The sum of two numbers is eleven. One number is thirty-eight less than six times the other. Find the numbers.

Answers

Answer 1

Answer:

One of the number is 4 while the other is 7

Step-by-step explanation:

The sum of two numbers is eleven

Let the numbers be x and y

X+ y = 11

One number is thirty-eight less than six times the other

X= 6y-38

X+ y = 11

6y-38 +y= 11

6y+y= 11+38

7y=49

Y= 49/7

Y= 7

X+ y = 11

X+7= 11

X= 11-7

X= 4


Related Questions

In the diagram,
AB =BC,AC = CD, and AD
12. Find the
lengths of all segments in the diagram. Suppose you
choose one of the segments at random. What is the
probability that the measure of the segment is greater
than 3? Explain your reasoning.

Answers

Answer:

Probability that the measure of a segment is greater than 3 = 0.6

Step-by-step explanation:

From the given attachment,

AB ≅ BC, AC ≅ CD and AD = 12

Therefore, AC ≅ CD = [tex]\frac{1}{2}(\text{AD})[/tex]

                                  = 6 units

Since AC ≅ CD

AB + BC ≅ CD

2(AB) = 6

AB = 3 units

Now we have measurements of the segments as,

AB = BC = 3 units

AC = CD = 6 units

AD = 12 units

Total number of segments = 5

Length of segments more than 3 = 3

Probability to pick a segment measuring greater than 3,

= [tex]\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}[/tex]

= [tex]\frac{3}{5}[/tex]

= 0.6

Derrick and Samantha are selling tickets for their school musical. Floor seats cost $7.50 and balcony seats cost $5.00. Samantha sells 60 floor seats and 70 balcony seats, Derrick sells 50 floor seats and 90 balcony seats. Write an expression to show how much money Samantha and Derrick have collected for tickets.

Answers

F(x) = 7.50x
B(x) = $5.00x

F(x) = 7.50(90)
B(x) = 5.00(160)

$7.50(90) = $675

$5.00(160) = $800

Solve the equation x2 = 5.

Answers

Answer:

±√5

Step-by-step explanation:

x² = 5

x = ±√5

The solution to the equation [tex]x^2=5[/tex] is [tex]x = \pm \sqrt{5}[/tex].

How to evaluate and solve the given equation?

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

[tex]x^2=5[/tex]

By taking the square root of both sides of the equation, we have:

[tex]x = \pm \sqrt{5}[/tex].

Read more on expression here: brainly.com/question/16729936

#SPJ6

a regular polygon of 2 k + 1 sides has 140 as
size of each interior angle find K​

Answers

Hope this can help.

Which statement is true about the two lines whose equations are given below?
y =
= 3x + 2
y = -4x + 9
A.
The lines are parallel.
B.
The lines are perpendicular.
The lines intersect but are not perpendicular.
C.
D.
The lines coincide.

Answers

Answer:

  C.  The lines intersect but are not perpendicular.

Step-by-step explanation:

The slopes (x-coefficients) of these lines are 3 and -4. They are different, but their product is not -1. Lines with different slopes are distinct lines that will intersect. If the product of their slopes is -1, they are perpendicular.

The lines intersect but are not perpendicular.

Please help. I’ll mark you as brainliest if correct!

Answers

Answer:
Width: 4
Length: 12

Work:
Length=Width times 2 + 4

What is 12 raised to the first power?

Answers

Answer:

12^1 = 12

Step-by-step explanation:

Any number raised to the power of one equals the number itself.

The temperature went from -6°F to -11°F. What was the change in temperature? 17°F -17°F -5°F 5°F

Answers

Answer:it got colder by more than 2 degrees

Answer:

well It would have been a change of -5ºF

what is five added to twice a number​

Answers

2x+5

Step-by-step explanation:

let the number be x

According to the question

2x+5

hope it whould help

The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70% of programmers remain in that position 20% are pro- moted to project manager and 10% are fired (state X). 95% of project managers remain in that position while 5% are fired. How long on the average does a programmer work before they are fired?

Answers

Answer:

it will take a programmer about 16.67 times to work before they are fired

Step-by-step explanation:

From the information given;

The transistion matrix for this study can be computed as:

       P          M         X

P     0.7      0.2        0.1

M     0        0.95     0.05

X      0        0            1

where;

The probability that the programmer remains a programmer = [tex](P *P)[/tex]

The probability that the programmer turns out to be a manager = [tex](P*M)[/tex]

The probability that the programmer is being fired = [tex](P*X)[/tex]

Thus, the required number of years prior to the moment being fired for an employee y(P), for programmer and y(M) for manager is represented by ;

[tex]y(P)=1+0.7y(P)+0.2y(M)[/tex]

[tex]y(M)=1+ 0.95y(M).[/tex]

[tex]0.05y(M)=1[/tex]

y(M) = [tex]\dfrac{1}{0.05}[/tex]

y(M) =20

y(P)=1+0.7y(P)+0.2y(M)

y(P) - 0.7y(P) = 1 + 0.2y(M)

0.3y(P) = 1 + 0.2(20)=1+4

0.3y(P) = 1 + 4

0.3y(P) =  5

[tex]y(P)=\dfrac{5}{0.3}[/tex]

[tex]y(P)=16.67[/tex]

Therefore, it will take a programmer about 16.67 times to work before they are fired

Each ounce of Food I contains 3 g of carbohydrate and 2 g of protein, and each ounce of Food II contains 5 g of carbohydrate and 3 g of protein. Suppose x ounces of Food I are mixed with y ounces of Food II. The foods are combined to produce a blend that contains exactly 73 g of carbohydrate and 46 g of protein.
a. Explain why there are 3x + 5y g of carbohydrate in the blend and why we must have 3x + 5y = 73. Find a similar equation for protein. Sketch the graphs of both equations.
b. Where do the two graphs in part (a) intersect? Interpret the significance of this point of intersection

Answers

Answer:

The answer is below

Step-by-step explanation:

a) Food I contains 3 g of carbohydrate and food II 5 g of carbohydrate. x is the number of ounce of food I while y is the number of ounce of food II.

Therefore, the amount of carbohydrate in food 1 is 3x while that of food II is 5y. Since the blend contains  exactly 73 g of carbohydrate, the total number of carbohydrate in both food I and food II is 73 g. Hence:

3x + 5y = 73                    (1)

Food I contains 2 g of protein and food II 3 g of carbohydrate. Therefore, the amount of protein in food 1 is 2x while that of food II is 3y. Since the blend contains  exactly 46 g of protein, the total number of protein in both food I and food II is 46 g. Hence:

2x + 3y = 46                   (2)

Using geogebra to Sketch the graphs of both equations.

b) The point of intersection is gotten from the graph, this gives x = 11, y = 8.

The point of intersection shows the amount of food I and food II that give the required amount of protein and carbohydrate.

11 ounce of food I and 8 ounce of food II would produce the required amount of protein and carbohydrate

What is the volume of the cube shown?

6 3/4
11 25/64
30 3/8
8 1/64

Please help !

Answers

Answer:

11 25/64 in ^3

Step-by-step explanation:

Volume of a cube is given by

V = s^3

s = 2 1/4 = 9/4

V = (9/4) ^3

  = 729/64

  =11 25/64 in ^3

Simplify the expression.
(2x^2y)^3

Answers

Answer:

=

4

x

4

y

6

Explanation:

(

2

1

x

2

y

3

)

2

Here

2

needs to be multiplied with each term within the bracket:

=

2

1

.

2

x

2

.

2

.

y

3

.

2

=

2

2

.

x

4

.

y

6

=

4

x

4

y

6=

4

x

4

y

6

Explanation:

(

2

1

x

2

y

3

)

2

Here

2

needs to be multiplied with each term within the bracket:

=

2

1

.

2

x

2

.

2

.

y

3

.

2

=

2

2

.

x

4

.

y

6

=

4

x

4

y

6=

4

x

4

y

6

Explanation:

(

2

1

x

2

y

3

)

2

Here

2

needs to be multiplied with each term within the bracket:

=

2

1

.

2

x

2

.

2

.

y

3

.

2

=

2

2

.

x

4

.

y

6

=

4

x

4

y

6=

4

x

4

y

6

Explanation:

(

2

1

x

2

y

3

)

2

Here

2

needs to be multiplied with each term within the bracket:

=

2

1

.

2

x

2

.

2

.

y

3

.

2

=

2

2

.

x

4

.

y

6

=

4

x

4

y

6=

4

x

4

y

6

Explanation:

(

2

1

x

2

y

3

)

2

Here

2

needs to be multiplied with each term within the bracket:

=

2

1

.

2

x

2

.

2

.

y

3

.

2

=

2

2

.

x

4

.

y

6

=

4

x

4

y

6

Step-by-step explanation:

Petra is making necklaces to sell at craft. the hardware for each necklace is 3.75 and each bead costs 0.50. The number of beads Petra needs depends on the design she chooses. which expression gives the total cost to make 30 necklaces.

Answers

Answer:

T=112.5+0.50*b (since there was not a given number of beads)

Can you please please help me with this please it’s so hard and i will give you a branlist

Answers

i think it’s the parallel sides “b”

A square calendar has sides that are 7 inches long. What is the calendar's area?

Answers

Answer:

49

Step-by-step explanation:

7x7=49

Answer:

49

Step-by-step explanation:

7x7=49

students surveyed about birthdays. How many more students were born on monday than friday?
a) 4 students
b) 1 students
c) 2 students
d) 3 students

Answers

C) 2 students
Explanation
Take Monday’s amount and subtract Friday’s
3-1=2

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(​1,6​), endpoint ​(-2​,​1)

Answers

Answer:

(4,11)

Step-by-step explanation:

Given two coordinates (x₁, y₁) and (x₂,y₂), the midpoint of the coordinates is expressed as M(X,Y) = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] where;

[tex]X = \dfrac{x_1+x_2}{2}\ and \ Y = \dfrac{y_1+y_2}{2}[/tex]

Given the midpoint (X, Y) = (1,6) and one end point to be ​(-2​,​1), to get the unknown endpoint (x,y), we will apply the formula above. from the coordinates given X = 1, Y = 6, x₁ = -2 and y₁ = 1

[tex]Given \ X = \dfrac{x_1+x_2}{2}\\1 = \dfrac{-2+x}{2}\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4[/tex]

Similarly to get y;

[tex]Given \ Y = \dfrac{y_1+y}{2}\\6 = \dfrac{1+y}{2}\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11[/tex]

Hence the unknown endpoint (x,y) is (4,11)

The function C(F) =5/9 (F - 32) is used to convert temperature from Fahrenheit (F) to Celsius (C).
The function K(C)= C + 273.15 is used to convert temperature from Celsius (C) to the Kelvin (K) scale. Write a function to convert 77°F to the Kelvin scale.

To express temperature in Kelvin as a function of Fahrenheit, compose the functions as(_*_)(_).

Now, derive the function described above and use it to express 77°F as ___K.

Answers

Answer:

K(F) = 5/9 (F - 32) + 273.15

K(F)=298.15k

Step-by-step explanation:

C(F) =5/9 (F - 32) is used to convert temperature from Fahrenheit (F) to Celsius (C).

C(F) =5/9 (F - 32)

The function K(C)= C + 273.15 is used to convert temperature from Celsius (C) to the Kelvin (K) scale.

K(C)= C + 273.15

K(c) - 273= C

Equating both values of C

K(F) - 273.15=5/9 (F - 32)

K(F) = 5/9 (F - 32) + 273.15

If F = 77°F

K(F) = 5/9 (F - 32) + 273.15

K(F) = 5/9(77-32) + 273.15

K(F) = 5/9(45) +273.15

K(F) = 25+273.15

K(F)=298.15k

Answer:

K

C

F

298.15

Step-by-step explanation:

Find the value of the expression for the given values.
6x-2 for x = -2, x = 6, and x = -5
If x= - 2. then 6x - 2 =
If x = 6, then 6x - 2 =
If x= - 5. then 6x-2=

Answers

Answer:

If x= - 2. then 6x - 2 = -14

If x = 6, then 6x - 2 = 34

If x= - 5. then 6x-2= -32

Step-by-step explanation:

You have to substitute the value of x in the expression.

If x = -2,

6x-2 = 6*(-2) - 2 = -12-2 = -14

If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?

Answers

2x- 6 is 5x + 3

your answwr

What is the value of this expression?
6 + 24 % 3 x 4 %2

Answers

Answer:

22

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

6 + 24 ÷ 3 x 4 ÷ 2

Step 2: Divide

6 + 8 x 4 ÷ 2

Step 3: Multiply

6 + 32 ÷ 2

Step 4: Divide

6 + 16

Step 5: Add

22

The sum of two even consecutive integers is 114. What is the smallest integer?

Answers

Answer:

56

Step-by-step explanation:

The sum of two even consecutive integers is 114.

Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

[tex](2n)+(2n+2)=114[/tex]

Solve for n.

Combine like terms:

[tex]4n+2=114[/tex]

Subtract 2 from both sides:

[tex]4n=112[/tex]

Divide both sides by 4:

[tex]n=28[/tex]

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!

Fruit juice in 4/5 pint cartons is sold by the park in 5/6 pint mugs. How many mugs are in a​ carton?

Answers

Answer:

Number of mugs in cartoon = 24 / 25

Step-by-step explanation:

Given:

Pints of cartoon = 4/5

Pints of mugs = 5/6

Find:

Number of mugs in cartoon

Computation:

Number of mugs in cartoon = Pints of cartoon / Pints of mugs

Number of mugs in cartoon = (4/5) / (5/6)

Number of mugs in cartoon = 24 / 25

If the length of rectangle is 8.26cm and its breadth is 5.5cm, the find the
area of the rectangle

Answers

Answer:

Area of a rectangle= L×B

=8.26cm×5.5cm

=45.43cm square

Answer:

45.43cm squared

Step-by-step explanation:

Length times breadth =

8.26cm x 5.5cm.

8.26cm x 5.5cm = 45.43cm squared.

Using an algorithm is a good way to figure out this question. There are useful websites to teach you about them :)

What is the image point of
(−5,−3) after a translation right 4 units and down 1 unit?

Answers

Answer:

(-1,-4)

Step-by-step explanation:

(-5,-3) if we're moving four units right on the x axis, it would be a bigger number near the center.  Think of it as adding -5 and 4, which would get you -1 for x (-1,x)

Now to get y, we would basically do the same thing except if it's going down, it would be a negative.  We would add both -1 and -3 together to get -4, hence the answer, (-1,-4)

I suggest drawing a graph and doing it yourself, it'll really help you.

(3 + 4i) - (8 -5i) Write answer in standard form a +bi Group of answer choices
A:-5+9i
B:-5 + 9i

Answers

Answer:

[tex]A=-5+9i[/tex]

Step-by-step explanation:

[tex]\left(3+4i\right)-\left(8-5i\right)\\\\\mathrm{Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number}\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3-8\right)+\left(4+5\right)i\\3-8=-5\\4+5=9\\\\=-5+9i[/tex]

Techside Real Estate, Inc. is a research firm that tracks the cost of apartment rentals in Southwest Virginia. In mid-2002, the regional average apartment rental rate was $895 per month. Assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. In a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.
a. Do the sample data enable Techside Real Estate, Inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? The sample mean is $915 and the sample standard deviation is $227.50. Make your decision based on α=0.10.
b. What is the P-value?

Answers

Answer:

1) we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

2) P - value = 0.116435

Step-by-step explanation:

We are given;

Population mean; μ = $895

Sample mean; x' = $915

Population standard deviation; σ = $225

Sample standard deviation; s = $227.50

Sample size; n = 180

Let's state the hypothesis;

Null hypothesis;H0: μ ≤ $895

Alternative hypothesis;Ha: μ > $895

Now, the z-score formula is;

z = (x' - μ)/(σ/√n)

Thus, we are making use of the population standard deviation

z = (915 - 895)/(225/√180)

z = 20/16.7705

z = 1.193

From online p-value from z-score calculator attached, with α = 0.10, one tail, we have;

The P-Value is 0.116435

This is more than the significance level of 0.1, thus we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.15%. They have 500 grams of substance B which decays at a rate of 0.37%. They are trying to determine how many years it will be before the substances have an equal mass.

Answers

Answer:

In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area

Step-by-step explanation:

In the blue area, people live closely because of its 1.Indutrialised area 2. The land is costly. 3.urbanisation In lighter color areas its farther because 1.Village 2.Farming area 3.Less popular rural area

what expression would be equivalent to 4+12? 6(8+6) 12(4+1) 4(44+3) 8(6+4)

Answers

Answer:

12(4+1) i think

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\large\textbf{4 + 12}[/tex]

[tex]\huge\textbf{Convert it to an easier way to}\\\huge\textbf{understand or keep it as it is:}[/tex]

[tex]\large\textbf{= 12 + 4}[/tex]

[tex]\huge\textbf{The answer:}[/tex]

[tex]\large\textbf{= 16}[/tex]

[tex]\huge\textbf{Now, let's see which one of your choices}\\\huge\textbf{are equivalent to your original equation.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\large\textbf{6(8 + 6)}[/tex]

[tex]\large\textbf{= 6(8) + 6(6)}[/tex]

[tex]\large\textbf{= 48 + 36}[/tex]

[tex]\large\textbf{= 84}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{6(8 + 6)}[/tex]

[tex]\large\textbf{= 6(14)}[/tex]

[tex]\large\textbf{= 84}[/tex]

[tex]\large\textbf{84 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\large\textbf{12(4 + 1)}[/tex]

[tex]\large\textbf{= 12(4) + 12(1)}[/tex]

[tex]\large\textbf{= 48 + 12}[/tex]

[tex]\large\textbf{= 60}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{12(4 + 1)}[/tex]

[tex]\large\textbf{= 12(5)}[/tex]

[tex]\large\textbf{= 60}[/tex]

[tex]\large\textbf{60 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\large\textbf{4(44 + 3)}[/tex]

[tex]\large\textbf{= 4(44) + 4(3)}[/tex]

[tex]\large\textbf{= 176 + 12}[/tex]

[tex]\large\textbf{= 188}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{4(44 + 3)}[/tex]

[tex]\large\textbf{= 4(47)}[/tex]

[tex]\large\textbf{= 188}[/tex]

[tex]\large\textbf{188 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option D.}[/tex]

[tex]\large\textbf{8(6 + 4)}[/tex]

[tex]\large\textbf{= 8(6) + 8(4)}[/tex]

[tex]\large\textbf{= 48 + 32}[/tex]

[tex]\large\textbf{= 80}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{8(6 + 4)}[/tex]

[tex]\large\textbf{= 8(10)}[/tex]

[tex]\large\textbf{= 80}[/tex]

[tex]\large\textbf{80 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\text{Therefore, your answer: \boxed{\textsf{None of the above}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Other Questions
How are creditor and investor claims reported on a balance sheet?A) The claims of creditors are liabilities and those of investors are assets.B) The claims of both creditors and investors are liabilities, but only the claims of investors are considered to be long-term.C)The claims of creditors are reported as liabilities while the claims of investors are recorded as stockholders' equity.D)The claims of creditors and investors are considered to be essentially equivalent. I need help with this question 6^2-3*(3^2*2)+5 Look at the "Introduction: 'Step out of the car!'" (pp. 1-13) of the Gladwell book. How is he using one of the rhetorical appeals in this introduction? Write a couple of sentences about how he uses either ethos, pathos, or logos, giving an example or two in a partial direct quote. Remember that you can apply one or more of the ways that the appeal is used from the Thonney book. Which state was NOT a restoration colony? A. New YorkB. Georgia C. New Jersey D. Carolina Generate the first 7 terms of the sequence defined by Q = 3n+ 5. Corporate procurement, also called corporate purchasing, deals with the transactional elements of buying products and services by an organization for its operational and functional needs.a) trueb) false Seven added to the product of 10 and k is less than or equal to 47 create a function f(x) such that f(3)=20 How is a combining of cultures reflected in the song excerpt?The song was sung in English in the colonies.O The Yoruba people were American Indians native to Brazil.O The slaves of Brazil replaced their traditions with Christianity.The words reflect both Christian and traditional African beliefs. You know 16 cups = 1 gallon. Convert 3.5 gallons into cups. i need help with these two questions A solid with a volume of 11cm is placed in a graduated cylinder with 50mL of water. The solid will displace how much water? The period of a pendulum T depends on a constant g and the length of the pendulum ????in a relation given by En su cuaderno o carpeta de trabajo realice la conversin del sistema de numeracin binario a octal segn este ejemplo de manera clara y sencilla de los siguientes nmeros. 110002 11011112 110000012 00101102 11002 Please help! Choose the correct word No puedes rebasar cuando hay una lnea____continuacortada Given directed line segment KM , find the coordinates of L such that the ratioof KL to KM is 1:3. Plot point L. Round to the nearest tenth.K What is the domain for the green segment in the piecewise functionbelow? *y61-81-4/o486- 12-181-24O (-10,10)O (2,10)O 13,10]O (1,9) Complete the Analysis section using formulas with statistical functions. Use named ranges instead of cell references in the formulas. Calculate the average, highest, and lowest values for each of the following:a. Price b. MPG City c. MPG Highway d. Average MPG e. Maintenance/Year f. Registration Fee g. Insurance /Year h. Amount to Borrow i. APR j. Years k. Loan Payment l. Gas m. Maintenance/Month n. Insurance/Month o. Total Monthly quick question please help! What is the net primary productivity of an algal bed if the gross primary productivity in an algal bed is 7 kcal/m2/yr and respiration is 3 kcal/m2/yr?