The mosquito population of a national park was 800,000 in 2003. If the population grew at a rate of 8.7% per year, approximately how many mosquitoes would havebeen in the park in 2008
Answers
Let P be the initial population of mosquitoes for a given year. Let k be the percentual increase of the population over a year.
To calculate the population after a year, first calculate the increase by multiplying k times P:
\(\text{Increase}=k\cdot P\)Add the increase to the initial population to know the population after a year:
\(\begin{gathered} \text{Population after a year }=\text{ Increase + initial population} \\ =P+kP \\ =(1+k)\cdot P \end{gathered}\)Therefore, to calculate the population after a year, we have to multiply the initial population by (1+k).
To calculate the population after two years, take (1+k)P as the new initial population:
\(\begin{gathered} \text{Population after 2 years }=(1+k)\cdot(1+k)P \\ =(1+k)^2\cdot P \end{gathered}\)By analogy, after n years, the population will be equal to:
\((1+k)^n\cdot P\)Since 5 years pass from 2003 to 2008, the initial population was 800,000 and the yearly percentual increase is 8.7%, then n=5, P=800,000 and k=8.7/100. Substitute in the formula to know the population of mosquitoes in 2008:
\(\begin{gathered} (1+\frac{8.7}{100})^5\cdot800,000 \\ =(1+0.087)^5\cdot800,000 \\ =(1.087)^5\cdot800,000 \\ =1.517566463\cdot800,000 \\ =1,214,053.17 \end{gathered}\)Therefore, the population of mosquitoes in the park in 2008 will be approximately (to the nearest tousand):
\(1,214,000\)Related Questions
the first four terms of a sequence are shown below:
7,4,1,-2
which of the following functions best defines this sequence?
A) f(1)=7, f(n+1)= f(n)+3; for n>= 1
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
C) f(1)=7, f(n+1)= f(n)-4; for n >= 1
D) f(1)=7, f(n+1)= f(n)+4; for n >= 1
Answers
9514 1404 393
Answer:
B) f(1)=7, f(n+1)= f(n)-3; for n >= 1
Step-by-step explanation:
The first term of the sequence is 7 and the next (4) is found by adding -3 to that: 4 = 7-3. This is described in answer choice B.
Identify whether or not the relation is a function a yes b no
And how does it change
Answers
Answer:
Not a function
Step-by-step explanation:
This is not a function. It will fail the vertical line test. For any value of x, there are two different y values. This tells us that it is not a function
Jake has a piece of rope that is 5.5 yards long. What is the length, in inches, of Jake's rope?
O 180.5 inches
O 187.2 inches
O 186 inches
O 198 inches
Answers
Item 2
Which of the following is not another way of expressing 88 out of 100?
22/25
0.088
88%
0.88
Answers
Answer:
The answer is B: 0.088
Step-by-step explanation:
22/25, multiply both sides by 4 to get 88/100
88% is 88/100
0.88 is 88/10
0.088 would be a lot less than a whole number
A gym asks its customers about the kinds of athletic activities they do outside of the gym and records the results in the
table below.
Answers
The probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.
Here, we have to solve the question:
To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem
P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)
Where:
P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.
P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.
P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).
P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).
Let's start by filling in the values we know from the table:
P(Part-Time) = (40 + 25) / 155 = 0.5484
P(Gym Membership) = (30 + 25) / 155 = 0.3226
P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545
To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:
P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)
Plugging in the values we know, we get:
P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463
Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):
P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667
Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.
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complete question:
a group of 155 students at a private university were asked if they are full-time or part-time and if they have gym memberships. the results are shown in the table below. given that a randomly selected survey participant is part-time, what is the probability that this student has a gym membership?
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
The equations of a circle are:
x² + (y - 3)² = 36
x² + (y - 5)² = 36
Options A and B are the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The equation of a circle is (x - h)² + (y - k)² = r².
We have,
Diameter = 12 units
Radius = 6 units
Centre = (h, k) = y-axis
This means,
h = 0
So,
Centre = (0, k)
Now,
The equation of a circle.
(x - 0)² + (y - k)² = r²
x² + (y - k)² = 6²
x² + (y - k)² = 36
If k = 3 or 5,
x² + (y - 3)² = 36
x² + (y - 5)² = 36
Thus,
The equation of a circle is x² + (y - k)² = 36.
Where k can be any value.
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Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answers
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?
13.3km/L=__________mi/gal
Answers
The rental car is getting approximately 37.56 miles per gallon.
To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:
1 km/l ≈ 2.82475 mpg
Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:
13.3 km/l x 2.82475 mpg ≈ 37.56 mpg
So, your rental car is getting approximately 37.56 miles per gallon.
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divide550six by 50six
Answers
The quotient of 550six and 50six is obtained by the calculation to be 11 six
What is the quotient?We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.
We could start by converting the both values to base 10 as follows;
(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten
(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten
Then we carry out the division in base ten; 210 ten/30 ten = 7 ten
We convert back to base six to obtain 11 six
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-3 |5 - 2^3| + 3 x -1.5
Answers
The Answer: 3 x − 10.5
Find the measure of angle T for the kite below
Answers
Answer:
Angle T = 43°
Step-by-step explanation:
118+118+81 = 317
360-317 = 43
SLOPE DIGITAL ESCAPE ROOM
I need help finding the code
Answers
By finding all the four slopes, we can see that the word is ECHA.
How to find the word?We know that the general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
With that formula we can get the slopes.
1) Using the points (0, 3) and (2, 4).
m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.
2)Using (-1, -12) and (1, -8)
m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.
3) We have (2, -6) and (-4, -3) so:
m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H
4)we can use the points (0, 3) and (1, 1), so:
m = (1 - 3)/(1 - 0) = -2, so the letter is A
Then the word is ECHA
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Graph the line x= -7.
Answers
Answer:
b
i hope this work for you
and sory if im wrang
Which purchase may people be required to save a small amount of money invested regularly that grows over time?
A) college
B) groceries
C) concert tickets
D) bus passes
Answers
Answer:
college
Step-by-step explanation:
75 POINTS PLS HELP! find
Answers
Answer:
should be a
Step-by-step explanation:
An experiment consists of recording, in order of their births, the sex composition of a four-child family in which the children were born at different times. (Let b represent the birth of a boy and g represent the birth of a girl. Enter your answers using letter combinations separated by commas. Example: bgbg, gggg, ...)
(a) Describe an appropriate sample space S for this experiment.
(b) Describe the event E that there are three boys and a girl in the family.
Answers
(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:
S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}
There are 2^4 = 16 possible outcomes in the sample space.
(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:
E = {bbbg, bbgb, bgbb, gbbb}
There are 4 possible outcomes in the event E.
Darius and Matthew have 3 fruit bars.They are both hungry after playing football and decide to split the fruit bar evenly.How much fruit bar will each boy get ?
Answers
Answer:
1 1/2 or 1.5
Step-by-step explanation:
If they split 1/2 of the bar with each other
3 bars x 1/2 split bar = 1.5 or 1 1/2 of the shared amount
3 *1/2=1.5 or 1 1/2
Make q the subject of the formula
P=2q+10
q=.......
Answers
p = 2q + 10
-2q = 10 - p
q = 10/-2 - p/-2
q = -5 - (-½p)
q = -5 + ½p
q = ½p - 5
The equation p = 2q + 10 is simplified for q and is written as q = (p - 10) / 2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
p = 2q + 10
Simplify the equation for q, then we have
2q + 10 = p
2q = p - 10
q = (p - 10) / 2
The equation p = 2q + 10 is simplified for q and is written as q = (p - 10) / 2.
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los alumnos de cuarto grado terminaron adornando también el foro de la celebración que mide de 3.5m de largo y 3.10m de ancho ¿cuánto liston compraron para el foro
Answers
Answer:
6.15
Step-by-step explanation:
Which of the following is the equation of a line with a slope of -5/9
Answers
Answer:
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Step-by-step explanation:
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assume point a is at a distance 0.1d from the left sheet. find the value of the electric field, in newtons per coulomb with its sign, at point a.
Answers
The expression gives us the magnitude of the electric field at point A is E = (σ1.L² + σ2.L²)/2ε₀.Ld
Electric charges create an electric field around them that affects the space and other charges present in it.
For the left rectangle, the total charge is:
q1 = σ1.L²
Where σ1 is the surface charge density of the left rectangle, and L is the length of the rectangle's side.
For the right rectangle, the total charge is:
q2 = σ2.L²
Where σ2 is the surface charge density of the right rectangle, and L is the length of the rectangle's side.
The total charge enclosed by the rectangular box is the sum of the charges on the two rectangles:
q = q1 + q2
Now we can apply Gauss's law:
Φ = E.A = q/ε₀
Where ε₀ is the permittivity of free space. Solving for E, we get:
E = (q/ε₀).1/A
Substituting the values of q and A, we get:
E = (σ1.L² + σ2.L²)/2ε₀.Ld
This expression gives us the magnitude of the electric field at point A.
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Complete Question:
Two large rectangular sheets of charge of side L are parallel to each other and separated by a distance d (d<L). The left and right sheets have surface charge densities of 12.5 uC/m² and -5.9 uC/m², respectively. Points A, B, C, and D are outside the sheets near the center of the squares. assume point a is at a distance 0.1d from the left sheet. find the value of the expression electric field, in newtons per coulomb with its sign, at point a.
Lightfoot Inc., a software development firm, has stock outstanding as follows: 20,000 shares of cumulative preferred 2% stock, $20 par, and 25,000 shares of $100 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $3,000; second year, $5,000; third year, $34,500; fourth year, $71,000.
Answers
The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.
To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.
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You cut a sheet of paper along its diagonal, as shown. What is the length of the diagonal? Round your answer to the nearest tenth
Answers
Answer:
c≈14.9 in
Step-by-step explanation:
What we have is a right triangle. We can use Pythagoreans theorem to solve for the hypotenuse.
\(a^2+b^2=c^2 = > c=\sqrt{a^2+b^2}\) ; \(a=10\) and \(b=11\)
\(c=\sqrt{(10)^2+(11)^2}\)
=> \(c=\sqrt{100+121}\)
=> \(c=\sqrt{221}\)
=> c≈14.9 in
Write in Slope Intercept Form :-)
Answers
y = -5x + 2
Explanation:
What is a name for the marked angle?
Answers
Have a nice day
PLEASE HELP! I am having trouble answering the last question. Given the function f(x)= -3+3x^2 Calculate the following values
Answers
Answer:
\frac{-3 + 3(a + h)^{2} + 3 - 3a^{2} }{h}
Step-by-step explanation:
All you have to do is take your values and plug them in and simplify!
\(\frac{-3 + 3(a + h)^{2} - (-3 + 3a^{2}) }{h}\)
\(\frac{-3 + 3(a + h)^{2} + 3 - 3a^{2} }{h}\)
The dot plots below show the results.
Students
Teachers
Which compares the medians of the data?
The median for the students is 4 and the median for the teachers is 8.
The median for the students is 2 and the median for the teachers is 3.
The median for the students is 4 and the median for the teachers is 3.
The median for the students is 2 and the median for the teachers is 8.
Answers
Answer: The median for the students is 2 and the median for the teachers is 3.
Step-by-step explanation:
Ordering the data for the students from the dot points:
0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4.
n = 20 which is positive so median position is average of:
= (n / 2) and = (n + 1) / 2
= 20 / 2 = 21 / 2
= 10 = 10.5
2 is in position 10 2 is in position 10.5
Average = (2 + 2) / 2 = 2
Student median is 2.
Teachers
0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8
3 is in position 10 as well as in position 10.5.
= (3 + 3) / 2
= 3
Teacher median is 3.
(In attachment, teacher plot is first and then the student follows)
Answer:
Students Median= 2
Teacher Median=3
Step-by-step explanation:
Clayton's mortgage payment was originally $2,460 per month. Now, after refinancing his home loan, Clayton's mortgage payment is $1,968. What is the percent of decrease in Clayton's mortgage payment?
please
Answers
Answer:
20%
Step-by-step explanation:
2460-1968=492
492/2460=0.20
Check answer2460 x 0.20 = 492
How does this problem works?
Answers
Answer:
I literally NEVER got this. it was the most complicated thing to me and still is.
Step-by-step explanation:
Find the sum and express it in simplest form.
(7t³ + 3t - 1) + (-9t³ + 2t)
DO
Enter the correct answer.
Answers
Answer:
-2\(t^{3}\) + 5t - 1
Step-by-step explanation:
(7\(t^{3}\) + 3t - 1) + (-9\(t^{3}\) + 2t)
7\(t^{3}\) - 9\(t^{3}\) + 3t + 2t - 1 Combine like terms
-2\(t^{3}\) + 5t - 1
Like terms have to have the same variable and the same exponents to be like terms.