Answer:
The area is 12.57, rounded to the nearest then is 13.
Step-by-step explanation:
A=πr2=π·22≈12.56637
suppose that you want to construct a 95% confidence interval for estimating a population mean. how does the margin of error with a sample size of 100 compare with the margin of error with a sample size of 2500 if both samples have the same standard deviation
The margin of error is directly proportional to the sample size. As the sample size increases, the margin of error decreases.
What is sample?
In statistics, a sample refers to a subset of individuals or observations taken from a larger population. It is a representative portion of the population that is selected to gather information and make inferences about the entire population.
Given that the standard deviation is the same for both samples, with a sample size of 100 and a sample size of 2500, the margin of error will be smaller for the sample size of 2500 compared to the sample size of 100.
This means that with a larger sample size of 2500, we can expect a more precise estimation of the population mean, resulting in a narrower confidence interval. Conversely, with a smaller sample size of 100, the margin of error will be larger, resulting in a wider confidence interval and a less precise estimation of the population mean.
Therefore, the margin of error is directly proportional to the sample size. As the sample size increases, the margin of error decreases.
To learn more about sample visit:
https://brainly.com/question/24466382
#SPJ4
linear algebreacompute anx from this formula for x for arbitrary n>0. what is a good approximation to anx for n large?
To compute anx from the given formula for x for any arbitrary n>0, we need to first determine the values of a1, a2, a3,...an. Once we have these values, we can substitute them into the formula and solve for x. However, since we don't have any information about the values of a1, a2, a3,...an, we cannot provide an exact solution for x.
Regarding the second part of your question, i.e., finding a good approximation for anx when n is large, we can make use of the concept of content loaded linear algebra. Specifically, we can use the principle of least squares to find the best fit line for a set of data points. In this case, the data points would correspond to the values of anx for different values of n.
Once we have the best fit line, we can use it to make predictions about the value of anx for large values of n. However, it's important to note that this will only be an approximation and not an exact solution.
In summary, to compute anx from the given formula, we need to determine the values of a1, a2, a3,...an. To find a good approximation for anx for large values of n, we can use the principle of least squares to find the best fit line for a set of data points.
To know more about Arbitrary visit :
https://brainly.com/question/30883829
#SPJ11
sabrina wants to test which brand of popcorn pops the most kernels. she picked a store brand, orville redenbacher, and popsecret. all three bags started with the same number of kernels. she popped each for 3 minutes in the same microwave, and then counted the number of kernels left over. what is her independent variable?
The independent variable in Sabrina's experiment is the brand of popcorn.
An independent variable is a variable that is manipulated by the experimenter and is expected to cause a change in the dependent variable. In this case, Sabrina wants to see which brand of popcorn pops the most kernels, so she is manipulating the brand of popcorn by testing three different brands: store brand, Orville Redenbacher, and PopSecret. The dependent variable in this experiment is the number of kernels left over after popping for 3 minutes in the same microwave. This variable is expected to change based on the brand of popcorn being tested. By manipulating the independent variable and measuring the resulting changes in the dependent variable, Sabrina can determine which brand of popcorn pops the most kernels.
To know more about independent variable visit:
https://brainly.com/question/1479694
#SPJ11
in a certain town, 65% of households own a cell phone, 23% own a ipad, and 12% own both a cell phone and ipad. the probability that a randomly selected household owns neither a cell phone or ipad is
To find the probability that a randomly selected household owns neither a cell phone nor an iPad, we need to subtract the probability of owning at least one device from 1.
First, we can find the percentage of households that own at least one device: 65% own a cell phone , 23% own an iPad , 12% own both
To find the percentage that own at least one device, we add the percentages of cell phone and iPad owners and then subtract the percentage that own both: 65% + 23% - 12% = 76%
Therefore, 76% of households own at least one device.
To find the percentage of households that own neither device, we subtract 76% from 100%: 100% - 76% = 24%
So the probability that a randomly selected household owns neither a cell phone nor iPad is 24%.
In summary, the three paragraph answer is: The probability that a randomly selected household owns neither a cell phone nor iPad in a certain town is 24%. Therefore, the probability that a randomly selected household owns neither a cell phone nor an iPad is 100% - 76%, which equals 24%.
To know more about probability visit:-
https://brainly.com/question/30034780
#SPJ11
A number, n, rounded to one. is 2.7. place Complete the inequality to show the lower and bounds upper of Is n decimal □
The number n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place
If a number n rounded to one decimal place is 2.7, then we know that n lies between two numbers:
The lower bound is the number that is 0.05 less than 2.7, which is 2.65 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).
The upper bound is the number that is 0.05 greater than 2.7, which is 2.75 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).
Therefore, we can write the inequality as:
2.65 ≤ n < 2.75
This means that n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place.
Learn more about Decimal place at
brainly.com/question/50455
#SPJ1
hi please help I don't want to pick the wrong question
Answer:
B
Step-by-step explanation:
[tex]\frac{4x^{2} }{12x^{2}-4}\\ = \frac{x^2}{3x^2-1}[/tex]
4 common leke cancel kar diya bas . nothing else
A six-foot man casts a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.
The same six-foot tall man wants to indirectly measure the streetlight in screen 3. But it is a cloudy day and there are no shadows. So holding his phone by his eye, he uses the "level" feature on the Measure app to sight the top of the streetlight. Standing 20 feet away he finds an angle of elevation of 52.5 degrees.
Write and solve an equation to determine the height of the streetlight.
The height of the streetlight is 30 feet.
Let's call the height of the streetlight "h".
When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.
When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.
Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.
Solving for h, we get:
96 / h > 3.2 * h
96 > 3.2h
30 > h
So, the height of the streetlight is less than 30 feet.
To determine the exact height of the streetlight, we can use the equation:
96 / h = 3.2 * h
96 = 3.2h
30 = h
For more questions on Finding height using Linear Equation
brainly.com/question/28122539
#SPJ1
complete question:
a six foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. when a person is 16 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. what is the height of the streetlight?
During a weekend, the manager of a mall gave away gift cards to every 80th person who visited the mall.
• On Saturday, 1,310 people visited the mall.
• On Sunday, 1,714 people visited the mall.
How many people received a gift card?
answer fast and explain pls
Answer:
37 people received a gift card over the weekend.
Step-by-step explanation:
To solve this problem, we need to find the total number of visitors who received a gift card on Saturday and Sunday separately and then add them.
For Saturday, we need to divide the total number of visitors by 80 to find how many received a gift card:
1,310 ÷ 80 = 16.375
We can't have a fraction of a person receiving a gift card, so we round down to 16. This means 16 people received a gift card on Saturday.
For Sunday, we do the same calculation:
1,714 ÷ 80 = 21.425
Again, we round down to 21. This means 21 people received a gift card on Sunday.
To find the total number of people who received a gift card, we add the number of people who received a gift card on Saturday and Sunday:
16 + 21 = 37
Therefore, a total of 37 people received a gift card over the weekend.
Answer: 404 gift cards to every person or either 202
Step-by-step explanation: because subtracting all the number you will get 404 then you have divided by 2 to get 202
Will give brainliest and 50 points!!!!!!
Answer:
I'm not the best at explaining but here it is...
Step-by-step explanation:
on each side of a line, there are 2 angles. These angles match the ones on the other side of the line. So with that and what we know. We can figure it out.
m<1 is 40. M<4 is opposite of this angle witch makes it the same size. That makes m<4 alo 40.
m<3 is 140. M<2 is opposite of this angle making it the same. This makes m<2 also 140.
now we move down to the bottom 4 angles. These are the same as the top 4 making the values the same.
for a more simple view of the answers...
m<1 is 40
m<2 is 140
m<3 is 140
m<4 is 40
m<5 is 40
m<6 is 140
m<7 is 140
m<8 is 40
33y-13=
Its pre algebra by the way.
Answer:
y = 1/3 i hope this is what you're looking for!
A survey was dispersed throughout the county in order to gather information about the amount of money spent on groceries.
Is this survey numerical or categorical?
Select a Value
Is this survey univariate or bivariate?
Select a Value
R
The survey is numerical because it involves gathering information about the amount of money spent on groceries.
The given survey about the amount of money spent on groceries can be classified as follows:
Because data on how much was spent on food is being gathered, the survey is numerical. Numerical data deals with quantitative measurements or values.
The survey can be considered univariate since it focuses on a single variable, which is the amount of money spent on groceries.
Thus, univariate data analysis involves examining and summarizing data related to a single variable.
For more details regarding survey, visit:
https://brainly.com/question/30392577
#SPJ1
Check the image..........................................................................
The combined cost of the notebooks and the pens will be; $5.5
We have been Given that Kendall bought 6 notebooks and 3 pens for a total of $27. The cost of one notebook is $1.50 more than the cost of one pen.
The two equations can be written;
6N + 3 P = 27
n = 1.5 +P
Solve the above equations by substitution method;
6(1.5 + P) + 3P = 27
9 +6p +3p = 27
9p = 18
p (pen): $2
N (notebook): $3.5
The combined cost will be;
Cost = 2 + 3.5
Cost = $5.5
To know more about an expression follow
brainly.com/question/14314939
#SPJ1
based on findings from a recent study on women's health, researchers created a 90 percent confidence interval of (0.42, 0.48) to estimate the percent of all women who do not find time to focus on their own health. based on the confidence interval, which of the following claims is not supported?
It provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the Sample data.
Based on the confidence interval of (0.42, 0.48), the claim that is not supported is that less than 42% of all women do not find time to focus on their own health. This is because the lower bound of the interval is 0.42, indicating that at worst, 42% of all women do not find time to focus on their own health. Therefore, any claim that suggests a lower percentage is not supported by the confidence interval.
On the other hand, the confidence interval does support claims that suggest the percentage of women who do not find time to focus on their own health is at least 42% and no more than 48%. For example, a claim that states "between 42% and 48% of all women do not find time to focus on their own health" is supported by the confidence interval.
It is important to note that the confidence interval does not tell us anything about the actual percentage of women who do not find time to focus on their own health. Rather, it provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the sample data.
To know more about Sample data.
https://brainly.com/question/30125349
#SPJ11
you know that the iq test scores are normally distributed with mean of 100 and standard deviation of 14. you test a class of 32 students and find that their mean iq is 109. what is the probability of finding a sample mean this high (or higher) by chance if we assumed that these students come from the general population?
Therefore, the probability of finding a sample mean of 109 or higher by chance is 1%.
We can use the central limit theorem to approximate the sampling distribution of the sample mean. The sampling distribution will also be normal with a mean of 100 and a standard deviation of (14 / sqrt(32)) ≈ 2.48.
To find the probability of finding a sample mean of 109 or higher by chance, we can standardize the sample mean:
z = (x - μ) / (σ / sqrt(n))
z = (109 - 100) / (14 / sqrt(32))
z = 2.33
Using a standard normal distribution table or calculator, we can find that the probability of a z-score of 2.33 or higher is approximately 0.01 or 1%.
To know more about probability,
https://brainly.com/question/13333458
#SPJ11
Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has been cut in half. The radius of the spherical ball is 8 centimeters. She wraps the first cord around the hemisphere of the ball until it is completely covered, as shown in Figure 1. She cuts the cord and removes it from the ball. She then wraps the second cord around the bottom circle of the ball until it is completely covered, as shown in Figure 2. She again cuts the cord and removes it from the circular base.
Which of the following correctly compares the lengths of the cords and best justifies the reason for this relationship?
A - The length of the first cord must be approximately equal to the length of the second cord because the surface area of the hemisphere is the same as the area of its circular base.
B - The length of the first cord must be approximately 2 times the length of the second cord because the surface area of the hemisphere is 2 times the area of its circular base.
C - The length of the first cord must be approximately 4 times the length of the second cord because the surface area of the hemisphere is 4 times the area of its circular base.
D - The length of the first cord must be approximately 8 times the length of the second cord because the surface area of the hemisphere is 8 times the area of its circular base.
The option that correctly compares the lengths of the cords and best justifies the reason for the relationship is B - The length of the first cord must be approximately 2 times the length of the second cord because the surface area of the hemisphere is 2 times the area of its circular base.
How to compare the lengths of the cords?We can compare the lengths of the cords by these steps:
First, find the length of cord needed to wrap around the hemisphere of the ball (cord 1), using the formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Since our focus is on a hemisphere, we find half the circumference, πr only.
So, the length of cord 1 is πr = π(8) = 8π cm.
Next, we find the length of cord needed to wrap around the circular base of the ball (cord 2), using the formula for the circumference of a circle, also.
So, the length of cord 2 is 2πr = 2π(8) = 16π cm.
Then, we compare the lengths of the cords:
Length of cord 1 = 8π cm
Length of cord 2 = 16π cm
Finally, we simplify:
Length of cord 1 = π(8) = 8π cm
Length of cord 2 = 2π(8) = 16π cm
So, the length of the first cord must be approximately 2 times the length of the second cord because the surface area of a hemisphere is 2 times the area of its circular base is correct.
Read more about cords at brainly.com/question/12394106
#SPJ1
In a class of 36 students, 19 read Biology, 16 read Chemistry and 5 were not allowed to read both subjects. Illustrate the information on a venn diagram. Find how many students read: 1. 11. both Biology and Chemistry; only Chemistry.
Step-by-step explanation:
let u represent the universal set
B represent biology
C represent chemistry
n(u)=36
n(b)=19
n(c)=16
n(bun)=5
n(bnn)=x
19-x+x+16-x+5=36
19+16-x+5=36
19+16+5-x=36
40-x=36
40-36=x
x=4
:.4 students read both biology and chemistry
number of students who read only chemistry is
16-x
but x=4
16-4
=12
:.12 students read only chemistry
Find the volume of the pyramid. Round your answer to the nearest tenth, if necessary.
6inch(height) and 4inch(base)
The volume of the pyramid is 8 [tex]in^{2}[/tex]
What is Pyramid?Pyramid is a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex.
How to determine this
Volume of pyramid = 1/3 * Base area * Height
Base area = 4 inches square
Height = 4 inches
Volume of pyramid = 1/3 * 4 * 6
Volume of pyramid = 1/3 *24
Volume of pyramid = 24/3
Volume of pyramid = 8 [tex]in^{3}[/tex]
Therefore, the volume of the pyramid is 8 [tex]in^{3}[/tex]
Read more about Pyramid
https://brainly.com/question/14980061
#SPJ1
Question
2 of 25
A teacher asked her students how many pets they own. Here are the results:
0,0,1,1,1,1,2,2,2,3,4,4,8
On a piece of paper, draw a dot plot to represent the data. Then determine
which answer choice matches the dot plot you drew.
Answer:
It's C
Step-by-step explanation:
You have two times 0 the the 2 points on 0 shows this,.....
A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without looking. What is the probability that you choose the tiles with the letters A, B, and C? Enter your final answer as a fraction in simplest form.
There is a probability of ___ that the 3 tiles will be A, B, and C.
There is a probability of 1/17,576 that the 3 tiles will be A, B, and C
Given data ,
A bag contains 26 tiles, each with a different letter of the alphabet written on it
Now , you choose 3 tiles from the bag without looking
Let the probability be represented as P ( A )
where the probability of choosing a letter = 1/26
So , probability that you choose the tiles with the letters A, B, and C is
P ( A ) = 1/26 x 1/26 x 1/26
P ( A ) = 1/17,576
Hence , the probability is 1/17,576
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ1
pLSSS HELP
Which of the following is not a step when drawing an angle? (1 point)
a
Draw a ray
b
Connect the arrows with a straight line
c
Line up the baseline on the protractor with the ray
d
Draw arrows on both ends to make them rays
Drawing a straight line and adding arrowheads is an easy way to create rays that are useful in geometry and other mathematical applications.
To connect the arrows with a straight line, you simply need to draw a line segment that passes through both arrowheads. This will create a line that extends infinitely in both directions.
To turn the arrows into rays, you can add an arrowhead on one end of the line segment to indicate the direction of the ray. This will create two rays that originate from the same point and extend infinitely in opposite directions.
It is important to note that a ray is named based on the direction in which it travels, so you may need to specify which direction each ray is pointing.
To learn more about : straight line
https://brainly.com/question/25969846
#SPJ11
trevor covered a cylindrical can with paper for a project. the can is 18 centimeters tall and has a 5-centimeter radius. which is closest to the minimum amount of paper trevor needed to cover the entire can ? responses
The minimum amount of paper that Trevor needs to cover the entire cylindrical can is approximately 565.2 square centimeters, which is closest to 565 square centimeters.
The minimum amount of paper that Trevor needs to cover the entire cylindrical can can be calculated by using the formula for the lateral surface area of a cylinder. Here's how to solve this problem: Given that the can is 18 centimeters tall and has a radius of 5 centimeters. Therefore, the diameter of the can be calculated as follows:
Diameter = 2 x Radius = 2 x 5 = 10 centimeters
The lateral surface area of the cylinder is given by:
Lateral surface area of cylinder = 2πrh
where, π is the mathematical constant pi (3.14)
r is the radius of the base
h is the height of the cylinder
Substituting the given values, we get:
Lateral surface area of cylinder = 2 x 3.14 x 5 x 18 = 565.2 square centimeters (rounded to one decimal place)
You can learn more about the surface area at: brainly.com/question/29298005
#SPJ11
Write the quadratic function g (x) = x² - 2x - 5 in vertex form.
Answer:
(x -1)2 = y - 4
Step-by-step explanation:
suppose that all people can be classified as either right-eye dominant or left-eye dominant. that is to say, right-eye dominant people see better with their right eye, and left-eye dominant people see better with their left eye. suppose that 78% of a population are right-eye dominant and that 61% of them are male. of those who are left-eye dominant, 53% are male. what percent of this population are left-eye dominant?
22% of the population is left-eye dominant.
To find the percentage of the population that is left-eye dominant, we need to subtract the percentage of right-eye dominant individuals from 100%.
Given that 78% of the population is right-eye dominant, the percentage of left-eye dominant individuals can be calculated as:
Left-eye dominant percentage = 100% - Right-eye dominant percentage
Left-eye dominant percentage = 100% - 78%
Left-eye dominant percentage = 22%
Know more about percentage here:
https://brainly.com/question/28998211
#SPJ11
gland, a small landlocked nation, has a population of rats that is growing at a rate proportional to its size. in 2019, there were 9,325 rats in gland, and in 2022, there were 12,140. how big will the population of glandian rats be in 2031?
The predicted population of Glandian rats in 2031 will be approximately 33,290.
In the case of Gland, the population of rats is growing at a rate proportional to its size. This means that the growth can be modeled using an exponential function. Given the data from 2019 (9,325 rats) and 2022 (12,140 rats), we can find the growth rate (r) and use it to predict the population in 2031.
Let's denote the initial population as P0, the population after t years as Pt, the growth rate as r, and the time elapsed in years as t.
1. Calculate the annual growth rate:
Pt = P0 * (1 + r)^t
12,140 = 9,325 * (1 + r)^(2022-2019)
12,140 = 9,325 * (1 + r)^3
2. Solve for r:
(1 + r)^3 = 12,140 / 9,325
(1 + r)^3 ≈ 1.301
1 + r ≈ 1.091
r ≈ 0.091 or 9.1%
3. Predict the population in 2031:
P2031 = P0 * (1 + r)^(2031-2019)
P2031 = 9,325 * (1.091)^(2031-2019)
P2031 = 9,325 * (1.091)^12
P2031 ≈ 33,290 rats
So, the predicted population of Glandian rats in 2031 will be approximately 33,290.
To know more about population visit:
https://brainly.com/question/31598322
#SPJ11
What is the equation of the line that passes through (0,2) and (-3,14) in slope intercept form?
Answer:
y = -4x + 2Step-by-step explanation:
Plug in the values of m and b that we found: y = -4x + 2 So, the equation of the line that passes through (0, 2) and (-3, 14) in slope-intercept form is y = -4x + 2.
Have a Nice Best Day : ) Please Give Me Brainliest
A cookie factory uses 1 1/5 barrels of oatmeal in each batch of cookies. The factory used 9 3/5 barrels of oatmeal yesterday. How many batches of cookies did the factory make?
Write your answer as a fraction or as a whole or mixed number.
The number of batches of cookies the factory made was 6.
Since, The fractions are represented as a numerical value, which defines a part of a whole. A fraction is a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that,
a cookie factory uses 1 1/5 of a barrel of oatmeal in each batch of cookies.
And, The factory is use 9 3/5 of a barrel of oatmeal yesterday.
Now, We can formulate;
Number of batches of cookies did the factory make,
= 9 3/5 ÷ 1 1/5
= 48/5 ÷ 6/5
= 48/5 x 5/6
= 6
Therefore, the number of batches of cookies the factory made was 6.
To learn more about the fraction visit:
brainly.com/question/1301963.
#SPJ1
darnell's grandparents sent him a magic kit for his birthday. it includes six-sided weighted dice. he rolls one of the dice repeatedly and records the results. the table below shows the outcomes he records.numbertimes rolled122338435167based on the data, what is the probability that darnell will roll a 3?
In order to calculate the probability of rolling a 3, we need to determine the number of times a 3 appears in the outcomes compared to the total number of rolls.
Looking at the table, we see that the number 3 appears twice, and there are a total of 20 rolls. Therefore, the probability of rolling a 3 is 2/20 or 1/10. In summary, the probability of rolling a 3 based on the data provided is 1/10. This can be calculated by dividing the number of times a 3 appears (which is 2) by the total number of rolls (which is 20).
Based on the data provided, the probability of rolling a 3 is 1/10. This is calculated by dividing the number of times a 3 appears (which is 2) by the total number of rolls (which is 20). Therefore, the likelihood of rolling a 3 is relatively low.
To know more about probability visit:-
https://brainly.com/question/32004014
#SPJ11
PLSPLSPLS WILL GIVE BRAINLY PLEASE
determine the vertical asymptotes and holes for the graph of the equation below.
x+1 / x^2-6x-7
Thee vertical asymptotes and holes for the graph of the equation are: B. Vertical asymptote, x = 7, Hole, x = -1.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the rational function shown above, we can logically deduce that its vertical asymptotes can be determined by factorizing the denominator as follows;
x² - 6x - 7 = 0
x² - 7x + x - 7 = 0
x(x - 7) + 1(x - 7) = 0
(x - 7)(x + 1) = 0
x = 7 or x = -1
Vertical asymptote, x = 7
Hole, x = -1.
Read more on vertical asymptotes and functions here: https://brainly.com/question/28184937
#SPJ1
The regular cost of a music system is $80 999 . During a sale it was sold for $69,999 . Calculate the rate of discount
Answer:
24.5%
Step-by-step explanation:
Consider the initial value problem y'=ty(4-y)/(1+t), y(0)=ysubnot. (a) Determine how the solution behaves as t goes to infinity. (b) If y subnot equals 2, find the time T at which the solution first reaches the value 3.99. (c) Find the range of initial values for which the solution lies in the interval 3.99
Thus, the range of initial values for which the solution lies in the interval [3.99, 4] is ysubnot in (0, 4).
(a) As t goes to infinity, the denominator of the right-hand side approaches infinity while the numerator approaches 4ty. Thus, the solution approaches the equilibrium solution y=4.
(b) Using separation of variables and partial fractions, we can obtain the solution: y = 4 / (1 + 3e^(2t^2/2 + C)). Setting y = 3.99 and solving for t, we obtain t = sqrt[ln(3.99/0.01) / 2].
(c) We can rearrange the differential equation to obtain y'/(y(4-y)) = t/(1+t) and then integrate both sides. This gives ln|y/(4-y)| = C + ln(1+t) - t, where C is the constant of integration. To find the range of initial values for which the solution lies in the interval [3.99, 4], we need to solve the inequality 3.99 <= y <= 4 for y in terms of t. This gives the condition -∞ < t <= ln(999/1).
To know more about initial values,
https://brainly.com/question/13465405
#SPJ11
