3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared the insect endangered and transplanted the insect to protected area. The population P(t) (in thousands) of insects in t months after being transplanted is
a. [3 pts] Determine the number of months until the insect population reaches 40 thousand (round to 2 decimal places).
b. [3 pts] What is the limiting factor on the insect population as time progresses? Explain your answer.
c. [3 pts] Sketch a graph of the function using the window and. Be sure to indicated the scale on the graph, label the axes, at least 2 points on the graph, and any asymptotes.
Answers
The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.
Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).
(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get
P(t)=40
(50(1+0.05t))/(2+0.01t)=40
Cross multiply both sides, we get
50(1+0.05t)=40(2+0.01t)
Apply the distributive property a(b+c)=ab+ac, we get
50+2.5t=80+0.4t
Subtract 0.4t and 50 from both sides, we get
50+2.5t-0.4t-50=80+0.4t-0.4t-50
2.1t=30
Divide both sides with 2.1, we get
t=14.29 months
(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get
[tex]\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end[/tex]
(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.
Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.
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Related Questions
How many pounds are in112 ounces? Enter only the number. Do not include units.
Answers
There are 7 pounds in 112 ounces
How to determine the number of pounds?There is 1 pound in 16 ounces
So, the number of pounds in 112 ounces is
Pounds = 116 ounces/16 ounces
Remove the unit
Pounds = 112/16
Evaluate the quotient
Pounds = 7
Hence, there are 7 pounds in 112 ounces
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The tables show proportional relationships between x and y. Match each table with its constant of proportionality.
xy
1 10
2 20
3 30
xy
4 20
8 40
12 60
x y
2 15
4 30
6 45
4
12/04
10
xy
14
2 8
3 12
Answers
Find DE
3x - 28
3x - 30
D
G
E
F
33
Answers
Answer:
11
Step-by-step explanation:
(3x-28) + (3x-30) + x = 33
7x - 58 = 33
7x = 91
x = 13
DE = 3x - 28 = 3*13 - 28 = 11
(02.05 LC)
Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) + 4?
The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Answers
Answer:
1st option
Step-by-step explanation:
given the graph of f(x) then the graph of f(x) ± c is a vertical translation of f(x)
• if - c then a shift down of c units
• if + c then a shift up of c units
then for f(x) + 4 is a shift up of 4 units
W
If 15 cans of food are needed for 7 campers for 2 days,
the number of cans needed for 4 campers for 7 days
is? (round up to nearest whole number)
Answers
Answer:
30 cans
Step-by-step explanation:
cross multiply
14x = 28 * 15
14x = 420
x = 420/14
x = 30 cans
How much will you have saved after 6 years by contributing $1,200 at the end of each year if you expect to earn 11% on the investment?
Answers
Savings after 6 years would be $ 1992.
What are savings?Savings is the money that remains after expenses and other commitments have been subtracted from income.
Savings are the sum of money that would otherwise be lying about, not being risked on investments or used for consumption.
Savings and investing can be compared because the latter includes putting money at risk in an effort to try to increase wealth.
Indicators of household debt or a negative net worth include negative savings.
According to the question,
Amount contributed(P)= $1200
Rate(R)= 11%
Time(T)= 6 years
Interest(SI)=P*R*T/100
= 1200*11*6/100
= 792
Savings after 6 years = P+ SI
= 1200 + 792
= $ 1992
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PLEASE HELP! And thank you so much! I will mark you brainliest. I just need an urgent response! Thank you for your time
Answers
Answer:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
Step-by-step explanation:
A)
x + y = 80
y = x + 20
B) x = 30 minutes
Replacing y with x + 20 in the first equation ->
x + x + 20 = 80
2x + 20 = 80
2x = 60
x = 30
C) No. If Pam dances for 60 minutes, and dances for 20 minutes longer than she does math, then she does math for 40 minutes. This means she spends 100 minutes total. 100 minutes is not 80 minutes, thus this is not possible.
Q1. A man wants to paint his house in 3 colors. If he can choose 3 colors out of 6 colors, how many
different color settings can he make?
(A) 216 (B) 20 (C) 18 (D) 120
Answers
the radius of the base is 4 inches and its height is 6 inches what is the surface area of the cylinder in terms of pi
Answers
Step by step
To find lateral_area = (2 * π * r) * h
Since it’s in term of pi,
(2 x radius x height) pi
2 x 4 x 6 = 48pi
base_area = 2 * π * r²
Since it’s in terms of pi
(2 x r^2)
(2 x 4^2)
= 32pi
Total surface area in terms of pi = 32+48
= 80pi
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
Answers
Using translation concepts, it is found that g(x) is positive on the following interval:
(3, ∞)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Function [tex]g(x) = \sqrt[3]{x - 3}[/tex] is a shift right of 3 units of [tex]f(x) = \sqrt[3]{x}[/tex], which is positive on the interval (0, ∞), hence g(x) is positive on the interval (3, ∞).
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A ______ function is a specific type of function that represents the relationship between two variables, usually x and y. The graph of this function is a line.the answer choices are
dependent
independent
parallel
slope
perpendicular
rate
scale
y
change
linear
Answers
Answer:
dependent
Step-by-step explanation:
because when x decreases y has to also decrease, so they are dependent on eachother
PLEASE HELP 80 POINTS!!!!!!
Answers
The sequence pattern for 3¹/₃, 3¹/₄, 3¹/₅, ...... is; f(n) = 3 + 1/(2 + n)
How to find the sequence pattern?We are given the sequence;
3¹/₃, 3¹/₄, 3¹/₅, ......
Now, we can see that;
First term is 3¹/₃.
However, for the second term, 1 has been added to the denominator.
Thus, we can suggest that the sequence pattern here is;
f(n) = 3 + 1/(2 + n)
where n is the nth term.
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how much must be deposited today to have $45,000 in 5 years with a quarterly compounding and an APR of 7.3%
Answers
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81
A model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house.
Answers
Answer: 13 in.
Step-by-step explanation:
All you need to do is divide 26 by 2 in this case.
Find the measure of MON
Answers
Answer: 77 degrees
mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.
A pitcher originally contains a juice drink with 20 percent cranberry juice. After 4 ounces of cranberry juice is added, the new drink is one-fourth cranberry juice. How many total ounces of juice drink are in the pitcher after the addition of the cranberry juice?
Answers
20%=0.2
1/4=0.25
0.2x+4=0.25x
-0.2x -0.2x
4=0.05x
4/0.05=x
80=x
80 total ounces
If you go out to eat with 3 friends and your meal was $72.50, there is 6.75% sales tax
and you should tip the waiter 15%. How much should each person pay?
Tax $
Total meal cost
Tip $
Total cost of meal with tip
Price for each person
Answers
After the tax and the tip are counted, we conclude that each friend must pay $30.
How much should each person pay?We know that the meal cost is $72.50.
Now, there is a 6.75% sales tax and a 15% tip on the waiter (we assume that the tip is based on the total meal cost, after the tax is applied).
Then the total meal cost is:
C = $72.50*( 1 + 6.75%/100%) = $72.50*(1 + 0.0675) = $77.39
Now we also need to add the tip, which is a 15% of that, so the total cost with the tip included is:
C' = $77.39*(1 + 15%/100%) = $88.998 = $90
(Where we rounded up).
Then, if there are 3 friends, each one must pay:
$90/3 = $30
Each friend must pay $30.
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11. What effect size do you use for parametric t-tests?
12. What effect size do you use for non-parametric t-tests?
13. What effect size would you use for chi-square tests?
Answers
The effective sizes for parametric tests, non parametric tests and chi square tests are as detailed below.
How to interpret the size of statistics test?
11) Parametric t-tests are statistical tests that assume the data approximately follows a normal distribution. Now, when trying to check for parametric t-tests, the effective size we use is Cohen's d which is an appropriate effect size for the comparison between two means.
12) Nonparametric t-tests are those statistical tests that don’t assume anything about the distribution followed by the data, and hence are also known as distribution free tests.
In non - parametric t - tests, we calculate effect size by using the formula;
r = z/√N
where;
r is effect size
z is z value
N is Observation number.
13) In the chi-square test, the effect size index (w) is calculated by dividing the chi-square value by the number of scores and taking the square root.
The effective size is considered small if w = 0.10, Considered medium if w = 0.30, and large if w = 0.50.
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If two numbers are selected at random ,one after the other with replacement from the set A=(5,6,7,8,9) find the probability of selecting at least one prime number
Answers
Answer:
16/25
Step-by-step explanation:
(at least 1 prime selected)=1−(no primes selected)
There are 3 numbers in the set that are not prime (6,8,9)
(no primes selected)=(35)2=925
(at least 1 prime selected)=1−925
=1625
cual es el valor de 4+x=9
Answers
Answer:
x=5
Step-by-step explanation:
Resolvamos tu ecuación paso a paso.
4+x=9
Paso 1: simplifica ambos lados de la ecuación.
x+4=9
Paso 2: Resta 4 de ambos lados.
x+4−4=9−4
x=5
Answer:
4+x=9
or, x=9-4
or, x=5
the value of x is 5
4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.
Answers
Answer:
8
Step-by-step explanation:
The definition of an average can be used with the given values to write an equation for the number of boys.
SetupThe average is the total divided by the number. If there were n original boys, the total was T, where ...
T/n = 145 ⇒ T = 145n
Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...
(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320
Equating the values of T, we have ...
T = 145n = 148(n +2) -320
SolutionSolving for n, we find ...
0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify
0 = n -8 . . . . . . . . . . . divide by 3
8 = n . . . . . . . . . . . add 8
The number of boys in the group at first was 8.
A client is instructed to drink 20 ounces of water with 1 hour. The client has only been able to drink 12 ounces. What portion of water remains? (express your answer as a fraction reduced to lowest terms)
Answers
Answer:
2/5
Step-by-step explanation:
20 ounces in all - 12 ounces drank = 8 ounces left
8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4
The portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A client is instructed to drink 20 ounces of water for 1 hour. The client has only been able to drink 12 ounces.
The remaining portion = 20 ounces - 12 ounces drank
The remaining portion = 8 ounces left
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
The fraction:
= 8 ounces left/20 ounces in all = 4/10 = 2/5 = 0.4
= 8/20
= 2/5
Thus, the portion of water remaining is 2/5 if the client is instructed to drink 20 ounces of water for 1 hour.
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Which statement is true about the slope of the graphed line?
A graph is a line that extends from second quadrant to first quadrant with y-intercept at 4.
A.
The slope is negative.
B.
The slope is positive.
C.
The slope is zero.
D.
The slope is undefined.
Answers
Answer:
c
Step-by-step explanation:
because I had a test on these
Find the remainder when f(x)=2x^3-x^2+x+1 is divided by 2x+1
Answers
Answer:
0
Step-by-step explanation:
By the remainder theorem, this is the same as finding f(-1/2), which is equal to 0.
The function f(X) =7^x + 1 is transformed to function g through a horizontal compression by a factor of 1/3
Answers
The equation of the function g(x) is g(x) = 7^(3x) + 1
How to determine the function g(x)The function f(x) is given as:
f(x) = 7^x 1
When compressed horizontally by a factor of 1/3.
We have:
g(x) = f(3x)
This implies that:
g(x) = 7^(3x) + 1
Hence, the equation of the function g(x) is g(x) = 7^(3x) + 1
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Y=x2+1 ordered pairs
Answers
The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
How to determine the ordered pairs?The function is given as:
y = x^2 + 1
the ordered pairs are the x and y values of the function
So, we stet x = 0, 1, 2, 3 and 4
y = 0^2 + 1 = 1
y = 1^2 + 1 = 2
y = 2^2 + 1 = 5
y = 3^2 + 1 = 10
y = 4^2 + 1 = 17
Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
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Which is the equation of an asymptote of the hyperbola whose equation is [tex]\frac{(x-2)x^{2} }{4} -\frac{(y-1)x^{2} }{36}[/tex]= 1?
y = −3x − 5
y = −3x − 7
y = 3x − 5
y = 3x + 7
Answers
The equation of the asymptote is y = 3x - 5. The correct answer is option C
What is Asymptote of an Hyperbola ?The distance from a point and the distance to a line in hyperbola is known as asymptote. The general equation is [tex]x^{2}/ a^{2} - y^{2}/b^{2} = 1[/tex]
From the given equation of hyperbola, which is
[tex]\frac{(x - 2)^{2}}{4}[/tex] - [tex]\frac{(y - 1)^{2} }{36}[/tex] = 1
The center (h , k) of the hyperbola = C(2, 1)
a = 2
b = 6
Where C = [tex]\sqrt{a^{2} + b^{2} }[/tex]
C = [tex]\sqrt{4 + 36}[/tex]
C = [tex]\sqrt{40}[/tex]
C = [tex]2\sqrt{10}[/tex]
The equation of the asymptote will be y - K = +/-(b/a)(x - h)
That is,
y - 1 = +/-(6/2)(x - 2)
y - 1 = +/-3(x - 2)
y - 1 = +/-3x - 6
y = +/-3x - 6 + 1
y = +/- 3x - 5
Therefore, the equation of the asymptote is y = 3x - 5.
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Tell whether the equation 3x - 6y = 0 is a direct variation. Explain. If the equation is a direct variation, identify the constant of variation.
Answers
The equation is in direct variation and have constant of variation is 2.
According to the statement
we have given equation is 3x - 6y = 0 and find that the equation is direct variation of not.
Direct variation is the mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
So, to find the direct variation equate the given equation equal to zero and solve it.
So, 3x - 6y = 0
3x=6y
or
x/ y=2 or x=2⋅y
here x is directly proportional to the y by 2 times.
∴x∝y
So, this equation in direct variations and constant of variation is 2.
From above this is clear that the equation is in direct variation and have constant of variation is 2.
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The difference of four times a number and seven is 21
Answers
Answer: 4n - 7 = 21, n = 7
Step-by-step explanation:
A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.
Hence, the equation that is represented by the question is
[tex]4x - 7 = 21[/tex]
We can also solve this equation (i.e., find the value of x that makes this equation true).
Adding 7 to both sides, we get
[tex]4x - 7 + 7 = 21 + 7[/tex]
Since the -7 and 7 add to 0, the equation becomes
[tex]4x = 28[/tex]
To get x by itself, we can divide both sides by 4, making the equation
[tex]x=7[/tex]
Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.
PLEASE HELPPPPPPPPPPPP!!!!!!! IM BEING TIMEDDDDDD
Answers
Answer:
119°
Step-by-step explanation:
the angles of a triangle make 180° (so does a straight line) therefore
180 (triangle) = a + c + 51
to find c:
180 (straight line) = 112 + c
c = 180 - 112
c = 68°
now we have
180 (triangle) = a + 68 + 51
to find a:
a = 180 - (68 + 51)
a = 180 - 119
a = 61°
to find b:
180 (straight line) = 61 + b
b = 180 - 61
b = 119°