A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000.
(a) What was the initial size of the squirrel population?

Answers

Answer 1

if this occurred over a span of 35 years and the population doubles every 7 years, we can divide 35 by 7 to find how many times the population has doubled, which would be 5 times. If we divide 60,000 by 2 (or multiply by 1/2) 5 times, you would get the answer, which would be 1,875.

Answer 2

Final answer:

To find the initial size of the grey squirrel population, we used the exponential growth formula. After calculating, we determined that the initial population size was 1,875 squirrels.

Explanation:

The student asked how to find the initial size of a grey squirrel population that doubles every 7 years and now has a population of 60,000 after 35 years.

To calculate the initial population size, we'll use the formula for exponential growth: P(t) = P0 × (2t/T), where P(t) is the population at time t, P0 is the initial population size, 2 is the base because the population doubles, t is the number of years, and T is the time it takes for the population to double.

The problem gives us 35 years (t) and a doubling time (T) of 7 years. Plugging these into the equation, we have 60,000 = P0 × (235/7). Simplifying, we get 60,000 = P0 × 25 or 60,000 = P0 × 32. Dividing both sides by 32, we find the initial population size is 1,875 squirrels.

Thus, the initial size of the grey squirrel population was 1,875.

Related Questions

Mr.chu is slicing 4 cantaloupes for his class.There are 24 students in class. If Me.Chu cut the cantaloupes to make an equal portion for each student , how much of a whole cantaloupe will each student get?

Answers

1/6 because 4/24 = 1/6

Final answer:

Each student will receive approximately 0.1667 parts of a whole cantaloupe when Mr. Chu evenly divides 4 cantaloupes among 24 students.

Explanation:

The subject of this problem is how to divide a quantity fairly between multiple recipients, also known as division. If Mr. Chu is slicing 4 cantaloupes and wants to divide them equally among 24 students, we need to find how much each student would receive.

This is solved by simply dividing the total quantity of cantaloupes by the number of students. So, 4 (whole cantaloupes) divided by 24 (students) equals 0.1667.

Therefore, each student will get approximately 0.1667 of a whole cantaloupe.

Learn more about division here:

https://brainly.com/question/2273245

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Joanne has 2a^3 number of animals. Ronnie has 3a^3 number of animals . Odessa has a^4 number of animals . How many animals do Joanne , Ronnie, and Odessa have altogether?

Answers

They have:

2a^3 + 3a^3 + a^4
= 5a^3 + a^4

how do you solve the following
6/13=3/c

Answers

Okay. This is set up as a proportion. What we do in this situation is cross multiply. When you do that, you get 6c = 39. Next, divide each side by 6 to isolate the c. 39/6 is 6.5. c = 6.5.

Mr. Thomas purchased a car for $30,000. in 4 years the value of the car decreased to $22,000. Which integer represents the average net change in value per year?

Answers

The change in value over 4 years is
$22,000 - 30,000 = -$8,000

so the average change in value per year is
-8000/4 = -2000

how many inches are equal to 30.48 cm

Answers

30.48 centimeters is 12 inches!

12 I think. Hope this helps!

The number of seats in the first row of a concert hall is 6. The second row has 9seats, the third row has 12 seats, and the fourth row has 15 seats. How many seats are in the eighth row?

Answers

Row eight would have 27 seats because each row adds 3 seats.

A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of π.)

452.16 cm3

840.54 cm3

1,055.04 cm3

1,456.96 cm3

Answers

Given:
Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³

Cylinder: height = 16 cm ; radius = 5 cm
cone: height = 12 cm ; radius = 4 cm

Volume of cylinder = 3.14 * (5cm)² * 16cm = 1,256 cm³
Volume of cone = 3.14 * (4cm)² * 12cm/3 = 200.96 cm³

Volume of air space = 1256 cm³ - 200.96 cm³ = 1,055.04 cm³

Q equal 1/2 p plus 15 solve for p

Answers

If Q=(1/2)(P)+15, we can multiply both sides by 2 to get 2Q=2(P/2+15)=P+30. Next, we can subtract 30 from both sides to get 2Q-30=P

Find the critical points of the function. (enter your answers as a comma-separated list.) g(x) = 4 − x2

Answers

Please use "^" to denote exponentiation: g(x) = 4 - x^2.

To find the critical point, differentiate g(x), set the result = to 0, and solve for x:

g '(x) = -2x = 0. Then x = 0 is the only critical value in this case.

The graph of g(x) is a vertical parabola opening down, and the horizontal tangent line is y = 4.

Complete te pattern 3,400,000 34,000

Answers

340 is the next number

3,400,000 34,000 340 is your next one

340 and 0.034 should be your answer

hope this helps

Solve for x. 2/3x=10 Enter your answer in the box.

Answers

Simply divide both sides by 2/3 to get x by itself.

= 10 ÷ 2/3

Keep, change, flip!

= 10 × 3/2

= 30 / 2

= 15

So, x = 15.

2 / 3x = 10
2 = 10 x 3x
2 = 30x
x = 2/30
x = 1/15

Suppose that 21 girls and 21 boys enter a mathemat- ics competition. furthermore, suppose that each entrant solves at most six questions, and for every boy-girl pair, there is at least one question that they both solved. show that there is a question that was solved by at least three girls and at least three boys.

Answers

Individuals shall draw a table consisting of 21 boys in each column and 21 girls in each row as shown on the image below.

The table will have 21x21 = 441 boxes. Mark each box with a letter showing the problem solved by both that boy and girl. Since at least one problem was solved by a girl and a boy, therefore each box will have a letter. Each entrant solved at most six questions, so there can be at most six letters in any row or column. This means six different letters can be there in a row only if at least 11 of the boxes contain letters appearing three or more times in the row. Individuals go through each row and color all the boxes, say blue. Therefore, 11 boxes in each row must be colored blue.

The number of the boxes that must be colored blue = 21 x 11 = 231. Individuals can apply the same process to the columns and color at least 231 boxes, say green. But the total boxes are 441 only. Therefore, by Pigeonhole principle, there will be some boxes which will be both blue and green. The problem of doubly colored boxes represents a problem solved by at least three boys and three girls.

The Pigeonhole Principle is used to show that there must be a question solved by at least three girls and three boys in a math competition with 21 girls and 21 boys.

To show that there is a question solved by at least three girls and three boys, we will use the Pigeonhole Principle.

We have 21 girls and 21 boys, each solving at most six questions.Let's assume no question is solved by at least three girls and three boys.The total number of questions solved would be at most 21 x 6 = 126, which is fewer than 21 x 2 + 21 x 2 = 84, a contradiction.Therefore, there must be a question solved by at least three girls and three boys.

Based upon a long period of record keeping the following represents the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.

x 0 1 2 3 4 5 6
p(x) .08 .17 .21 k .21 k .13

a. What is the value of k?

b. Calculate the expected value of x.

c. Calculate the expected value of x^2
.

d. Calculate the variance of x.

e. Calculate the standard deviation of x

f. Calculate the variance of 3x.

g. Suppose that network slowness is independent from week to week. What is the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks?

h. Calculate the variance of the random variable x^2

Answers

Given a table representing the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.

[tex]\begin{tabular} {|c|c|c|c|c|c|c|c|} x&0&1&2&3&4&5&6\\[1ex] p(x)&.08&.17& .21& k& .21& k& .13 \end{tabular}[/tex]

Part A:

The total value of p(x) = 1.

Thus,

.08 + .17 + .21 + k + .21 + k + .13 = 1

0.8 + 2k = 1

2k = 1 - 0.8 = 0.2

k = 0.2 / 2 = 0.1

Therefore, the value of k is 0.1

Part B:

The expected value of x is given by

[tex]E(x)=\Sigma xp(x) \\ \\ =0(0.08)+1(0.17)+2(0.21)+3(0.1)+4(0.21)+5(0.1)+6(0.13) \\ \\ =0+0.17+0.42+0.3+0.84+0.5+0.78=3.01[/tex]

Therefore, the expected value of x is 3.01

Part C:

The expected value of [tex]x^2[/tex] is given by

[tex]E(x^2)=\Sigma x^2p(x) \\ \\ =0^2(0.08)+1^2(0.17)+2^2(0.21)+3^2(0.1)+4^2(0.21)+5^2(0.1)+6^2(0.13) \\ \\ =0(0.08)+1(0.17)+4(0.21)+9(0.1)+16(0.21)+25(0.1)+36(0.13) \\ \\ =0+0.17+0.84+0.9+3.36+2.5+4.68=12.45[/tex]

Therefore, the expected value of [tex]\bold{x^2} [/tex] is 12.45

Part D:

The variance of x is given by

[tex]Var(x)=E(x^2)-(E(x))^2 \\ \\ =12.45 - (3.01)^2=12.45-9.06 \\ \\ =3.39[/tex]

Therefore, the variance of x is 3.39.

Part E

The standard deviation of x is given by

[tex] \sqrt{Var(x)} = \sqrt{3.39} =1.84[/tex]

Therefore, the standard deviation of x is 1.84.

Part F:

The variance of ax, where a is a constant is given by

[tex]Var(aX)=a^2Var(X)[/tex]

Thus, the variance of 3x is given by

[tex]Var(3X)=3^2Var(X)=9(3.39)=30.51[/tex]

Therefore, the variance of 3x is 30.51.

Part G:

The probability that the network has no more that 4 slow times in one week is given by

[tex]P(x\leq4)=P(0)+P(1)+P(2)+P(3)+P(4) \\ \\ =0.08+0.17+0.21+0.1+0.21=0.77[/tex]

Since, the network slowness is independent from week to week, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is given by

[tex](0.77)^5=0.27[/tex]

Therefore, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is 0.27

Part H:

The variance of x^2 is given by

[tex]Var(x^2)=E((x^2)^2)-(E(x^2))^2=E(x^4)-(E(x^2))^2[/tex]

[tex]E(x^4)=\Sigma x^4p(x) \\ \\ =0^4(0.08)+1^4(0.17)+2^4(0.21)+3^4(0.1)+4^4(0.21)+5^4(0.1) \\ +6^4(0.13) \\ \\ =0(0.08)+1(0.17)+16(0.21)+81(0.1)+256(0.21)+625(0.1)\\+1,296(0.13) \\ \\ =0+0.17+3.36+8.1+53.76+62.5+168.48=296.37[/tex]

Thus,

[tex]Var(x^2)=296.37-(12.45)^2=296.37-155.00=141.37[/tex]

Therefore, the variance of the random variable [tex]\bold{x^2}[/tex] is 141.37

Answer:.1

Step-by-step explanation:

how do logarithms work

Answers

A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100:

log 100 = 2

because

102 = 100

This is an example of a base-ten logarithm. We call it a base ten logarithm because ten is the number that is raised to a power. The base unit is the number being raised to a power. There are logarithms using different base units. If you wanted, you could use two as a base unit. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight:

log2 8 = 3

because

23 = 8

In general, you write log followed by the base number as a subscript. The most common logarithms are base 10 logarithms and natural logarithms; they have special notations. A base ten log is written

log

and a base ten logarithmic equation is usually written in the form:

log a = r

A natural logarithm is written

and a natural logarithmic equation is usually written in the form:

ln a = r

So, when you see log by itself, it means base ten log. When you see ln, it means natural logarithm (we'll define natural logarithms below). In this course only base ten and natural logarithms will be used.

Final answer:

Logarithms are used in Mathematics to solve exponential equations by converting them into linear equations. They involve finding the exponent to which a base must be raised to equal a given number. Properties of logarithms, such as the product and quotient rules, help manipulate and solve logarithmic equations.

Explanation:

Logarithms are mathematical tools used to solve exponential equations and simplify complex calculations. They are the inverse function of exponential functions and help us solve for the unknown exponent in an equation.

Logarithms work by converting exponential equations into linear equations. When we take the logarithm of a number, we are finding the exponent to which a base must be raised to equal that number. For example, the logarithm (base 10) of 100 is 2, because 10 raised to the power of 2 equals 100.

The properties of logarithms allow us to manipulate them to solve equations. Some key properties include:

The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number.The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

Answers

A quick way to solve this problem involves copying the given equation:

2x + 5y = 10

dropping the final 10, and
substituting the given x and y values: (5, -4).

Then:

2(5) + 5(-4) = C C = 10-20 = -10

Thus, the equation of this new, parallel line is 2x + 5y = -10.

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line 2x + 5y = 10 is:

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 10

Hence the slope of the line 2x + 5y = 10 is -2/5

Since both lines are parallel, hence the slope of the other line is the same (-2/5). Hence the equation of the line is:

[tex]y-y_1=m(x-x_1)\\\\y-(-4)=-\frac{2}{5} (x-5)\\\\y+4=-\frac{2}{5} x+2\\\\y=-\frac{2}{5} x-2[/tex]

The equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10 is y = (-2/5)x - 2

Find out more at: https://brainly.com/question/18880408

What is the greatest common factor of 49 and 84? 3 4 7 9

Answers

49: 1 7, 49
84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The GCF is 7

The answer is 7 since neither 49 nor 84 are divisible by 9

Find the unit rate,Kenny reads 5/8 pages in 2/3 minute.Please show your work.

Answers

Unit rate in this case would be pages per minute so divide (5/8)pages÷(2/3)minute.
Dividing a fraction can be done as multiplying by the reciprocal.
(5/8)·(3/2)=15/16pages per minute or 0.9375 pages/min.

in a student council election Martha and Hillary received a total of 1600 votes, Martha received 81 more votes than Hillary, how many votes did Martha receive

Answers

total of votes: 1600-> this means votes for Martha plus the votes for Hillary

If we divide 1600 by 2 people, this leaves 800 votes for each girl.

800-81=719 for Hillary
800+81=881 for Martha

We take 81 votes, from those 800,and place them in martha's votes

Just to confirm: 881+719=1600 total votes

What is the difference of (4-5y)-2(3.5y-8)?

Answers

20 - 12y Simplify parentheses: 4 - 5y - 7y + 16 Combine similar terms: 4 + 16 - 5y - 7y Simplify: 20 - 12y

Nicolas has three fewer than twice the number of songs downloaded as Sabrina does. Interpret the meaning of the expression 2x – 3. The expression 2x – 3 represents

Answers

The number of songs is x so twice the nb of songs is 2x and 3 fewer than gives -3 so we obtain 2x-3

The expression 2x-3 represent's: The number of songs downloaded by Nicholas.

The variable x represents: The number of songs downloaded by Sabrina.

The florist has 63 roses and carnations. If she has 27 roses how many carnations does she have?

Answers

63-27=36 carnations

She have 36 roses. You subtract 63 from 27

A room has an area of 60 square meters and a perimeter of 32 meters what are the length and width of the room

Answers

10 by 6
10*6=60
10+10+6+6=32

A line passes through (2, −1) and (4, 5).

Which answer is the equation of the line?

Answers

y= 3x - 7
subract 5 by -1 which is 6 and divide that by 4-2 which is 2 so 6 divided by 2 is 3. then subtract the y value by 6 to get 0,-7

How would you write 1+1 in distributive property

Answers

You would put it in as 1(1x1)

Hope this helps

PLS HELP! 20 POINTS AND BRAINLIEST!
25 POINTS!!!!!
In the figure below, lines m and n are parallel:

Two parallel lines are shown crossed by a transversal. The angles are labeled with number 1-8. The angles on line m where the line is crossed by the transversal are 1, 2, 3, and 4 in clockwise order from top left. The angles on line n where the line is crossed by the transversal are 5, 6, 7, and 8 in clockwise order from top left.

In the diagram shown, ∠7 measures 92 degrees. What is the measure of ∠8?

8 degrees
88 degrees
92 degrees
180 degrees

Answers

7 and 8 have to equal 180 degrees

180- 92 = 88

so angle 8 is 88 degrees

Answer:

The correct option is B) 88°.

Step-by-step explanation:

Consider the provided information.

Consider the figure 1,

m∠7=92°, then by using the property of liner pair angles, we have

m∠7 + m∠8 = 180° (Liner pair angles)

⇒m∠8 + 92° = 180°

⇒m∠8 = 180 - 92

⇒m∠8 = 88°

Therefore, the measure of m∠8 is 88°.

Hence, the correct option is B) 88°.

What does n equal in: -6(n+1) = 42 . Need help quickly. Thank you!

Answers

It is -7.83 because you distribute the -6 to the n and the 1 inside the parentheses which makes you get -6n-5=42. Since 5 is negative you add it to -5 and the 42 on the other side of the equation which turns out to -6n=47. You then divide -6 on both sides of the equation. -6n divided by -6 cancels out so 47 divided by -6 equals -7.83333333 which rounds to -7.8

At the beginning of a basketball season, the Panthers won 30 games out of 66 games. At this rate, how many games will they win in a normal 106-game season?

Answers

You would divide 66 by 30 which give you 2.2. Then you divide 106 by 2.2 which gives you an anwser of 48 games

Evaluate the expression below when x = -2. x2 − 8 x + 6

Answers

Solve for x over the real numbers:x = -2. x^2 - 8 x + 6
Hint: | Rewrite the right hand side of the equation.-2. x^2 - 8 x + 6 = -2 x^2 - 8 x + 6:x = -2 x^2 - 8 x + 6
Hint: | Move everything to the left hand side.Subtract -2 x^2 - 8 x + 6 from both sides:2 x^2 + 9 x - 6 = 0
Hint: | Write the quadratic equation in standard form.Divide both sides by 2:x^2 + (9 x)/2 - 3 = 0
Hint: | Solve the quadratic equation by completing the square.Add 3 to both sides:x^2 + (9 x)/2 = 3
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.Add 81/16 to both sides:x^2 + (9 x)/2 + 81/16 = 129/16
Hint: | Factor the left hand side.Write the left hand side as a square:(x + 9/4)^2 = 129/16
Hint: | Eliminate the exponent on the left hand side.Take the square root of both sides:x + 9/4 = sqrt(129)/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the first equation: Solve for x.Subtract 9/4 from both sides:x = sqrt(129)/4 - 9/4 or x + 9/4 = -sqrt(129)/4
Hint: | Look at the second equation: Solve for x.Subtract 9/4 from both sides:Answer: x = sqrt(129)/4 - 9/4 or x = -9/4 - sqrt(129)/4

(-2)²-8(-2)+6=4+16+6=26.

A bank offers a CD that pays a simple interest rate of 6.0. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 6 years.

Answers

Since its simple interest then we shouldn't me calculating compound interest, Rate of interest = 6.0 Time period = 6 years Expecting amount after 6 years = â€‹$4500 There for , 4500/(1 + (3*6/100)) which is 4500/(1 + 0.18) It gives us 4500/1.18 = 3813.56 so we have to put $3813.56

You play video games online. When you sign up with the game site, you get 400400 points. You earn 5050 more points for each hour that you play. How many hours do you have to play to get to 1,000 points?

Answers

The answer to your question would be 12 because you would subtract 400 from 1000 and get 600 then youbdivide 50 into 600, therefore giving you the answer 12.

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A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000. (a) What was the initial size of the squirrel population?

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A grey squirrel population was introduced in a certain county of Great Britain 35 years ago. Biologists observe that the population doubles every 7 years, and now the population is 60,000.
(a) What was the initial size of the squirrel population?