At least 95% of the observed values are expected to lie between mu minus 2 sigma and mu plus 2 sigma.
This is because of the empirical rule, also known as the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the observations will fall within one standard deviation of the mean, about 95% of the observations will fall within two standard deviations of the mean, and around 99.7% of the observations will fall within three standard deviations of the mean.
In this case, we are given that x has mean mu and standard deviation sigma. Therefore, about 95% of the values of x are expected to lie between mu minus 2 sigma and mu plus 2 sigma, as this interval covers two standard deviations on either side of the mean.
Mathematically, we can express this as:
P(mu - 2sigma < x < mu + 2sigma) ≈ 0.95
where P is the probability that x falls within the interval mu - 2sigma to mu + 2sigma.
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Consider the expression 16 - y^2/square root of 49 + 12. What is the value of the expression when y=-5?
Answer:
Step-by-step explanation:
16 - (y^2/sqrt(49)) +12
at y = -5
16 - ( (-5)^2 / sqrt(49)) +12
16 - ( 25 / 7) + 12
28 - (25/7)
(28*7 - 5) / 7 (LCM)
(196 - 5) / 7
(191/7)
27.2857 = Ans
Consider the quadratic function: f(x)=x^2-6x+8
Identify the coordinates of the x(intercepts if any
Answer:
x-intercepts (4,0) (2,0)
y-intercepts (0,8)
Step-by-step explanation:
have a good day :)
A convention center is hosting a home show where different businesses provide information and examples for improvements that can be made to homes. The sponsors are also holding a lottery to give away $10,000 in home improvements. In a giant bin, 20 balls numbered 1 - 20 are mixed together. Then , 3 balls are selected from the bin, without replacement For $5. 00a customer can try to predict the 3 numbers that will be selected. If the order in which the numbers are selected does not matter , how many different predictions are possible for this game of chance ?
There are 1140 different predictions possible for this game of chance.
In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.
To solve this problem, we can use the formula for combinations, which is
=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]
where n is the total number of items, and x is the number of items to be selected.
In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes
=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]
Using a calculator or simplifying the equation, we get:
[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]
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Does anyone have answers 3 and 4 for 4. 4. 3 Practice: Modeling: Solids?
Extremely lost and help with be appreciated :)
Answer:
search them up it should give you the answers
Step-by-step explanation:
What’s the answer I need help plsease
Answer: B
Step-by-step explanation:
Your original matrix:
1 0
0 1
after dilation
3 0
0 3
after reflection... it only changes sign of y because its reflected across x-axis
3 0
0 -3
B
Frank keeps his pet iguana in a glass tank that is shaped like a rectangular prism.the height of the tank is 11 inches, the width is 34.5 inches, and the length is 25 inches.what is the best estimate for the volume of the tank in cubic feet?remember 12 inches = 1 foot.
The best estimate for the volume of the tank in cubic feet is 5.5 cubic feet.
The volume of the tank is:
V = l x w x h
where l is the length, w is the width, and h is the height.
Substituting the given values, we get:
V = 25 x 34.5 x 11 = 9547.5 cubic inches
To convert cubic inches to cubic feet, we divide by (12 x 12 x 12), since there are 12 inches in a foot and 12 x 12 x 12 cubic inches in a cubic foot:
V = 9547.5 / (12 x 12 x 12) cubic feet
V ≈ 5.5 cubic feet
Therefore, 5.5 cubic feet is the best estimate for the tank's cubic foot capacity.
Hence , the volume of the rectangular glass tank is 5.490 feet³
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[tex]\frac{4}{-2} -\frac{3}{-6}[/tex]
The value of the fraction is 3/-2
What is a fraction?A fraction can simply be described as the part of a whole variable, a whole number or a whole element.
The different types of fractions in mathematics are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
4/-2 - 3/-6
find the lowest common factor
12 - 3/-6
subtract the value, we get;
9/-6
Divide the values into simpler forms
3/-2
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Ray kl and ray hk are two sides of an angle. what is a name of this angle?∠lkh∠khl∠hlk∠lhkthis is very urgent and i need the answer now please!!
The name of the angle formed by Ray KL and Ray HK is ∠LKH or ∠HKL.
An angle is formed by two rays that share a common endpoint, called a vertex. In this case, Ray KL and Ray HK share the endpoint, K, which is the vertex of the angle. The name of an angle is determined by the letters assigned to its three points, with the vertex letter in the middle.
In this case, the angle can be named ∠LKH or ∠HKL, depending on the order in which the points are listed. The symbol ∠ is used to represent an angle. Therefore, the correct way to refer to the angle formed by Ray KL and Ray HK is ∠LKH or ∠HKL.
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BRAINLEST AND 40 POINTS!!
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water.
Enter an estimate for the land area on the planet. Round the answer to the nearest million.
An estimate for the land area on the planet is
mi?
A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²
The surface area of a sphere is given by the formula:
S = 4πr²
where S is the surface area and r is the radius.
Substituting the given radius, we get:
S = 4π(2,812)²
S ≈ 99,392,252.4 mi²
Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:
Land area ≈ (1/3) x 99,392,252.4
Land area ≈ 33,130,750.8 mi²
Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.
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Find the derivative.
f(X) = (2e^3x + 2e^-2x)^4
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule and the power rule.
First, we need to find the derivative of the function inside the parentheses, which is:
g(x) = 2e^(3x) + 2e^(-2x)
The derivative of g(x) is:
g'(x) = 6e^(3x) - 4e^(-2x)
Now, using the chain rule and power rule, we can find the derivative of f(x):
f'(x) = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))
Simplifying this expression, we get:
f'(x) = 24(2e^(3x) + 2e^(-2x))^3 * (e^(3x) - e^(-2x))
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
Let u = 2e^(3x) + 2e^(-2x). Then f(x) = u^4.
First, find the derivative of the outer function with respect to u:
df/du = 4u^3
Next, find the derivative of the inner function with respect to x:
du/dx = d(2e^(3x) + 2e^(-2x))/dx = 6e^(3x) - 4e^(-2x)
Now, use the chain rule to find the derivative of f with respect to x:
df/dx = df/du * du/dx = 4u^3 * (6e^(3x) - 4e^(-2x))
Substitute the expression for u back into the equation:
df/dx = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))
This is the derivative of f(x) with respect to x.
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the average time it takes a salesperson to finish a sale on the phone is exponentially distributed with a mean of 18 minutes. find the probability that more than 2 minutes pass before a sale is completed.
The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.
The CDF of the exponential distribution is given by:
F(x) = 1 - e^(-λx)
where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.
To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:
P(X > 2) = 1 - P(X ≤ 2)
Substituting into the CDF formula:
P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]
Plugging in the value of λ:
P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895
This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.
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Nick is building a kaleidoscope by making a cylinder case with height of 11 inches and a diameter of 2 3/4 inches. What is the volume of the cylinder in cubic inches? Round to the nearest tenth. ( Use 3. 14 for pi ) Right Awnser will be marked brainliest!!
The volume 33.5 cubic inches
To calculate the volume of the cylinder, we need to use the formula:
V = π[tex]r^2[/tex]h
where V is the volume, π is the constant pi, r is the radius of the base (which is half the diameter), and h is the height.
First, we need to convert the diameter of the cylinder to inches:
2 3/4 inches = (2*4 + 3)/4 inches = 11/4 inches
The radius of the cylinder is half the diameter, so:
r = (11/4)/2 = 11/8 inches
Now we can plug in the values into the formula:
V = π[tex](11/8)^2[/tex](11) cubic inches
V ≈ 33.5 cubic inches (rounded to the nearest tenth)
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After Paul and Marlena got married, they decided they wanted to take a
Caribbean cruise to celebrate their ten year anniversary. The cruise will cost them
$5,800. How much should they deposit into an account now that pays 5.3%
interest, compounded daily, in order to have enough for their cruise in ten years?
A. $550.81
B. $2,431.23
C. $2,957.82
D. $3,414.04
PLEASEEE
Paul and Marlena should deposit approximately $2,431.23 into an account now to have enough for their cruise in ten years.
So, the correct answer is B. $2,431.23.
To calculate the amount Paul and Marlena should deposit into an account now in order to have enough for their cruise in ten years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{ (nt)}[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is what we need to find.
The future value (A) is given as $5,800.
The interest rate (r) is 5.3% or 0.053 as a decimal.
The interest is compounded daily, so n = 365 (number of days in a year).
Using the formula, we can rearrange it to solve for P:
[tex]P = A / (1 + r/n)^{(nt)[/tex]
Substituting the given values:
[tex]P = 5800 / (1 + 0.053/365)^{(365\times 10)[/tex]
Calculating this expression:
P ≈ 2,431.23
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the average weight of 40 randomly selected minivans was 4,150 pounds. the minivan population standard deviation was 490 pounds. find the 99% confidence interval of the true mean weight of minivans.
The 99% confidence interval of the true mean weight of minivans with 4150 pounds is CI = (3950, 4350).
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
Point estimate is the sample mean, which is 4150 pounds. It is the best "guess" one has.
selected minivans was 4,150 pounds,
(z < 0.99) = 2.58
99% CI = ±2.58
Standard Error of the mean.
It is the = [tex]\frac{standard \ deviation}{\sqrt{sample \ size} }[/tex]
SE = [tex]\frac{490}{\sqrt{40} }[/tex]
SE = 77.475
To the nearest decimal ,
z x SE = ±200
CI = (3950, 4350) units are pounds.
Therefore, the confidence interval of the true mean weight of minivans is (3950, 4350).
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A pet border keeps a dog-to-cat ratio 5;2. If the boarder has room for 98 animals then how many of them can be dogs?
Answer:
70 dogs
Step-by-step explanation:
sum the parts of the ratio , 5 + 2 = 7 parts
divide total by 7 to find the value of one part of the ratio
98 ÷ 7 = 14 ← value of 1 part of the ratio , then
5 × 14 = 70 ← number of dogs
The value of a car is worth 40,000, and it declines by 3% every year. Which function best represents the the value of the hybrid car.
40000(0. 03)^t
40000(1. 03)^t
The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is [tex]40,000(0.97)^{t}[/tex]
The value of the car = 40,000
The value of car declines at the rate of 3% every year
function is represented as F(t)
F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]
P is principal amount value of the car which is 40,000
R is rate at which it declines every year which is 3%
t is no. of year
Putting all the values in the equation we get
F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]
F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]
F(t) = [tex]40000(0.97)^{t}[/tex]
The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .
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Please help me with this math
Answer:
mean decreases by 15
median stays the same
The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points
The values on the relative frequency table indicates;
Part A; 55%
Part B; 20%
Part C; There is an association between passing the exam and completing the exam review
What is a relative frequency table?The relative frequency table shows the mode of a dataset, from the sample obtained from a population.
The data in the table can be expressed as follows;
[tex]{}[/tex] Passed exam Did not pass exam Row totals
Completed exam review [tex]{}[/tex] 55% 10% 65%
Did not completed exam review[tex]{}[/tex] 20% 15% 35%
Column Total [tex]{}[/tex] 75% 25% 100%
Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%
Part B; The percentage that passed the exam given that they did not complete exam review is 20%
Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review
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Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are
4
44 apples and
5
55 bananas in his pantry.
What is
P(select an apple
)
P(select an apple)start text, P, left parenthesis, s, e, l, e, c, t, space, a, n, space, a, p, p, l, e, end text, right parenthesis?
If necessary, round your answer to
2
22 decimal places.
If Cam randomly selects a piece of fruit from his pantry, the probability of selecting an apple is 4/9 or 0.44.
To find the probability of selecting an apple, we need to divide the number of apples by the total number of fruits in Cam's pantry.
Total number of fruits = number of apples + number of bananas = 4 + 5 = 9
P(select an apple) = number of apples / total number of fruits = 4/9
So, the probability of selecting an apple is 4/9 or approximately 0.44 when rounded to two decimal places.
Therefore, the probability is 4/9 or 0.44.
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Complete question is:
Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 4 apples and 5 bananas in his pantry.
What is P(select an apple)?
If necessary, round your answer to 2 decimal places.
Are the events mutually exclusive?
event a: rational numbers
event b: irrational numbers
no - overlapping
yes - mutually exclusive
Answer:
Yes they are mutually exclusive
Step-by-step explanation:
You cannot both be a rational number and an irrational number
The first floor of a tiny house has has a length of 11 feet. The width of the kitchen if is 7 feet and the width of the bathroom is 4 feet. The expression 11(7+4) represents the total area in square feet. Write an expression to represent the total area as the sum of the areas of each room
The total area of the first floor of the tiny house is 121 square feet
The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:
Total area = Area of kitchen + Area of bathroom
The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:
Area of kitchen = 11 x 7 = 77 square feet
Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:
Area of bathroom = 11 x 4 = 44 square feet
Substituting these expressions into the equation for the total area, we get:
Total area = Area of kitchen + Area of bathroom
= 77 + 44
= 121 square feet
Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.
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Hamid's soccer game will start at 10:00 am but the players must arrive to the field three quarters of an hour early to warm up. the game must end by 1:15
Hamid's soccer game starts at 10:00 am with players warming up 45 minutes earlier and ends by 1:15.
How long is Hamid's soccer game?Hamid's soccer game is scheduled to start at 10:00 am, but the players must arrive at the field 45 minutes early to warm up. This means that they need to be there at 9:15 am. The duration of the game is not given, but we know that it must end by 1:15 pm.
Assuming that the game will last for 90 minutes, it would end at 11:30 am. This would give the players ample time to change, clean up, and leave the field by 12:00 pm. However, if the game were to last longer, say for 2 hours, it would end at 12:00 pm, leaving only 15 minutes for the players to get ready to leave.
Therefore, it is important for the players to play efficiently and within the time allotted so that they have enough time to change and leave before the deadline. It is also important for the players to arrive at the field on time to ensure that they have enough time to warm up and prepare for the game.
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The population of pine trees in a 200-acre area has decreased by roughly the same percentage over the past 4 years. The table below shows data values for the population of these trees, p (t) , after t years.
The function that would best represent this is given as p(t) = 1150 (0.8769)^t
What is an exponential function?An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a constant called the base and "x" is the variable. The base is usually a positive number greater than 1, but it can also be a fraction between 0 and 1, or even a negative number.
Exponential functions are characterized by the fact that the variable "x" appears as an exponent. As a result, these functions grow or decay very rapidly as "x" increases or decreases, depending on the value of the base "a".
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5
The consumer group's claim that the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0.3 is correct.
This can be calculated by subtracting the sample proportion of Brand S from the sample proportion of Brand R, resulting in a difference of 0.03 or 3%. This matches the consumer group's claim that the mean of all possible differences in sample proportions is 0.3. It is important to note that this result only applies to the specific samples taken and cannot be generalized to all samples from these brands.
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Find the solution of the following initial value problem. 3x N이 =3 f'(u) = 5( cosu - sin u) and f(u)= Use Newton's method to approximate all the intersection points of the following pair of curves. Some preliminary graphing or analysis may help in choosing good intro y=16/* and y=x+1 The graphs intersect when x (Do not round until the final answer. Then found to six decimal places as needed. Use a comma to separate med
the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.
To solve this problem, we can separate the variables and integrate both sides as follows:
f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C
Using the initial condition f(3xN) = 3, we can solve for the constant C:
f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)
Thus, the solution to the initial value problem is given by:
f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)
For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:
f(x) = 16/x - (x + 1)
The intersection points correspond to the roots of f(x), which can be found using Newton's method:
x_{n+1} = x_n - f(x_n)/f'(x_n)
where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:
x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421
Thus, the intersection point is approximately (2.215421, 3.256684).
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Use Newton's method to approximate a root of the equation In (4x) = arctan(x -0.1) as follows. Let x1 = 0.1 be the initial approximation. The fourth approximation x4 is and the fifth approximation x5 is
To use Newton's method to approximate a root of the equation
In (4x) = arctan(x -0.1),
we will need to find the first derivative of the function f(x) = In(4x) - arctan(x-0.1). f(x) = In(4x) - arctan(x-0.1) f'(x) = 4/(4x) - 1/(1+(x-0.1)^2) Using the initial approximation x1 = 0.1,
We can find the second approximation x2: x2 = x1 - f(x1)/f'(x1) x2 = 0.1 - [In(4*0.1) - arctan(0.1-0.1)] / [4/(4*0.1) - 1/(1+(0.1-0.1)^2)] x2 = 0.1076
We can repeat this process to find the third approximation x3: x3 = x2 - f(x2)/f'(x2) x3 = 0.1076 - [In(4*0.1076) - arctan(0.1076-0.1)] / [4/(4*0.1076) - 1/(1+(0.1076-0.1)^2)] x3 = 0.1078
Now we can find the fourth approximation x4: x4 = x3 - f(x3)/f'(x3) x4 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x4 = 0.1078
Finally, we can find the fifth approximation x5: x5 = x4 - f(x4)/f'(x4) x5 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x5 = 0.1078
Therefore, the fourth approximation x4 is 0.1078 and the fifth approximation x5 is also 0.1078.
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An object is shot upwards from ground level with an initial velocity of 3 meters per second; it
is subject only to the force of gravity (no air resistance). Find its maximum altitude and the
time at which it hits the ground.
The maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.
To find the maximum altitude and the time at which the object hits the ground after being shot upwards from ground level with an initial velocity of 3 meters per second and subject only to the force of gravity,
we can use the following steps:
1. Calculate the time it takes to reach its maximum altitude:
To do this, we can use the formula vf = vi - gt, where vf is the final velocity (0 m/s at the peak), vi is the initial velocity (3 m/s), g is the acceleration due to gravity (9.81 m/s²), and t is the time. Rearranging and solving for t:
0 = 3 - 9.81t
t = 3 / 9.81 ≈ 0.306 seconds
2. Calculate the maximum altitude:
We can use the formula h = vit - 0.5gt², where h is the maximum altitude. Plugging in the values:
h = (3 m/s)(0.306 s) - 0.5(9.81 m/s²)(0.306 s)²
h = 0.459m
3. Calculate the time it takes to hit the ground:
Since the object will take the same amount of time to fall from its maximum altitude to the ground as it took to reach the maximum altitude, the total time to hit the ground is double the time it took to reach the maximum altitude:
total time = 2 × 0.306 s ≈ 0.612 seconds
So, the maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.
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The distance from city a to city b is 256. 8 miles. The distance from city a to city c is 739. 4 miles how much farther is the trip to city c than the trip to city b
Answer:
482.6 mi
Step-by-step explanation:
a to b = 256.8 mi
a to c = 739.4 mi
(a to c) - (a to b) = 739.4 - 256.8 = 482.6 mi
Find x.
Please help thank you
(-10x-4y) and (7x-5y) in simplest form
The simplification of the given algebraic expression is: -3x - 9y
How to simplify Algebraic Expressions?Algebraic expressions are defined as the idea of expressing numbers with the aid of letters or alphabets without really specifying their actual values.
Now, the algebraic operations are known by the acronym PEMDAS which denotes:
P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
We want to find the sum of the algebraic expressions given as (-10x - 4y) and (7x - 5y) in simplest form.
Thus, we have:
(-10x - 4y) + (7x - 5y)
= -10x - 4y + 7x - 5y
= -3x - 9y
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Complete question:
Find an expression which represents the sum of (-10x - 4y) and (7x - 5y) in simplest terms.