One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. If P represents the number of female insects in a population, S the number of sterile males introduced each generation, and r the population's natural growth rate, then the female population is related to time t by
t =
P+S
P[(r−1)P − S]
dP
Suppose an insect population with 10,000 females grows at a rate of r = 0.10 and 900 sterile males are added in each generation. Evaluate the integral to give an equation relating the female population to time. (Note that the resulting equation cannot be solved explicitly for P.)
The equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the female population is related to time t by;
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
Now, to do partial fraction;
(P+S)/P((r-1)P-S) = A/P + B/((r-1)P-S)
P + S = A((r-1)P -S) + PB
if P = 0, then:
A = -1
If (r-1)P - S = 0
p = S/(r-1)
B = 1 + r - 1
B = r
Therefore,
[tex]t = \int\limits {\frac{(P+S)}{P((r-1)P-S)} } \, dP[/tex]
t = -ln|P| + ln|(r-1)P-S| + 1/r-1 x integral((r-1)/[(r-1)P-S])
t = -ln|P| + ln|(r-1)P-S| + ln|(r-1)P-S|/(r-1)
t = -ln|P| + (r/r-1)ln|(r-1)P-S|
Now substituting known constants then;
t = -ln|P|-1/9(ln|-0.9P - 900|)
t = -ln|P| - 1/9(ln|-0.9P -900|)
t = -ln|P| - 1/9(ln(|(-9/10)(P + 1000)|))
t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
as P >= 0, ln(P) and ln(P + 1000) doesn’t need abs value
Therefore, the equation relating female population with time requested by t = -ln(P) - 1/9ln(P + 1000)- 1/9ln(9/10)
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Find the perimeter of the rectangle
= 2(2 + 3) units
= 2 × 5 units
= 10 units.
Answer:The perimeter of the rectangle is 10 units.
Hope it helps.
Do comment if you have any query.
solve for x! please help giving BRAINLIEST.
Answer:
its 45
Step-by-step explanation:
Greg received 3/8 of the votes cast for class secrectary. How many votes did he receive
Write your answer in simplest form
( show me how you got your answer like an explanation please Thanks! :)
Answer: 3/8
Step-by-step explanation: We don't know how many votes are there for the class secretary.
A sample in which each element in a population has a equal chance of being selected
Answer:
simple random sample
Step-by-step explanation:
I hope that's it
Where do I put the parenthesis to make it true?
5 – 6w – 5 – 95 + 2w = –48w – 70
Answer:
i just stole your points thank you
Step-by-step explanation:
5 – 6w – 5 – 95 + 2w = –48w – 70
-6w + 2w + 48w = -70 -5 + 5 +95
44w = 25
w=25/44
What is the equation of the line??
Answers:
m = -2/3
b = 1
equation: y = (-2/3)x + 1
This is the same as writing [tex]y = -\frac{2}{3}x+1[/tex]
===========================================================
Explanation:
There are a few approaches, but I like to start at the y intercept whenever it is an integer. The y intercept is where the diagonal line crosses the vertical y axis. In this case, that location is (0,1) telling us that b = 1 is the y intercept.
From that starting anchor point, we need to find a way to get to another point on this line. There are a few ways to do this, but we can move down 2 and to the right 3 units to go from (0,1) to (3,-1). This "down 2 right 3" motion directly leads to the slope of rise/run = -2/3
---------------
Alternatively, you can start at something like (-3,3) and move down 4 and move right 6 to arrive at (3,-1). Note how rise/run = -4/6 = -2/3. No matter where you start, moving along this line will involve a "down 2 right 3" movement pattern. Be sure to reduce any fractions as much as possible.
Yet another alternative is to apply the slope formula using any two points on the line. Preferably they have integer coordinates.
----------------
However you determine the slope, it's m = -2/3 after fully reducing. It along with b = 1 is plugged into y = mx+b to get y = (-2/3)x+1 as the equation of this line. It's in slope intercept form.
I need help with part a and b please
Answer:
The total answer should be 38 on the top
Step-by-step explanation:
a) So the first partial quotient would be equal to 30 as 31 x 30 = 930
b) Second partial quotient would be 8 as 31 x 8 = 248
Answer:
0
38
I hope it's help byeeee
Write 5/6% as a decimal number.
Answer: 5/6 as a decimal is 0.833
Step-by-step explanation:
just divide 5 by 6
A ruler 30 cm long is broken into two parts in the ratio 8:7. How long
are the two parts?
Answer:
Step-by-step explanation:
Length of each part of the ruler will be
8x and 7x
. Hence, 8x+7x=30 => 15x=30 =>x=2
Hence, the lengths will be
8x=8×2=16
7x=7×2=14
Jerome makes and sells his own energy drinks. He mixes a liquid drink mix with water to create his own special blend. Jerome usually uses 8 cups of water and 3 cups of drink mix. Tomorrow, there is a road race in town, however, and Jerome thinks he’ll be able to sell a lot more of his energy drinks than usual. Jerome’s brother told him to add one cup of water for every one cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. Jerome’s sister told him to multiply both the amount of water and the amount of drink mix by the same number to keep the ratio the same and still increase the total amount of energy drink. Who is correct: Jerome’s brother or Jerome’s sister? As you complete the task, keep this question in mind: Based on what you know about ratios, what do you think the answer will be? Directions: Complete each task, reading the directions carefully as you do. You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given partial credit based on the work you show and on the completeness and accuracy of your explanations. Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy. Now let’s get started! Step 1: Finding the part-to-part and part-to-whole ratios To make his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix. What is the ratio of water to drink mix? (2 points) What is the ratio of drink mix to water? (2 points) What is the ratio of drink mix to mixed energy drink? (2 points) What is the ratio of water to mixed energy drink? (2 points) Step 2: Testing Jerome’s brother’s approach Jerome’s brother told him to add one cup of water for every one cup of drink mix he add
Answer:
not well explained??
Step-by-step explanation:
?? explain it better bro.
Help I have a C in math. I don't understand this Alegbra. If you get it right then I will give you Brainlist!
I know I already got the right answer so please give an explanation too!
Answer:
11
Step-by-step explanation:
to find the area of a square: base times height, we know that all sides of a square are the same. So, 11*11
=121, the answer is 11
Answer:
11 in.
Step-by-step explanation:
The canvas has the shape of a square.
The area of a square is the side times the side, but since in a square, all sides have equal lengths, then the area of a square is the square of the side.
You are given the area. You need to find the side.
The area is the square of the side, so the side is the square root of the area.
side = √area
side = √(121 in.²)
side = 11 in.
need help, im confused
Answer:
Part A: correct
Part B: $20
Step-by-step explanation:
Part B:The amount Vanessa pays for her printer and 2 cartridges is ...
$90 +2(25) = $140
The amount Tia pays for her printer and 2 cartridges (c=2) is ...
t = 80 +20(2) = 120 . . . . dollars
Then the difference in the amounts they pay is ...
$140 -120 = $20
Sum of the Angles of a Triangle
If the three angles of a triangle
are equal, what is the
measurement of each angle?
B
C
[?] degrees
9514 1404 393
Answer:
60°
Step-by-step explanation:
If the measure of the angle is represented by A, then the sum of the three angles in the triangle is ...
A +A +A = 180°
3A = 180° . . . . . . . simplify
A = 180°/3 = 60° . . . . . divide by the coefficient of A
The three angles in an equi-angular triangle are all 60°.
__
Additional comment
If the angles are equal, so are the opposite sides. The three sides in an equi-angular triangle are also equal. Generally, such a triangle is called an equilateral triangle. It is useful to remember the angles in an equilateral triangle are all 60°.
One interesting consequence of this is that the smallest angle in any triangle can never be larger than 60°.
Customers at a gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the scenario.
What is the slope of the line?
Find the value of e.
Step-by-step explanation:
sum of three angles in a triangle is 180
55+35+x=180
90+x=180
x=180-90
x=90
Two students are working on the same homework assignment. Antonia has completed 18 out of 45 questions. Oliver has completed 20% of the questions. Which student has completed the most questions, and why?
Answer: Your anwser who has the most completed it would be the person with 18 questions anwsered out of 45
Step-by-step explanation:
The reason of this is becuase 20 percent of 45 if 9 and thats 9 questions out of 45 so 18 questions out of 45 is more
please mark brainliest thank you
in an auditorium,there are 104 rows with 24 seats in each row.how many seats are available?
Answer:
2,496 seats
Step-by-step explanation:
If there are 104 rows with 24 seats in EACH row, we must multiply to find the answer. Which is gives you the equation: 104 x 24 = 2,496
hope this helps!
mark me brainliest :D
hen Max was a puppy, he weighed 512 pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.
How much weight did Max gain between the time he was a puppy and his 1-year check-up?
Enter your answer as a decimal or simplified mixed number in the box.
Answer:
10.3lbs or 10 3/10 as a mixed number
Step-by-step explanation:
i have the same question on my test so i know this is right but here's an explanation: so 5 1/2 pounds is the same as 5.5 pounds, and if you add 10 pounds to 5.5 pounds, you get 15.5 pounds, which is 3 ounces away from 15.8 pounds. so adding 3 ounces to the 10 pounds, then adding that to the 5.5 pounds, you would get 15.8. therefore, your answer is 10.3lbs.
The puppy gained 10.3 pounds of weight in 1 year.
What is subtraction?Subtraction is one of the arithmetical operations, to subtract means to take away from a group or a number of things.
Given that, Max was a puppy, he weighed [tex]5\frac{1}{2}[/tex] pounds. At his 1-year check-up with the vet, Max weighed 15.8 pounds.
[tex]5\frac{1}{2}[/tex] pounds = 5.5 pounds
Weight before 1 year = 5.5 pounds
Weight after 1 year = 15.8 pounds
Weight gained by the puppy in 1 year = 15.8-5.5 = 10.3 pounds
Hence, the puppy gained 10.3 pounds.
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78 divided by 21?:-:
Answer:
3.7 or 3.71428571429
Step-by-step explanation:
:/
Answer:
3.714
Step-by-step explanation:
78/21 is 3.71428571429 but you can round that to 3.714
Weverton Cliffs is a hiking trail in Maryland. This trail is 3 inches long on a map that has a scale of 7 ½ inches = 15 miles.
If Sarah hikes Weverton Cliffs from beginning to end and returns along the same trail, what is the total distance she hikes?
A. 3 miles
B. 6 miles
C. 12 miles
D. 18 miles
Answer: Is 6
Step-by-step explanation: Because 1 mile = 1/2. Is this helpful?
1. You are interested in recycling behavior and whether it varies between urban and
rural residents. You know that the statewide recycling rate is 48.89%, and you
survey 140 rural residents and 310 urban residents to find out if they recycle.
180 urban residents respond that yes, they recycle. 130 do not. 40
rural residents recycle, and 100 do not.
a) Construct an expected frequencies crosstab, based on the sample size and the
statewide recycling rate.
b) Construct an observed frequencies crosstab, based on your actual data.
(NOTE for 1a and 16: Be sure to include both percentages and frequency values, in
Answer:
65
Step-by-step explanation:
If I am ordering a custom wood frame costing $1.27 per inch and the entire area needing framing is 17" on all4 sides, how is price tabulated?
14. Explain why a rotation of positive 180 degrees is the same as a rotation of -180 degrees.
Answer:
t is the same because...
Step-by-step explanation:
turning -180 is like turning right turning left no matter how you turn you will still be in the opposite from which you started
I have to get this done by today pls help me
Answer:
16
Step-by-step explanation:
d = 800
t = ( 1 / 500 ) d
t = ( 1 / 500 ) 800
= 800 / 500
t = 1.6 hours
Simplify to the form of a square root of b
Answer:
If we substitute a and b to equal 6 for example
it would be
√
6
2
+
6
2
it would equal 8.5(1.d.p) as it would be written as
√
36
+
36
giving a standard form as
√
72
However if it was
√
6
2
+
√
6
2
it would equal 12 as the
√
and
^
2
would cancel out to give the equation 6+6
Therefore
√
a
2
+
b
2
cannot be simplified unless given a substitution for a and b.
I hope this isn't too confusing.
Step-by-step explanation:
I need help with my algebra.
Answer:
f(-2) =-2
Step-by-step explanation:
f(-2) means what is the output of the function when the input of the function is -2
When x =-2, y =-2
f(-2) =-2
WHAT IS 159 DIVIDED BY 3 (ITS NOT HARD PLEASE ANSWER I DON'T HAVE A CACULATER)
Answer:
Step-by-step explanation:
The asked quotient of 159 divided by 3 is the number 51.
What is divide?It is the inverse of multiplication, and it is used to find out how many times one number can be divided by another. In mathematics, the division is an arithmetic operation that involves splitting a quantity into equal parts or groups.
Here,
As mentioned in the question, we have to determine the quotient of 159 divided by 3
So let the quotient be y,
y = 159/3
y = 51
Thus, the asked quotient of 159 divided by 3 is number 51.
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WILL GIVE BRAINLIEST
These two triangles are congruent by ....
O SSS
O SAS
O HL
O ASA
O AAS
O the triangles are NOT congruent
SAS postulate states that if two sides and one angle of the two triangles are congruent then the corresponding triangles are congruent.
These two triangles are congruent by SAS postulate
Proof
Statements Reasons
In ΔNHJ ↔ ΔKHJ
mHJ≅mHJ common to both Δs∠N≅∠K right anglesmHN≅mHK givenFrom 1,2, and 3 ΔNHJ ≅ ΔKHJ SAS≅SAS
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If AZ = 85 ZE=51 find Bc
