Mathematics College

Sea grass grows on a lake. The rate of growth of the grass is ????????/???????? = ????????, where ???? is a constant.
a. Find an expression for ????, the amount of grass in the lake (in tons), in terms of ????, the number of years, if the amount of grass is 100 tons initially, and 120 tons after one year.
b. In how many years will the amount of grass available be 300 tons?
c. If fish are now introduced into the lake and consume a consistent 80 tons/year of sea grass, how long will it take for the lake to be completely free of sea grass?

Answers

Answer 1

Answer:

[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]

[tex](b)\ t = 6[/tex]

[tex](c)\ t = 1.7[/tex]

Step-by-step explanation:

Given

[tex]G_0 = 100[/tex] --- initial

[tex]G(1) = 120[/tex] --- after 1 year

[tex]r \to rate[/tex]

Solving (a): The expression for g

Since the rate is constant, the distribution of G follows:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(1) = 120[/tex] implies that:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]120 = G_0 * e^{r*1}[/tex]

Substitute [tex]G_0 = 100[/tex]

[tex]120 = 100 * e^{r[/tex]

Divide both sides by 100

[tex]1.2 = e^{r[/tex]

Take natural logarithm of both sides

[tex]\ln(1.2) = \ln(e^r)[/tex]

[tex]0.1823 = r[/tex]

[tex]r = 0.1823[/tex]

So, the expression for G is:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(t) = 100 *e^{0.1823t}[/tex]

Solving (b): t when G(t) = 300

We have:

[tex]G(t) = 100 *e^{0.1823t}[/tex]

[tex]300 = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]3 = e^{0.1823t}[/tex]

Take natural logarithm

[tex]\ln(3) = \ln(e^{0.1823t})[/tex]

[tex]1.099 = 0.1823t[/tex]

Solve for t

[tex]t = \frac{1.099}{0.1823}[/tex]

[tex]t = 6[/tex] --- approximated

Solving (c): When there will be no grass

Reduction at a rate of 80 tons per year implies that:

[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]

To solve for t, we set G(t) = 0

[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]

Rewrite as

[tex]80t = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]0.8t = e^{0.1823t}[/tex]

Take natural logarithm of both sides

[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]

[tex]\ln( 0.8t) = 0.1823t[/tex]

Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]

[tex]t = 1.7[/tex]

Related Questions

What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta

Answers

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]

(2x - y + 3) (2x - y - 3)using identities ​

Answers

Step-by-step explanation:

(2x-y+3)(2x-y-3)=

4x²-2xy-6x-2xy+y²+3y+6x-3y-9=

4x²-4xy+y²-9=

(2x-y)²-9

A driver leaves home for a business trip and drives at a constant speed of 60 miles per hour for 2 hours. Her car gets a flat tire, and she spends 30 minutes changing the tire. She resumes driving and drives at 30 miles per hour for the remaining one hour until she reaches her destination. For what interval of time would a graph that models the driver's distance from home consist of a horizontal line?​

Answers

Answer:

The 30 minutes that she is changing the flat

Step-by-step explanation:

find f(1)' If u know that
g(1)=1 , g'(1)= -1
h(1)= -2 , h'(1) 3
​

Answers

Step-by-step explanation:

[tex]f(x) = g(x)h(x)[/tex]

Taking the derivative of f(x), we get

[tex]f'(x) = g'(x)h(x) + g(x)h'(x)[/tex]

Then [tex]f'(1)[/tex] becomes

[tex]f'(1) = (-1)(-2) + (1)(3) = 5[/tex]

QUESTION 1
Determine the work done by the force
F=31+] + k in moving an object through
displacement T = 7 -7 -K​

Answers

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is

W = F • r cos(θ)

The cosine of the angle between the vectors can be obtained from the dot product identity,

a • b = ||a|| ||b|| cos(θ)   ==>   cos(θ) = (a • b) / (||a|| ||b||)

so that

W = (F • r)² / (||F|| ||r||)

For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is

W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==>   W ≈ 5.12 J

(assuming F and r are measured in Newtons (N) and meters (m), respectively).

..A tin of paint was 2/3 litres full. Tom used 1/2 of
the paint to paint his table. How much was left ?

Answers

Multiply the amount of paint started with by the amount used:

2/3 x 1/2 = (2 x 1) / (3 x 2) = 2/6 = 1/3

There is 1/3 liter left

PLEASE HELP ME WILL MARK IF YOU CAN HELP

Answers

Answer:

d = 52°

Step-by-step explanation:

The two sides with little marks are congruent.

That means that the opposite angles are congruent.

One angle measures 76°.

The other to angles measure d each.

d + d + 76 = 180

2d + 76 = 180

2d = 104

d = 52

Find the coefficient of the t4
term in the expansion of
(4t – 375
a

Answers

9514 1404 393

Answer:

  -3840t^4

Step-by-step explanation:

The k-th term, counting from k=0, is ...

  C(5, k)·(4t)^(5-k)·(-3)^k

Here, we want k=1, so the term is ...

  C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4

__

The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.

A fair charges an admission fee of 4 dollars for eacg person. Let C be the cost of admission in dollars for P people. Write an equation relating C to P. Then graph your equation using the axes

Answers

Answer:

Equation is C = 4P

Graph is shown below

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

Explanation:

The equation is C = 4P since it costs $4 per person. We just multiply 4 with the number of people (P) to get the cost (C).

Let's say 0 people show up, so that means C = 4*P = 4*0 = 0

The input P = 0 leads to the output C = 0. This is basically the same as saying x = 0 leads to y = 0. The point (0,0) is on the graph.

Repeat for P = 1 and you'll find that C = 4. This is the same as x = 1 leading to y = 4. The point (1,4) is on the graph.

If you keep going for various values of P, you'll get corresponding values of C. It turns out that all you need are 2 points to graph this line. Plot (0,0) and (1,4) on the same xy grid. Draw a line through them to complete the graph.

The graph is shown below.

A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative

Answers

Answer:

a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.

Analyze the key features of the graph of f(x) shown below.

Use rules of transformations and the parent function to formulate an equation for the rational function shown in the graph. Show all your work.​

Answers

Answer:

y = -2+1/3x

Step-by-step explanation:

Slope = -2

x - intercept = -3

To make the x-intercept positive you make it 1/3.  

y = -2 +1/3x

Please help I have gotten through every problem except this one!

Answers

I think it’s 83 maybe

Answer:

Step-by-step explanation:

BUG is 30 degrees more than GUY

So that means if <GUY = x

< BUG = <GUY + 30

Together they make 180 degrees

<BUG + <GUY = 180        Substitute for <BUG

<GUY + 30 <GUY = 180  Combine

2*<GUY + 30 = 180          Subtract 30 from both sides

2*<GUY = 150                   Divide by 2

<GUY = 150/2

<GUY = 75

<BUG = 75 + 30

<BUG = 105

Let a, b, c be the three observations. The mean of these observations is.
(a) a+b+c2 (b) a×b×c2 (c) a+b+c3 (d) a+bc

Answers

Answer:  a+b+c/3

Step-by-step explanation:

mean= sum of all values/number of values

Find each. a. za_2 for the 99% confidence interval b. za_2 for the 98% confidence interval c. za_2 for the 95% confidence interval d. za_2 for the 90% confidence interval e. za_2 for the 94% confidence interval

Answers

Answer:

a) Z = 2.575.

b) Z = 2.327.

c) Z = 1.96.

d) Z = 1.645.

e) Z = 1.88.

Step-by-step explanation:

Question a:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Question b:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Question c:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Question d:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Question e:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.94}{2} = 0.03[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.03 = 0.97[/tex], so Z = 1.88.

Solve this equation:


7d

___________

(2d+1)(3d-1)

Answers

Answer:

Step-by-step explanation:

(2d + 1)(3d - 1)

2d(3d - 1) + 1(3d - 1)

6d^2 - 2 + 3d + 1

6d^2 - 1 + 3d

6d^2 + 3d - 1 (after arranging in standard form)

Answer:

7d/(2d+1)(3d-1)=6d^2 + 3d - 1

Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered.

What is the equation of the line? Plsss helppp

Answers

Answer:

y = -7

Step-by-step explanation:

Slope: 0

y-intercept: (0,−7)

Since the line doesn't change up, down, right, or left, and it stays on the y-axis, that's how u get y = . The straight line runs along -7 . That's how u get -7 . so when u put it all together u get: y = -7 .

Hope that helps. Tried to explain the best I could :)

a tank is 2m long, 1.4m wide and 1.8m high.find the volume of water in the tank when it is half full.

Answers

Answer:

2.52m³

Step-by-step explanation:

volume=L x W x H

V=2 x 1.4 x 1.8

V=5.04

WE DIVIDE 5.04m³ by 2 to get 2.52m³

Have a nice day

LxBxH
2x1.4x1.8=5.04
Half filled means divide by 2
V=5.02/2=2.52

Calculate the mean and the standard deviation of the age of individuals that purchased skateboarding shoes. Use 10 as the midpoint of the first class. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answers

Answer:

Mean = 19.84

Standard deviation = 11.12

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.

The explanation of the answer is now given as follows:

Note: See the attached excel file for the calculation of the total of fx and total of f*x^2.

N = Number of individuals sampled = 200

From the attached excel file, we have:

Total of fx = 3,967

Total of f*x^2 = 103,425.50

Therefore, we have:

Mean = Total of fx / N = 3,967 / 200 = 19.84

Variance = (Total of f*x^2 / N) - Mean^2 = (103,425.50 / 200) - 19.84^2 = 517.13 - 393.43 = 123.70

Standard deviation = Variance^0.5 = 123.70^0.5 = 11.12

Suppose a jar contains 8 red marbles and 25 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.

Answers

Answer: [tex]\dfrac{7}{132}[/tex]

Step-by-step explanation:

Total marbles in the jar =  8+25 = 33

Using combinations, the number of ways of choosing two marbles out of 33=  [tex]\dfrac{33!}{2!(33-2)!}\\\\=\dfrac{33!}{2\times31!}\\\\=\dfrac{33\times32}{2}=528[/tex]  (total outcomes)

Similarly, the number of ways of choosing two red marbles =

[tex]\dfrac{8!}{2!6!}\\\\=\dfrac{8\times7}{2}=28[/tex](favorable outcomes)

Required probability = [tex]\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]

[tex]=\dfrac{28}{528}\\\\=\dfrac{7}{132}[/tex]

hence, required probability = [tex]\dfrac{7}{132}[/tex]

how many kilometers are there in 9000000cm​

Answers

Answer:

90 kilometers

Step-by-step explanation:

https://www.bing.com/search?q=kilometers+are+there+in+9000000cm

PROBIBILITY HELP ME PLZ Mike is playing a game where a ball is hidden under one of 5 cups. Mike guesses which cup contains the ball 20 times and chooses correctly 6 times. Mike wants to simulate the game to determine if his results are the same as what would be expected by random chance.

Answers

Answer:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

Step-by-step explanation:

Given

[tex]Cups = 5[/tex]

[tex]Ball=1[/tex]

[tex]Trials = 20[/tex]

See attachment

Required

Simulate the above experiment (fill in the gaps)

The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:

[tex]P(Correct) = \frac{Ball}{Cups}[/tex]

This gives:

[tex]P(Correct) = \frac{1}{5}[/tex]

The number of times (i.e. 6) he chose correctly is not a factor in his simulation

So, a correct simulation of the experiment is as follows:

Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.

The selected ball represents the number of balls hidden (i.e. 1 ball).

The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)

The 20 times represent the number of times the experiment is repeated.

What is the 13th term of 5,15,45,135

Answers

Answer:

2657205.

Step-by-step explanation:

This is a Geometric Sequence with common ratio 3.

13th term = 5*(3)^(13-1)

=5(3)^12

= 2657205.

Answer:

2657205.

Step-by-step explanation:

Two similar triangles are shown below:
Which two sets of angles are corresponding angles

Answers

Answer:

angle w and angle v; angle x and angle y (option 1)

Step-by-step explanation:

the little arc things are what tell you two angles are corresponding m

angles w and v both have two arc drawing things.

angle x and y have one

and the other angles that aren't labeled have three

The weight, in pounds , of Mike's five pet dogs are listed below.What is the mean absolute deviation (MAD) of the weights?

16 , 23 , 27 , 41 , 53

Type the answer in the box.

______ pounds​

Answers

Answer:

it would be 32

Step-by-step explanation:

you would add them all up then divide it by five

Answer: The answer is 32

Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.

You borrow $16,000 with a term of four years at an APR of 5% to buy a truck. What is your monthly payment? (Round your answer to the nearest cent.)
$


How much total interest is paid? (Round your answer to the nearest cent.)
$

Answers

Answer:

368.47

1686.56

Step-by-step explanation:

effective rate: .05/12=.00416666667

payment=x

[tex]16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47[/tex]

Interest:

368.47*48-16000=1686.56

Answer:

Answer:

368.47

1686.56

Step-by-step explanation:

effective rate: .05/12=.00416666667

payment=x

\begin{gathered}16000=x\frac{1-(1+.00416666667)^{-48}}{.00416666667}\\x=368.47\end{gathered}

16000=x

.00416666667

1−(1+.00416666667)

−48

x=368.47

Interest:

368.47*48-16000=1686.56

A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.

Answers

Answer:

$30.21

Step-by-step explanation:

100% -25%= 75%

Discounted price of the book

= 75% ×$38

= $28.50

Since the customer must pay an additional 6% of the discounted price,

percentage of discounted price paid

= 100% +6%

= 106%

Total amount paid

= 106% × $28.50

= $30.21

_________________________________

Alternative working:

Original selling price= $38

Since the book is discounted 25%,

100% ----- $38

1% ----- $0.38

75% ----- 75 ×$0.38= $28.50

Since the sales tax is based on the discounted price, we let the discounted price be 100%.

100% ----- $28.50

1% ----- $0.285

106% ----- 106 ×$0.285= $30.21

∴ The total amount the customer pays for the discounted book is $30.21.

Trig Equation from a Graph

Answers

Answer:

Step-by-step explanation:

What happens when the multiplicity of a real root is even?

Answers

Answer:

Step-by-step explanation:

The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.

A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.


Treating the fee as interest paid, what is the equivalent annual interest rate?

Answers

Answer:

1460

Step-by-step explanation:

What does a right angle look like

Answers

Answer:

It's a 90 angle, straight up and down, moving into straight right and left.

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