Let A=La 'a] be ] be a real matrix. Find necessary and sufficient conditions on a, b, c, d so that A is diagonalizable—that is, so that A has two (real) linearly independent eigenvectors.

Answers

Answer 1

The necessary and sufficient conditions for A to be diagonalisable are:

The quadratic equation (ad - aλ - dλ + λ^2 - bc = 0) must have two distinct real roots.

These distinct real roots correspond to two linearly independent eigenvectors.

To determine the necessary and sufficient conditions for the real matrix A = [[a, b], [c, d]] to be diagonalizable, we need to examine its eigenvalues and eigenvectors.

First, let λ be an eigenvalue of A, and v be the corresponding eigenvector. We have Av = λv.

Expanding this equation, we get:

[a, b] * [v1] = λ * [v1]

[c, d] [v2] [v2]

This leads to the following system of equations:

av1 + bv2 = λv1

cv1 + dv2 = λv2

Rearranging these equations, we get:

av1 + bv2 - λv1 = 0

cv1 + dv2 - λv2 = 0

This can be rewritten as:

(a - λ)v1 + bv2 = 0

cv1 + (d - λ)v2 = 0

To have non-trivial solutions, the determinant of the coefficient matrix must be zero. Therefore, we have the following condition:

(a - λ)(d - λ) - bc = 0

Expanding this equation, we get:

ad - aλ - dλ + λ^2 - bc = 0

This is a quadratic equation in λ. For A to be diagonalisable, this equation must have two distinct real roots.

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Related Questions

PLZZZ HELP!! BRAINLIEST FOR WHOEVER GETS RIGHT ANSWER
The graphs below have the same shape. What is the equation of the red graph.

Answers

Answer:

2 - x^2

Step-by-step explanation:

use the information provided to write the equation of each circle​

Answers

Answer:

1.

centre(h,k)=(-13,9)

radius (r)=6

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x+13)²+(y-9)²=6²

x²+26x+169+y²-18y+81=36

x²+y²+26x-18y+169+81-36=0

x²+y²+26x-18y +214=0

is a required equation of the circle.

2.

centre(h,k)=(1,-1)

radius (r)=11

we have

equation of the circle is

(x-h)²+(y-k)²=r²

(x-1)²+(y+1)²=11²

x²-2x+1+y²+2y+1=121

x²+y²-2x+2y=121-2

x²+y²-2x+2y=119

is a required equation of the circle.

Find the unit rate.
2 2/5 to 3 3/4

Answers

Answer:

2 2/5=5/5+5/5+2/5=12/5

3 3/4= [(3•4)+3]/4=15/4

(12/5) / (15/4)= 12/5 • 4/15=12•4/5•15=

48/75 kilometers in 1 minute

Step-by-step explanation:

How that this helps! :)

Have a great rest of your day/night!

Which graph represents all the real numbers, , where ≥−2? THIS IS LAST QUESTION PLEASE ANSWER! I WILL GIVE BRAINLYST.

Answers

Answer:

It's the one right under the first one

Which is the proper interpretation of a 95% confidence interval of a proportion of U.S. adults who own a sports car with an upper limit of 27% and a lower limit of 22%? O l am 5% confident the true proportion of U.S. adults who own a sports car is between 22% and 27%. I am 95% confident the sample proportion of U.S. adults who own a sports car is between 22% and 27%. I am 95% confident the true proportion of U.S. adults who own a sports car is between 22% and 27%. o I am 5% confident the sample proportion of U.S. adults who own a sports car is between 22% and 27%.

Answers

There is a high level of confidence that the true proportion lies within the interval of 22% to 27%

The proper interpretation of a 95% confidence interval of a proportion of U.S. adults who own a sports car with an upper limit of 27% and a lower limit of 22% is:

I am 95% confident that the true proportion of U.S. adults who own a sports car is between 22% and 27%.

This interpretation accurately conveys the meaning of a confidence interval. It means that if we were to take multiple random samples and calculate 95% confidence intervals using the same methodology, approximately 95% of those intervals would contain the true proportion of U.S. adults who own a sports car. Therefore, there is a high level of confidence that the true proportion lies within the interval of 22% to 27%.

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Ben rolls a number cube 50 times. He records the result of each roll in the table below.
RESULTS OF ROLLING NUMBER CUBE
Outcome 1 2 3 4 5 6
Frequency 7
6
5
11
10
11
Based on the data, which statement is true?
Ben will roll an even number about 250 times if the number cube is rolled 500 times.
Ben will roll an even number about 220 times if the number cube is rolled 500 times.
Ben will roll an even number about 700 times if the number cube is rolled 1,000 times.
Ben will roll an even number about 560 times if the number cube is rolled 1,000 times.

Answers

Answer:

picture ?

Step-by-step explanation:

Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function f(x) = 2ex + e6x n=0 TABLE 1 | l = Sx" = 1 + x + x2 + x3 + . Important Maclaurin Series and Their Radii of Convergence R 1 no n! 2n+1 otsin x = n=0(-1)" (2n + 1).-x-31+51-71 R=0 0 2n+1 R 1 -0ntl k(k-1) (1+x)" = (k)x" = 1 +kx + k(k-1)(k-2) , x3 + , R=1

Answers

The  radius of convergence for the Maclaurin series of f(x) is R = 1.

To obtain the Maclaurin series for the given function f(x) = 2ex + e6x, we can use the Maclaurin series expansions of the exponential function. The Maclaurin series for ex is given by e^x = Σ(x^n/n!) from n=0 to infinity, with a radius of convergence of R = ∞.

Using this, we can rewrite the given function as f(x) = 2e^x + e^6x. Substituting the Maclaurin series expansion of ex into the first term and the Maclaurin series expansion of e^6x into the second term, we get:

f(x) = 2(Σ(x^n/n!)) + (Σ((6x)^n/n!))
= 2Σ(x^n/n!) + Σ((6^n)(x^n)/n!)

Now we can combine the two series by collecting like terms and coefficients. The resulting Maclaurin series for f(x) is:

f(x) = Σ((2/n! + (6^n)/n!)(x^n))

The radius of convergence of this series will be determined by the smaller of the radii of convergence of the individual series used, which is R = 1 for the series of ex and R = 1 for the series of e^6x. Therefore, the radius of convergence for the Maclaurin series of f(x) is R = 1.

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pls solve this
(-21) x [(-4) + (-6)] = [(-21) (-4)] +[(-21)×(-6)]​

Answers

Answer:

ree kid it is 3409,3567

Step-by-step explanation:

Can someone help me with this. Will Mark brainliest . Need answer and work/explanation. Thank you.

Answers

Answer:

Hope it helps...

Step-by-step explanation:

Write an equation in terms of x and y for the function that is described by the given characteristics. a cosine curve with a period of , an amplitude of 1, a left phase shift of , and a vertical translation down by 9/2 of a unit.

Answers

The equation for the described function can be written as:

y = cos(x - π) - 9/2

Let's break down the components of the equation:

The cosine function, cos(x), produces a periodic wave with an amplitude of 1.

The period of the cosine curve is determined by the coefficient in front of the angle, which is 1 in this case. A period of 1 corresponds to one complete cycle of the cosine curve.

The left phase shift of π shifts the entire curve to the right by π units.

The vertical translation down by 9/2 units shifts the entire curve downwards by 9/2 units.

Therefore, the equation y = -cos(x - π) - 9/2 represents a cosine curve with the given characteristics.

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MATH
NATION
The data from a survey of ages of people taking an exercise class was skewed to the left.
Part C: The box plot represents the data. Calculate the appropriate measure of spread.
Answer choices:
A. IQR= 45
B. IQR= 13
C. Standard deviation = 8
D. Standard deviation=55

Answers

Answer:

IQR=13 im pretty sure

Step-by-step explanation:

The measure interquartile range is 13 option (B) IQR= 13 is correct.

What is the box and whisker plot?

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

We have a box plot, and the data from a survey of ages of people taking an exercise class was skewed to the left.

We know on the left side skewed has more data on the right and on the left side, there are fewer data.

From the dot plot, the end point is not given, so we are assuming the end point is 58.

IQR = 58 - 45 = 13

Thus, the measure interquartile range is 13 option (B) IQR= 13 is correct.

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WHAT IS THE SLOPE IF I HAVE (-3,5) AND (4,-5)

Answers

Answer:

-10/7

Step-by-step explanation:

Use slope formula

[tex]\frac{y2-y1} {x2-x1}[/tex]

x1= -3

y1 = 5

x2 = 4

y2 = -5

[tex]\frac{-5-5}{4--3}[/tex]

[tex]\frac{-5 + -5}{4 +3}[/tex]

[tex]\frac{-10}{7}[/tex]

which point is on the line that passes through point h and is perpendicular to line fg?

Answers

The point on the line that passes through point H and is perpendicular to line FG is (–6, 10).

First, we need to find the slope of line FG. The slope of a line can be calculated by dividing the change in the y-coordinate by the change in the x-coordinate. In this case, the change in the y-coordinate is 10 and the change in the x-coordinate is 3, so the slope of line FG is 10/3.

Since the lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of 10/3 is -3/10.

Now, we need to find the equation of the line that passes through point H and has a slope of -3/10. The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, we know that m = -3/10 and the y-coordinate of point H is 10. Plugging these values into the equation, we get y = -3/10*x + 10.

To find the x-coordinate of the point we are looking for, we can substitute in the y-coordinate of point H. 10 = -3/10*x + 10, so x = –6.

Therefore, the point on the line that passes through point H and is perpendicular to line FG is (–6, 10).

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please help me ......​

Answers

Answer:

no solution

Step-by-step explanation:

which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p qi)i p = 3, q = 7 p = –3, q = 7 p = 3, q = –7 p = –3, q = –7

Answers

The values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

Let's expand the expression:

(3 - 7i)(p + qi)i = (3 - 7i)(pi - q)

Using the distributive property, we have:

= 3pi - 7pi^2 - 3qi + 7qi^2

Since i^2 is equal to -1, we can substitute -1 for i^2:

= 3pi - 7p - 3qi - 7q

Now, equating the imaginary part to 58i:

-7p - 7q = 58

Dividing both sides by -7:

p + q = -8

From the given options, only p = 3 and q = -7 satisfy this equation:

3 + (-7) = -4

Therefore, the values p = 3 and q = -7 would make the expression (3 – 7i)(p + qi)i equal to 58i.

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2
Select the correct answer from each drop-down menu.
Consider polynomial function f.
f(x) = (1 - 1)?(1 + 3)3 (+ 1)
Use the equation to complete each statement about this function.
The zero located at x = 1 has a multiplicity of , and the zero located at x = -3 has a multiplicity of
The graph of the function will touch, but not cross, the x-axis at an x-value of
Reset
Next

Answers

Answer:

2 of the 3 answers in picture

Step-by-step explanation:

Answer:

The answers are 2, 3, and 1 only

Step-by-step explanation:

This is the correct answer for plato users

which statement best explains why ben uses the width hi to create the arc at j from point k?

Answers

By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.

Which statement best explains why Ben uses the width BI to create the arc JK from point E?

A.  ∠DEF ≅ ∠ABC when BH = EK, BI = JK, and HI = EJ.

B.  BI = JK when ∠DEF ≅ ∠ABC.

C.  BI = EJ when ∠DEF ≅ ∠ABC.

D.  ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

The statement Ben explains why Ben uses the width BI to create the arc JK from point E is  ∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

The correct option is (D).

Ben ensuring that for making an arc JK,

BH = EJ

BI = EK

HI = JK

These are the three congruent corresponding sides for making an arc.

then, he will use the congruence criteria to ΔDEF ≅ ΔABC.

By using the property of CPCTC (corresponding parts of congruent triangles are congruent) he can prove ∠DEF ≅ ∠ABC.

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Which statement best explains why Ben uses the width BI to create the arc JK from point E.

a converging lens with a focal length of 6.70 cmcm forms an image of a 4.80 mmmm -tall real object that is to the left of the lens. the image is 1.50 cmcm tall and erect.

Answers

A converging lens with a focal length of 6.70 cm forms an erect image of a 4.80 mm tall real object positioned to the left of the lens. The resulting image is 1.50 cm tall.

A converging lens is a lens that bulges in the middle and causes light rays to converge. In this case, the lens has a focal length of 6.70 cm, which means that parallel rays of light incident on the lens will converge to a point 6.70 cm away from the lens. The object, positioned to the left of the lens, has a height of 4.80 mm. When the light rays from the object pass through the lens, they refract and intersect at a point to form the image. The image formed is erect, meaning it is in the same orientation as the object. The height of the image is 1.50 cm.

The magnification of the image can be calculated using the formula: magnification = height of image / height of object. In this case, the magnification is 1.50 cm / 4.80 mm. To convert the height of the object to centimeters, we divide 4.80 mm by 10, which gives us 0.48 cm. Therefore, the magnification is 1.50 cm / 0.48 cm, which equals approximately 3.125.

Since the image is erect and the magnification is greater than 1, we can determine that the image is larger than the object. The positive magnification indicates that the image is virtual, which means it cannot be projected onto a screen. The image is formed on the same side of the lens as the object, which is the left side in this case. The image distance can be calculated using the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Since the image is formed on the same side as the object, the object distance is negative (-u). By plugging in the values, we can solve for the image distance. However, additional information, such as the object distance, would be needed to calculate the exact position of the image.

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Similar to the univariate t-test, the bivariate t-test

a. requires ratio or interval data.
b. assumes that samples are drawn from populations with normal distributions.
c. is especially helpful when the sample size is large (n>80).
d. is useful when the population standard deviation is known.
e. All of the above

Answers

Similar to the univariate t-test, the bivariate t-test has all of the mentioned characteristics, so, E. All of the above.

What are the similarities?

The univariate and bivariate t-tests are different in the fact that while one measures only one variable, the other measures two variables.

The similarities between these tests include the fact that they both require ratio or interval data, they are both drawn from populations with normal distributions and they are useful for analyzing large sample sizes. Also, the two tests ate useful when the population's standard deviation is known.

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The ages of student volunteers at an event are: 13, 11, 12, 15, 16, 11, 12, 14, 15,
and 11. Find the median *

Answers

Answer:

12.5

Step-by-step explanation:

Median = middle number
Put the values in order from least to greatest

11, 11, 11, 12, 12, 13, 14, 15, 15, 16
Which number is in middle?
12 and 13 so find what’s in between

Solution: 12.5


HELP ME FIND AREA I WILL MARK BRAINLEST

Answers

Answer:

472

Step-by-step explanation:

break it up into two rectangles

1) 12x18=216 in

2) 8x32=256

Hope this helped

Answer:

472 in²

Step-by-step explanation:

The figure is composed of 2 rectangles , then

area = area of lower rectangle + area of upper rectangle, that is

area = (8 × 32) + (12 × 18) = 256 + 216 = 472 in²

PLS PLS HELP WILL MARK BRAINLIEST

Answers

Answer:

d: 83

e: 97

f: 83

Step-by-step explanation:

d: We first have to find out f, so f and d can be alternate interior angles, which means they can be congruent to each other.

e: e is a vertical angle to the given angle, which means they are congruent, making it also 97 degrees.

f: f is a supplementary angle to the given angle, which means we can subtract 97 from 180 to give us 83.

Going back to angle d, now that we know f is 83 degrees, then d is an alternate interior angle, so d=f, meaning d is also 83 degrees.

Hope this helps! :)

21) Michelle has just been informed that her cell phone plan will be increasing in price. Her new pricing
plan has a flat fee of $25.00 per month, plus a cost of $0.09 per minute of usage. Based on her budget,
Michelle has determined she can only afford to use a maximum of 209 minutes per month. Based on
this information, what is the highest amount Michelle will pay for her cell phone per month?
a) $18.81
b) $5.23
c) $43.81
d) $25.09

Answers

Answer:

c) $43.81

Step-by-step explanation:

= $25.00 + ($0.09 × 209)

= $25.00 + $18.81

= $43.81

An angle measures 52° more than the measure of its complementary angle. What is the measure of each angle?

Answers

Answer:
First angle is 71, and the other is 19

A complementary angle is 90, so 71 + 19 = 90, while having a 52 degree difference

identify the vertical asymptote(s) of each function. check all of the boxes that apply. x = -8 x = -2 x = -1 x = 1 x = 2 x = 8

Answers

The correct boxes to check are x = 1 and x = 2.

To identify the vertical asymptotes of the function f(x) = (x - 8) / ([tex]x^{2}[/tex]- 3x + 2), we need to determine the values of x for which the denominator of the function becomes zero. These values will give us vertical asymptotes.

Breaking the denominator into the factors :

[tex]x^{2}[/tex] - 3x + 2 = (x - 1)(x - 2)

Setting the denominator equal to zero:

x - 1 = 0 --> x = 1

x - 2 = 0 --> x = 2

So, the vertical asymptotes of the function are:

x = 1 and x = 2.

Now, let's check for diffrent values of x:

x = -8 (This is not a vertical asymptote as it is not related to the function's denominator.)

x = -2 (This is not a vertical asymptote as it is not associated with the function's denominator.)

x = -1 (This is not a vertical asymptote as it is not related to the function's denominator.)

x = 1 (This is a vertical asymptote.)

x = 2 (This is a vertical asymptote.)

x = 8 (This is not a vertical asymptote as it is not related to the function's denominator.)

Therefore, the correct boxes to check are x = 1 and x = 2.

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The correct question is given below -

Identify the vertical asymptote(s) of each function. Check all of the boxes that apply. f(x)=x-8/[tex]x^{2}[/tex]-3x+2

x = -8

x = -2

x = -1

x = 1

x = 2

x = 8

Answer:

D and E for the first one. B and D for the second one

Step-by-step explanation: edg is stinky, i hope this helped a little

19. Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left. What was the weight of each bag? Use a tape diagram and show your calculations. Focus

Answers

The weight of each bag of the mixture can be determined by using a tape diagram. Given that Linda mixed 5.15 lb of cashews with 4.32 lb of pistachios, and after filling up 6 bags that were the same size with the mixture, he had 0.05 lb of nuts left.

A tape diagram is a bar model that is used to represent fractions and ratios visually. It is useful when comparing different quantities that are related to each other.Tape DiagramTo solve the problem using a tape diagram, we begin by representing the total weight of the mixture and the weight of each bag using a single length unit. For example, we can choose 1 inch to represent the weight of 1 pound.

In this case, we would represent the total weight of the mixture as 5.15 + 4.32 = 9.47 inches. Next, we divide the total length by the number of bags to find the length of each bag. If the total length of the mixture is 9.47 inches and there are 6 bags, then the length of each bag is:9.47 ÷ 6 = 1.578 inches. Finally, we convert the length of each bag back to pounds by multiplying by the weight of 1 pound, which is 1 inch in our tape diagram. Thus, the weight of each bag is:1.578 × 1 = 1.578 lb. Therefore, the weight of each bag of the mixture is 1.578 lb.

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In the June 1986 issue of Consumer Reports, some data on the calorie content of beef hot dogs are given. Here are the numbers of calories in 20 different hot dog brands: 186, 181, 176, 149, 184, 190, 158, 139, 175, 148, 152, 111, 141, 153, 190, 157, 131, 149, 135, 132. Assume that these numbers are the observed values from a random sample of independent normal random variables with standard deviation o= 4 calories. Find a 90% confidence interval for the mean number of calories u.

Answers

The 90% confidence interval for the mean number of calories is 155.3 to 158.4

Finding a 90% confidence interval for the mean number of calories u.

From the question, we have the following parameters that can be used in our computation:

The dataset

The mean is calculated as

x = sum/count

So, we have

x = (186 + 181 + 176 + 149 + 184 + 190 + 158 + 139 + 175 + 148 + 152 + 111 + 141 + 153 + 190 + 157 + 131 + 149 + 135 + 132) / 20

x = 156.85

Calculate the margin of error using

E = t * σ/√n

Where t = 1.729 i.e. the critical value

So, we have

E = 1.729 * 4/√20

Evaluate

E = 1.55

The confidence interval is then calculated as

CI = x ± E

So, we have

CI = 156.85 ± 1.55

Evaluate

CI = 155.3 to 158.4

Hence, the 90% confidence interval for the mean number of calories is 155.3 to 158.4

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A recipe for cooking rice indicates that 14 cups of boiling water are needed for 8 cups of rice.

if henri has 28 cups of boiling water how much cups of rice should he add


(WILL GIVE BRAINLIST FOR BEST ANSWER!)

Answers

Hello!

This is a question about ratios and relating them to multiples of the ratio.

We are given that a recipe for cooking rice requires 14 cups of boiling water for every 8 cups of rice.

Then we are asked how many cups of rice are needing to be added if we have 28 cups of boiling water.

Since 28 is two times 14, and assuming that this ratio is proportional, we can multiply the cups of rice by 2 to find the equal ratio.

That means that 16 cups of rice should be added if we have 28 cups of boiling water.

In terms of ratios, we can set up the following proportion.

[tex]\frac{14}{8}=\frac{28}{x}[/tex]

Then here, we can cross multiply and solve for [tex]x[/tex].

[tex]14x=224[/tex]

[tex]x=16[/tex]

Hope this helps!

I need help with this ( see image). Please show workings.​

Answers

Answer:

32. (E)stopped at 2pm

33. (A)

Step-by-step explanation:

32. on the graph you go across the x axis and find where the straight line starts and look for the time

33. look at the y-axis and see what line and the number it is on

Please help.
Is algebra.

Answers

Number 6 is letter “C”
Other Questions
In a longitudinal wave the particles are pushed _________________.A.In and out.B.Round and round.C.Over the edge.D.Back and forth. I WILL GIVE BRAINLIESTDo you think Jackson was right to initiate the use of the spoils system to appoint government officials? support your opinion. What is the area of a rectangle whose length is 4 2/3 cm and width is 8 cm? Need answer please !! 3. A runner sprints 50 ft each day for 7 days. How many inches does she sprint during this week? (Again please hurry) how do you find the radius when given the volume and height? Apple manufactures 20 laptops with four distinct components: processor, memory, hard drive and motherboard. Under the disaggregate option, Apple designs specific components for each laptop, resulting in 20x4=80 distinct components. Under the common-component option, Apple designs laptops such that two distinct processors, two distinct memory units, two distinct hard drives and two distinct motherboards can be combined to create 20 laptops. Monthly demand for each of the 20 laptops is independent and normally distributed, with a mean of 10,000 and a standard deviation of 2,000. The replenishment lead time for each component is one month. Apple is targeting a CSL of 95 percent for component inventory.a. Evaluate the safety inventory requirements with and without the use of component commonality.b. Calculate the percentage of safety inventory that was reduced by using component commonality. Solve.t8.4=1.5=Help plzzzz bdaIf mza = 2.m2b, mzc = 60', and the right angles are labeled in the figure, which of the followingproduce an acute angle? Select all that apply find the area of the triangle La semana pasada, yo ________ cmo llegar a las cascadas. saban sabas supe supiste Find the formula for the nth term in this arithmetic sequence a1=0 a2=.5 a3=1 a4=1.5 Read the excerpt from John Muir's "Calypso Borealis" and answer the question. [1] After earning a few dollars working on my brother-in law's farm near Portage [Wisconsin], I set off on the first of my long lonely excursions, botanising in glorious freedom around the Great Lakes and wandering through innumerable tamarac and arbor-vitae swamps, and forests of maple, basswood, ash, elm, balsam, fir, pine, spruce, hemlock, rejoicing in their bound wealth and strength and beauty, climbing the trees, revelling in their flowers and fruit like bees in beds of goldenrods, glorying in the fresh cool beauty and charm of the bog and meadow heathworts, grasses, carices, ferns, mosses, liverworts displayed in boundless profusion. [2] The rarest and most beautiful of the flowering plants I discovered on this first grand excursion was Calypso borealis (the Hider of the North). I had been fording streams more and more difficult to cross and wading bogs and swamps that seemed more and more extensive and more difficult to force one's way through. Entering one of these great tamarac and arbor-vitae swamps one morning, holding a general though very crooked course by compass, struggling through tangled drooping branches and over and under broad heaps of fallen trees, I began to fear that I would not be able to reach dry ground before dark, and therefore would have to pass the night in the swamp and began, faint and hungry, to plan a nest of branches on one of the largest trees or windfalls like a monkey's nest, or eagle's, or Indian's in the flooded forests of the Orinoco described by Humboldt. [3] But when the sun was getting low and everything seemed most bewildering and discouraging, I found beautiful Calypso on the mossy bank of a stream, growing not in the ground but on a bed of yellow mosses in which its small white bulb had found a soft nest and from which its one leaf and one flower sprung. The flower was white and made the impression of the utmost simple purity like a snowflower In a paragraph of 35 sentences, explain Hi please zoom in to see it clearly, uh you dont have to answer them all but it would be nice !!! (no links please) :D Ina paragraph consisting of several sentences, please identify theprimary sources of bank income and expenses. How does Antigone justify breaking the law after she is caught? What is the mode of the set of data points given below? 1 15 12 6 12 9 12 3 6 12 15 9 15 12 15 Marking as brainiest Each student in a class recorded how many books they read during thesummer. Here is a box plot that summarizes their data. What is the Rangeof the data?. 810 1 18number of booksYour answerThis is a required question six and fifty-three hundredths as a decimal-Yes, I'm D-U-M-B! can anyone tell me how this puzzle goes together please