Mathematics College

please help
answer choices:
A:0.125
B:0.20
C:0.80
D:1.0

Please Help Answer Choices:A:0.125B:0.20C:0.80D:1.0

Answers

Answer 1

9514 1404 393

Answer:

  B:  0.20

Step-by-step explanation:

Green was selected 8 of the 40 times. We expect its probability of selection to be about ...

  8/40 = 1/5 = 0.20 . . . p(green)

Answer 2

Answer:

B 0.2

Step-by-step explanation:

First find out how many marbles are in total

16 + 8 + 6 + 9 + 1 = 40

Then simply divide the number of green marbles by the total.

8 / 40 = 0.2

Related Questions

six times 4 less than three times x

Answers

Answer:

6 (3x-4)

Step-by-step explanation:

putting the words together. Pls trust me

Answer: 18x - 24

In equation form this would be 6(3x-4) then distribute.

Step-by-step explanation:

Cos Milky said it. Milky smart.

Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes

Answers

Answer:

24

Step-by-step explanation:

im an expert but I did this on my calculator

hope this helped tho

Determine whether the underlined number is a statistic or a parameter. Choose the correct statement below. because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a . because the value is a numerical measurement describing a characteristic of a .

Answers

Complete question :

Determine whether the underlined number is a statistic or a parameter.

"In a study of all 4841 students at a college, it is found that 55% own a computer."

Answer:

because the value is a numerical measurement describing a characteristic of a population.

Step-by-step explanation:

The difference between statistic and parameter lies in the fact that, statistics are used in describing the numerical value obtained from a sample of data. While parameter are used to describe the numerical characteristics of a population.

Hence, all students of a college refers to the population(entire students). Therefore, the numerical characteristics obtained from such data would be called a parameter.

A triangle has side lengths of 10,11,15. What type of triangle is it?

Answers

Answer: ACUTE triangle!

Step-by-step explanation:

simplify the above expression, then tell me what rule you used, (product rule, power rule, quotient rule.) then explain how you did the problem

Answers

Answer:

Step-by-step explanation:

You have to use the power rule for this. The way I teach my Algebra 1 students to do this is take everything inside the parenthesis and put it into its own set of parenthesis, and then raise each one to the outside power. One thing at a time makes it not so overwhelming. Like this:

[tex](4)^2(x^5)^2(y^3)^2[/tex]

Now follow the power rule. Multiply the power of each element in the parenthesis by the 2 outside.

[tex](4^1)^2=4^2=16[/tex], then [tex](x^5)^2=x^{10[/tex], and finally, [tex](y^3)^2=y^6[/tex].

Now put it all together to get:

[tex]16x^{10}y^6[/tex]

Vuzile bought 24 marbles lost 1/6 marbles. how many did he lose?​

Answers

Answer:

4 marble lost

Step-by-step explanation:

1/6×24=4

so 4 marble lost

PLS HELP ASAP!!

not sure how to do this or how this works.

Answers

Answer:

d -3

Step-by-step explanation:

The answer is probably D

Which table represents a linear function

Answers

The first table ...

Answer:

the first one

Step-by-step explanation:

its a table increasing by 5 for every 1 thing

like example

5 dollars for every 1 candy bar sold at a fundraiser

Need help please number 3

Answers

3x° = (5x-20)° [Interior Alternate Angle]

=> 3x° = 5x° - 20°

=> 5x° - 3x° = 20°

=> 2x° = 20°

=> x° = [tex]\frac{20°}{2}[/tex]

=> x° = 10°

[tex]\\\\\\[/tex]

HOPE IT HELPS

PLEASE MARK ME BRAINLIEST ☺️

Anna sold 1 tie for every 4 shirts. Which proportion would determine how many shirts she would need to sell along with 16 ties?​

Answers

Answer:

64 shirts

Step-by-step explanation:

The ratio of ties to shirts is 1:4, so if the number of ties was 16, then you would have to multiply 16(number of ties) by 4(number of shirts), 16 x 4=64. therefore the awnser will be 64 shirts. Your welcome

Which statement would be a reasonable prediction based on the scatterplot and trend line? O A box with 10 books should weigh about 2 pounds. A box with 10 books should weigh about 4 pounds. A box with 10 books should weigh about 6 pounds. O A box with 10 books should weigh about 12 pounds.​

Answers

Answer:

D

Step-by-step explanation:

please give brainliest I need five brain to go to next level

Answer:

its b

Step-by-step explanation:

its not d i took a test and got it wrong

Complete the first step in the solution.

8 = n ÷ 3
8⋅ __ = ( n ÷ 3)⋅ __

Answer:

Answers

Answer:

24

Step-by-step explanation:

8=n÷3

8*3=n

n=24

When solving for n It’s 24. Simplify on both sides of the equation isolating the variable .
N=24.

factor x^2-2x-8 step by step please

Answers

Factors of 8
1 and 8
2 and 4

We need to add to -2
We can use +2 and -4

(x + 2)(x - 4)

Check using FOIL
x^2 + 2x - 4x -8
x^2 - 2x - 8 :)

What is the answer for x²+9x-10

Answers

(X-1) (X+10) it should be correct

4/5 divided by 7/10 in fraction form help

Answers

Answer:

Divide 4/5 with 7/10

45 ÷ 710 is 87.

Step-by-step explanation:


There is sales of 40% off of the original price. If a mobile phone has a sale price of $180, what was the original price? Choose the correct answer.
A) $200
B) $280
C) $300
D) 320$

Answers

100%-40%=60%
60%=180
100%=? 180*100:60=300$ c)

Answer:

$300

Step-by-step explanation:

If the phone has a discount of 40% that means it cost 60% of the original price

X= original price (100%)

$180  =  60% of the original price

    X   =  100%

 CROSS MULTIPLICATION

60X   =   180x100

60X =  18000

Divide both sides by 60

X  = 300

PLEASE HELP MEEE!!!!!!
Point J is located at (-2, -5) and Point K is located 5 units right and 9 units up Which measurement is closest to the distance between Point J and Point K?
A. 3.7 units
B. 7.5 units
C. 10.3 units
D. 12 units

Answers

Answer:

Step-by-step explanation:

d^2=(x2-x1)^2+(y2-y1)^2

Here we are told dx=5 and dy=9 so

d^2=25+81

d^2=106

d=10.3 units

Answer:  C) 10.3 units

This value is approximate. This also means that segment JK is roughly 10.3 units.

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

Explanation:

The "5 units right and 9 units up" means we have a right triangle with legs 5 and 9. The hypotenuse is unknown, which I'll call c.

a = 5b = 9c = unknown

Apply the pythagorean theorem. Solve for c.

a^2 + b^2 = c^2

5^2 + 9^2 = c^2

25 + 81 = c^2

106 = c^2

c^2 = 106

c = sqrt(106)

c = 10.2956301 approximately

c = 10.3 approximately

The distance from J to K is roughly 10.3 units

------------------------------------

A slightly different method:

Start at point J (-2, -5) and move 5 units to the right and 9 units up to arrive at K(3, 4)

Let's use the distance formula to find the distance from (-2,-5) to (3,4)

Define the following

(x1,y1) = (-2,-5) which means x1 = -2 and y1 = -5(x2,y2) = (3,4) which means x2 = 3 and y2 = 4

Those values are then plugged into the distance formula

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-3)^2 + (-5-4)^2}\\\\d = \sqrt{(-5)^2 + (-9)^2}\\\\d = \sqrt{25 + 81}\\\\d = \sqrt{106}\\\\d \approx 10.2956301\\\\d \approx 10.3\\\\[/tex]

The distance from J to K is roughly 10.3 units

One thing to point out, as you probably already noticed, is that the distance formula and pythagorean theorem effectively are saying the same thing when computing distances like this. The distance formula is based off the pythagorean theorem. Note the x1-x2 portion which represents the horizontal distance from J to K. This is the "move 5 units right" portion. Then the "y1-y2" is the vertical change in distance, which is the "move 9 units up". Also, we can see that the square root of 106 shows up again; a lot of elements are repeated (just phrased in a slightly different way) from the last section.

Which graph represents the function f (x) = 3 x minus 2 Over x minus 2?

Answers

Answer:

C

Step-by-step explanation:

Christopher works as a translator of
literature. He gets paid different
amounts for translating articles and for
translating book chapters. In January,
he was paid $340 for translating 3 book
chapters and 2 articles. In February,
he was paid $380 for translating 1 book
chapter and 6 articles. How much is
Christopher paid, in dollars, to translate
each article?

Answers

Answer:

50$

Each book is equal to 80 now here's the math

50x2=100 340-100=240/3=80

380-80=300/6=50

This is all coming from a high schooler so I may be wrong however this is pretty basic and if I'm wrong flame me man

A figure was translated 4 units down and 3 to the left then reflected over the y-axis. The figures are

Answers

Answer:

Congruent and similar

Step-by-step explanation:

because you did not change anything about the shape that shape is still the same size and shape just in a different spot

B. Congruent but not similar because translation and reflection does not change the size or shape of the figure

Find the measure of angle w

Answers

Answer: Angle w=90

Step-by-step explanation: A line is 180 degress,so 90 plus w = 180. 180-90 is 90, so w is 90.

Answer:

90

Step-by-step explanation:

There is  perpendicular bisector separating a given angle of 90, and a variable of w

We can assume the other ray is at a 180 degree angle, this means we can find w by using this simple equation; 180 - (given number) = remaining number, in this case, w.

The area of a square screen is 100 cm². Find the side length
of the screen.

Answers

Answer:

10 cm

Step-by-step explanation:

From the question,

Area of a square = (Length)²

A = L²............................ Equation 1

Where A = Area of the screen, L = Length of the Screen

make L the subject of the equation

L = [tex]\sqrt{A}[/tex].................... Equation 2

Given: A = 100 cm²

Substitute into equation 2

L = [tex]\sqrt{100}[/tex]

L = 10 cm

Hence the length of the screen is 10 cm


Form a paragraph proof for the following. Make sure you include all the
explanations.
HELP ASAP PLS

Answers

Answer:

Line BD is Congruent to Line BD due to the Reflexive property. Angle Bad is congruent to angle BCD because of the third angle theorem therefore triangle ABD is congruent to triangle CBD because all angles and sides are congruent

I don't know if that will satisfy your teacher because some prefer different things but that leaves no ground to be inferred and explains everything word for word.

Classifying Quadrilateral

Answers

top right would be rhombus

Answer:

Step-by-step explanation:

Answer 12.9

14.5% of 90 is n. The value of n is 15​

Answers

Answer:

dddddddddddddddddddddddddd

Step-by-step explanation:

dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

LITERALLY GIVING LIKE 30 POINTS OR WHATEVER IM DESPERATE PLEASE I NEED MODULE 4 NOTES FOR FLVS 8TH GRADE PRE-ALGEBRA?? I HAVE A DBA AND NEED NOTES I BEG ITS FOR MRS. MEURER'S CLASS

Answers

Answer:  While I am not in your class and can not unfortunately specifically help with this I can still give you a basic overview of what you need to know in most pre algebra courses and you can hopefully then use this information in the best way possible.

Step-by-step explanation:  Some of the basic pre algebra concepts include:

Knowing your basic addition, subtraction, multiplication, and division.  I am assuming you know how to do this sort of math.  For example, I mean problems such as 5+4 or 10/5, but if you do need help with these just ask me and I can help you further.

Basic variable usage:  This means being able to solve problems such as x + 10 = 15.  I can help walk you through this sort of problem.  The variable (which is usually represented by the letter x) is used as a placeholder for an unknown number that you need to solve for.  You can think of this more simply in the example I gave as What plus 10 is equal to 15.  That might help you get the basics down if you can think of a problem that way.  As you can probably tell now the answer would be 5.  There may be also more advanced problems regarding variables but not all pre algebra classes will include this material so if you need a review in this you can ask me as well.

Another basic concept is the concept of solving equations.  This can also mean using both addition and multiplication within one equation or things of that nature.  These equations can look something like 18 - (5 + 3^2) + 7 and I can help walk you through a problem like this.  An important fact to remember is the order of operations, which is the way in which you must solve more complex equations like this or if you need to think of it another way it can mean the way you break down an equation.  You probably have heard of PEMDAS before and this is the way you can remember the order of operations.  It is an acronym with each of the letters representing an operation.  P = parenthesis E = exponents M = Multiplication D = division A = addition and S = subtraction.  Now we can use this to solve the equation!  First we should start within the parenthesis so lets only look at that portion of the problem for now to keep things simpler.  Inside the parenthesis it said 5 + 3^2  We see addition and exponents within the parenthesis so because of PEMDAS we should start with the exponent.  Exponents just mean the amount of times you need to multiply the base number by itself.  The base number is the number the exponent is "attached" to.  Our base number is 3 and the exponent is 2 which means we should do the following math 3 * 3 which equals 9  Now we can go back to our original problem inside the parenthesis.  In place of the 3^2 we can instead put 9 now as we know its the answer for that part of the problem.  What we have now is 5 + 9  and we can simply add that to get 14.  This means inside the parenthesis we can replace with just the number 14 as we have already solved everything we need for it.  The equation now looks like --> 18 - (14) + 7.  Now what we have left is addition and subtraction.  Remember on PEMDAS how multiplication and division were next to each other along with addition and subtraction?  For these 4 just because they are next to each other does not dictate the other rather when you are dealing with either just multiplication and division in a problem you work left to right and the same goes for addition and subtraction and since our resulting problem only has addition and subtraction left we will simply just work from the left of the equation to the right.  Our problem as of now is 18 - (14) + 7.  18 - 14 = 4 so we can now have the equation be 4 + 7 and after adding we get our answer which is 11!  I hope you were able to follow along with that and my explanations were satisfactory.

Hopefully at least some of this included in your module 4 but if you would elaborate more I would more than happily assist you more so please do not hesitate to reach out :)

Edit for extra information:

https://rb.gy/qslgfv

If you have anymore questions regarding this information if you would still like me to go over equations with inequalities just let me know!

Is an example of money

Answers

Answer:

Gold coins are an example of commodity money. ... Dollar bills are an example of fiat money because their value as slips of printed paper is less than their value as money. Bank money consists of the book credit that banks extend to their depositors.

Step-by-step explanation:

Paper money is an example

Each student needs 2/5 of cup of play dough to build a house how many cups of Play-Doh and waiting for nine students?

Answers

Answer: 3 3/5 cups (decimal form 3.6 cups)

Steps:
2/5 * 9 = 18/5
18/5 = 3 3/5

What is the solution to negative 3 over 7 EndFraction m less-than 21?

Answers

Answer:

the answer is c

Step-by-step explanation:

I promise

A bouncing ball reaches a height of 54 inches at its first peak, 36 inches at its second peak, and 24 inches at its third peak. Which formula represents this scenario?

f(x) = 54(two-thirds) Superscript x
f(x) = 54(two-thirds) Superscript x minus 1
f(x) = Two-thirds(54)x
f(x) = Two-thirds(54)x – 1

Answers

Answer:

f(x) = 54(two-thirds) Superscript x minus 1

Step-by-step explanation:

Given that:

First peak : 36 / 54=2/3

Second peak : 24 / 36 = 2/3

The common ratio here is 2/3 ; which mean each bounce height is 2/3 of previous height

Modeling this using geometric progression :

An=a1r^(n-1)

An = nth term of a geometric progression

a1=first term

r=common ratio = 2/3

n = nth term

a1=54

Substituting into the above formular :

An=54(2/3)^(n-1)

Answer: B

Step-by-step explanation:

Just took the test

Other Questions
Ill cash app you if you help me please if the answer is right drop your cash app when you drop the answer plz Mr. Smith decided to regularly wash his head with an antidandruff shampoo every three days. He began on January 1st, 2017 on Saturday. On what day of the week will he wash his head for the last time in 2017? Read 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. No other bloom was near it, for the bog a short distance below the surface was still frozen, and the water was ice cold. It seemed the most spiritual of all the flower people I had ever met. I sat down beside it and fairly cried for joy.[4] It seems wonderful that so frail and lovely a plant has such power over human hearts. This Calypso meeting happened some forty-five years ago, and it was more memorable and impressive than any of my meetings with human beings excepting, perhaps, Emerson and one or two others. When I was leaving the University, Professor J.D. Butler said, "John, I would like to know what becomes of you, and I wish you would write me, say once a year, so I may keep you in sight." I wrote to the Professor, telling him about this meeting with Calypso, and he sent the letter to an Eastern newspaper [The Boston Recorder] with some comments of his own. These, as far as I know, were the first of my words that appeared in print.[5] How long I sat beside Calypso I don't know. Hunger and weariness vanished, and only after the sun was low in the west I splashed on through the swamp, strong and exhilarated as if never more to feel any mortal care. At length I saw maple woods on a hill and found a log house. I was gladly received. "Where ha ye come fra? The swamp, that awfu' swamp. What were ye doin' there?" etc. "Mony a puir body has been lost in that muckle, cauld, dreary bog and never been found." When I told her I had entered it in search of plants and had been in it all day, she wondered how plants could draw me to these awful places, and said, "It's god's mercy ye ever got out."[6] Oftentimes I had to sleep without blankets, and sometimes without supper, but usually I had no great difficulty in finding a loaf of bread here and there at the houses of the farmer settlers in the widely scattered clearings. With one of these large backwoods loaves I was able to wander many a long wild fertile mile in the forests and bogs, free as the winds, gathering plants, and glorying in God's abounding inexhaustible spiritual beauty bread. Storms, thunderclouds, winds in the woodswere welcomed as friends.The words that Muir uses in his essay reveal that he relates to nature as a(n) emotional professor objective notetaker passionate observer removed reporter Consider the equation y = 4x - 10. Find y if x = 3. What do the remains of Kennewick Man indicate about early migrants to Washington?They migrated over only one thousand years.They came from warm climates.They may have come from islands.They traveled north from Mexico. What can a database designer create to make it easy for people to create records?A. A queryB. A formC. A reportD. A field Evaluate 11.3v + 10.7w when v=7 and w=8 Si no tuviera que ir a la escuela, Luz no.a las seis todos los das.O A. se levantarB. levantabanC. levantaraD. se levantara What is the main feature of primary succession Solve this equation: 10x10=10x10 How does the section "Types of Rocks" prepare the reader for the information in the rest of the text? Use evidence from the text in your response. He is still here (into negative) A person invests 7000 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars? Anybody good at political cartoon in history & know how do #7-9? Math. Find Mid point and fx check the items which are included as an expense for transportation 1. electricity 2. location 3. license and registration 4. insurance 5.monthly payment 6. maintenance 7. fuel 54:39Read the following excerpt from a report about some of the possible reasons college costs are increasing.A major concern related to higher education's business model is that colleges and universities cannot or willnot control their cost increases. In for-profit industries when productivity goes up, salaries usually go up. Thisis different in public education.Based on the excerpt, how is higher education different from for-profit industries?O Salaries in higher education are higher because of business costs.O Salaries in higher education are based on productivity.O Salaries in higher education are lower because of business costs.Salaries in higher education are based on additional factors. A student graphed distance versus time for an object that moves 14 m every 2 seconds. What is the slope of the ling on the graph. Please explain! Please help me will give brainlyest Memories of a MemoryHave you ever witnessed something amazing, shocking or surprising and found when describing the event that your story seems to change the more you tell it? Have you ever experienced a time when you couldn't really describe something you saw in a way that others could understand? If so, you may understand why some experts think eyewitness testimony is unreliable as evidence in scientific inquiries and trials. New insights into human memory suggest human memories are really a mixture of many non-factual things.First, memory is vague. Imagine your room at home or a classroom you see every day. Most likely, you could describe the room very generally. You could name the color of the walls, the floors, the decorations. But the image you describe will never be as specific or detailed as if you were looking at the actual room. Memory tends to save a blurry image of what we have seen rather than specific details. So when a witness tries to identify someone, her brain may recall that the person was tall, but not be able to say how tall when faced with several tall people. There are lots of different kinds of "tall."Second, memory uses general knowledge to fill in gaps. Our brains reconstruct events and scenes when we remember something. To do this, our brains use other memories and other stories when there are gaps. For example, one day at a library you go to quite frequently, you witness an argument between a library patron and one of the librarians. Later, when telling a friend about the event, your brain may remember a familiar librarian behind the desk rather than the actual participant simply because it is recreating a familiar scene. In effect, your brain is combining memories to help you tell the story.Third, your memory changes over time. It also changes the more you retell the story. Documented cases have shown eyewitnesses adding detail to testimony that could not have been known at the time of the event. Research has also shown that the more a witness's account is told, the less accurate it is. You may have noticed this yourself. The next time you are retelling a story, notice what you add, or what your brain wants to add, to the account. You may also notice that you drop certain details from previous tellings of the story.With individual memories all jumbled up with each other, it is hard to believe we ever know anything to be true. Did you really break your mother's favorite vase when you were three? Was that really your father throwing rocks into the river with you when you were seven? The human brain may be quite remarkable indeed. When it comes to memory, however, we may want to start carrying video cameras if we want to record the true picture.Part A and Part B below contain one fill-in-the-blank to be used for all three question responses. Your complete response must be in the format A, B, C including the letter choice, commas, and a space after the commas.Part A:Which of the following best summarizes the main point of the essay "Memories of a Memory"?Fill in blank 1 using A, B, or C. Humans cannot recall their earliest memories accurately. Humans have interesting brains that do many things to memories. Humans have trouble recalling details of spaces.Part BSelect one quotation from the text that supports your answer to Part A. Add your selection to blank 1 using D, E, or J. With individual memories all jumbled up with each other, it is hard to believe we ever know anything to be true. You may understand why some experts think eyewitness testimony is unreliable as evidence in scientific inquiries and trials Research has also shown that the more a witness's account is told, the less accurate it is.Select one quotation from the text that supports your answer to Part A. Add your selection to blank 1 using F, G, or H. New insights into human memory suggest human memories are really a mixture of many non-factual things. The image you describe will never be as specific or detailed as if you were looking at the actual room. In effect, your brain is combining memories to help you tell the story. Bugle Corp. approved a plan of merger with Stanley Corp. One of the determining factors in approving the merger was the strong financial statements of Stanley which were audited by Dennis & Co., CPAs. Bugle had engaged Dennis to audit Stanley's financial statements. While performing the audit, Dennis failed to discover certain instances of fraud which have subsequently caused Bugle to suffer substantial losses. In order for Dennis to be liable under common law, Bugle, at a minimum, must prove that Dennis:Failed to exercise due care.Acted recklessly or with lack of reasonable grounds for belief.Was grossly negligent.Knew of the instances of fraud.