Biologists stocked a lake with 800 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6600 . The number of fish grew to 1020 in the first year.
a) Find a logistical model for the number of fish P(t) after t years
P(t)=
b) How long will it take for the population to increase to 3300 hhalf of the carrying capacity)?
It will take years.

The missing numbers are 3 hours = 180 minutes 24 hours = 1 day

24 months = 2 years

What are numbers ?

A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.

An arithmetic value used to indicate amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. For instance, this is a single butterfly, and these are four.

1. 5 × x = 45

   45 / 5 = x

    x = 9

45 ÷ 5 = 9

2. 200 + 600 = 800

300 + 400 = 700

3. 3 hours = 180 minutes

     3 * 60 minutes

24 hours = 1 day

24 months = 2 years

12 * 2 = 24

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On solving the question, we got that - Maricopa Success invested $45000 in stocks, Maricopa Success invested $75000 in bonds and Maricopa Success invested $50000 in CD's.

A theorem of equality between two expressions consisting of equations, variables and/or numbers. Essentially, equations are problems, and the development of mathematics has been driven by attempts to find answers to these problems in a systematic way. The equations vary in complexity from simple algebraic equations (containing only addition or multiplication) to differential, exponential equations (containing exponential terms), and integral equations. They are used to express many of the laws of physics. See also system of equations.

Equations -

s + b + C = 170000

11.4s + 4.4b + 3.25C = 1005500

b = C + 25000

And,

Rearrange::

s + b + C = 170000

1140s + 440b + 325C = 100550000

0 + b - C = 25000

Now,

Use any method you know to solve the system to get:

stocks = 45000

bonds = 75000

CD's = 50000

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For the third part of the batch, 1 :1/2 gallon of yellow is needed and for the second batch part 1/4 gallon is needed.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since we know that there should be the same amount of yellow and green (they are each 1/4 of the recipe) and there is a half a gallon of green there should same amount the yellow. Hence, the answer is 1/2 gallon.

For the second part of the question, we know that 2 gallons is 1/4 of the recipe, and we know that 1/4 * 2= 1/2 (2/4) we just have to multiply 2 by 2 and get 4, our answer.

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Answer:

third part of the batch 1 :1/2 gallon of yellow Second batch part 1: 4

Step-by-step explanation:

have a nice day.

The decision for rejecting the null hypothesis is μ = 8.4

In statistics the term hypothesis refers a tentative statement about the relationship between two or more variables.

Here we have given that engineer designed a valve that will regulate water pressure on an automobile engine and he is designed the valve such that it would produce a mean pressure of 8.0 pounds/square inch. Then it is believed that the valve performs above the specifications. Where the valve was tested on 24 engines and the mean pressure was 8.4 pounds/square inch with a standard deviation of 1.0 Here the level of significance of 0.05 will be used.

Here we have to determine the decision for rejecting the null hypothesis.

While we looking into the the given question we have identified the following values,

Standard deviation = 1.0

Mean pressure = 8.4 pounds/square

Level of significance = 0.05

Sample size = 24

According to these values the null and alternative hypothesis is written as,

H0 = μ = 8.4

Hx = μ ≠ 8.4

Therefore, H0 = μ = 8.4 is the decision for this one.

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The polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the zeroes of the polynomial are, x= -2, x=7

The polynomial expression is obtained as,

=(x+2)(x-7)

=x²-7x+2x+14

=x²-5x+14

Thus, the polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.x= -2, x=7 ,will be P(x)=x²-5x+14.

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Step-by-step explanation:

[tex](8 - 12) \times (8 \times 4) + {7}^{2} \\ [/tex]

[tex]( - 4) \times (32) + 49[/tex]

[tex] -12 8 + 49 =79 [/tex]

Time taken by the bicyclist is 8 hours.

Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Given slope = 35 / 2 = 17.5

Distance = 140 miles.

then time is calculated by 140 /17.5

 = 8 hours

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

As x grows, there are 4 different sorts of slopes: negative, positive, zero, and undefined. The "average rate of change" can also be thought of as the slope of a line.

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It will take Omari 7 months to pay off the computer.

What is a percentage?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) besides the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

To find the amount of the down payment, multiply the price of the computer by the down payment percentage:

down payment = $1,099 * 20% = $219.80

The remaining balance on the computer after the down payment is:

remaining balance = $1,099 - $219.80 = $879.20

To find the total number of months it will take Omari to pay off the computer, divide the remaining balance by the monthly payment:

total months = $879.20 / $144/month = 6.1 months

Since it is not possible to have a fraction of a month.

Hence, it will take Omari 7 months to pay off the computer.

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a) The mean of this distribution is of: 0.35.

b) The standard error of this distribution is of: 0.0382.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has mean and standard deviation defined as follows:

(the standard deviation can also be called standard error).

The sample size and the proportion for this problem are given as follows:

n = 156, p = 0.35.

Then the standard error for this distribution is calculated as follows:

s = square root(0.35 x 0.65/156) = 0.0382.

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Answer:

C.

Step-by-step explanation:

For the first letter there are 26 choices, then, since one has been used, for the second letter there are only 25 choices left. And so on. You multiply them to get the total number of combinations.

For the digits, the initial choice is from 10 digits (0..9), which invalidates answer B.

The following excel commands would give you the critical value is T.INV(0.95,25)

What is excel commands?

The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.

Population sd is not available so we have to use t test.

0.95 is for upper bound and 25 is df of t test.

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Answer:

x = 222:2 and x = 2

Step-by-step explanation:

(2x-123):3=33

(2x – 123):3 = 33

2x – 123 = 33.3

2x – 123 = 99

2x = 99 + 123

2x = 222

x = 222:2

x = 111

200-8.(2x+7)=112

200 – 8.(2x + 7) = 112

-8.(2x + 7) = 112 – 200

-8.(2x + 7) = -88

2x + 7 = (-88):(-8)

2x + 7 = 11

2x = 11 – 7

2x = 4

x = 4:2

   x = 2

I hope my answer helps you.

Answer:

q. point of intersection

Step-by-step explanation:

Both systems in two variables contains two lines that may be intersecting, parallel, or the same line.

The value of (5x2−14x+24)÷(x−4)  is 5x + 6

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given ,

5x2 - 14x - 24

         x - 4    

  5x2 multiplied by 14x, then 24.

The first term is 5x2, and 5 is its coefficient.

The coefficient of the middle term, which is -14x, is -14.

"The constant," the final term, is -24.

Step 1: Multiply the first term's coefficient by the constant 5 • -24 to get a result of -120.

Find two factors of -120 whose combined value is equivalent to the middle term's coefficient, which is -14, in step two.

    -120    +    1    =   -119  

    -60    +    2    =    -58  

    -40    +    3    =    -37  

    -30    +    4    =    -26  

    -24    +    5    =    -19  

    -20    +    6    =    -14    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6  

                   5x2 - 20x + 6x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                  5x • (x-4)

            Add up the last 2 terms, pulling out common factors :

                  6 • (x-4)

Step-5 : Add up the four terms of step 4 :

                 (5x+6)  •  (x-4)

Therefore  The value of (5x2−14x+24)÷(x−4)  is 5x + 6

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Simplified term is 5x + 6. Simplification is the process of reducing an expression/fraction/problem to a simpler form.

A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.

Mathematical expressions are made up of different numbers and operations. To simplify them, we must first understand the rule known as the order of operations. It specifies the order in which operations must be performed when simplifying a mathematical expression.

Factoring  5x2 - 14x - 24

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -14x  its coefficient is  -14 .

The last term, "the constant", is  -24

Multiply the coefficient of the first term by the constant   5 • -24 = -120

Find two factors of  -120  whose sum equals the coefficient of the middle term, which is   -14 .

-120    +   1   =   -119

-60    +   2  =   -58

-40    +   3  =   -37

-30    +   4  =   -26

-24    +   5  =   -19

-20    +   6  =  -14  

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -20  and  6

5x2 - 20x + 6x - 24

Add up the first 2 terms, pulling out like factors :

                   5x • (x-4)

Add up the last 2 terms, pulling out common factors :

                   6 • (x-4)

Add up the four terms of step 4 :

                   (5x+6)  •  (x-4)

Which is the desired factorization

Cancel out  (x-4)  which appears on both sides of the fraction line.

 5x + 6

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The percentage of the council members who voted in favor of the tax is 50%.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the council has 76 members out of which 38 members voted in favor of the tax.

The percentage amount of members who favor the tax is:
(38/76) × 100%

= 50%

Hence, the percentage of the council members who voted in favor of the tax is 50%.

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$23.76 is the value of XYZ stock when the required return is 12 percent.

percentage, a relative value indicating hundredth parts of any quantity.

Let the price per share be P

growth rate, g = 8% = 0.08

D = Next years dividend = $0.88 × 1.08 = $0.9504

Required rate of return r = 12% = 0.12

P=D/r-g

P=0.9504/0.12-0.08

P=$23.76

Hence,$23.76 is the value of XYZ stock when the required return is 12 percent.

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By using trigonometry, it can be calculated that

Value of x is [tex]\frac{2\pi}{3}[/tex]

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

Trigonometry is a very important tool in mathematics.

Trigonometry has a very good application in heights and distance.

Trigonometry has also a very good application in calculus and differential equation and also in physics, trigonometry plays a very vital role

Here,

The trigonometric equation is

4cos x + 2 = 0 where 0 ≤ x ≤ π

4cos x = -2

cos x = [tex]-\frac{2}{4}[/tex]

cos x = [tex]-\frac{1}{2}[/tex]

cos x = cos [tex]\frac{2\pi}{3}[/tex]

x = [tex]\frac{2\pi}{3}[/tex]

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The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

From the graph, the zeroes are -4 and 3. Then the factor of will be (x + 4) and (x - 3). Then the polynomial 'y' is given as,

y = a(x - 3)(x + 4)

At (1, -20), we have

- 20 = a(1 - 3)(1 + 4)

- 20 = a (-2)(5)

a = 2

Then the inequality is given as,

y < 2(x - 3)(x + 4)

y < 2(x² + x - 12)

y < 2x² + 2x - 24

The value of the coefficients a, b, and c will be 2, 2, and negative 24. And the sign will be (<).

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The minimum number of dogs that have a mass of more than 24kg is 6 and the maximum number of dogs that could have a mass of more than 24kg is 18  

Using fundamental algebraic principles, rearrange the function to get the value of x at the derivative value of 0. The maximum or minimum will be at the vertex of the function, which is indicated by the response's x-coordinate. Rewrite the answer into the original function to determine the minimum or maximum.    

Here we have

The given shows the masses of various dogs  

Mass (x) kg          frequency  

0 ≤ x < 10                    2

10 ≤ x < 20                  7

20 ≤ x < 30                12

30 ≤ x < 40                 6      

a) The minimum number of dogs that have a mass of more than 24kg.

If we observe the given table the mass of 24 kg will lie in class intervals 20 ≤ x < 30, 30 ≤ x < 40                      

In class interval 20 ≤ x < 30, mass ranges from 20 kg to 30 kg there is a possibility that the mass of dag will be less than 24 since it started from 20 kg,  

In class interval 30 ≤ x < 40, mass ranges from 30 kg to 40 here there is no possibility that the mass will be less than 24 kg.

So here we can take the frequency of class interval 30 ≤ x < 40 as the Minimum value or number of dogs that could have a mass of more than 24 kg

Therefore,

The minimum number of dogs that have a mass of more than 24kg is 6

b) The maximum number of dogs that have a mass of more than 24kg.

In the above case since we are calculating minimum value, we didn't consider class interval 20 ≤ x < 30.

In this case, to get the maximum value or a maximum number of dogs we will consider class interval 20 ≤ x < 30 as there is a possibility that the mass could be more than 24 kg

In class interval 30 ≤ x < 40 the mass will always be more than 24 kg.

Thus, the Maximum number of dogs with more than 24 kg = 12 + 6 = 18

Therefore,

The maximum number of dogs that could have a mass of more than 24kg is 18  

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The pressure of 28 inches of mercury occurs at 6.03 miles from the eyes of the hurricane

From the question, we have the following pressure function that can be used in our computation:

f(x) = 0.48 ln(x + 2) + 27

Also from the question, we have

Pressure = 28 inches

This means that

f(x) = 28

So, we have the following equation

0.48 ln(x + 2) + 27 = 28

Subtract 27 from both sides

0.48 ln(x + 2) = 1

Divide 0.48 from both sides

ln(x + 2) = 2.083

Take the exponent of both sides

x + 2 = 8.03

So, we have

x = 6.03

Hence, the distance is 6.03 miles

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The coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

What are the coordinates of the axis?

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

We have,

The graph shows the sketch of y = f(x).

The graph crosses the y-axis at the point (0,-2), and the x-axis at the point (8,0).

The coordinates of the intersection with the x-axis are:

x = 8

y = 0

The coordinates of the point where x = -3,

y = 0.

Hence, the coordinates of the intersection with the x-axis are

(8,0), and the coordinates of the point where x = -3, (-3 0).

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Answer:

Step-by-step explanation:

Although the answer is correct, the Step 3 is not correct.

Answer:

C(-6, -3)

Step-by-step explanation:

In a square, all four sides have the same length and all four angles have the same measure (90 degrees). Therefore, the line segments connecting the vertices of a square are all perpendicular to each other and all have the same length.

Since the line segment AB has a length of 8 (the difference in the y-coordinates is 8) and a horizontal component (the difference in the x-coordinates is 0), the line segment CD must also have a length of 8 and a horizontal component of 0. This means that the x-coordinate of point C is the same as the x-coordinate of point A, which is 2.

The line segment CD also has a vertical component equal to the difference in the y-coordinates of points D and A, which is 5 - (-3) = 8. Therefore, the y-coordinate of point C is the same as the y-coordinate of point D minus 8, or -3.

Therefore, the coordinates of point C are (-6, -3).

2/ ( 1 + x) ( 1 - x) is express  into partial fractions.

With an example, what is a partial fraction?

The division of an algebraic fraction into smaller, "partial fractions," components is possible. Think about the algebraic fraction (3x+5) (2x2-5x-3). This formula can be broken down into its simplest form, [2/(x - 3)] - [1/(2x + 1)]. Partial fractions are the more straightforward pieces [2/(x - 3)] and [1/(2x + 1)].

                        The four categories of partial fractions are linear factors, degree 2 irreducible factors, repeated linear factors, and repeated irreducible degree 2 factors.

= 2/(1-(x^2))

= 2 / (1)² - (X)²

=  2/ ( 1 + x) ( 1 - x)

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Answer:

c. |11|

Step-by-step explanation:

When it comes to absolute value, we're talking about the distance from 0. Even though 11 is greater than -19 and -34, the distance from 11 and 0 is smaller than the distance from -19 and 0 and the distance from -34 and 0.

|11-0|=11

|0-19|=19-0=19

|0-34|=34-0=34

The value of x = 3.8 cm and y = 3.44 cm

What are some examples of consistency?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

What are the five different types of congruence?
Two triangles are congruent if they satisfy all five conditions for congruence. Right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).

This can be solve by congruence

these two triangle can be congruent by AAS

so x = 3.8 com

in this triangle we have all angle 60 degree

so this is an equivalent triangle

hence down side = 3.8 cm

hence y = (3.8)^2-(1.6)^2 = 14.44 - 2.56 = √11.88 = 3.44

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The correct option for the equation is C.

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main Body:

Using distance=rate multiplied by time as the  formula,  

mountaineer climbed 1,000 feet at a rate of x feet per hour  

1000 = xt₁           <--eq.1  

"He climbed an additional 5,000 feet at a different rate."  

5000 = x't₂         <--eq.2  

"This rate was 10 feet per hour less than twice the first rate."  

x' = 2x - 10 <--eq.3  

We now have 3 equations/expressions to solve for the number of hours:  

From eq. 1 and 2:  

Total time = t₁ +t₂ = t

t = 1000/x + 5000/x'  

but x' = 2x - 10  

t = 1000/x + 5000/(2x-10)  

t = 1000/x + 5000/[2(x-5)]  

t = 1000/x + 2500/(x-5)

Hence correct option is C.

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Using the Final Exam Grade formula above, I want a 90 in the class and I currently have an 85 . The final is worth [tex]$40 \%$[/tex] of the term grade.

First, convert the weight of the final exam from percent to decimal: [tex]$40 \div 100=0.40$[/tex]

[tex]$$\begin{gathered}F=\frac{90-((1-0.4) \times 85)}{0.4} \\F=\frac{90-((0.6) \times 85)}{0.4} \\F=\frac{90-51}{0.4} \\F=\frac{39}{0.4} \\F=97.5\end{gathered}$$[/tex]

So if I have an 85 in the class, I want a 90, and the final exam is worth 40%, I need a 97.5 to get a 90 in the class.

Using the Final Class Grade formula above, [tex]$F=88.6, w=15$, and $C=91$.[/tex]

First, convert the weight of the final exam from percent to decimal: 15 div 100=0.15

So I went into the final with a class grade of 91 . I got 88.6 on the final which was worth $15 \%$ of the course grade. My final grade in the class was 90.64.

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