A species of fish was added to a lake. The population size P (t) of this species can be modeled by the following function, where t is the number of years from the
time the species was added to the lake.
P(t)=-2000/1+6e^-0.42
Find the initial population size of the species and the population size after 7 years.
Round your answers to the nearest whole number as necessary.

Initial population size:

Population size after 7 years:

Answer:

The amount in 20 years is $6,050.24

Step-by-step explanation:

Given the following information:

Principal (Present Value, or PV)= $3,100

Interest rate ( r )= 3.4% or 0.034

Number of compounding period (n )= 1 (annually)

Number of years ( t )= 20

We can use the Future Value formula to find out the value of $3,100 in 20 years:

\(FV = PV(1 + \frac{r}{n})^{nt}\)

\(FV = 3100(1 + \frac{0.034}{1})^{1*20}\)

\(FV = 3100(1.034)^{20}\)

FV = 3100(1.95169)

FV = $6,050.24

Therefore, the future value of the amount deposited is $6,050.24

Answer:

(a) therefore the equation is

a(t) = -1000t + 32800

Step-by-step explanation:

(a) a(t) = mt + b

(8, 24800). ( 20, 12800)

(t, a). ( t¹ , a¹)

slope or gradient, m = a¹ - t¹

a - t

m = 12800 - 24800

20 - 8

m = -12000

12

m = -1000

The slope is -1000

let's use (8, 24800) to find b.

24800 = -1000 (8) + b

24800 = -8000 + b

b= 24800 + 8000

b = 32800

therefore the equation is

a(t) = -1000t + 32800

(b) Since the slope is negative (-1000), it means that the altitude is decreasing at a constant rate of 1000 feet per minute. The negative sign indicates the descent, as the altitude is decreasing over time.

Therefore, the slope tells us that the plane is descending at a constant rate of 1000 feet per minute.

(c) The value 32800 tells us the initial altitude of the plane before descending. It indicates the starting point or the initial position of the aircraft above the ground level.

Therefore, the value 32800 represents the initial altitude of the plane before it began descending.

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

\( A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} \)

The initial amount occurs at t = 0.

\( A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} \)

\( A(0) = 934 (\dfrac{1}{2})^0 \)

\( A(0) = 934 \times 1 \)

\( A(0) = 934 \)

After 80 years, t = 80.

\( A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} \)

\( A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} \)

\( A(80) = 934 (0.15749) \)

\( A(80) = 147 \)

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)

\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)

Answer:

23 years.

Step-by-step explanation:

It is given that the initial price of painting is $150 and its values increasing by 3% annually.

We need to find how many years will it take until it is doubled in value.

The value of painting after t years is given by

\(y=150(1+0.03)^t\)

\(y=150(1.03)^t\)

The value of painting after double is 300. Substitute y=300.

\(300=150(1.03)^t\)

Divide both sides by 150.

\(2=(1.03)^t\)

Taking log both sides.

\(\log 2=\log (1.03)^t\)

\(\log 2=t\log (1.03)\)

\(t=\dfrac{\log 2}{\log (1.03)}\)

\(t=23.44977\)

\(t\approx 23\)

Therefore, the required number of years is 23.

1.order of operations

2.12 or variable

3.error

4.Line(12¨

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A parabola is a group of points inside a plane that are equidistant from the focus, as well as a straight line or directrix.

\(\to y-5=\frac{1}{16} (x-3)^2\)

The formula for the parabola:

\(\to y = a(x-h)^2 + k\)

Solving the above-given equation:

\(\to y=\frac{1}{16} (x-3)^2+5\)

Compare the value and write the value that is:

\(\to\)  a = \(\frac{1}{16}\)

\(\to\)  h = 3

\(\to\)  k = 5

Solving the value:

\(\to y=\frac{1}{16} (x-3)^2+5\)

\(\to y=\frac{1}{16} (x^2+9-6x)+5\\\\\to y=\frac{x^2}{16} +\frac{9}{16}- \frac{6x}{16}+5\\\\\to y=\frac{x^2}{16} +\frac{9}{16}- \frac{3x}{8}+5\\\\\to y=\frac{x^2}{16} - \frac{3x}{8}+5 +\frac{9}{16}\\\\\to y=\frac{x^2}{16} - \frac{3x}{8}+\frac{80+ 9}{16}\\\\\to y=\frac{x^2}{16} - \frac{3x}{8}+\frac{89}{16}\\\\ \to 16y=x^2 - 6x+89\\\\\)

by solving the above expression we get (0, 5.563).

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer: True

The set of whole numbers is {0, 1, 2, 3, 4, 5, ...}

The set of natural numbers is {1, 2, 3, 4, 5, ...}

Both sets describe numbers that are positive and without any fractional or decimal component. The only difference is that 0 is included in the first set, but exclude from the second. If you want to include negative whole numbers as well, then you'd use the set of integers.

The given statement is true.

A number is an arithmetic value used to represent quantity. Hence, a number is a mathematical concept used to count, measure, and label. Thus, numbers form the basis of mathematics.

The statement given is says that, the set of whole numbers includes zero, but the natural numbers do not.

So, if we see the definition of both types of numbers, we can say that the whole numbers are the natural starting from 0, and the natural numbers are the one which includes only counting numbers used in our daily life.

Hence, the given statement is true.

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0.7745 is the probability that a randomly selected college student will take between 4.0 and 6.5 minutes to find a parking lot in the library lot.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Given

Mean, μ = 5.5 minutes

Standard Deviation, σ = 1 minute

We are given that the distribution of length of time is a bell-shaped distribution that is a normal distribution.

z(score) = (x -  μ)/σ

P(college student will take between 4.0 and 6.5 minutes)

= P(4.0 ≤ x ≤ 6.5)

=  P((4.0 - 5.5)/1 ≤ z ≤ (6.5 - 5.5)/1)

= P(-1.5 ≤ z ≤ 1)

= P(z ≤ 1) - P(z < - 1.5)

= 0.8413 - 0.0668

= 0.7745 = 77.45%

Hence, 0.7745 is the probability that a randomly selected college student will take between 4.0 and 6.5 minutes to find a parking lot in the library lot.

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answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer:

what statement

Step-by-step explanation:

Answer:

I would say C. 2/3 + n = 6/5

Step-by-step explanation:

Hope it helps. Let me know

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

given

Rewrite the above expression as:

\(2ab\sqrt[3]{3*4^{3} *ab^{2} } - 5\sqrt[3]{3*3^{3} * a^{4}b^{5} }\)

Evaluate the cube roots

\(2ab {4\sqrt[3]{3ab^{2} } } - 5 {3ab\sqrt[3]{3ab^{2} }\)

Evaluate the differences

-7ab(2√3ab²)

Expressions with equal values are considered equivalent expressions. the difference is 2ab(√/192ab²)-5[√/81a¹b³ is -7ab(2√3ab²)

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Answer:

hey

Step-by-step explanation:

Answer:

11 people could enter for $100

Step-by-step explanation:

According to the information given:

$28=3 people

$20=2 people

so it goes up by 8 dollars for every person added

20-8= 16, the original fee, meaning the sequence formula would be:

8n+8 (n being the number of people)

if 8n+8=100

8n=92

n=11.5 rounded down would be 11

Answer:

The correct answer is A.

Step-by-step explanation:

The correct answer is A.

To find the length of one side of the square, we need to take the square root of the area. Therefore, the square root of 90 is approximately 9.49 feet. Since this value falls between 9 feet and 10 feet, but is closer to 9 feet, the statement "√90 feet is between 9 feet and 10 feet but is closer to 9 feet" is true. So, Jimmy should cut the carpet to 9.49 feet to fit the square-shaped room.

Answer:

14(x-7)

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

Angle ABE is a 180 as ABE forms a line

so angle ABC + ANGLE CBE = 180

x + 20 = 180

x = 180-20

= 160

I hope im right!!

Step-by-step explanation:

answer is 160

hope it helps

The 70 meters by 50 meters rectangular field having a path with an area of 104 m² around it indicates that the width of the path, found using the quadratic formula is about 0.43 meters.

The quadratic formula is a formula that is used to find the values of x that are the solutions to the the the quadratic equation of the form, a·x² + b·x + c = 0.

The length of the rectangular field = 70 meters

The width of the rectangular field = 50 meters

The width of the path around the field = Uniform width

Area of the path around the field = 104 m²

Let x represent the width of the path, we get;

(70 + 2·x) × (50 + 2·x) - 70 × 50 = 104

4·x² + 240·x = 104

4·x² + 240·x - 104 = 0

The quadratic formula which can be used to find the value of x in the equation a·x² + b·x + c = 0, is presented as follows;

\(x = \dfrac{-b\pm \sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}\)

Comparing the equation 4·x² + 240·x - 104 = 0 to the quadratic equation for the quadratic formula; a·x² + b·x + c = 0, we get;

a = 4, b = 240, c = -104

Therefore;

\(x = \dfrac{-240\pm \sqrt{240^2-4\times 4 \times (-104)} }{2\times 4}\)

x ≈ 0.430 or x ≈ -60.4

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Answer:

4%

Step-by-step explanation:

(|600-625|)/625 x 100

=4%

Answer:

The percent error for this estimate was 4%.

Step-by-step explanation:

Teacher's estimated students = 600

Actual students = 625

625-600 = 25 students are more than the teacher's estimate.

In other words, the measurement error = 25 students

Now the percent error can be calculated by dividing 25 (measuring error) by the actual students.

Percent error = 25/625 = 0.04 which is 4%

Therefore, the percent error for this estimate was 4%.

Using the permutation formula, it is found that there are 840 ways to place the letters.

The order in which the letters are placed is important, as PAST is a different arrangement that PTAS, for example, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this problem, 4 letters are taken from a set of 7, hence:

\(P_{7,4} = \frac{7!}{3!} = 840\)

There are 840 ways to place the letters.

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Answer:35

Step-by-step explanation:

The radian measure of the central angle is 1.4 radian

Given :

           radius of circle r = 7cm

           Arc length l = 10cm

           Take arc length formula l = r x θ

                    l = r x θ

                   10 = 7 x θ

                    θ = 10/7 = 1.4

           Therefore, the radian measure of the central angle is 1.4 radian

      The degree of rotation from the initial side to the terminal side establishes how large an angle is. Radians are one unit of measurement for angles. Use a circle's centre angle to define a radian (an angle whose vertex is the centre of the circle). A central angle that intersects an arc that is the same length as the circle's radius (r) is measured in radians.

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Answer:

D

Step-by-step explanation:

m angle b equals 77 now we have to find the arc of andle b.

so use the equation arc AC = 2(77)

arcAC = 154

360 - 154

=206

206/2

= 103

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

Step-by-step explanation:

The perimeter is:

Total:

Correct choice is A

Answer:

A is correct

Step-by-step explanation:

9514 1404 393

Answer:

  C.  $166.50

Step-by-step explanation:

The rate Sara pays for parking is ...

  $10.50/(3 hours) = $3.50 /hour

So, Sara's net pay, after paying for parking, is ...

  $12.75/hour - 3.50/hour = $9.25 /hour

If she works 18 hours per week, her net earnings are ...

  (18 h)($9.25/h) = $166.50 . . . . weekly earnings

57/6 = $9.50 per shirt

9.50 x 4 = $38

Answer: $38

Answer:

$38

Step-by-step explanation:

57 ÷ 6 = 9.5

9.5 x 4 = 38

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Answer:

Mark 3 and subtract 1 from each division

Step-by-step explanation:

Tara will mark the number line at point 3.

Then she will subtract 1 from 3 and mark at point 2.

Again subtracting 1 from 2 the next mark is at 1.

And the last mark is at 0.

The first mark at point 3 shows that the string is 3 feet long.

Now we need 1 foot divisions. So we subtract from 1  division  from point 3  to get 1 foot long string. So we continue to get 3 equal parts each of 1 foot long by dividing the 3 feet long string into 3 equal divisions.

so the first piece is from 0-1 gives 1 foot long string

The 2nd piece is from 1-2 gives 1 foot long string

The 3rd piece is from 2-3 gives 1 foot long string

Answer:

\(S_{10} = 3069\)

Step-by-step explanation:

Given

\(Sequence = \{3, 6, 12, 24, 48...\}\)

Required

Determine the sum of the first terms

First, we calculate the common ratio (r)

\(r = \frac{T_2}{T_1}\)

\(r = \frac{6}{3}\)

\(r = 2\)

The required sum is:

\(S_n = \frac{a(r^n-1)}{r-1}\)

Substitute 3 for a, 2 for r and 10 for n

\(S_{10} = \frac{3(2^{10}-1)}{2-1}\)

\(S_{10} = \frac{3(1024-1)}{2-1}\)

\(S_{10} = \frac{3(1023)}{2-1}\)

\(S_{10} = \frac{3(1023)}{1}\)

\(S_{10} = \frac{3069}{1}\)

\(S_{10} = 3069\)