A given field mouse population satisfies the differential equation dp/dt=.4p-450 where p is the number of mice and t is the time in months.
(a) Find the time at which the population becomes extinct if p(0)=1075
Round your answer to two decimal places in months.
(b) Find the initial population Po if the population is to become extinct in 1 year.
Round your answer to the nearest integer.
Po= mice
Answers
Answer:
a) 7.78 months
b) 1116
Step-by-step explanation:
Given -
\(\frac{dP}{dt} = 0.4p-450\)
Integrating the above equation with respect to time, we get -
\(\int\ \frac{dP}{0.4p-450} = \int\ dt\\\)
let us define new variable x
\(x = 0.4p - 450 \\dx = 0.4 dy\)
substituting these values in above integral equation, we get -
\(\frac{1}{0.4} \int\ \frac{dx}{x} = \int\ dt\\ln x = 0.4 t + C\\x = ce^{0.4t}\)
\(P (t) = \frac{C}{0.4} e^{0.4t} +1125\\\)
at t = 0, P (0) = 1075, using this condition, we get -
\(\frac{c}{0.4} = -50\\P(t) = 50 e^{0.4t} +1125 \\t = 7.78\\P(0) = 1125 - \frac{1125}{e^{4.8}} = 1116\)
Related Questions
y=9/4×2
sketch the graph of f and f on the same set of axes
Answers
The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.
The graph represents a parabola that opens upward. As x increases, the corresponding y-values increase, forming a curved shape. The vertex of the parabola is at the origin (0,0). The graph is symmetric with respect to the y-axis, meaning that the left and right sides of the parabola are mirror images of each other.The slope of the graph gradually increases as x moves away from the origin. The steepness of the curve becomes more pronounced, indicating a faster rate of increase in y-values for larger x-values.The graph does not intersect the x-axis, indicating that there are no real roots or solutions for the equation f(x) = 0. The y-intercept of the graph is at (0, 0), and the y-values increase indefinitely as x approaches positive or negative infinity.Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.
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please help me ASAP :)
Answers
c.) 1/2³ i got it right on assignment
Pharoah Company had the following adjusted trial balance.
Pharoah Company
Adjusted Trial Balance
For the Month Ended June 30, 2020
Adjusted Trial Balance
Account Titles
Cash
Debit - $3,820
Accounts Receivable
Debit - 4,040
Supplies
Debit - 490
Accounts Payable
Credit - $1,800
Unearned Service Revenue
Credit - 180
Owner’s Capital
Credit - 4,180
Owner’s Drawings
Debit - 770
Service Revenue
Credit - 5,990
Salaries and Wages Expense
Debit - 1,500
Miscellaneous Expense
Debit - 390
Supplies Expense
Debit - 1,700
Salaries and Wages Payable
Credit - 560
$12,710
Prepare a post-closing balance.
Answers
Answer:
The solution is given below
Step-by-step explanation:
The preparation of the post closing trial balance is given below
Particulars Debit amount Credit amount
Cash $3,820
Account receivable $4,040
Supplies $490
Account payable $1,800
Unearned service revenue $180
Owner capital ($4,180 + $5,990 - $1,500 - $390 - $1,700 - $770) $5,810
Salary and wages payable $560
Total $8,350 $8,350
Solve for x 3(x-8)=-29.7
Answers
Answer: x= -1.9
Step-by-step explanation:
Craig likes to collect vinyl records. Last year he had 10 records in his collection. Now he has 12 records. What is the percent increase in his collection?
Answers
Answer:
20%
Step-by-step explanation:
Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?
Answers
Based on the given parameters, the length of c is 8.0 units
How to determine the side length of c?The given parameters are
Angle c = 76 degrees
Side a = 20
Side b = 13
The length of c is then calculated using the following law of sines
c^2 = a^2 + b^2 - 2absin(C)
Substitute the known values in the above equation
So, we have
c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)
Express 20^2 as 400
c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)
Express 13^2 as 169
c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)
Evaluate the product and sin(76)
c^2 = 400 + 169 - 520 * 0.9703
Evaluate the product
c^2 = 400 + 169 - 504.55
Evaluate the exponents
c^2 = 400 + 169 - 504.55
So, we have
c^2 = 64.45
Evaluate the square root
c = 8.0
Hence, the length of c is 8.0 units
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I need help on this problem for 50 points 3000x9000
Answers
Answer:
The answer is 27,000,000
help me find the slope please
Answers
Answer:
3/4
Step-by-step explanation:
Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)
Slope is rise/run
Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.
Feel free to tell me if I did anything wrong! :)
Also, if you're still confused, I could explain it another way.
New Hope School started with only 94 students. Now the school has grown to 750% of the original size. How many students are in school now?
94
x7.5
--------
705 students
Answers
Answer:
Use maths papa
Step-by-step explanation:
y = |x - 5| + |x + 5| if x >5
Answers
Answer:
y = 2x
Step-by-step explanation:
You want the simplified form of y = |x -5| +|x +5| if x > 5.
Turning pointsThe graph of the whole function will have turning points where the absolute value expressions are 0:
x -5 = 0 ⇒ x = 5
x +5 = 0 ⇒ x = -5
For values of x > 5, we are concerned with that portion of the graph that is to the right of both of these turning points. Hence, both absolute value expressions are positive and unchanged by the absolute value bars.
y = (x -5) +(x +5) . . . . . . if x > 5
y = 2x . . . . . . . . . . . . . . collect terms
The simplified function is y = 2x.
__
Additional comment
The attached graph shows y=2x and the given function for x > 5. They are identical. (The y=2x graph is shown dotted, so you can see the red graph of the given function.)
please help image attached! x=?
Answers
Answer:
90°
Step-by-step explanation:
from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.
which value of x makes the equation 2+4(6-2x)
Answers
Answer:
8=8 so it is true
Step-by-step explanation:
Where should he plot he third point
Answers
Answer:
I think he should plot the point at (4, 2)
The attachment is a repost showing what I see if Jeff attaches the 3rd point to the listed points.
Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work.
Part C: Determine the average rate of change between station 2 and station 4. Show your work.
Answers
Answer:
She will need a time of 1024 units to complete the 10th station.
Step-by-step explanation:
A. As the quotient between consecutive terms is the same, the data is a geometric sequence.
B. The recursive formula is:
C. She will need a time of 1024 units to complete the 10th station.
In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.
If the quotient between consecutive terms is the same, the sequence is geometric.
Item a:
When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.
-(-v+y)-4(2y-4v)
How do I simplify this?
Answers
Step-by-step explanation:
hope you understand.
first simplify it by arranging correct signs then it's just subtraction or addition.
What is the greatest whole number that rounds to 2,600 when rounded to the nearest hundred? The
least whole number?
Answers
Answer:
Greatest- 2,649
Least- 2,550
4 times 1
8 over 9 equal
Answers
Step-by-step explanation:
4*1 = 4
this indicates multiplication
8/9 = 0.88888888888 which when simplified would go back to 8/9 or .889
8 "over" 9 indicates division!
Extra Credit #4
What are the next two numbers in this pattern?
431
141311
1114111321
311431131211
Answers
Answer:
The next two numbers following:
431
141311
1114111321
311431131211
are:
132114132113111221
AND
11131221141113122113312211
Step-by-step explanation:
I shall explain the pattern below:
431 (just the digits 4, 3, and 1)
141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)
1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)
311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)
NEXT TWO NUMBERS:
one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)
that makes: 132114132113111221
one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)
that makes: 11131221141113122113312211
The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.
Consider the marginal cost function
C′(x)=0.09x^2 − 4x+60.
a. Find the additional cost incurred in dollars when production is increased from 4 units to 20 units.
b. If C(4)=203, determine C(20) using your answer in (a).
(Do not round until the final answer. Then round to two decimal places as needed.)
Answers
The additional cost that is incurred in dollars when production is increased from 4 units to 20 units is $516.80.
If C(4)=203, C(20) is given as $719.80
How to determine the additional cost and C(20)To determine the additional cost incurred when production is increased from 4 units to 20 units, we need to first obtain the difference between the cost of producing 20 units and the cost of producing 4 units.
The result is obtained by integration as follows:
C(x) = ∫ C'(x) dx = ∫ (0.09x^2 - 4x + 60) dx = 0.03x^3 - 2x^2 + 60x + C
Note that the constant is 'c'.
The additional cost when there is an increment from 4 to 20 units will be:
C(20) - C(4)
= (0.03*20^3 - 2*20^2 + 60*20 + C) - (0.03*4^3 - 2*4^2 + 60*4 + C)
= $516.80
To solve the second part of the question, We are given these values:
C(4) = 203.
Also, from the expression we derived in part (a) for C(x), we can solve for the constant of integration C by substituting C(4) = 203 this way:
C(4) = 0.03*4^3 - 2*4^2 + 60*4 + C = 203
C = 83
To obtain C(20) we substitute C = 83 and x = 20 into the expression we derived in part (a) thus
C(20) = 0.03*20^3 - 2*20^2 + 60*20 + 83
= $719.80.
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QUESTION 6 1 POINT
Using the table, what is the average daily balance of the credit card for the August 1 through August 31 billing period?
Round your answer to the nearest dollar.
Provide your answer below:
Day
1
8
16
24
Activity
Payment
Purchase
Purchase
Adjustment Closing Balance
-550
4
+200
+150
850
300
500
650
Answers
Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.
To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.
Let's calculate the daily balances for each day:
Day 1: Closing Balance = $850
Day 8: Closing Balance = $300
Day 16: Closing Balance = $500
Day 24: Closing Balance = $650
To calculate the daily balances, we need to consider the activities that occurred on each day.
On Day 1, there was no activity recorded, so the closing balance remains at $850.
On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.
On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.
On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.
Now, let's calculate the average daily balance:
Sum of daily balances = $850 + $300 + $500 + $650 = $2300
Number of days in the billing period = 31
Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19
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please help me to answer the question
Answers
Answer:
D
B
E
C
B
Step-by-step explanation:
NO WORRIES!!!! This is easy, you just need to try out each choice add it by the other number and divide by 6 and get the number on top!! :D
Ex:
#1) 39+51= 90, 90 divided by 6= 15
#2) 33+21= 54, 54 divided by 6= 9
#3) 60+60= 120, 120 divided by 6= 20
#4) 18+30= 48, 48 divided by 6 = 8
#5) 34+38= 72, 72 divided by 6= 12
:)
24 356 ÷ 5 using long division.
Answers
Answer:
24 356 ÷ 5 using long division.
Step-by-step explanation:
See the image
Yesenia drove 45.3 miles on Monday and 3.8
miles more on Tuesday. How many miles did she
drive in all?
Answers
Answer:
The answer is 49.1
Step-by-step explanation:
45.3 + 3.8 = 49.1
Calificación mínima. Para obtener una A en un curso, Stephen Heasley debe
obtener una calificación promedio de 90 o mayor en cinco exámenes. Si en los
primeros cuatro exámenes de Stephen sus calificaciones son 92, 87, 96 y 77,
¿cuál es la minima calificación que Stephen puede recibir en el quinto examen
para obtener una A en el curso?
Answers
Answer:
La mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso es 98.
Step-by-step explanation:
La media (también llamada promedio o media aritmética) de un conjunto de datos es una medida de posición central. Es el valor obtenido al sumar todos los datos y dividir el resultado entre el número total de datos.
En este caso, el número total de datos es 5 y el valor de los datos de los cuales debes obtener el problema es 92, 87, 96, 77 y un valor desconocido de un quinto examen. Y sabes que este valor debe ser igual o mayor a 90.
Esto se expresa matemáticamente como:
\(\frac{92+87+96+77+nota}{5}\)≥90
donde "nota" es la mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso.
Resolviendo:
\(\frac{352+nota}{5}\)≥90
352+nota≥90*5
352+nota≥450
nota≥450 - 352
nota≥98
La mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso es 98.
Can y’all please help me answer this, this My last question
Answers
Answer:
x ft is the answer since X = 10
so it means 10 ft
Multiply.
(2x+6)²
NEED ANSWER ASAPP
Answers
Answer:
4x² + 24x + 36
Step-by-step explanation:
(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36
help please I need help very bad
Answers
Answer:
(8,2)
Step-by-step explanation:
the third option
Answer:
i guess (8,2)
Step-by-step explanation:
it's where both lines intercept
12% de descuento por articulo cuyo valor es $5,600.00
Answers
The price of article after 12 percent discount is $4928
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
The given amount of article is $5,600.00,
And discount percent is 12%.
The amount of discount = 56,00×12/100
= 672
The price of article after discount = 5600-672 = 4928
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Express the answers in simplest form. A list contains the names of six anthropology students, two sociology students, and four psychology professor's new study, find the probability that the chosen student (a) A psychology student (c) A psychology student or an anthropology (d) Not a sociology student.
Answers
a) P(psychology student) = 1/3. b) P(psychology or anthropology student) = 5/6. c) P(not sociology student)= 5/6
How to find the probability that the chosen student(a) The probability of choosing a psychology student is the number of psychology students divided by the total number of students:
P(psychology student) = 4/(6+2+4) = 4/12 = 1/3
(b) The probability of choosing a psychology student or an anthropology student is the sum of the number of psychology and anthropology students divided by the total number of students:
P(psychology or anthropology student) = (4+6)/(6+2+4) = 10/12 = 5/6
(c) The probability of not choosing a sociology student is the number of non-sociology students divided by the total number of students:
P(not sociology student) = (6+4)/(6+2+4) = 10/12 = 5/6
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some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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