The number
N(t)
of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem
dN
dt
= N(1 − 0.001N), N(0) = 1. A and B please
Answers
The solution of the given differential equation is
\($N(t) = \frac{0.001^t}{1 - 0.001^t}$$\)
The limiting value of N(t) is 1000.
The given initial-value problem is a differential equation of the form:
\($\frac{dN}{dt} = N(1 - 0.001N), N(0) = 1$$\)
This differential equation can be solved to find the value of N(t) for any given time t. To solve this equation, we need to use the method of separation of variables. We start by rewriting the equation in the form
\($\frac{dN}{N(1 - 0.001N)} = dt$$\)
Then, we integrate both sides of the equation and get
\($\int{\frac{dN}{N(1 - 0.001N)}} = \int{dt}$$\)
Integrating the left side of the equation gives
\($$\ln{|N|} - 0.001\ln{|1 - 0.001N|} = t + C$$\)
where C is an integration constant.
Now, solve for N(t), we take the exponential of both sides and rearrange to get
\($N(t) = \frac{e^{Ct}}{1 - 0.001e^{Ct}}$$\)
Finally, by setting t = 0 and using the initial condition N(0) = 1, we can determine the value of the integration constant to be \($C = -\ln{(0.001)}$\).
Thus, the solution to the initial-value problem is given by
\($N(t) = \frac{0.001^te^{-\ln{(0.001)}}}{1 - 0.001^te^{-\ln{(0.001)}}} \\= \frac{0.001^t}{1 - 0.001^t}$$\)
Hence, the number N(t) of supermarkets throughout the country that are using a computerized checkout system at time t is given by the above equation.
For getting the limiting value of N(t) as t approaches infinity, we can take the limit as t approaches infinity of the general solution:
lim(N(t)) as t → ∞ Since the denominator approaches 1 as t approaches infinity, we have:
lim(N(t)) as t → ∞ = 1000 / 1 ⇒ 1000.
Therefore, the limiting value of N(t) as t approaches infinity is 1000, which means that eventually, all supermarkets throughout the country will be using a computerized checkout system.
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Related Questions
Express the following in the simplest form 1575:1190 answer
Express the following in the simplest form 1575:1190
Answers
Answer:
45:34
Step-by-step explanation:
1575:1190
Divide both numbers by 35:
45:34
What is the median of data 4 6 8 9 11?
Answers
Answer:
8
Step-by-step explanation:
its the middle number when the given values are listed least to greatest.
*count from each minimum and maximum values til you have the number in exact center.
a researcher obtain a statistically significant r=-.91 when n=30. how would you report this?
Answers
A statistically significant negative correlation coefficient of r = -0.91 was obtained from a sample of n = 30. This indicates a strong and significant negative relationship between the variables.
The researcher conducted a correlation analysis and found a correlation coefficient (r) of -0.91, which indicates a strong negative relationship between the variables under investigation. The negative sign indicates that as one variable increases, the other variable tends to decrease, and vice versa.
The statistical significance of the correlation coefficient is crucial in determining whether the observed relationship is likely to be due to chance or if it truly exists in the population. In this case, the report should highlight that the obtained correlation coefficient is statistically significant.
To establish statistical significance, the researcher likely conducted a hypothesis test, such as a t-test or a permutation test, to determine the probability of obtaining a correlation coefficient as extreme as -0.91 under the null hypothesis of no correlation. Since the obtained correlation coefficient is statistically significant, it suggests that the observed negative relationship is unlikely to be a result of chance and provides evidence for a genuine association between the variables in the population from which the sample was drawn.
Reporting this finding is important for conveying the strength and significance of the negative relationship to the readers, providing valuable insights for further analysis and interpretation of the variables under investigation.
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The midpoint of AB is M(3, -2). If the coordinates of A are (8,4), what are the
coordinates of B?
Answers
Answer:
B(-2, -8)Step-by-step explanation:
M being midpoint of AB means:
\(x_B-x_M=x_M-x_A\qquad\quad\ \wedge\qquad y_B-y_M=y_M-y_A\\\\x_B-3=3-8\qquad\quad\wedge\qquad\quad y_B-(-2)=-2-4\\\\x_B-3=-5\qquad\quad\ \wedge\qquad\quad y_B+2=-6\\\\x_B=-5+3\qquad\quad\ \wedge\qquad\quad y_B=-6-2\\\\x_B=-2\qquad\qquad\ \wedge\qquad\qquad y_B=-8\)
itaimle fentan' th the yen +1 Mime chose Sowe Mitide chices asccereiond pls: * attonach 7= Which of the liliswing in a cintical ritik to the wocest of yod tritivees plan? Mrryin Dreite hisculte ievitor: porinumalike Q.wide Orete be Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager. Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following plans is most useful for demonstrating a new technology or service or to reach a market that is widely spread out? Mutiple Choice an irvertion plan a proof-of-concept website an operational plan a screening plan Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan Connie is in trouble because she does not know what a business plan looks like. Which of the following statements about the market section of the classic business plan is not true? Muniple Choice The market section bullds on material you may have developed in the IDEO, business model canvas, and feasibility analyses done eatilier, Marketing plans remain the same across any multiple target audiences; Target audiences are aiso ealled custamer segments. Some people prefer to relocate the compettion and competilve advantage section from the market section to the industry section. Connie decides to open "Connie's Corner Café" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following is a critical risk to the success of your business plan? Mulitiple Choice overlooked competition assumptions given for the financials adequate paybock direct customer connection Connie decides to open "Connie's Corner Café" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. Which of the following pitch deck categories is sometimes given in the form of a user's experience? Multiple Cholce product sides problem slide solution slide introductory slide Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks like. There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is get the listener Multiple Choice to make a micro-commitment. provide feedback look at your invention plan, to piedge money Connie decides to open "Connie's Corner Cafe" and finds the ideal location for her venture. However, it appears that Connie will have to approach Investors or bankers for financial backing. When she talks to her local bank manager, Mr. Johnson, he immediately asks for Connie's business plan. Connie is in trouble because she does not know what a business plan looks llike. A good marketing strategy is most likely to focus on Multiple Choice productiservice description. key activities and operations: value proposition. the longerterm competitive plan.
Answers
The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website
How to explain the informationThe statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.
A critical risk to the success of your business plan is Overlooked competition.
The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.
There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment
A good marketing strategy is most likely to focus on the longer-term competitive plan.
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A snack-size bag of pretzels contains 0.5 ounce. How many ounces of pretzels come in a bulk pack that contains 64 snack size bags.
Answers
\(__________________________\)
Given:Each bag of pretzels contain = 0.5 ozAnswer & Solution:64 x 0.5 oz = 32 oz
Therefore, 64 bags of pretzels contains 32 oz of pretzels.
The Spanish Club has 40 members, 5 girls and 35 boys. What is the ratio of
girls to boys in the Spanish Club?
O A. 1:4
B. 1:7
C. 7:1
Answers
Answer:
B. 1:7
Please give me brainliest, thank you!
Step-by-step explanation:
Information given and needed:
- 40 members
- 5 girls
- 35 boys
Solve:
girls to boys
5 to 35
(You can now simplify)
1 to 7
Answer:
B. 1:7
Answer:
1:4
Step-by-step explanation:
What is the value of the missing side
length?
5.6
x
3.4
Answers
Answer:
the missing value of the side length is 19.04
What is the rate of change of y with respect to x for 9x - 11y + 2 = 0?
a. 9/11
b.2/11
c.11/9
d.2/9
Answers
Answer:
The answer is A: 9/11
Bob walked 20 miles in 4 hours. Kelly walked 14 miles in 3 hours. Are these rates proportional
Answers
Answer:
No
Step-by-step explanation:
20/4=5
14/3=4.67
Since they're not the same, they're not proportional.
Answer:
not proportional
Step-by-step explanation:
First , let's find the speed of each person by dividing the distance traveled and the time.
Using B to represent Bob's speed and K to represent Kelly's speed , we have:
\(B=\frac{20}{4} = 5 mph\\K=\frac{14}{3}= 4.666 mph\\\\\)
The speeds 5 and 4.666 are not multiples , so they are NOT proportional.
PLEASE MARK ME BRAINLIEST
Complete the sentence: Squares, rectangles, and rhombi are all types of ______________.
parallelograms
kites
triangles
trapezoids
Answers
Answer:
Parallelograms.
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Answer:
Parallelograms!
Step-by-step explanation:
Why? Well we all know that Square and a rectangle is probally a parallelogram and then you see rhombi your wonder rhombus? Well rhombi is basically a plural form of rhombus and since square and rectangle is a parallelogram that confirms it! (TRUST+)
If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of Response area.
Answers
Answer:
1,2,3,6
Step-by-step explanation:
6x1, 2x3, 3x2, 6x1
The winning team
in a 400-meter relay race had a time of
198.608 seconds. Suppose all 4 of the split
times were the same. Write and solve an
equation to find the split times.
Answers
The equation for split times is 4x= 198.608 and the value of x is 49.652
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the split time
all 4 of the split times were the same.
4x= 198.608
=> x= 198.608/4 = 49.652
The equation for split times is 4x= 198.608 and the value of x is 49.652
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Order these numbers from least to greatest.
NEEDS HELP NOW!
Answers
Answer:
5.275, 146/25, 5 17/20, 6.27
Step-by-step explanation:
This how you but this decimals and fractions from least to greatest. I hope this helps
146/25 is 5.84. 5 17/20 as an improper fraction is 117/20 because 20 times 5 is 100 and then add 17. 117/20 is 5.85.
In order from least to greatest would be 5.275, 146/25, 5 17/20, and then 6.27
me question is in the screen shot
Answers
The area of the regular heptagon in this problem is given as follows:
1278.12 yd².
How to obtain the area of an heptagon?The area of a regular heptagon of apotemn h and side length l is given by the equation presented as follows:
A = 3.5lh.
The parameters for this problem have the values given as follows:
l = 7 yd, h = 7.27 yd.
Hence the area of the regular heptagon in this problem is obtained as follows:
A = 3.5 x 7 x 7.27
A = 1278.12 yd².
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Fiona rolls a fair dice 144 times.
How many times would Fiona expect to roll a number greater than 2?
Answers
Answer:
34
Step-by-step explanation:
A square patio has a perimeter of (32x+8) feet. What is the length of the patio? Thanks!
Answers
Answer:
The side length is 8x+2 ft
Step-by-step explanation:
The perimeter of a square is found by
P =4s where s is the side length
32x +8 = 4s
Divide each side by 4
32x/4 +8/4 = 4s/4
8x+2 = s
The side length is 8x+2 ft
what is the first step when solving this equation: 2(x-4)+6=3x+19
Answers
Answer: The first step is to follow order of operations so parenthesis goes first e potential next multiplication and division and finally adding and subtracting.
Step-by-step explanation:
_____ is the process of drawing conclusions about unknown characteristics of a population from which data were taken.
Answers
Answer:
Statistical inference
Step-by-step explanation:
25. 0 grams of sodium chloride (NaCl) is dissolved in 100 grams of solution. What is the concentration of the solution in parts per million (ppm)?
Answers
The concentration of the sodium chloride solution is 250,000 parts per million (ppm).
To calculate the concentration of the solution in parts per million (ppm), we need to determine the amount of solute (sodium chloride) present in relation to the total solution.
The concentration of a solution is typically expressed as the ratio of the mass of solute to the mass of the solution or the volume of solute to the volume of the solution. In this case, we have 0 grams of sodium chloride dissolved in 100 grams of solution.
To convert this into parts per million (ppm), we need to multiply the concentration by 1,000,000. Since ppm represents one part in a million, it is equivalent to mg/L or µg/g.
Using the given values, we have:
Concentration (ppm) = (mass of solute / mass of solution) * 1,000,000
Substituting the values, we get:
Concentration (ppm) = (0 grams / 100 grams) * 1,000,000
Concentration (ppm) = 0 * 1,000,000
Concentration (ppm) = 0
Therefore, the concentration of the solution is 0 parts per million (ppm), indicating that there is no sodium chloride present in the solution.
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Beatrice has a rectangular swimming pool in her backyard. The dimensions are 16 feet by 8 feet. She decides to build a deck of uniform
width around the pool. Together the pool and the deck will have an area of 384 square feet.
a) write the expression to represent the length and the width of the swimming pool with the deck around it
b) find x, the width of the deck
Answers
Hi can someone help me with this. Find the slope
Answers
Answer:
5/2
Step-by-step explanation:
Answer:
2/5
Step-by-step explanation:
goes 2 to the right then up 5
The dinner bill came to $72.48 and Julio tipped the waiter 15%. What is the total price of dinner?
Answers
Answer: $83.35
Step-by-step explanation:
Find 15% of 72.48 = 10.87
10.87 + 72.48 = 83.35
Find the lower quartile of this data set: 593, 588, 540, 434, 420, 398, 390, 375
420
564
394
427
alsoo im like rly booorrredddd any one wanna talk??
female 14 bdays todayy!!!
Answers
Answer:
Quartiles Quartiles:
Q1 --> 396
Q2 --> 423.5
Q3 --> 552
Step-by-step explanation:
Mean x¯¯¯ 461.91666666667
Median x˜ 423.5
Mode 420
Range 218
Minimum 375
Maximum 593
Count n 12
Sum 5543
Quartiles Quartiles:
Q1 --> 396
Q2 --> 423.5
Q3 --> 552
Interquartile
Range IQR 156
Outliers none
Smallest to biggest. 0.43,3/7,43.8%,7/16
Answers
Answer: 3/7 (Smallest), 0.43, 7/16, 43.8% (largest)
Step-by-step explanation:
0.43
3/7 = 0.4286
43.8% = 0.438
7/16 = 0.4375
a discipline technique that may damage a child's math achievement is:
Answers
Excessive punishment or negative reinforcement can harm a child's math achievement by creating fear, undermining confidence, and discouraging engagement with the subject. Positive discipline techniques and a supportive environment are crucial for fostering math success.
Excessive punishment or negative reinforcement as a discipline technique can have detrimental effects on a child's math achievement. When a child makes mistakes or struggles with math concepts, responding with punishment, criticism, or harsh consequences can create a negative association with math. This can lead to anxiety, fear, and a lack of motivation to engage with the subject.
Mathematics requires a growth mindset, where mistakes are seen as opportunities for learning and improvement. By punishing or negatively reinforcing a child's math mistakes, we discourage them from taking risks, trying new strategies, and seeking help when needed. It hampers their ability to develop problem-solving skills and critical thinking abilities.
Furthermore, negative discipline approaches can damage a child's self-esteem and confidence in their mathematical abilities. They may develop a belief that they are "bad at math" or incapable of improving, leading to a self-fulfilling prophecy where their performance suffers.
To support a child's math achievement, it is essential to employ positive discipline techniques. This includes providing constructive feedback, offering assistance and guidance, creating a safe and supportive learning environment, and promoting a growth mindset. Encouraging effort, perseverance, and celebrating small successes can foster a positive attitude towards math and enhance a child's mathematical abilities.
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Mary puts 200 fish into a pond. If the fish are guaranteed to increase at an annual rate of 14%, how many fish will be in the pond in 5 years?
Answers
Answer:
340
Step-by-step explanation: 200 * .14 = 28 then 28*5= 140 then 140+200=340
Answer:
340 in 5 years
Step-by-step explanation:
I set it up as a fraction so I could find 14% of 200.
14/100 = x/200
Then I cross multiplied
100x = 2800
Simplify
x=28
Twenty-eight is 14% of 200. Multiply 28 by 5.
28 x 5 = 140
Add 140 to 200
340
resolve into factors : a^3 + 35b^3 + (a -b)^3
Answers
Step-by-step explanation:
a^3+35b^3+a^3-b^3
2a^3+34b^3
Answer:
2a^3 + 34b^3 - 3a^2b + 3ab^2
If x and y are in direct proportion and y is 42 when x is 6, find y when c is 11
Answers
When x and y are in direct proportion, the value of y when the value of x is 11 is 77.
What is meant by direct proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Sometimes, we notice that changes in one quantity's value are similar to changes in another quantity's value, meaning that when one quantity's value rises, the other quantity's value rises in the same proportion and vice versa. Two quantities are said to exist in direct proportion when such circumstances occur. According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant.
When x and y are in direct proportion, we can write,
x/y = c
where c is a constant.
Now it is given that y = 42 , when x = 6
then c = x/y = 6/42 = 1/7
We are asked to find the value of y when x = 11.
The c remains constant.
so 11/y = 1/7
y = 11*7 = 77
Therefore when x and y are in direct proportion, the value of y when the value of x is 11 is 77.
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Marathon Digital Movies is having a sale. Customers can download 13 movies for $15.99. How much does each movie cost with the sale?
Answers
Given:
Cost of 13 movies = $15.99
To find:
Cost of each movie
Steps:
Lets assume the cost of each movie as 'x'.
So,
\(\frac{15.99}{13} =\frac{x}{1}\)
\(1.23 = x\)
\(x = $1.23\)
Therefore, the cost of one movie is 1.23 dollars
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