what is the domain explain any restrictions

Answers

Answer 1

A function's domain is the set of all possible inputs to the function. Domains can be limited if the function is rational and the denominator is 0 for some x value or values.

What are the 3 domain restrictions?

The square root function, log function, and reciprocal function are the three functions with limited domains. Because you cannot take square roots of negative numbers and produce real numbers, the square root function has a limited domain.

To find the domain restriction of an expression, take the expression's denominator. Put that denominator to zero. Solve the resulting equation for the denominator zeroes. The domain consists of all other x-values.

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Related Questions

Which of the following is a geometric sequence?

A. 7, 4, 1, -2, …

B. 2, 4, 6, 8, …

C. 1, 1/2, 1/4, 1/8, …

D. 1, 1, 2, 3, 5, …

Answers

Answer: C

Step-by-step explanation:

Each term is half the previous term.

Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.

Answers

so discount means 33% of £999 is subtracted from £999 so 33% of 999 is 329.67 so to calculate the discounted price 999-329.67

A linen napkin, in the shape of a square, has sides that are 10 inches long.

If the napkin is folded along the diagonal, whats the length of the diagonal?
round to the nearest tenth.

Answers

Answer: A=187.5,2

Step-by-step explanation:

answer would be 187.5

Laurel appears at Comedy Cafe at a random time between 1:00 and 2:00. Hardy turns up at a random time between 2:00 and 2:30. The probability that Laurel waits for no more than 40 minutes for Hardy can be expressed in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m n$.

Answers

Answer:

i need more info please

Step-by-step explanation:

How many three-digit numbers use only the digits 0,1 and 5

Answers

The number of three digit numbers which use only the digits 0,1, and 5 is; 18.

How many three digit numbers use 0,1 and 5?

Since, it follows from the task content that three digit numbers are to be considered, Hence, it follows that the choice for the first digit is between 1 and 5, for the second number and third number, the choice lies within all three numbers.

On this note, we have;

= 2× 3 × 3.

= 18.

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rationalize the denominator
PLS HELP

Answers

Answer:

x = 5, y = sqrt6, z = 3

Step-by-step explanation:

[tex]\frac{10}{\sqrt{6} } \\\\\frac{(10)(\sqrt{6} )}{(\sqrt{6} )(\sqrt{6}) } \\\\\frac{10\sqrt{6} }{6} \\\\or\\\\\frac{5\sqrt{6} }{3}[/tex]

❄ Hi there,

let us revise the way we rationalize the denominator before we get down to the actual process.

__________

Suppose you had a problem, and you did all the steps, and you arrived at the following answer: [tex]\sf{\dfrac{10}{\sqrt6}}[/tex].

Well, this answer is not in its simplest form, because it has an irrational number in its denominator.

So what we do is we get rid of that irrational number in the denominator  by multiplying the fraction's top & bottom by [tex]\sqrt6[/tex]:

[tex]\sf{\dfrac{10\sqrt6}{\sqrt6\times \sqrt6}}[/tex]

Now we simplify

[tex]\sf{\dfrac{10\sqrt6}{6}}[/tex]

Reduce

[tex]\sf{\dfrac{5\sqrt6}{3}}[/tex]

- - - - -  - - -

According to a secret government report, 1/3 of
all the jelly beans in the world are red. If that
1/3 amounts to 38,567,942 red jelly beans, how
many jelly beans are there in total?

Answers

Proportionately, the total jelly beans in the world will be 115,703,826.

What is a proportion?

A proportion refers to a fraction of a whole.

A proportion is a ratio or a number relationship between two or more values or variables.

The proportion of a whole value can be represented as a fraction, decimal, or percent.

Data and Calculations:

Red jelly beans in the world = 1/3

And 1/3 = 38,567,942

1/1 = 115,703,826 (38,567,942/1/3)

Thus, if 1/3 of the jelly beans in the world is 38,567,942, then the whole jelly beans will be 115,703,826.

Thus, proportionately, the total jelly beans in the world will be 115,703,826 because 1/3 of 115,703,826 is 38,567,942.

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The Random Variable is normally distributed with mean = 98 and standard deviation =
20.41.
On the sampling distribution with n = 81, for what value of the sample mean (X) would have
10% of the possible sample means less than it? Round your answer to 2 decimal places.

Answers

If mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

Given that mean is 98,standard deviation is 20.41,n=81 and significance level be 10%.

We are required to find the value of sample mean.

Because the value of n is greater than 30 so we will use z statistics in the problem.

We know that,

Z=(X-μ)/σ  in which μ is population mean, σ is standard deviation.

Confidence level=1-0.01=0.09 means 90%.

Z value for 90% confidence level be 1.645.

we have to put the value of Z=1.645 , μ=98,σ=20.41 to get the value of X.

1.645=(X-98)/20.41

1.645*20.41=X-98

33.57445=X-98

X=98+33.57445

X=131.57445

Hence if mean is 98, standard deviation is 20.41, n=81 then sample mean will be  131.57445 which would have 10% of the possible mean less than it.

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Q.estimate the area of each polygon in square units.
i cant understand the question can someone help me and provide detailed explanation with the solution. please provide reasons so i can grasp the concept.

Answers

Answer is estimate 12 square units

Step by step
An estimate is a close guess.

To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12.

You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units.

If you had a figure that was NOT on the lines you would estimate the area because you would not have exact measurements.

The area of the polygon is 12 square units.  In mathematics and everyday life, an estimate is an approximate calculation or guess that is close to the actual value but may not be exact.

To make an estimate or guess, you can square off the parallelogram and create a rectangle and add your squares (or multiply 3x4) to = 12": This part explains a method for estimating the area of a parallelogram. It suggests that if you take a parallelogram and "square it off" (convert it into a rectangle by drawing a perpendicular line), you can then find the area of the rectangle, which is easier to calculate. In this case, the dimensions of the rectangle are given as 3 units for the base and 4 units for the height, and the estimated area is 12 square units.

You can use the formula for the exact area using base x height (3x4) you get the same answer of 12 square units": This part emphasizes that the estimation method used in step 2 (multiplying 3 by 4) produces the same result as the exact formula for finding the area of a parallelogram, which is base times height. In this case, both the estimation and the formula give an area of 12 square units.

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If p(a) = 2/3, p(b) = 4/5, and p(anb) = 3/5, what is P( AuB) ( the n is the arc shape direction, so is the u)

Answers

By the inclusion/exclusion principle,

[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]

[tex]P(A\cup B) = \dfrac23 + \dfrac45 - \dfrac35[/tex]

[tex]P(A\cup B) = \dfrac{10}{15} + \dfrac{12}{15} - \dfrac9{15}[/tex]

[tex]P(A\cup B) = \boxed{\dfrac{11}{15}}[/tex]

Which equation gives the lines show on Graph y= 2x+4
y= -1/2x-4
y=1/2x+4
y=2x-4

Answers

the answer is the second one y=1/2x+4

Explain why the triangles are similar, and then find the values of x and y.

Answers

The values of x and y from the figure is 9 and 5 respectively

Similarity theorem of triangle

Two triangles are similar if the ratio of the similar sides is equal to a constant. From the given diagrams;

x/(8+4) = 6/8

x/12 =6/8

8x = 6 * 12

8x = 72

Divide both sides by8 to have:

8x/8 = 72/8

x = 9

Similarly;

10+y/x = 10/6

10+y/9 = 10/6

10+y/9 = 5/3

Cross multiply

3(10+y) = 5(9)

30 + 3y = 45

3y = 45-30

3y = 15

y = 5

Hence the values of x and y from the figure is 9 and 5 respectively

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HELP IM BEING TIMED I NEED THE ANSWER QUICKLY AS POSSIBLE!!
What is the range of the absolute value function below?

Answers

According to the graph

It's a Translated modulus functionIt has vertex at (4,1)

Maximum value is 1

So

Range is

f(x)≤1

Option C

x/4 ÷ 2/3 = 1/5

solve for x

Answers

The value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

Fraction

x/4 ÷ 2/3 = 1/5

x/4 × 3/2 = 1/5

(x × 3) / (4 × 2) = 1/5

3x / 8 = 1/5

cross product

3x × 5 = 8 × 1

15x = 8

x = 8/15

Therefore, value of x from the equation x/4 ÷ 2/3 = 1/5 is 8/15

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Mediciones recientes del fondo del mar que se extiende a lo largo de las crestas a medio océano muestran que la deriva continental es del orden de 4 cm. Suponga que este valor ha sido constante a través del tiempo y considere la distancia actual entre Sudamérica y África como 5000 millas. ¿Cuánto tarda Aproximadamente pangea en fragmentarse?

Answers

Usando proporciones, hay que la pangea tardra aproximademente 20,116,750 años para fragmentar-se.

¿Qué es una proporción?

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

La deriva continental es del orden de 4 cm al año. La distancia actual entre Sudamérica y África es de 5000 millas. En cm, esta distancia es la seguiente:

5000 millas = 5000 x 160934 cm = 80,467,000 cm.

Asi, el tiempo que levará para la pangea fragmentar-se es:

t = 80,467,000/4 = 20,116,750 años

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3. Today, Dahlia folded 29 paper cranes. Now there are 41 paper cranes in class. How many cranes were there in class yesterday? Each paper crane has a length of 10 centimetres. How many centimetres were there total for all the paper cranes?​

Answers

Answer:

There were 12 cranes in class yesterday. For all the cranes, there were a total of 290 centimeters.

Step-by-step explanation:

41-29=12.

29*10=290

please helppp I really don't understand this lol

Answers

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Order the following expressions from least to greatest

(Quick Please)

Answers

square root (3) < square root (pie) < 2

A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, she estimates that 5 fewer students will participate. If the company needs to bring in $6,210 per week to stay in business, what price must be charged for a 1-hour tutoring session to produce this amount of revenue?

Answers

The price that must be charged for a 1-hour tutoring session to produce this amount of revenue is 24.5 dollars

How to solve Word Problem

The first thing to do with word problem is to understand the question. After that, make analysis of the question.

It is given that a A private tutoring company charges $20 for a 1-hour session. Currently, 300 students are each tutored for an hour each week. Since the company is losing money, the owner has decided to increase the price. For each 50¢ increase, That is $20.5 for each students.

If she estimates that 5 fewer students will participate, that is, 295 students, and the company needs to bring in $6,210 per week to stay in business.

Let us assume that 1 hour per day. And there are 7 days in a week.

Divide the money by 7 to know the value per day

6210/7 = 887.14

Now, divide the amount per day by 250 students to know the amount per student per hour

887.14/295 = 3.007

The price that must be charged for a 1-hour tutoring session to produce this amount of revenue should be 20.5 + 4 = 24.5 dollars

Therefore, each student will pay $24.5 per hour

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Fifty people enter a contest in which three identical prizes will be awarded. In how many different ways can the prizes be awarded to the entrants

Answers

There are 117600 ways for the distribution of the prizes.

According to the statement

We have given that the number of people enter in a contest is 50.

And

Number of prizes given identically is 3.

And we have to find that the by how many ways can be prizes be awarded.

So,

Provided that no one can receive more than one prize,

It means The first prize can be given to any of the 50 people, the second to any of the remaining 49, and the third to the remaining of the 48,

Here we use Permutation

Then the possibilities become is

50*49*48= 117600

So there are above written ways to distribute the prizes.

There are 117600 ways for the distribution of the prizes.

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The volume of a cylinder is 100. Another cylinder has twice the height but half the base radius. What is the volume of the second cylinder

Answers

Answer:

50 units³

Step-by-step explanation:

Cylinder volume formula:

V = πr²h

Given:

The first cylinder, has base radius - r and height - h. Its volume is:

V₁ = πr²h = 100

The second cylinder has:

R = r/2 and H = 2h

Its volume is:

V₂ = πR²H = π(r/2)²*(2h) = πr²h/2 = V₁/2

Substitute the value of the first cylinder:

V₂ =  V₁/2 = 100/2 = 50

pls help me..
look at the pic below!!

Answers

Answer:

y = 3(x - 2)² - 5

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

Given equation

y = 3x² - 12x + 7

Convert this to vertex form

y = a(x - h)² + k

Follow the steps

y = 3x² - 12x + 7 =

     3(x² - 4x) + 7 =                                  Factor out 3

     3(x² - 4x + 4) - 3*4 + 7 =                   Complete the square

     3(x - 2)² - 5                                       Simplify

Answer:

  y = 3(x -2)² -5

Step-by-step explanation:

It looks like you want to write the standard-form quadratic ...

  y = 3x² -12x +7

in vertex form.

The process is similar to that of "completing the square."

Steps

Factor out the leading coefficient

Do this for the variable terms only.

  y = 3(x² -4x) +7

Identify the x-term coefficient

The x-term coefficient (inside parentheses) divided by 2 is the opposite of the x-coordinate of the vertex. It is the constant term in the squared binomial of the vertex form. Square this value.

  x coefficient: -4

  binomial constant: -4/2 = -2

  square of this: (-2)² = 4

Add this inside parentheses

To keep the overall equation unchanged, you must also subtract an equal amount outside parentheses.

  y = 3(x² -4x +4) +7 -3(4)

Simplify to vertex form

Write the trinomial in parentheses as a square, and simplify the y-coordinate of the vertex.

  y = 3(x -2)² -5

WILL GIVE BRAINLIEST
The number of lattes sold daily by two coffee shops is shown in the table.


Shop A Shop B
55 36
52 40
50 34
47 39
51 44
48 41
53 40
53 38


Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
Mean for both coffee shops because the data distribution is symmetric
Median for both coffee shops because the data distribution is not symmetric
Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric

Answers

Answer:

It will be a more accurate thing to put it into the mean.

Step-by-step explanation:

Mainly, there is a lot of numbers in the data. So the reason Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric.

Hoped this helped. Please mark me brainliest!

At the movie theatre, child admission is and adult admission is . On Wednesday, tickets were sold for a total sales of . How many child tickets were sold that day

Answers

The child tickets were sold that day is 82.

Given the cost of child admission $6.30 and the cost of adult admission $9.80 and on Wednesday 144 tickets were sold for a total sales of $1124.20.

Let the child tickets are x and adult tickets are y.

On Monday, 144 tickets were sold for a total sales.

x+y=144              ........(1)

Total sales = $1124.20

Need to find the child tickets sold on Wednesday.

Total sales = 6.30x+9.80y

Total sales = $1124.20

So,6.30x+9.80y=1124.20                        .......(2)

Find the value of y from equation (1), we get

x+y-x=144-x

y=144-x

Now, we will substitute the value of y in equation (2) to find the value of x, we get

6.30x+9.80(144-x)=1124.20

Apply the distributive property that is a(b+c)=ab+ac, we get

6.30x+9.80×144-9.80x=1124.20

6.30x+1411.2-9.80x=1124.20

Combine the variable terms on left side, we get

1411.2-3.5x=1124.20

subtract 1411.2 from both sides, we get

1411.2-3.5x-1411.2=1124.20-1411.2

-3.5x=-287

Divide both sides with -3.5x, we get

-3.5x/(-3.5)=-287/(-3.5)

x=82

Therefore, 82 child tickets were sold on Wednesday when cost of child admission $6.30 and the cost of adult admission $9.80.

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On friday , march 16, mr posts beginning checking balance is 80 and his account is created for a deposit is for 50 the same day, several transactions are posted totaling 90 mr posts bank charges a 25 overdraft fee. his bank credits deposits before it post checks. what will mr. posts account balance be at the end of the day?

Answers

Account balance at the end of day is 195.

word problem

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation.

now according to question

initial balance in account on march 16 =80

deposit in account on the same day = 50

overdraft fee charged by bank=25

several transactions amount deposited in bank=90

total amount deposited /available in bank account.

=80+50+90

=220

total amount deducted from account

=25

account balance at the end of day

=220-25

=195

hence answer is 195

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An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers.

Answers

What is sequence ?A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}Sequence and series is one of the basic topics in Arithmetic. An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements. An arithmetic progression is one of the common examples of sequence and series.

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."  

The general form an arithmetic sequence is:

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

The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.

So, the statement provided is True.

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In the triangle below, what is the measure (in degrees) of angle X?
66°
55°
X

Answers

Answer:

59

Step-by-step explanation:

Angle degrees in a triangle add up to 180

66+55+x=180

121+x=180

x=59

Answer

59°

Step-by-step explanation:

A triangle's angles add up to 180°.

So to find the last angle of the shape, you need to add the given angles and then subtract the answer from 180° looking like this:

66° + 55° = 121°

180° - 121° = 59°

A civil engineer is designing a public parking lot for the new town hall. The number of cars in each row should be six less than the number of rows in the lot. The mayor has requested that the new lot should hold twice as many cars as the current parking lot, which has space for 56 cars.

Determine which equation the civil engineer can use to find the number of rows, x, he should include in the new parking lot.

A.
6x2 − 56 = 112
B.
x2 − 6 = 112
C.
x2 − 6x = 112
D.
2x2 − 12x = 112

Answers

The equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

How to determine the equation

Let the number of rows be x

Number of cars in each row = x - 6 = 56

Number of rows for parking lot = 2x

Then,

Number of cars for new parking lot = 2x ( x - 6 = 56)

Expand the expression,

2 ( x - 6 = 56)

2x² - 12x = 112

Thus, the equation which the civil engineer can use to find the number of rows is 2x² - 12x = 112. Option D

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If a person stands 40 ft from a tree and the angle of elevation made from their eyes (5 ft above the ground) to the top of the tree is 47°, how tall is the tree? Round your answer to the nearest foot.

Answers

Using the given information, the height of the tree is 48 ft

Trigonometry

From the question, we are to determine the height of the tree

In the given diagram, the height of the tree is (x + 5) feet

First, we will determine the value of x

tan 47° = x / 40

x = 40 × tan47°

x = 42.89 ft

∴ The height of the tree = (42.89 + 5) ft

Height of the tree = 47.89 ft

Height of the tree ≈ 48 ft

Hence, the height of the tree is 48 ft.

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Alex has 84 quarters and nickels worth a total of $17.80.

Which equation can be used to find q, the number of quarters Alex has?

Answers

The equation which can be used to find the number of quarters and nickels is; n + q = 84, 0.05n + 0.25q = 17.80.

Quarters and nickels

Total coins = 84Total value = $17.80

let

Number of quarters = qNumber of nickels = n

n + q = 84

0.05n + 0.25q = 17.80

From equation (1)

n = 84 - q

Substitute into (2)

0.05n + 0.25q = 17.80

0.05(84 - q) + 0.25q = 17.80

4.2 - 0.05q + 0.25q = 17.80

- 0.05q + 0.25q = 17.80 - 4.2

0.20q = 13.60

q = 13.60 / 0.20

q = 68

Substitute q = 68 into

n + q = 84

n + 68 = 84

n = 84 - 68

n = 16

Therefore, the number of quarters and nickels are 68 and 16 respectively.

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What ishappening to the overall population total?a. the overall population is increasing b.the overall population is decreasing c.there is no change in the overall population d.there is not enough evidence Question 9 of 10If a reader wants to evaluate a text, which is the best question to ask whilereading it? A. How well do elements of the text help the text achieve its goals? B. What elements in this text are ones likewell?to use in my writing asC. How interesting do I find the elements of the text, and do I careabout its goals?D. When did the author write this text, and how did he decide on itsgoals? Marcella wants to earn a total of at least $4,000 per month. For each company, find the least number of office machines she would need to sell each month in order to meet this goal. Show your work. Terrorism has changed some things about the face of war, while other things have stayed the same. As an example of a change, the threat of terrorism has influenced the National Guards training and missions. Now, U.S. civilians are at risk of terrorist threats at home. This situation has caused the National Guard to have to rethink its mission in regard to offering support to local and domestic government and policies. The fact of terrorist threats in the United States has also radically changed some things about how the Coast Guard is trained and what its mission parameters are. In 150 words or more, explain how the threat posed by terrorists has changed some features of Coast Guard training and missions while other features have stayed the same. SCENARIO FOURIn 1959, William Malloy was arrested for gambling by the police in Hartford, Connecticut. Afterpleading guilty, he was sentenced to one year in jail and fined $500. After three months into his jailsentence, Malloy was placed on two years probation. While Mallow was still on probation, aConnecticut Superior Court ordered Malloy to testify about gambling and other criminal activities inHartford County. When Malloy refused, on the grounds that it might incriminate him on othercharges, he was put in jail and held until he was willing to answer questions.What right has been violated?What Amendment in the Bill of Rightsprotects this right? Why should you pursue a Diploma in Electronics and Communication Engineering? A gear wheel with 9 teeth plays into a gear wheel with 27 teeth. When the smaller wheel has made 42 revolutions, how manyrevolutions has the larger wheel made?A) 14B) 16C) 120D) 126Show work please Need help ASAPUse the map to answer the question.(A) In several sentences, summarize the outcome of the 2016 Senate elections in the United States. Identify which party won more states and the regions of the country in which this party had the most victories.(B) In one paragraph, describe the political behavior that contributed to Republican victories in Alabama, Georgia, North Carolina, South Carolina, and Florida.(C) In one paragraph, explain why this chart is either sufficient or insufficient to show whether the 2016 Senate would be more or less likely to confirm appointments made by a Republican president. Construct a dichotomous key to classifying classes of invertebrates without jointed legs : annelids , molluscs , cnidarians , sponges , echinoderms , nematodes , flatworm