Mathematics High School

A lake has the capacity to support 10,000 trout. Suppose that the conditions are such that the current population of trout will grow logistically up until it stabilizes at the amount that the lake can support. Currently there are 1,500 trout in the lake. Which of the following is a possible model for P(t), the trout population in t years?

Answers

Answer 1
I just got this problem, I'm not sure if it's right but I got P(t) = 10,000/ (1+9e^0.48t)
Answer 2

Answer:

P(t) = 10,000/ (1+9e^-0.48t)

Step-by-step explanation:

i think because it starts at around 1500 for t=1 and then when t=2 and so on it grows exponentially.

Related Questions

How many of the first 200 positive integers are multiples of neither 6 nor 15

Answers

There are
.. floor(200/6) = 33 multiples of 6
in the range 1 .. 200.

There are
.. floor(200/15) = 13 multiples of 15
in the range 1 .. 200, half of which are also multiples of 6.

So, there are 33 +13 -6 = 40 numbers in the range 1 .. 200 that are multiples of either 6 or 15 or both.

The remaining 200 -40 = 160 numbers are not multiples of either.

how many fluid ounces are in 3 quarts and 2 cups ?

Answers

15 fluid ounces.
1quart= 4 cups

First, convert it all down to cups. Since there are 4 cups in a quart, we have 14 cups total. Then, there are 8 fluid ounces in one cup. Multiply 14 by 8, and we have the answer 112 fluid ounces!
I hope this helped you.

Please helplpppp solve each equation 9.4k + 3.5 + 4.8k =46.2

Answers

9.4k+4.8k+3.5=46.2
we subtract 3.5 from both sides
14.20 k=42.70 divide both sides by 14.20
k=3.007

Seven pounds of birdseed is used to fill 4 identical bird feeders.

A.How many pounds of birdseed are used to fill each bird feeder?

Answers

to find that out you would do 7 divided by 4 and you get 1.75. 1.75 is how many pounds are used to fill each bird feeder

A person at ground level measures the angle of elevation to the top of a building to be 74degrees if at this point the person is 34 feet away from the base of the building, then how tall is the building round to the nearest tenth.

Show work

Will give brainliest to best answer

Answers

see the attached figure 

Let
h---------> building tall

we know that
tan 74°=h/34---------> h=34*tan 74°--------> 34*3.487------> 118.57 
h=118.6 ft

the answer is h=118.6 ft

Evaluate the determinant for the following matrix:
                                                                                -4 -4 -3 
                                                                                 3  3 -5 
                                                                                -5  2 -5
 A. –203 B. 75 C. –152 D. –263

Answers

Looks like it is from China, but... I color coded the numbers. Multiply across the dashed lines.

Answer:

The determinant of matrix is -203            

Step-by-step explanation:

Given the matrix of order 3 i.e

[tex]A=\begin{bmatrix}-4&-4&-3\\ 3&3&-5\\ -5&2&-5 \end{bmatrix}[/tex]

we have to find the determinant of matrix A

[tex]|A|=-4(-5(3)-(-5)(2))-3((-4)(-5)-(-3)(2))+(-5)((-5)(-4)-(-3)(3))\\\\|A|=-4(-15+10)-3(20+6)-5(20+9)\\\\|A|=-4(-5)-3(26)-5(29)\\\\|A|=20-78-145\\\\|A|=-203[/tex]

Hence, the determinant of matrix is -203

Option A is correct.

A trapezoid has an area of 150 square meters. If the bases are 14 meters and 16 meters, what us the height of the trapezoid?

Answers

To find the area of a trapezoid, we use the following formula:
[tex]a = \frac{1}{2} (b1 + b2) \times h[/tex]
In this formula a represents the area and b1 and b2 each represent a base of the trapezoid.

So, we have got the following information
[tex]a = 150[/tex]
[tex]b1 = 14[/tex]
[tex]b2 = 16[/tex]

Filling in the formula gives us:
[tex]150 = \frac{{1} }{2} \times (14 + 16) \times h[/tex]
[tex]150 = \frac{1}{2} \times 30 \times h[/tex]
[tex]150 = 15 \times h[/tex]
Finally we have to divide both sides by 15.
[tex]h = 150 \div 15 = 10[/tex]
Therefore, the height of the trapezoid is 10 meters.

helpppppppppppppppppppppppppp

Answers

For this case we evaluate the function when x = 0
 We then have to evaluate:
 y = -2sinx - 1
 y = -2sin (0) - 1
 y = -1
 Then, the intersection with the y-axis is -1 and the amplitude is 2.
 Answer:
 y = -2sinx - 1
 option 2

Last question thanks guys!! (only 1!)

Answers

The correct answer is:  [C]:  " x² = √32 " .
_________________________________________________
Explanation:
_________________________________________________
Note:  Working backward,   "(± 4√2)" , squared, equals what value(s)?
_________________________________________________
Note:  We are actually given 2 (TWO) solutions:

  " +4√2" and "–4√2" ; 
_______________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;

- √32 = -1 * √32  =   - 4√2
_______________________________
or:  

√32 = √16 √2  = 4√2 ; 

-1 * √32  =   - 4√2
______________________________________________________
However, BOTH these values, when "squared" (i.e. raised to the exponential power of "two"; will result in the same value— which is:  "32" ; 
_______________________________________________________

 is equal to:  "(4√2)²  = (4)² *(√2)²  =  (4*4) (√2*√2) = 16*2 = " 32 " .

______________________________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;

- √32 = -1 * √32  =   - 4√2
_______________________________
or:  

√32 = √16 √2  = 4√2 ; 

-1 * √32  =   - 4√2
_________________________________________________
          " (4√2)²  =  (4)²  * (√2)²  =  (4 * 4) (√2*√2)  =  16 * 2 = " 32 " .  

         " (-4√2)²  = (-4)²  * (√2)²  = (-4 *-4) (2) = 16 * 2 = " 32 " .
_________________________________________________
The correct answer is:  " 32 " ; which is:  Answer choice:  [D]:  " x² = 32 " .

We know that the answer is: " " {" ± 8 "}; since we are dealing with equations that contain "x SQUARED"; that is, " x²"; and when we solve for the 'square root of all values of a [variable raised to an even positive integer] ;

we take the "plus or minus" square root values ;  since the value, "x" could be plus or minus;  since a "negative value" multiplied by a "negative value" is a "positive value" ; 
______________________________________________
So, the correct answer is:  Answer choice:  [B]:  " x² = ± 8 " .
______________________________________________
Let us check our answer:  

√32 = √16*√2 = 4√2 ;

– √32  =  – 4√2 ;
________________________________________________
Also, note:
________________________________________________

   x²  =  32 ;  Solve for "x" ; 

→ Take the square root of "each side" of the equation ; 
     to isolate "x" on one side of the equation; & to solve for "x" ;

→  √(x²)  =  √32 ; 

→  | x |   = √32 ;

→  x = ±   √32 . Yes!
____________________________________________________
[tex]x=\pm4 \sqrt{2} \\ x^2=(4 \sqrt{2} )^2 \\ x^2=4^2\cdot(\sqrt{2} )^2 \\ x^2=16\cdot (2) \\ x^2=32[/tex]

A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in. What is the length of the actual wall?
A) 6.67 inches
B) 80 feet
C) 960 feet
D) 6.67 feet

Answers

B 80 Feet, 8 x 10 would be 80, therefore 80 feet . 

Answer:

the length of the actual wall= 80 feet

Step-by-step explanation:

A blueprint for a house has a scale of 1:10. A wall in the blueprint is 8in.

Blueprint has a scale ratio of [tex]\frac{1}{10}[/tex]

As per the scale, the wall in the blue print is 1 in then the length of the actual wall is 10 feet

A wall in the blueprint is 8 inches, the length of the actual wall is [tex]10*8= 80[/tex] feet

the length of the actual wall= 80 feet

Choose the BEST answer.
1. What is a Web page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
2. What is a home page? (1 point)
A single page of a Web site that consists of an HTML document
The entry page of the Web site
Web page that is located in the same group of Web pages or Web Site as th
document
3. What is the object of storyboarding? (1 point)
To help you visualize your Web site before writing any pages in HTML. To help prevent duplicati

Answers

1. A web page is a single page of a Web site that consists of an HTML document
 2. A home page is the entry page of the Web site
 3.The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.

Answer:

1)

A single page of a Web site that consists of an HTML document.

2)

The entry page of the Web site.

3)

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML.

Step-by-step explanation:

Web page:

A web page or webpage is a document commonly written in HTML (Hypertext Markup Language) that is accessible through the Internet or other networks using an Internet browser.

Hence, option: A is true.

Home page:

A home page also refers to the first page that appears upon opening a web browser, sometimes called the start page.

Hence, option: B is correct.

( The entry page of the Web site )

object of storyboarding:

The object of storyboarding is to help you visualize your Web site before writing any pages in HTML

PLEASE HELP! ^^
A 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. What is the volume of 100 pages of the book?

A. 20 in^3
B. 60 in^3
C. 188 in^3
D. 6,000 in^3

I think it's 600 and I think they made a typo but, help please.,

Answers

The volume of 100 pages of the book is 20 in³.

Explanation:
Since the book is rectangular, we use the formula for the volume of a rectangular prism: V = l*w*h.

Using the measurements of the book we have
V = 10*8*(3/4) = 80*(3/4) = 240/4 = 60 in³.

However, 100 out of 300 pages means we want 100/300 = 1/3 of the book: 60(1/3) = 60/3 = 20 in³.

Answer:

A. [tex]20\text{ in}^3[/tex]

Step-by-step explanation:

We have been given that a 300-page book is 10 inches long, 8 inches wide, and 3/4 inches tall. We are asked to find the volume of 100 pages of the book.

First of all, we will find the volume of whole book using volume of cuboid formula.

[tex]\text{Volume of cuboid}=l\cdot w\cdot h[/tex], where,

l = Length of cuboid,

w = Width of cuboid,

h = Height of cuboid.

Upon substituting our given values in volume formula we will get,

[tex]\text{Volume of entire book}=10\text{ in}\times 8\text{ in}\times \frac{3}{4}\text{ in}[/tex]

[tex]\text{Volume of entire book}=10\text{ in}\times 2\text{ in}\times 3\text{ in}[/tex]

[tex]\text{Volume of entire book}=60\text{ in}^3[/tex]

Since there are 300 pages in entire book and 100 is 1/3 of 300, so the volume of 100 pages will be the 1/3 of the volume of entire book.

[tex]\text{Volume of 100 pages}=\frac{60\text{ in}^3}{3}[/tex]

[tex]\text{Volume of 100 pages}=20\text{ in}^3[/tex]

Therefore, the volume of 100 pages will be 20 cubic inches and option A is the correct choice.

Yesterday , the snow was 2 feet deep in front of archies house. Today, the snow depth dropped to 1.6 feet because the day is so warm.What is the percent change in the depth of the snow?

Answers

earlier snow depth = 2 feet
later snow depth = 1.6 feet

change 
2 - 1.6
0.4 feet

percentage change
(0.4 / 2) * 100
20 %
80% is still left, therefor the percent change is 20%

help, please simplify.. thank you

Answers

[tex]\bf \cfrac{3.7\times 10^{-12}(42)}{(.000000025)(4.0\times 10^{-15})}\implies \cfrac{37\times 10^{-13}(42)}{(25\times 10^9)(4\times 10^{-15})}[/tex]

[tex]\bf \cfrac{37(42)\times 10^{-13}}{25(4)\times 10^910^{-15}}\implies \cfrac{1554\times 10^{-13}}{100\times 10^{9-15}}\implies \cfrac{1554\times 10^{-13}}{1\times 10^2\times 10^{9-15}} \\\\\\ \cfrac{1554\times 10^{-13}}{10^{2+9-15}}\implies \cfrac{1554\times 10^{-13}}{10^{-4}}\implies 1554\times 10^{-13}\times 10^4 \\\\\\ 1554\times 10^{-13+4}\implies 1554\times 10^{-9}\implies \cfrac{1554}{10^9}\implies 0.000001554[/tex]

Troy’s canoe is 18 feet long. Ariel’s canoe is 5/6 the length of Troy’s canoe.

What is the length of Ariel’s canoe?
Express your answer in simplest form

Answers

18 * 5 = 90
90/6 = 15
 it is 15 feet

Which of the following are continuous functions of time?
The quantity of gas in the tank of a car on a journey between New York and Boston (continuous or discontinuous)
The number of students enrolled in a class during a semester (continuous or discontinuous)

I want to verify my answers:
Discontinuous for the car
Continuous for the students,

Answers

Continuous functions of time are a function if small changes are made to the source then the result will have those small changes in them. The quantity of gas is a continuous function of time because small variations can be made to the quantity of the gas in use to the extent of molecules and atoms whereas same cannot be done to the student as we cannot half them.
Final answer:

The quantity of gas in a car's tank during a journey is continuous, whereas the number of students enrolled in a class is discontinuous due to discrete changes.

Explanation:

Continuous functions of time imply that values can change smoothly without jumps or breaks. For the quantity of gas in the tank of a car on a journey between New York and Boston, this would be a continuous function because the gas level decreases gradually as the car is driven. However, for the number of students enrolled in a class during a semester, this is a discontinuous function, because the enrollment can only change through discrete additions or subtractions when students enroll or drop out of the class.

This figure shows circle O with inscribed ∠XYZ. m∠XYZ=76∘ What is the measure of XYZ?

Answers

check the picture below.

now, the inscribed angle is at ∡XYZ and is 76°, that means by the "inscribed angle theorem", the intercepted arcXZ, in red, is twice as much, namely 152°.

keeping in mind that a circle has a total of 360°, and since the red arc has already taken up 152°, the arcXYZ in blue, will pick up the slack from 360° - 152°, namely 208°.

can anyone find an irrational number between 7.7 and 7.9??



Answers

[tex] \sqrt{62} [/tex] is an irrational number; then, [tex] \sqrt{62} [/tex]≈ 7,8 and 7,7 < 7,8 < 7,8.

A store owner paid $15 for a book she marked up the price of the the book by 40% to determine its selling price part A what is the selling price of the book? Part B a customer buys a different book that has an original selling price of $38 the book is discounted 25% the costumer must pay 6% sales tax on the discounted price of the book .what is the total amount the customer must pay for the discounted book

Answers

A:

40% = 0.4

15*0.4 = 6 

15 + 6 = 21

The marked up price is $21

B:

To find the discounted price:

25% = 0.25

38*0.25 = 9.5

38 - 9.50 = 28.50 

To find the tax and price after tax:

6% = 0.06

28.50*0.06 = 1.71

So tax is $1.71

28.50 + 1.71 = 30.21 

Price after tax is $30.21

Jennifer is 30 years old. She has $1200 in a checking account, $8000 in a savings account, $6000 in stock investments, $12,000 in a retirement account, and owns a car worth $8000. What is the total value of her liquid assets?

A. $20,000
B. $15,200
C. $23,200
D $25,200

APEX

Answers

Answer:

B.15,200

Step-by-step explanation:


Medals and Fan!

Given a segment with endpoints A and B, what figure can you construct using the steps below?
Step 1: Draw a ray with endpoint C.
Step 2. Open the compass to the length of AB
Step 3: With the same compass setting, put the compass point on point C. Draw and arc that intersects the ray. Label the point of intersection D.

A. A perpendicular Bisector
B. A congruent segment
C. an angle bisector
D. a congruent angle,

Answers

The answer here is B , congruent segment. Because by opening the compass to the length of AB you are setting the radius of the circle the compass could create to the same length of AB then by intersecting with the ray C, you have copied the length of AB to ray C. For that reason, CD and AB will be congruent.

In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Find the values of x and y.
x = 5, y = 12
x = 5, y = 9
x = 4, y = 9
x = 9, y = 4

Answers

We have that in this case the following equalities are met:
 DH = HF
 x + 3 = 3y
 GH = HE
 3x - 3 = 5y + 4
 We then have the following system of equations:
 x-3y = -3
 3x-5y = 7
 Resolving the system graphically we obtain the following values:
 x = 9
 y = 4
 Note: see attached image.
 Answer:
 The values of x and y are:
 x = 9, y = 4

Final answer:

In parallelogram DEFG, DH = x + 3, HF = 3y, GH = 3x – 3, and HE = 5y + 4. Solving the equations yields x = 9, y = 4.

Explanation:

To find the values of x and y in parallelogram DEFG, we'll use the properties of parallelograms. In a parallelogram, opposite sides are equal in length.

Given that DH = x + 3 and HF = 3y, and that DH is opposite to HF, we have:

x + 3 = 3y   ...(1)

Similarly, given GH = 3x - 3 and HE = 5y + 4, and that GH is opposite to HE, we have:

3x - 3 = 5y + 4   ...(2)

Now, we have a system of two equations (1) and (2) to solve for x and y.

From equation (1):

x = 3y - 3   ...(3)

Substitute equation (3) into equation (2):

3(3y - 3) - 3 = 5y + 4

9y - 9 - 3 = 5y + 4

9y - 12 = 5y + 4

4y = 16

y = 4

Now, substitute the value of y into equation (3):

x = 3(4) - 3

x = 12 - 3

x = 9

So, the values of x and y are x = 9 and y = 4. Thus, the correct answer is x = 9, y = 4.

Which of the following statements describes a correct method for solving the equation below?
3x + 3 = 6x

A. Subtract 3x from both sides of the equation, and then divide both sides by 3.
B. Add 3x to both sides of the equation, and then divide both sides by 3.

C. Divide both sides of the equation by 6, and then subtract 3 from both sides.

D. Divide both sides of the equation by 6, and then add 3 to both sides.

Answers

Selection A works best.

_____
The other choices get you to a place where further work is necessary. They don't really contribute to solving the equation.
A) is the correct answer. 

3x + 3 = 6x
3x-3x + 3 = 6x - 3x
(3x -3x cancel each other out, leaving you with 3)
3 = 3x
3/3 = 3x/3
1 = x
x = 1

Now Verify- 
3x + 3 = 6x
3(1) + 3 = 6(1)
3 +3 = 6
6 = 6

Now can also use the guess and check way. But this is my way of solving it. I hope it helped.

A tent forms an equilateral triangular prism, with both triangular faces exposed. each side of the triangular face has a length of 196196196 centimeters (\text{cm})(cm)left parenthesis, c, m, right parenthesis, and the tent is 250\,\text{cm}250cm250, space, c, m long. what is the height, in centimeters, of the tent?

Answers

Given:
Equilateral Triangular Prism
Each side of the triangular face has a length of 196cm
The tent is 250cm long

I have attached an image of the tent. Since the height of the tent is also the height of the triangle, I will solve for the height of the triangle using Pythagorean theorem.

I divided the equilateral triangle into 2 right triangle. The height then becomes the long leg of the triangle. The hypotenuse is 196cm and the short leg is 98cm, half of one side of the triangle.

a² + b² = c²
a² = c² - b²
a² = (196cm)² - (98cm)²
a² = 38,416cm² - 9,604cm²
a² = 28,812cm²
a = √28,812cm² 
a = 169.74cm

The height of the tent is 169.74 centimeters. 

How many numbers less than 1000 are divisible by 7?

Answers

==> The number of positive integers divisible by 7 but not by 11 is 142 - 12 = 130. ==>the number of positive integers less than 1000 that are divisible by either 7 or 11is 142 + 90 - 12 = 220. ==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and 11 is 220 - 12 = 208.

Find the least common multiple of x² + x – 12 and x² + 2x – 15.

Answers

Solution:

we have been asked to find the Least Common multiple of the given polynomial x² + x – 12 and x² + 2x – 15.

To find the least common multiple. Lets first find the factors.

[tex] x^2+x-12=x^2+4x-3x-12\\
\\
x^2+x-12=x(x+4)-3(x+4)\\
\\
x^2+x-12=(x+4)(x-3)\\ [/tex]

[tex] x^2+2x-15=x^2+5x-3x-15\\
\\
x^2+2x-15=x(x+5)-3(x+5)\\
\\
x^2+2x-15=(x+5)(x-3)\\ [/tex]

Hence the LCM of the given set of Polynomials is (x+4)(x-3)(x+5).

The LCM is (x+4)*(x-3)*(x+5)

Many 1/2 inch cubes can fit into a box that is 15 inches tall, 1 1/2 inches wide, and 3 inches long?

Answers

The answer is 20, I hope this helps!

What exponential function is the best fit for the data in the table?

x f(x)
2 -3
3 0
4 12




A. f(x) = 4(4)^x - 1 + 4

B. f(x) =4(4)^ x - 1 - 4

C. f(x) = 1/4(4)^x -1 + 4

D. f(x) = 1/4(4)^ x - 1 - 4

Answers

Answer: The correct answer is choice D.

There are multiple ways to get to the right answer. You could plot the points on a graphing calculator. Then, graph each function to determine which equation matches the points.

You could also input the x values and see which equation produces the y values in the chart. 

On thing to notice is the we have negative output values, there we need to pick either B or D, so the values go beneath the x-axis.

Answer:

option D.

Step-by-step explanation:

Data given in the table is

x           2         3          4

f(x)       -3        0          12

Now we will plug in the values of x in the given functions to find the correct exponential function.

For x =2

A). f(x) = 4(4)[tex]^{(x-1)}[/tex] + 4

     f(2) = 4(4)[tex]^{2-1}[/tex] + 4 = 4 × 4 + 4 = 20

B). f(x) = 4(4)[tex]^{(2-1)}[/tex] - 4

    f(2) = 4(4)[tex]^{2-1}[/tex] - 4 = (4)(4) - 4 = 16 - 4 = 12

C).  f(x) = 1/4(4)[tex]^{x-1}[/tex] +4

      1/4(4)[tex]^{2-1}[/tex] + 4 = [tex]\frac{1}{4}[/tex] × 4 + 4

     = 1 + 4 = 5

D). f(x) = [tex]\frac{1}{4}(4)^{x-1}-4[/tex]

     f(2) = [tex]\frac{1}{4} (4)^{2-1}-4=\frac{1}{4}(4)-4[/tex]

      = 1 - 4 = -3

We find option D in which f(2) = (-3). so the answer would be option D.

what's the numerator for the following rational expression?
2/f + 5/f = ?/f

Answers

We have 2/f + 5/f = (2+5)/f = 7/f;

Can someone please help me.

The polygons are similar. Write a similarity statement and give the scale factor

Answers

the scale factor is
[tex] \frac{4}{3} [/tex]
all you need to so is take one of the sides from the larger figure and divide it by the corresponding side on the smaller figure for example
[tex] \frac{24}{13} [/tex]
which simplifys to your answer
[tex] \frac{4}{3} [/tex]

Other Questions
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