}\:x\:\mathrm{approaching}\:7\:\mathrm{from\:the\:left},\:x<7\quad \Rightarrow \quad \:x-7<0 \\ The\:denominator\:is\:a\:negative\:quantity\:approaching\:0\:from\:the\:left \\ Hence \\ \operatorname{\lim}_{x\to7^-}(\frac{1}{x-7})=-\infty \end{gathered}[/tex]

For the vertical asymptote

[tex]\begin{gathered} Vertical-asymptote \\ For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points \\ also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function. \end{gathered}[/tex]

The denominator of the rational function given is

[tex]\begin{gathered} denominator:x-7 \\ x-7=0 \\ x=7 \end{gathered}[/tex]

Hence:

limit = - ∞

Vertical asymptote: x = 7

5. an elevator in a building starts with five passengers and stops at 7 floors. if each passenger is equally likely to get off at any floor and all the passengers leave independently of each other, what is the probability that no two passengers will get off at the same floor?

Answers

The probability that no two passengers gets off at the same floor will be 0.15.

As per the question statement, an elevator in a building starts with five passengers and stops at 7 floors where each passenger is equally likely to get off at any floor and all the passengers leave independently of each other.

We are required to calculate the probability that no two passengers gets off at the same floor.

Here, since repetition is not allowed,

That is, the total number of ways for 5 passengers are to be assigned to seven floors but no two passengers on the same floor

= 7P5 = [(7!)/(7 - 2)!] = [(7!)/(2!)] = (7 * 6 * 5 * 4 * 3) = 2520

And, the total number of ways to assign 5 passengers to 7 floors, with repetition being allowed will be

= (7)⁵ = 16807.

Therefore, the probability that no two passengers gets off at the same floor will be = (2520/16807) = 0.14993 ≈ 0.15

Probability: It is that branch of Mathematics which deals with the numerical descriptions concerning the extent to which an event is likely to occur, or how likely it is for a proposition to be true, and is measured by the ratio of the favorable cases to the whole number of cases possible.

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Standard Form & Scientific Notation• 3 examples of converting from standard form to scientific notation• 3 examples of converting from scientific notation to standard form

Answers

Required:

We need to convert from standard form to scientific notation and also scientific notation to standard form.

Explanation:

a) Convert from standard form to scientific notation:

1) Consider the number 4,520,000.

The given number can be written as follows.

[tex]4,520,000=452\times10000[/tex]

[tex]=452\times10^4[/tex]

[tex]=452\times10^4\times\frac{10^2}{10^2}[/tex]

[tex]=452\times\frac{10^4\times10^2}{10^2}[/tex]

[tex]=\frac{452}{100}\times10^6[/tex]

[tex]=4.52\times10^6[/tex]

The scientific notation of s

[tex]4.52\times10^6[/tex]

2) Consider the number

[tex]35.98\times10^3[/tex]

Multiply and divide by 10.

[tex]35.98\times10^3=35.98\times10^3\times\frac{10}{10}[/tex]

[tex]=\frac{35.98}{10}\times10^3\times10[/tex]

[tex]=3.598\times10^4[/tex]

The scientific notation is

[tex]3.598\times10^4[/tex]

3) Consider the number.

[tex]600.89\times10^{-8}[/tex]

Multiply and divide by 100.

[tex]600.89\times10^{-8}=600.89\times10^{-8}\times\frac{100}{100}[/tex]

[tex]=\frac{600.89}{100}\times10^{-8}\times10^2[/tex]

[tex]=6.0089\times10^{-6}[/tex]

The scientific notation is

[tex]6.0089\times10^{-6}[/tex]

b) convert from scientific notation to standard form:

1)

Consider the notation:

[tex]6.285\times10^{-5}[/tex][tex]Use\text{ }10^{-5}=\frac{1}{100000}.[/tex]

[tex]6.285\times10^{-5}=\frac{6.285}{100000}[/tex]

[tex]=0.00006285[/tex]

The standard form is 0.00006285.

2) Consider the notation.

[tex]7.9\times10^4[/tex][tex]Use\text{ }10^4=10000.[/tex]

[tex]7.9\times10^4=7.9\times10000[/tex]

[tex]=79000[/tex]

The standard form is 79,000.

3) Consider the notation.

[tex]9.008\times10^5[/tex][tex]Use\text{ }10^5=100000.[/tex]

[tex]9.008\times10^5=9.008\times100000[/tex]

[tex]9.008\times10^5=900800[/tex]

The standard form is 900,800.

What is the function g(x) that results when translating the function
f(x)=|x|
to the left 12 units and reflecting it over the x-axis?

g(x) =

Answers

The image of the function after the translation is g(x) = -|x - 12|

How to determine the equation of g(x) after the transformation?

From the question, the given parameters are:

f(x) = |x|

The transformation is given as

Translate the function to the left 12 units and reflect it over the x-axis

Mathematically, this transformation can be represented as

(x, y) = (x - 12, -y)

When represented as a function, we have

g(x) = -f(x - 12)

So, we have

g(x) = -|x - 12|

So, we have the following equation

f'(x) = -|x - 12|

Hence, the equation of g(x) is g(x) = -|x - 12|

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_1) Given: L = √2
M-3√3
N =√16
P = √9
Which expression results in a rational number?
(3) N + P
(4) P+L
(1) L + M
(2) M + N

Answers

The expression that results in rational number is P+N

What is rational numbers?

Any integer that can be expressed as p/q, where q ≠ 0, is referred to as rational.

The form of a rational number, which is a type of real number in mathematics, is p/q when q is not equal to 0.  Examples of rational numbers include 1/2, 1/5, 3/4, and other such values. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1.

Here,  L = √2

M=3√3

N =√16

P = √9

we know [tex]\sqrt{16} =4 , \sqrt{9} =3[/tex]

only P and N are rational numbers.

P+N = 4+3 = 7/1

which is a rational number.

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Did anybody see my question for 24 I really need help

Answers

Answer:

48

hope its right sorryyyy

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Using your notes from the video and the reading, create an argument on what YOU think started the French and Indian War. Be sure to use CER (Claim, Evidence, Reasoning) method when creating your answer. Your answer should have 2 piece of evidence and reasoning;BoldItalicUnderline HELP ASAP Instructions: Identify the type of sequence and write the explicit rule. Use the chemical reaction to answer the question. 4Fe+3O22Fe2O3 What happens to atoms of Fe and O2 during the reaction? (1 point) Identify the nature and point of action of the third force acting on the wheelbarrow.Write down an equation showing the relationship between the three forces Shen runs each lap in 4 minutes. He will run at least 48 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.Write your answer as an inequality solved for n. Read the paragraph below aloud and with expression. Emphasize different words to change the meaning of the passage. Write one or two sentences discussing how the emphasis changes the meaning of the sentence. Imagine a morning in late November. A coming of winter morning more than twenty years ago. Consider the kitchen of a spreading old house in a country town. A great black stove is its main feature; but there is also a big round table and a fireplace with two rocking chairs placed in front of it. Just today the fireplace commenced its seasonal roar. Read the excerpt from act 3, scene 1, of Julius Caesar[ANTONY] First, Marcus Brutus, will I shake with you-Next, Caius Cassius, do I take your hand-Now, Decius Brutus, yours;-now yours, Metellus,-Yours, Cinna;-and my valiant Casca, yours;-Though last, not last in love, yours, good Trebonius.Gentlemen all,-alas, what shall I say?My credit now stands on such slippery groundThat one of two bad ways you must conceit me:Either a coward or a flatterer.That I did love thee, Caesar, O, 'tis true.If then thy spirit look upon us now,Shall it not grieve thee dearer than thy death,To see thy Antony making his peace,Shaking the bloody fingers of thy foes-Most noble! In the presence of thy corse?Mark this and returnWCSa what are the central ideas of this soliloquy? factors affecting flotation A bag contains 80 more red marbles than black marbles. Ifthe ratio of red marbles 9 to 4, how many marbles are in the bag in total? what is cancer explain what a doctor means when he or she says cancer has "metastasized." is a benign tumor cancerous? Provide examples of various types of cancer. Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive integer value. x^2=4(x-9) Which are physical properties (Select all that apply)science N N Which of the following is an equation of line k in the xy-plane above? (A) y=-x-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4 A storage tank 20 m high is filled with pure water. (Assume the tank is open and exposed to the atmosphere at the top.)(a) Find the gauge pressure at the bottom of the tank.(b) Calculate the magnitude of the net force that acts on a square access hatch at the bottom of the tank that measures 0.6 m by 0.6 m.PLEASE HELP ASAP!!! How do I solve this problem 2 5/12 = 3 1/4 + k In your opinion, what group (African American, Native American, Woman, Wealthy White Man, or Poor White man) had the most to lose by going to war with Britain? Explain a fisherman catches one trout from each of two ponds. pond a contains 100 trout and pond b contains 1,000 trout. which population is more affected by the fisherman? group of answer choices pond b; the fisherman is more likely to catch a fish that is undergoing evolution in a bigger population. pond a; fewer fish are able to move into a small pond and find mates. pond b; the process of evolution occurs more slowly in large populations and removing a fish speeds up the process. pond a; the fisherman has a greater likelihood of completely removing alleles from the gene pool by taking a fish from the smaller population. Explain how colonialism and trade have had a significant historical impact on cultural diffusion. in which direction (into or out of the cell) will water flow in cells of escherichia coli (an organism found in your large intestine) suddenly suspended in a solution of 20% nacl? what if the cells were suspended in distilled water? if growth nutrients were added to each cell suspension, which (if either) would support growth, and why? suppose a consumer has preferences between two goods that are perfect substitutes. can you change prices in such a way that the entire demand response is due to the income effect?