The differential equation to describe the situation is:
dP/dt = 0.000508 * P * (1 - P/732)
We can write a logistic differential equation to describe the rate of change of students who heard the rumor. The equation is:
dP/dt = k * P * (1 - P/M)
where dP/dt is the rate of change in the number of students who heard the rumor, k is a constant, P is the number of students who have heard the rumor at a given time, and M is the maximum capacity of the school (732 students).
At 12 PM, P = 227 and dP/dt = 24 students per hour. We can plug these values into the equation:
24 = k * 227 * (1 - 227/732)
Now, solve for k:
k ≈ 0.000508
So, the differential equation to describe the situation is:
dP/dt = 0.000508 * P * (1 - P/732)
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Elena is trying to figure out how many movies she can download to her hard
drive. The hard drive is supposed to hold 500 gigabytes of data, but 58
gigabytes are already taken up by other files. Each movie is 8 gigabytes. Elena
wrote the inequality 8x + 58 ≥ 500 and solved it to find the solution x ≥ 55. 25.
4a) Explain how you know Elena made a mistake based on her solution.
4b) Fix Elena's inequality and explain what each part of the inequality represent.
Based on Elena's solution, x represents the number of movies that can be downloaded. However, her inequality is incorrect as it states that the total amount of downloaded data (8x + 58) is greater than or equal to the total capacity of the hard drive (500 gigabytes).
This means that Elena is considering the amount of data taken up by other files in addition to the movies she wants to download. Therefore, her solution of x ≥ 55.25 is incorrect as it would allow Elena to download more movies than the remaining capacity of the hard drive.
The corrected inequality should be 8x ≤ 442, as the remaining capacity of the hard drive is 500 - 58 = 442 gigabytes. This means that Elena can download a maximum of 55 movies (8 x 55 = 440), leaving 2 gigabytes of space remaining on the hard drive. Therefore, each part of the inequality represents the total amount of data used by the movies downloaded (8x) and the remaining capacity of the hard drive (442).
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Karmen is buying a new car. For the car's exterior, she can choose from three colors-black, gray, or white. For the interior, she can choose between
belge and gray. She can also choose between a manual and an automatic transmission
if Karmen picks a car at random, what is the probability of picking a car that has a black exterior and a belge interior?
What is the probability of picking a car with a belge interior and an automatic transmission?
The probability of Karmen picking a car with a black exterior and a belge interior is
The probability of Karmen picking a car with a belge interior and an automatic transmission is
The probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6
How to find the probability?To find the probability, we need to start by identifying the event or situation for which we want to calculate the probability.
Since Karmen has three choices for the exterior color, two choices for the interior color, and two choices for the transmission, the total number of possible car configurations is:
3 x 2 x 2 = 12
This means there are 12 different cars to choose from.
To find the probability of picking a car that has a black exterior and a belge interior, we need to determine how many cars meet these criteria. There is only one car that has a black exterior and a belge interior, so the probability of picking this car is:
1/12
Therefore, the probability of Karmen picking a car with a black exterior and a belge interior is 1/12.
To find the probability of picking a car with a belge interior and an automatic transmission, we need to determine how many cars meet these criteria. There are two cars that have a belge interior and an automatic transmission, so the probability of picking one of these cars is:
2/12
Simplifying this fraction gives:
1/6
Therefore, the probability of Karmen picking a car with a belge interior and an automatic transmission is 1/6.
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Ryann is filing Chapter 7 bankruptcy. She will be able to include $10,148.22 of her total debt of $112,758.00Calculate what percent of Ryann's total debt is included in the bankrup
Answer:
Step-by-step explanation:
To calculate the percentage of Ryann’s total debt that is included in the bankruptcy, you can divide the amount of debt included in the bankruptcy by the total debt and then multiply by 100.
So, the calculation would be: ($10,148.22 / $112,758.00) * 100 = 9%.
This means that 9% of Ryann’s total debt is included in the bankruptcy.
A window in the shape of a parallelogram has a base of 36 inches, and a height of 45 inches. What is the area?
The area of a parallelogram is given by the formula:
$\sf\implies{\boxed{A = bh}}$
where $b$ is the length of the base and $h$ is the height.
In this case, the base is 36 inches and the height is 45 inches, so the area of the parallelogram is:
$\sf\implies\:A = bh = 36 \cdot 45 = 1620$
Therefore, the area of the parallelogram-shaped window is 1620 square inches.
[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]
[tex]{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
Answer:
1620 inches ^2
Step-by-step explanation:
The area of a parallelogram is simply put as:
A=bh
where b is base and h is height
Given b is 36 and 45 is our h, we can now solve for the area.
A=(36)(45)
A=1620
Friendly reminder:
When multiplying two of the same units, remember to square them to have the correct labeling, so in conclusion, our answer is:
1620 inch.^2
Write the equation for the circle graphed below. Center = (-5, -5) Radius= 4
Answer:
(x + 5)^2 + (y + 5)^2 = 16.
Step-by-step explanation:
(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the centre and r =- the radius.
Here (a, b) = (-5, -5) and r = 4, so:
(x - (-5))^2 + (y - (-5))^2 = 4^2
(x + 5)^2 + (y + 5)^2 = 16
At the Royal Dragon Chinese restaurant, a slip in the fortune cookies indicates a dollar amount that will be subtracted from your total bill. A bag of 10 fortune cookies is given to you from which you will select one. If six fortune cookies contain "1$ off," three contain "$3 off," and one contains "$8 off," determine the expectation of a selection.
Answer:
im sorry this makes absolutely no sense
Step-by-step explanation:
During their team meeting, both managers shared their findings. Complete the statement describing their combined results.
Select the correct answer from each drop-down menu.
The initial number of video views was ____ the initial number of site visits, and the number of video views grew by _____ the number of site visits.
The difference between the total number of site visits and the video views after 5 weeks is _____.
More than
the same as
fewer than
a smaller factor than
the same factor as
a larger factor than
20,825
52,075
15,625
36,450
The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits. The difference between the total number of site visits and the video views after 5 weeks is 20,825.
During their team meeting, both managers shared their findings. Complete the statement describing their combined results.
The initial number of video views was fewer than the initial number of site visits, and the number of video views grew by a larger factor than the number of site visits.
The difference between the total number of site visits and the video views after 5 weeks is 20,825.
Therefore the correct answer are fewer, larger factor than and 20,825.
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A golfer at G wishes to hit a shot between two trees P and Q, as shown in the
diagram to the right. The trees are 31 metres apart, and the golfer is 74 metres
from P and 88 metres from P. Find the angle within which the golfer must play
the shot, correct to the nearest degree.
Answer:
20°
Step-by-step explanation:
You want the measure of angle G in triangle GPQ with side lengths GP=74, PQ=31, QG=88 meters.
Law of cosinesThe law of cosines tells you the relevant relationship is ...
PQ² = GP² +GQ² -2·GP·GQ·cos(G)
Solving for angle G gives ...
G = arccos((GP² +GQ² -PQ²)/(2·GP·GQ))
G = arccos((74² +88² -31²)/(2·74·88)) = arccos(12259/13024)
G ≈ 19.735° ≈ 20°
The golfer must play the shot within an angle of about 20°.
The sixth-graders at Ayana's school got to choose between a field trip to a museum and a field trip to a factory. 39 sixth-graders picked the museum. If there are 50 sixth-graders in all at Ayana's school, what percentage of the sixth-graders picked the museum?
Answer:
78% of sixth-graders picked a field trip to a museum.
Step-by-step explanation:
39 out of 50 kids picked the museum field trip. This is 39/50. We can change this like so:
39/50 × 2/2
= 78/100
78/100 is 78% (because percent literally means "per hundred)
Another way is to just divide. 39/50 means 39 ÷ 50.
39 ÷ 50 is .78 then times by 100 to change to a percent. This works for all kinds of fractions.
78% of sixth graders at Ayana's school selected the museum field trip.
A manufacturer makes aluminum cups with a volume of 10 cubic centimetres cach, in the form of right circular cylinders open at the top. Find the dimensions that would require the least amount of material.
The dimensions that require the least amount of material are r = (10/π)^(1/3) cm for the radius and h = (10/π)^(1/3) cm for the height.
To minimize the amount of material used for making aluminum cups with a volume of 10 cubic centimeters, you will need to optimize the dimensions of the right circular cylinders.
Given the volume (V) is 10 cm³, the formula for the volume of a right circular cylinder is V = πr²h, where r is the radius and h is the height.
10 = πr²h
To minimize the material used, we want to minimize the surface area (SA) of the open cylinder, which is given by the formula SA = 2πrh + πr² (the first term represents the lateral surface and the second term the base).
Using the volume formula, we can find a relationship between r and h:
h = 10 / (πr²)
Now substitute this expression for h in the surface area formula:
SA(r) = 2πr(10 / (πr²)) + πr²
SA(r) = 20/r + πr²
To find the minimum surface area, differentiate SA(r) with respect to r and set the result equal to zero:
d(SA)/dr = -20/r² + 2πr
Now solve for r:
0 = -20/r² + 2πr
20/r² = 2πr
r³ = 10/π
Now take the cube root of both sides:
r = (10/π)^(1/3)
To find the height, substitute this value of r back into the expression for h:
h = 10 / (π((10/π)^(1/3))²)
h = (10/π)^(1/3)
The dimensions that require the least amount of material are r = (10/π)^(1/3) cm for the radius and h = (10/π)^(1/3) cm for the height.
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Simplify the expression
600 is writtena s 2^a x b x c^d
where a , b, c and d are all prime numbers
Find the value of a,b,c and d
Answer:
a = 3
b = 1
c = 5
d = 2
Step-by-step explanation:
To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
Therefore, the prime factorization of 600 is:
600 = 2^3 × 3^1 × 5^2
So, a = 3, b = 1, c = 5, and d = 2.
Suppose that the future price p(t) of a certain item is given by the following exponential function. In this function, p(t) is measured in dollars and r is the
number of years from today.
pt) = 2000(1. 039)'
QD
Find the initial price of the item.
SU
Does the function represent growth or decay?
O growth O decay
By what percent does the price change each year?
The price of the item increases by approximately 3.93% each year.
Find out what is the initial price of the item and what percentage of the price changes each year?The initial price of the item is the value of p(0), which can be obtained by setting r=0 in the given function. Therefore:
p(0) = 2000(1.039)^0 = 2000
So the initial price of the item is $2000.
To determine whether the function represents growth or decay, we need to look at the value of the base of the exponential function, which is 1.039 in this case. Since this value is greater than 1, the function represents growth.
To find the percentage change in price each year, we can calculate the percentage increase from the initial price to the price after one year (r=1):
p(1) = 2000(1.039)^1 = 2078.60
The percentage increase from $2000 to $2078.60 is:
((2078.60 - 2000)/2000) x 100% ≈ 3.93%
Therefore, the price of the item increases by approximately 3.93% each year.
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What is the value of 200 + 3 (8 3/4) + 63.25
Answer:
289.5
Step-by-step explanation:
200+26.25+63.25
289.5
Para el periódico mural, los alumnos decidieron representar un pino por medio de un triángulo que tiene una superficie de 1. 5m si la base mide 1. 5 m ¿cuanto mide la altura? 
The height of the triangle is 2 meters.
How tall is triangle?Para encontrar la altura del triángulo, podemos utilizar la fórmula para calcular el área de un triángulo:
Área = (base x altura) / 2
Sabemos que el área es de 1.5 m² y que la base mide 1.5 m, por lo que podemos despejar la altura de la siguiente manera:
1.5 m² = (1.5 m x altura) / 2
Multiplicando ambos lados por 2:
3 m² = 1.5 m x altura
Despejando la altura:
altura = 3 m² / 1.5 m
altura = 2 m
Por lo tanto, la altura del triángulo que representa al pino en el periódico mural es de 2 metros.
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Morris shovels driveways during a big snowstorm. He charges $25 to shovel a drive way. He can shovel a drive way in a half hour assuming that he worked back to back how much could he make in 5 hours
Answer:
250
Step-by-step explanation:
5 x 2= 10
25 x 10= 250
Please I need your help!
Select each equation that the number 10 to the 3rd power makes true.
6.01 × ⬜ = 601
0.305 × ⬜ = 305
0.54 × ⬜ = 540
0.097 × ⬜ = 970
0.97 × ⬜ = 97
Jason borrowed $5000 to go with the money he'd saved to buy a tractor. The finance charge on the loan was $55 and the term on the loan was 360 days. What was the APR for Jason's loan?
O 0. 011%
O 1. 116%
O 4. 015%
O 1. 527%
The answer is option B: 1.116%.
To find the APR(Annual Percentage Rate) for Jason's loan, we first need to calculate the total amount of interest he paid.
The finance charge of $55 is the interest paid for the 360-day term.
To find the total interest, we can use the formula:
Total interest = (finance charge / loan amount) x (days in a year / loan term in days)
Plugging in the values, we get:
Total interest = (55 / 5000) x (365 / 360)
Total interest = 0.011 x 1.01389
Total interest = 0.01116 or 1.116%
Therefore, the APR for Jason's loan is 1.116%.
The answer is option B: 1.116%.
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To the nearest cubic centimeter, what is the volume of the regular hexagonal prism?
a hexagonal prism has a height of 7 centimeters and a base with a side length of 3 centimeters. a line segment of length 2.6 centimeters connects a point at the center of the base to the midpoint of one of its sides, forming a right angle.
the volume of the regular hexagonal prism is about ___ cm3
Rounded to the nearest cubic centimeter, the volume of the regular hexagonal prism is approximately 82 [tex]cm^3.[/tex]
To calculate the volume of the regular hexagonal prism, we need to find the area of the base and multiply it by the height.
The base of the prism is a regular hexagon with side length 3 centimeters. The formula for the area of a regular hexagon is:
[tex]Area = (3√3/2) * (side length)^2.[/tex]
Substituting the given side length of 3 centimeters:
[tex]Area = (3√3/2) * 3^2[/tex]
= (3√3/2) * 9
= (27√3/2).
Now, let's calculate the volume by multiplying the base area by the height:
Volume = Area * height
= (27√3/2) * 7
≈ 81.729[tex]cm^3[/tex].
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Write the product 5x2/3 as the product of a whole number and a unit fraction
The product 5x^(2/3) can be written as the product of the whole number 5 and the unit fraction 1/x^(-2/3), which simplifies to x^(2/3)/1 or just x^(2/3). So, we have:
5x^(2/3) = 5 * (1/x^(-2/3)) = 5x^(2/3) = 5 * (x^(2/3) / 1) = 5x^(2/3) = 5x^(2/3)
To write the product 5x^(2/3) as the product of a whole number and a unit fraction, we need to express x^(2/3) as a unit fraction.
Recall that a unit fraction is a fraction with a numerator of 1, so we need to find a fraction that has 1 as the numerator and x^(2/3) as the denominator. We can do this by using the reciprocal property of exponents:
x^(2/3) = 1 / x^(-2/3)
Now we can substitute this expression into the original product:
5x^(2/3) = 5 * (1 / x^(-2/3))
Simplifying the right-hand side of the equation, we can write it as:
5 / x^(-2/3) = 5x^(2/3)
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A bacteria population doubles every eight minutes if the population with one cell, how long will it take to grow to 2097152
The time that it will take the bacteria to grow to 2097152 is: 2 hours 48 minutes
How to solve Exponential functions?An exponential function is defined as a Mathematical function in the form f(x) = [tex]a^{x}[/tex].
where:
“x” is a variable.
“a” is a constant which is called the base of the function and it should be greater than 0
However; the exponential function is:
1([tex]2^{x}[/tex]) = 2097152
log 2x = log 2097152
x log 2 = log 2097152
x = log 2097152/log 2
x = 6.32162/0.3010
x = 21 times the population doubles
21(8) = 168 minutes = 2 hours 48 minutes
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Terri is beginning a science experiment in the lab. The instructions call for 227 milligrams of potassium. Calculate the difference between this amount and 1 gram
The difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
The amount of potassium called for in the experiment is 227 milligrams. To convert milligrams to grams, we divide by 1000: 227/1000 = 0.227 grams.
The amount of 1 gram is larger than 0.227 grams. To find the difference between the two amounts, we subtract the smaller amount from the larger amount:
1 gram - 0.227 grams = 0.773 grams
Therefore, the difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
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Find the length of the midsegment of the trapezoid
2n-2
N+12
4n+6
Answer: To find the length of the midsegment of a trapezoid, you need to add the lengths of the two bases together and divide by 2.
The length of the top base is 2n-2 and the length of the bottom base is 4n+6.
Adding the two bases together gives:
(2n-2) + (4n+6) = 6n + 4
Dividing by 2 gives:
(6n + 4) / 2 = 3n + 2
Therefore, the length of the midsegment of the trapezoid is 3n + 2.
Which term can be put in the blank to make the statement below true?
3,000,000=30________________
A. Thousands
B.Ten-Thousands
C.Hundred-Thousands
D.Millions
100 points Please help asap!
The solution of the system of equations is given by the ordered pair (-2, 2).
Based on the table, a x-value that is a solution to the equation is -2.
The solution to the equations are (-6, 3) and (-4, -5).
An ordered pair which is the best estimate for the solution of the system is: A. (-0.5, -1.75).
How to graphically solve this system of equations?In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
8x - 4y = -24 ......equation 1.
4x - 12y = -32 ......equation 2.
Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant II, and it is given by the ordered pairs (-2, 2).
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pls show work its due tomorrow
Answer: 325
Step-by-step explanation:
15*30-5*5-20*5=325
Answer: 875 square feet.
Step-by-step explanation: (25x30)+(5x20)+25
Mrs.lane makes a 22% commission on commercial advertising sales for the local newspaper plus $8.25/hr. working 40hrs/week. her average bi-weekly commercial sales are $5,625. how much would her average gross monthly income be?
Mrs. Lane's average gross monthly income would be $3,135.
How to find the income?To find the monthly income of Mrs. Lane's,
First, we need to find Mrs. Lane's commission for her bi-weekly commercial sales:
Commission = 22% of $5,625 = 0.22 x $5,625 = $1,237.50
Next, we need to find her hourly wage for a week:
Hourly wage = $8.25 x 40 = $330
Her gross bi-weekly income is the sum of her commission and hourly wage:
Gross bi-weekly income = Commission + Hourly wage
= $1,237.50 + $330
= $1,567.50
To find her gross monthly income, we can multiply her gross bi-weekly income by the number of bi-weekly pay periods in a month:
Gross monthly income = Gross bi-weekly income x Number of bi-weekly pay periods in a month
= $1,567.50 x 2
= $3,135
Therefore, Mrs. Lane's average gross monthly income would be $3,135.
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1) Amy deposits $2,300 in an account that pays 8.5% interest. How much money will Amy have after 4 years?
2)Andres deposits $10,000 in an account that pays 8% interest. How much money will Andres have after 4 years?
a
$ 13,604.89
b
$ 604.90
c
$ 20,004.98
3) Kara deposits $500 in an account that pays 5% interest. How much money will Kara have after 2 years?
a
$ 1,009.34
b
$ 13.97
c
$ 551.25
1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.
2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.
3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.
How the future values are determined:The future values represent the present investment compounded at an interest rate.
The future values can be determined using an online finance calculator as follows:
1) N (# of periods) = 4 years
I/Y (Interest per year) = =8.5%
PV (Present Value) = $2,300
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $3,187.48
Total Interest = $887.48
2) N (# of periods) = 4 years
I/Y (Interest per year) = =8%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $13,604.89
Total Interest = $3,604.89
3) N (# of periods) = 2 years
I/Y (Interest per year) = 5%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $551.25
Total Interest = $51.25
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If Mikal uses all his money to buy one type of flour, he has exactly enough money to buy either 12 pounds of wheat flour, or 6 pounds of rice flour, or 4 pounds of almond flour. If Mikal uses all his money to buy an equal number of pounds of all three types of flour, what is the total number of pounds of flour that he can buy?
The total number of pounds of flour he can buy is 7 pounds of flour
Let's assume that Mikal has $1 to spend on flour. According to the problem, he can buy:
- 12 pounds of wheat flour for $1, which means that the price of wheat flour is 1/12 = $0.0833 per pound.
- 6 pounds of rice flour for $1, which means that the price of rice flour is 1/6 = $0.1667 per pound.
- 4 pounds of almond flour for $1, which means that the price of almond flour is 1/4 = $0.25 per pound.
If Mikal spends $1 on an equal amount of all three types of flour, he will spend $1/3 = $0.3333 on each type of flour. To determine how many pounds of each type of flour he can buy, we need to divide $0.3333 by the respective price per pound of each type of flour:
- Wheat flour: $0.3333 / $0.0833 per pound = 3.9996 pounds (rounded to 4 pounds)
- Rice flour: $0.3333 / $0.1667 per pound = 1.9998 pounds (rounded to 2 pounds)
- Almond flour: $0.3333 / $0.25 per pound = 1.3332 pounds (rounded to 1 pound)
Therefore, Mikal can buy 4 pounds of wheat flour, 2 pounds of rice flour, and 1 pound of almond flour with $1. The total number of pounds of flour he can buy is:
4 + 2 + 1 = 7 pounds of flour.
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Write the equation in factored form:
so x= what values?
What do the solutions for x mean?
x2−4x−21=0
