In a small forest, a certain species of tenrecs doubles in number every
year. Write a function, f(x), that models the number of tenrecs after X
years if there were originally 698 tenrecs.

Answers

Answer 1

The function, f(x), that models the number of tenrecs after x years is f(x) = 698(2)^x

How to determine the equation of the function

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

Initial value, a = 698

Rate, b = 2 i.e. doubles

Using the above as a guide, we have the following:

f(x) = ab^x

Substitute the known values in the above equation, so, we have the following representation

f(x) = 698(2)^x

Hence, the function is f(x) = 698(2)^x

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Related Questions

Find the explicit equation.

Answers

Answer:

f(n) = 23-5n

Step-by-step explanation:

The initial number everywhere is always 23, so that's the start number. Than for every "n" it subtracts 5.

Exponents please help me!

Answers

Answer:

Step-by-step explanation:

(5/3)[tex]d^{3}[/tex]*(-1/3)[tex]x^{3}[/tex]=(-5/9)[tex]d^{3} x^{3}[/tex]

Mmusi borrows an amount of money from Aggie. After two years, Mmusi pays back money, plus 18% simple interest per year. He has to pay back an amount of R4080 much money did he borrow from Aggie?​

Answers

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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The total land are of the United States is about 3,483,511 square miles more than the total land are of Tennessee, which is about 53,927 square miles. Write and solve and equation to find the total land are of the United States.

Answers

The total area of the US is equal to 3,537,438 square miles.

What is an equation?

An equation is an expression shows the relationship between two or more numbers and variables.

A equation is a statement with two equal sides and an equal sign in between. An equation is, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that the total land area of the United States is about 3,483,511 square miles more than the total land area of Tennessee, is about 53,927 square miles.  

We need to write and solve an equation to find the total land area of the United States.

Now, according to the given information,  

Total land area of the United States is 3,483,511 square miles more than the total land area of Tennessee, is 53,927 square miles  

Total land area = 3,483,511 + 53,927

= 3,537,438

Hence, the total area of the US =  3,537,438 square miles.

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how to count to 20 in spanish?

Answers

Counting to 20 in Spanish is a relatively straightforward process. The first step is to learn the numbers from 1 to 10, which are:

1 - uno

2 - dos

3 - tres

4 - cuatro

5 - cinco

6 - seis

7 - siete

8 - ocho

9 - nueve

10 - diez

Once you have these numbers memorized, it's easy to continue counting up to 20. Simply add the numbers from 11 to 19 to the base number, diez.

11 - once (diez + uno)

12 - doce (diez + dos)

13 - trece (diez + tres)

14 - catorce (diez + cuatro)

15 - quince (diez + cinco)

16 - dieciséis (diez + seis)

17 - diecisiete (diez + siete)

18 - dieciocho (diez + ocho)  

19 - diecinueve (diez + nueve)

20 - veinte

As you can see, the only exception is the number 15, which has its own unique word, "quince." Other than that, all of the numbers from 11 to 19 follow the same pattern of adding "diez" to the appropriate digit. And once you reach 20, you're done! It's important to note that Spanish has gendered nouns, so when counting objects, you will need to use the appropriate article and adjective to match the gender of the noun. For example, if you are counting "dogs," you would say "uno perro," but if you were counting "cats," you would say "una gata."

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Answer:

1  uno

2  dos

3  tres

4  cuatro

5 cinco

6 seis

7 siete

8 ocho

9 nueve

10 diez

11 once

12 doce

13 trece

14 catorce

15 quince

16 dieciséis

17 diecisiete

18 dieciocho

19 diecinueve

20 veinte

Step-by-step explanation:

Due to inflation, a fixed quantity of money can buy 5% less every year. If camille has enough in her wallet to buy 86 movie tickets right now, how many movie tickets could the same amount of money buy in 4 years?.

Answers

Due to inflation, a fixed quantity of money can buy 5% less every year. If camille has enough in her wallet to buy 86 movie tickets right now, the same amount of money could buy 69 movie tickets in 4 years.

Inflation is the sustained increase in the general price level of goods and services in an economy over a period of time. When inflation occurs, each unit of currency buys fewer goods and services; consequently, inflation reduces the purchasing power of money. Here, inflation reduces the purchasing power of money by 5% every year.

Let's assume that Camille has enough in her wallet to buy 86 movie tickets right now. After 1 year, the same amount of money would be able to buy 86 * (100 - 5) / 100 = 81.7 movie tickets, since the purchasing power of the same amount of money would have decreased by 5%.

After 2 years, the same amount of money would be able to buy 81.7 * (100 - 5) / 100 = 77.6 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 3 years, the same amount of money would be able to buy 77.6 * (100 - 5) / 100 = 73.7 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

After 4 years, the same amount of money would be able to buy 73.7 * (100 - 5) / 100 = 69.9 movie tickets, since the purchasing power of the same amount of money would have decreased by another 5%.

However, since movie tickets cannot be bought in fractional amounts, we would round down to the nearest whole number, so the same amount of money could buy 69 movie tickets in 4 years.

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A sundae cost 2 dollars additional topings 0.50 write and graph the equation of two variables

Answers

Let x be the number of toppings and y be the cost of the sundae. We know that a sundae costs $2 without any toppings, and each topping costs $0.50. Therefore, the equation that describes the relationship between x and y is:

y = 2 + 0.5x

This equation can be represented on a graph, with x on the horizontal axis and y on the vertical axis. As x increases, y increases by $0.50 for each additional topping. The graph will be a line with a slope of 0.5 and y-intercept of 2, meaning that the line passes through the point (0,2) and rises by $0.50 for each unit increase in x.

An aerial photograph is taken of a building. The photograph is made when the angle of elevation of the sun is 24 degrees. The shadow is determined to be 60 feet long. How tall is the building?

Answers

Answer:

36

Step-by-step explanation:

Solve for x. Round to the nearest tenth.
Thank you!

Answers

The value of the hypotenuse x is 19.1

How to determine the value of the hypotenuse x

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

Rise = 17

Angle = 63 degrees

The hypotenuse, x is then calculated using the following laws of sines

sin(63) = 17/x

Make x the subject

So, we have the following representation

x = 17/sin(63)

Evaluate the expression

This gives

x = 19.1

Hence, the value of x is 19.1

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The dimensions of a rectangular prism are (x + 1) feet by (x + 2) feet by 4 feet. The volume of the prism is (24x - 1) cubic feet. What is the value of x?

Answers

Answer:

x=3/2

Step-by-step explanation:

(x+1)(x+2)(4) = (24x-1)
4(x^2+3x+2) = 24x-1
4x^2+12x+8 = 24x-1

4x^2-12x^2+9 = 0

(2x-3)^2 = 0

2x-3 = 0

x = 3/2

The possible values of variable {x] are -

{x} = 1.146   or   {x} = 1.854.

What is volume?Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write → V = ∫∫∫ F(x, y, z) dx dy dz.

Given is that the dimensions of a rectangular prism are (x + 1) feet by (x + 2) feet by 4 feet.

We can write the volume of the rectangular prism as -

Volume = length x width x height

4(x + 1)(x + 2) = (24x - 1)

(x + 1)(x + 2) = 6x - 1/8

6x - (x + 1)(x + 2) = 1/8

Solving the equation graphically, we get -

x = 1.146   or   x = 1.854

Therefore, the possible values of variable {x] are -

{x} = 1.146   or   {x} = 1.854.

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What is 101 Inches in Feet?

Answers

Answer:

8.417

Step-by-step explanation:

The amount of 101 inches is equal to 8.4167 feet.

To convert inches to feet, we divide the number of inches by 12, since there are 12 inches in 1 foot.

As 1 foot= 12 inches

Therefore, to convert 101 inches to feet, we divide 101 by 12:

= 101 inches / 12 inches/foot

= 8.4167 feet

So, 101 inches is equal to 8.4167 feet.

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Write a function in any form that would match the graph shown

Answers

The function which would match the graph shown as in the task content is; y = -1/2 (x - 6) (x + 5).

Which function would match the graph shown?

It follows from the task content that; the zeroes of the parabola are; -5 and 6;

Therefore, we have that;

y = a (x - 6) (x + 5).

To determine the value of a; use the y-intercept such that we have; (0, 15).

15 = a (0 - 6) (0 + 5)

15 = -30a

a = -1/2.

Ultimately, the required function to match the graph is; y = -1/2 (x - 6) (x + 5).

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ANSWER THE FOLLOWING

Answers

For a cardboard:

Area = (d) 8400 cm²Area in sqm = (b) 0.84 m(b) 3700 cm². (b) 4700 cm².(a) ₹11.75.

How to calculate area and cost of painting?

The area of the cardboard is:

Length = 1 m 5 cm = 105 cm

Breadth = 80 cm

Area = Length x Breadth = 105 cm x 80 cm = 8400 cm²

The area of the cardboard in square meters is:

1 m = 100 cm

Length = 1 m 5 cm = 105 cm = 1.05 m

Breadth = 80 cm = 0.8 m

Area = Length x Breadth = 1.05 m x 0.8 m = 0.84 m²

The area covered by the ribbons is the area of the cardboard that is not painted. From the previous calculations, we know that the area of the cardboard is 8400 cm² and the area that was painted is 4700 cm². Therefore, the area covered by the ribbons is:

Area covered by ribbons = Total area of the cardboard - Area that was painted

Area covered by ribbons = 8400 cm² - 4700 cm²

Area covered by ribbons = 3700 cm²

The area of the cardboard is (105 cm) x (80 cm) = 8400 cm².

The area covered by the ribbons is 3700 cm².

So, the area of the cardboard that was painted is 8400 cm² - 3700 cm² = 4700 cm².

The area of the cardboard is 8400 cm² or 0.84 m². The area covered by the ribbons is 3700 cm². So, the area that needs to be painted is the difference between the area of the cardboard and the area covered by the ribbons, which is:

8400 cm² - 3700 cm² = 4700 cm²

To convert to square meters, we divide by 10000:

4700 cm² ÷ 10000 = 0.47 m²

Therefore, the cost of painting the remaining area is:

0.47 m² × ₹25/m² = ₹11.75

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In linear​ regression, one​ variable, called a​ __________ variable, is related to one or more​ ____________ variables by a linear equation.
A.​ dependent; response
B. ​independent; dependent
C.​ response; dependent
D. ​dependent; independent

Answers

In linear regression, one variable, called a dependent variable, is related to one or more independent variables by a linear equation.

What is the relation between a function and the dependent and independent variables?

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

In the case of multiple inputs, all the inputs are independent variables.

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Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the most accurate rate of speed Morris is traveling?

1 mile = 5,280 feet

45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour

Answers

Answer:

48 miles per hour

Step-by-step explanation:

To convert Aneesha's speed from miles per hour to feet per second, we can use the formula:

speed in feet per second = speed in miles per hour * feet per mile / seconds per hour

So, Aneesha's speed in feet per second is:

50 miles per hour * 5,280 feet per mile / 3600 seconds per hour = 792 feet per second

Morris is traveling 3 feet per second less than Aneesha, so his speed in feet per second is:

792 feet per second - 3 feet per second = 789 feet per second

To convert Morris's speed back to miles per hour, we can use the formula:

speed in miles per hour = speed in feet per second * seconds per hour / feet per mile

So, Morris's speed in miles per hour is:

789 feet per second * 3600 seconds per hour / 5,280 feet per mile = approximately 48 miles per hour.

select all the possible solutions of 20y> -5 + 18y

Answers

Answer:

Step-by-step explanation:

2y>-5

y>-2.5

30 Point for some help!!

Answers

Answer:

The second option!

Step-by-step explanation:

Sorry if i was wrong... :(


At your floral business, you can sell 400 bouquets for a total benefit of $4,800. If you
earn $7,200 when selling 600 bouquets, what is your marginal benefit in this range?

Answers

The marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

How to find the marginal benefit

To find the marginal benefit in this range, we need to calculate the additional benefit of selling one more bouquet within this range.

First, let's find the benefit per bouquet in the range between selling 400 and 600 bouquets:

Total benefit in the range = $7,200 - $4,800 = $2,400

Number of bouquets in the range = 600 - 400 = 200

Benefit per bouquet in the range = Total benefit / Number of bouquets = $2,400 / 200 = $12

So for each bouquet sold within the range between 400 and 600, the benefit is $12.

Therefore, the marginal benefit of selling one more bouquet within the range between 400 and 600 is $12.

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5/6/p = 2/3/1/2 Enter answer as a simplified fraction in the box. show all work

Answers

The value of p is 5/8

What are complex fraction?

A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.

Examples of complex fraction include ½/¾, ⅚/½

⅚/p = ⅔/½

= 5/6 ÷ p = ⅔ ÷ 1/2

= 5/6 × 1/p = 2/3 × 2/1

= 5/6p = 4/3

15 = 24p

divide both sides by 24

p = 15/24

p = 5/8

therefore the value of p is 5/8

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picture below........

Answers

The area of the given figure above can be calculated through the addition of the area of a rectangule and the area of a trapezium would be = 110km²

How to calculate the area of the given figure?

The area of the rectangle= length× width

where length = 17km

width = 4km

area = 17×4= 68km²'&&&&&&

The area of trapezium; = ½(a+b)h

where a= 12 km

B= 17-12 = 5 km

h = 3+4 = 7 km

area = ½(5+7)×7

= ½× 12×7

= 6×7 = 42km²

Therefore the area of the figure = 68+42 = 110km²

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PLEASE HELP!!!!!!!!!!!
Which of the following inequalities does the graph represent?

Answers

Answer:

- 1/2< x ≤ 3

Step-by-step explanation:

The filled circle (at point 3) indicates that 3 is included in the inequality and the clear circle at -1/2 indicates that -1/2 is not included

Find the measure of missing angle

Answers

D = 105°
They are vertical angles
Same thing goes for E

E = 32°

105° + 32° + f = 180°
137 + f = 180°
Subtract for both sides

F = 43°

How long does it take for $250 to grow to $600 at 4% annual percentage rate compounded continuously? Round to
the nearest year.

Answers

Answer:

22yrs

Step-by-step explanation:

So, the money will grow to $600 in about$$ 22 years.

According to the U. S. Mint, the number of quarters minted in 2018 was about 2 x 10°. The mass of a quarter is about 6 X 10-3 kg. Write the number of quarters and the mass of a quarter in standard form

Answers

The number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg

About the mass

The number of quarters minted in 2018 is 2 x 10°, which in standard form is simply 2. The mass of a quarter is 6 x 10^-3 kg, which in standard form is 0.006 kg. So, the number of quarters minted in 2018 is 2 and the mass of a quarter is 0.006 kg

A unit of mass is a unit used to measure mass. Mass is a physical property of an object that is used to explain various observed object behaviors.

In everyday life, mass is always synonymous with weight. But in reality, mass and weight are different. The weight is caused by the interaction between the mass and the Earth's gravitational field.

For example, an object with a weight on earth, when it is sent into outer space or to another planet, the object has no weight because there is no gravity. However, the object still has the same mass.

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Find the value of x

Answers

The value of the angles x is 121 degrees

How to determine the value of the variable

It is important to note that the sum of interior angles of a polygon takes the expression

(n -2) 180

Then, we have;

(6-2) 180

720

Then, add all the angles and equate to 720. we get;

105 + 88 + 142 + 140 + 124 + x = 720

Add the values

599 + x = 720

Collect the like terms

x = 720 - 599

x = 121 degrees

Hence, the value is 121 degrees

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How do you find the inverse of a modulo?

Answers

You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended Euclidean algorithm, and the resulting inverse is the residue of the coefficient modulo the modulus.

Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed integer modulus.

To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.

The steps for finding the inverse of a modulo are as follows:

1. Identify the number you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").

2. Use the extended Euclidean algorithm to find the greatest common divisor of "a" and "m", and the coefficients x and y such that ax + my = gcd(a,m).

3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x mod m.

4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".

In step 3, x mod m represents the residue of x modulo m, which is the unique non-negative integer less than m that is congruent to x modulo m. In other words, it is the remainder when x is divided by m.

For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.

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4x(3+5)-10=4x3+5-10=??

Answers

Answer:

x = 17/32

Step-by-step explanation:

Firstly, you want to simplify by combining like terms:

4x(3+5)—10 = 4 · 3 + 5 – 10

32x—10 = 7

Add ten to both sides:

32x - 10 = 7

+10             +10

32x = 17

Divide both sides by 32:

32x = 17

/32      /32

32 divided by 32x makes x

so we get x = 17/32

(we dont divide 17/32 since we would get an irrational number (0.53125))

Evan runs a circular loop around his neighborhood after he ran a lap he calculated that he had run 744 feet what is the diameter across this loop

Answers

The diameter across this loop was 236.6 feet

What is the perimeter?

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

However, if we assume that Evan ran around the loop's outer edge and not inside the loop,

we can use the formula for the circumference of a circle,

which is C = πd,

where C is the circumference, d is the diameter, and π is approximately 3.14.

We can rearrange the formula to solve for the diameter,

which is d = C/π.

Plugging in the given value for the circumference, we get:

d = 744/π ≈ 236.6 feet

Therefore, if Evan ran around the outer edge of the loop, the diameter of the circle is approximately 236.6 feet.

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What is the measurement of AB?
I will give brainiest to whoever answers it right.

Answers

The measurement of AB is given as follows:

AB = 16.23.

What are the trigonometric ratios?

The three trigonometric ratios are defined as follows:

Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.

For the angle of 52º, we have that:

AB is the hypotenuse.10 is the length of the adjacent side.

Hence the measurement of AB is obtained as follows:

cos(52º) = 10/AB

AB = 10/cos(52º)

AB = 10/0.616

AB = 16.23.

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I need help on this one

Answers

Answer:

24

Step-by-step explanation:

2x3=6

6x4=24

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