2.
Suppose the population of kangaroos in a different province of Australia is modeled by
the following, with t = 0 representing the year 2020:
P() = 76(0.92)
a.) Using a calculator, find P(10) and interpret it in the context of the problem. Be
specific.
b.) What is happening to the population of kangaroos in this problem? What specific value
in the equation causes this? By what percentage is the kangaroo population decreasing
each year?
c.) As the value of t increases to very large numbers, do you think this model will be
realistic? Explain. Using a calculator, find P(100) to help support your answer.

Answers

Answer 1

Answer:

  a) 30 kangaroos in 2030

  b) decreasing 8% per year

  c) large t results in fractional kangaroos: P(100) ≈ 1/55 kangaroo

Step-by-step explanation:

We assume your equation is supposed to be ...

  P(t) = 76(0.92^t)

__

a) P(10) = 76(0.92^10) = 76(0.4344) = 30.01 ≈ 30

In the year 2030, the population of kangaroos in the province is modeled to be 30.

__

b) The population is decreasing. The base 0.92 of the exponent t is the cause. The population is changing by 0.92 -1 = -0.08 = -8% each year.

The population is decreasing by 8% each year.

__

c) The model loses its value once the population drops below 1/2 kangaroo. For large values of t, it predicts only fractional kangaroos, hence is not realistic.

  P(100) = 75(0.92^100) = 76(0.0002392)

  P(100) ≈ 0.0182, about 1/55th of a kangaroo


Related Questions

17.9% of what number is 14.857?

Answers

Answer:

83

Step-by-step explanation:

.179 of x = 14.857

x = 14.857/.179

x = 83

Answer: a = 83

Explanation:

17.9% = 17.9/100

Let a be the number that a • 17.9% = 14.857:

17.9/100 • a = 14.857
a = 14.857 x 100/17.9
a = 83

Will mark brainliest

Answers

D is the correct answer.

pt 2 7-7 Please helppp If you guys want lol ill do 7 moreeee LOL

Answers

Answer:

c = 72

Step-by-step explanation:  

8        

        x   ___c__     =   9  x   8

                   8

c = 72

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------

Answer: c = 72~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{c}{8} = 9[/tex]

Multiply both sides by 8.

[tex]c = 9 \times 8[/tex]

Multiply 9 and 8 to get, you guessed it, 72!

How do i answer these questions

Answers

Answer:

well basically for the first question it gives you

The rate that increases. which is 0.03 per second

And that R = 48 inches at time.

and T= 0.

The question wants you to determine the volume of the balloon at the time and find the volume when t= 300 seconds. so just replace 0 to 300.

press the question and type the answer

9 + 8r = −7 − 4(−r + 3)

Answers

Answer:

r = -7

Step-by-step explanation:

Solve for r:

8 r + 9 = -4 (3 - r) - 7

-4 (3 - r) = 4 r - 12:

8 r + 9 = 4 r - 12 - 7

Grouping like terms, 4 r - 12 - 7 = 4 r + (-7 - 12):

8 r + 9 = 4 r + (-7 - 12)

-7 - 12 = -19:

8 r + 9 = 4 r + -19

Subtract 4 r from both sides:

(8 r - 4 r) + 9 = (4 r - 4 r) - 19

8 r - 4 r = 4 r:

4 r + 9 = (4 r - 4 r) - 19

4 r - 4 r = 0:

4 r + 9 = -19

Subtract 9 from both sides:

4 r + (9 - 9) = -9 - 19

9 - 9 = 0:

4 r = -9 - 19

-9 - 19 = -28:

4 r = -28

Divide both sides of 4 r = -28 by 4:

(4 r)/4 = (-28)/4

4/4 = 1:

r = (-28)/4

The gcd of -28 and 4 is 4, so (-28)/4 = (4 (-7))/(4×1) = 4/4×-7 = -7:

Answer:  r = -7

toss two dice. the probability of rolling an even number on both sides is 1/2x1/2= 1/4. predict in 120 tosses how many times an even number will appear on both dice?

Answers

Answer:

Chances of both even number = 30 times

Step-by-step explanation:

Given:

Chances of both even number = 1/4

Total number of tosses = 120

Find:

How many times both dice show even number

Computation:

Chances of both even number = [Chances of both even number][Total number of tosses]

Chances of both even number = 1/4 [120]

Chances of both even number = 30 times

What are two lines that lie within the same plane and never intersect.

Answers

Answer:

Step-by-step explanation:

Parallel lines

The present value of R8052.55 received in 5 years at 9% interest is

Answers

Answer:

The present value of a bond is calculated by discounting the bond's future cash payments by the current market interest rate. In other words, the present value of a bond is the total of: The present value of the semiannual interest payments, PLUS. The present value of the principal payment on the date the bond maturaes.Calculate the present value investment for a future value lump sum return, based on a constant interest rate per period and compounding. This is a special instance of a present value calculation where payments = 0. The present value is the total amount that a future amount of money is worth right now.

NEED TO SHOW ALL WORK) For each of the equations given below, use the triangle method to solve for the
desired variable.

Answers

Answer:

1) [tex]a=\dfrac{F}{m}[/tex]

2) [tex]m=\dfrac{p}{v}[/tex]

Step-by-step explanation:

1) The given equation is

[tex]F=ma[/tex]

We need to solve this for a.

In the given triangle place single variable i.e., F, on the top and variables in the product in the bottom (order of m and a does not matter) as shown in the below figure.

Using the triangle and the operations (× and ÷), we get

[tex]F=ma[/tex]

[tex]a=\dfrac{F}{m}[/tex]

[tex]m=\dfrac{F}{a}[/tex]

Therefore, the required answer is [tex]a=\dfrac{F}{m}[/tex].

2) The given equation is

[tex]p=mv[/tex]

We need to solve this for m.

In the given triangle place single variable i.e., p, on the top and variables in the product in the bottom (order of m and v does not matter) as shown in the below figure.

Using the triangle and the operations (× and ÷), we get

[tex]p=mv[/tex]

[tex]m=\dfrac{p}{v}[/tex]

[tex]v=\dfrac{p}{m}[/tex]

Therefore, the required answer is [tex]m=\dfrac{p}{v}[/tex].

A box contains 65 balls numbered from 1 to 65. If 9 balls are drawn with replacement, what is the probability that at least two of them have the same number

Answers

Answer:

Probabilty= 7.66*10^-3

Step-by-step explanation:

A box contains 65 balls numbered from 1 to 65.

9 balls are drawn with replacement.

Probabilty of selecting a number = 1/65

Probabilty of selecting a number

= 0.0154

Probabilty of at least 2 numbers out of 9 selected to have Same number

Probabilty= 9C2(0.0154)^2(0.9846)^7

Probabilty= 7.66*10^-3

the weight of earth is about 66 metric ton what is the standard form of 6,600,000,000,000,000,000,000, metric tone​

Answers

Answer: 6.6 x 10^21 metric ton

Please help...............

Answers

Answer:

C' ( -10 , 4)

D' (-10 , 6)

E' (-8 , 6)

F' (-8 , 4)

John says 1/3 is smaller than 1/8 because 3 is less than 8. Jane
says 1/3 is greater than 1/8 because the pieces are bigger. Who is
right? How do you know?

Answers

Answer:

Jane is correct

Step-by-step explanation:

100 divide by 3 is 33.333 recurring

100 divided by 8 is 12.5

El recibo del servicio de celular del mes de abril facturó un monto de S/52,50 por un consumo de 69 minutos; y el del mes de mayo, facturó S/32 por un consumo de 28 minutos. El monto que cobran cada mes incluye un costo fijo por mantenimiento y un precio establecido por minuto de consumo. ¿Cuántos minutos se debería consumir como máximo para pagar menos de S/30 el siguiente mes?

Answers

Answer:

x  = 24  minutos

Step-by-step explanation:

Llamaremos  "y" el costo fijo mensual y "x" la cantidad de minutos consumidos al mes, según lo cual:

El enunciado del problema establece que la facturación en pesos es igual a un costo fijo  y   más el consumo en minutos del mes, entonces

En Abril    52,50  =  y  +  b*x     ⇒   52,5  =  y  +  69*b

y en Mayo   32   =  y  +  b*x      ⇒   32  =  y  + 28*b

Así obtuvimos un sistema de dos ecuaciones con dos incógnitas, que resolveremos y obtendremos los valores de b y de y

y  =  52,50  -  69*b

32 = ( 52,50  -  69*b ) + 28*b

- 20,50  =  - 41*b

b  =  0,5

y    y  =  52,5  - 69*0,5

y =  18

Entonces la ecuación de facturación es :

F(x) = 18  + 0,5*x

Para pagar como máximo 30 pesos en el mes siguiente

F(x) =  30  =  18 + 0,5*x

30 -  18  =  0,5*x

x  = 24  minutos

i need help asap !!!!!!

Answers

Answer:

B. ZJ = 85

C. KH = 68

Step-by-step explanation:

Given that ZK, ZL, ZM are perpendicular bisectors of ∆GHJ, they form a circumcenter which is equidistant from the vertices of ∆GHJ. According to the circumcenter theorem, ZH = ZG = ZJ = 85.

Also each median formed is equal. This means: KH = GH, LH = LJ, MG = MJ

Since HG = 136, KH = ½ of 136 = 68.

The two options that are true are:

B. ZJ = 85

C. KH = 68

A ladder leans against a vertical wall of
height 5 m. If the foot of the ladder is
12 m away from the wall, calculate
the length of the ladder.​

Answers

Answer: 13m

Step-by-step explanation:

Use Pythagorean theorem: a²+b²=c²

5²+12²=c²

25+144=c²

c²=169

c=13 (even if it is true that there are positive and negative solution, but length cannot be negative)

Given:

A ladder is leant against a wall of height 5m.The foot of ladder is 12m away from the wall.

To Find:

The length of ladder.

Concept Used:

We will use Pythagoras Theorem.

Answer:

Here given

Vertical height = 5m.Base = 12m.

Here the length of ladder is equal to hypotenuse of ∆ so formed.

Now in a right angled ∆ ,

=> (hypotenuse)² = (pependicular)²+(base)².

=> h ² = (12m)²+(5m)²

=> h² = 144m² + 25m².

=> h² = 169m².

=> h = √169m².

=> h = 13m.

Hence the required answer is 13m.

WILL GIVE BRAINLIEST THANKS AND 5 STARS FOR CORRECT ANSWER Desmond ran a lemonade stand in front of his house for the fans walking to the football game. On the first Saturday, he sold 80 cups of lemonade. The second Saturday was cold and rainy so he sold only 70% of what he had sold the previous Saturday. How many cups did he sell on the second Saturday?

Answers

Answer:

56

Step-by-step explanation:

First, convert the 70% so that we can use it with the 80 cups. To do this, convert the percent to a decimal by moving the decimal 2 spaces to the left:

70% → 70.00 → 0.70 → 0.7

70% percent can be seen as 0.7. Multiply this by 80:

[tex]80*0.7=56[/tex]

So, 70% of 80 is 56. Desmond sold 56 cups on the second Saturday.

:Done

Which symbols could be used to make the folllowing statement true -15 -19

Answers

Answer:

-15 > -19

Step-by-step explanation:

-15 > -19

-15 is closer to 0 than -19 so it is greater than

9. Find the area of rectangle.
2x
A=
5x?
please help

Answers

Answer:

[tex] \boxed{\sf Area \ of \ rectangle = 10x^3} [/tex]

Given:

Length of rectangle = 5x²

Width of rectangle = 2x

To Find:

Area of rectangle

Step-by-step explanation:

[tex]\sf Area \ of \ rectangle = Length \times Width[/tex]

[tex] \sf = 5 {x}^{2} \times 2x[/tex]

[tex] \sf = 5 \times 2 {x}^{2 + 1} [/tex]

[tex] \sf = 5 \times 2 {x}^{3} [/tex]

[tex] \sf = 10 {x}^{3} [/tex]

Answer:

[tex]\huge\boxed{Area\ of\ Rectangle = 10x\³}[/tex]

Step-by-step explanation:

Area of Rectangle = Length * Width

Where Length = 2x and Width = 5x²

Area of Rectangle = (2x)(5x²)

Area of Rectangle = 10x³

Write all the steps plzzzzzz

Answers

Answer:

Step-by-step explanation:

See attachment

Write 645,300 in expanded form using exponents

Answers

Answer:

Step-by-step explanation:

(6 x 10^5) + (4 x 10^4) + (5 x 10^3) + (3 x 10^2)

DESPERATE! Please answer any of the questions :(( And explain bc im super confused

Answers

Answer:

Step-by-step explanation:

4. when bases are equal ,powers are also equal.

x+4=3x-1

3x-x=4+1

2x=5

x=5/2=2.5

Consider this expression.

x^2 + x - 72

Replace the values of a and b to rewrite the given expression.

( x + a )( x + b )

Answers

Answer:

Step-by-step explanation:

Hello, first we can develop (x+a)(x+b)

[tex](x+a)(x+b)=x(x+b)+a(x+b)=x^2+bx+ax+ab=x^2+(a+b)x+ab[/tex]

We know that this should be equal to

[tex]x^2+x-72[/tex]

So, we can identify the coefficients of the like terms

1 = 1 (terms in [tex]x^2)[/tex]

1 =  a + b (terms in x)

-72 = ab (constant term)

72 is 8 * 9 so, -72=9*(-8)

and we have 9 - 8 =1

so, a = 9 and b = -8

[tex]\Large \boxed{\sf \bf \ x^2+x-72=(x+9)(x-8) \ }[/tex]

Thank you

We are to consider the given expression:

x² + x - 72

The above expression is a quadratic expression and the objective is to determine its roots in form of (x + a) (x + b)

In form of (x + a) (x + b), the values of the expression x² + x - 72 in form of (x + a) (x + b) are 9 and -8 respectively.

From the given expression;

x² + x - 72

So; we will look for two factors of 72 in such a way that if those factors are multiplied together; they will give -72 and the addition of those two numbers will give +1.

So, the factors of 72 are:

1, 2, 3, 6, 8, 9, 12, 36, 72

From the above factors;

the multiplication of (-8) × (9) will give us  = -72and the addtion of -8 + 9 = +1

Our factors are:  (-8)  and (9)

From  x² + x - 72, we have:

x² + (-8x) + (9x) - 72 = 0

(x² - 8x) + (9x -72) = 0

Opening the brackets by factorization;

x(x -8) + 9(x -8) = 0

(x + 9) or (x - 8) = 0

(x + 9) (x - 8) = 0

Recall that, we are to replace the values of a and b with the roots derived from the expression x^2 + x - 72.

Therefore, we can conclude that the values of a and b are 9 and -8 respectively.

Learn more about quadratic equations here:

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The sum of two numbers is eight. Using y to represent the smaller number,
translate "three times the larger number" into a variable expression and thenuh
simplify.​

Answers

Answer:

24 - 3y

Step-by-step explanation:

Since the sum of the two numbers is 8, the larger number is 8 - y.

Three times the larger number: 3 (8 - y).

Simplify using Distributive property: 3 (8 - y) = 24 - 3y.

So the answer is 24 - 3y

Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).

Answers

Answer:

x  = - 2 is confirmed to be the real solution of the equation.

Step-by-step explanation:

We are tasked with the following activities

Conjecture: How many solutions do [tex]x^3 - 5x^2 + 28 = 0[/tex]  have?

Find the real solution(s) of the equation.

Then use polynomial long division to find the other solution(s).

To start with the how many solutions that  [tex]x^3 - 5x^2 + 28 = 0[/tex]  have

suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :

[tex](-2)^3 - 5(-2)^2 + 28 = 0[/tex]

[tex]-8 - 5\times 4 + 28 = 0[/tex]

-8 - 20  + 28 = 0

-28 - 28 = 0

0 = 0

The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation

So , as x = - 2

x + 2 = 0  

x  = - 2 is confirmed to be the real solution of the equation.

A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.

NEED HELP QUICK! Points P, Q, and R are shown on the number line. What is the distance between point P and point R? A) 47 units B) 61 units C) 121 units D) 132 units ' The numberline is below.

Answers

C ) 121

Explanation : Add 91 + 30 to get 121

Answer:

plz give hlamberttx the brainliest!

Step-by-step explanation:

he saved my grade and helped me sooo much with this question. he is 100% correct i got an 100 on my usa test prep

Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.

Answers

Answer:y=0 So its A

Step-by-step explanation:3(-y+7)=3(y+5)+6

We move all terms to the left:

3(-y+7)-(3(y+5)+6)=0

We add all the numbers together, and all the variables

3(-1y+7)-(3(y+5)+6)=0

We multiply parentheses

-3y-(3(y+5)+6)+21=0

We calculate terms in parentheses: -(3(y+5)+6), so:

3(y+5)+6

We multiply parentheses

3y+15+6

We add all the numbers together, and all the variables

3y+21

Back to the equation:

-(3y+21)

We get rid of parentheses

-3y-3y-21+21=0

We add all the numbers together, and all the variables

-6y=0

y=0/-6

y=0

   

   

Answer:

y = 0

Step-by-step explanation:

Which of the following could be a rational number? Group of answer choices the sum of a rational number and an irrational number the product of a rational number and an irrational number the product of two irrational numbers the sum of two irrational numbers

Answers

Answer:

Is the number rational or irrational?

30‾‾‾√

rational

irrational

Step-by-step explanation: help ;-;

Option (3) the product of two irrational numbers is a rational number is a correct option.

What is a rational number?

"Rational numbers are numbers that can be expressed as a fraction or part of a whole number. It includes the integers, plus all fractions, or terminating decimals and repeating decimals".

What is an irrational number?

"Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers".

For the given situation,

We need to analyze the all options.

Option 1:

The sum of a rational number and an irrational number is an irrational number.

Option 2:

The product of a rational number and an irrational number is an irrational number.

Option 3:

The product of two irrational numbers is a rational or an irrational number based on the numbers taken.

Option 4:

The sum of two irrational numbers is an irrational number.

Hence we can conclude option(3), the product of two irrational numbers is a rational number is a correct option.

Learn more about rational numbers here

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Simplify (7 + 1)2 - (11 +32) 4.
O A. 59
O B. 17
O C. -3
O D. -13

the 32 is an exponent. so it’s 3 to the second power.
help !

Answers

Answer:

59

Step-by-step explanation:

I think your equation is supposed to look like this:

(7 + 1)² - (11 + 3²)/4

Follow PEMDAS to solve (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

(7 + 1)² - (11 + 9)/4

(8)² - (20)/4

64 - (20)/4

64 - 5

59

HELP PLEASE
Select the correct answer.
Over which interval of the domain is function m
negative?

Answers

Answer:

C, (6, ∞)

Step-by-step explanation:

The x intercept is 6, and it continues downward for infinity. :) I had this question on my assignment today and it was right!

Interval of the domain for which function is negative is equals to ( 6, ∞).

What is function?

" Function is defined as relation between two variable is such that for all the inputs there is exactly one output."

Standard equation of the line

y = mx + b

b = y-intercept

m = slope

According to the question,

For the given line in graph,

y- intercept = 4

x- intercept = 6

Therefore ,

For the function y = mx + b  we have,

b = 4

y = mx + 4

Substitute the value of x- intercept in the function y = mx +4 we get,

when x = 6 , y= 0

[tex]0 = m(6) + 4\\\\\implies m= \frac{-4}{6}\\ \\\implies m= \frac{-2}{3}[/tex]

Function [tex]y = \frac{-2}{3}x+ 4[/tex]

Interval of the domain is function is  negative.

[tex]y < 0 \\\\\implies \frac{-2}{3}x+ 4 < 0\\\\\implies -2x + 12 < 0\\\\\implies -2x < -12\\\\\implies 2x > 12\\\\\implies x > 6[/tex]

Interval of the domain is function is  negative is ( 6, ∞).

Hence, Option (C) is the correct answer.

Learn more about function here

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A book review may include the opinions of the person writing the review, while a summary should not include opinions.d. A book review includes the most important details in the book, while a summary includes only the main ideas.What is the best definition of a summary?choose all of the abovea. an essay presenting an opinion of a textb. a review of a range of opinions on a textc. a collection of important quotations from a textd. a brief, objective statement of the central ideas of a text In a working diode, the junction Diode