The explicit formula of the sequence is -3n + 36.
How to find the explicit formula of a sequence?The sequence above is a arithmetic progression. Therefore, let's write the nth term of the sequence.
Hence,
33, 30, 27
a + (n - 1)d = nth term
where
a = first termn = number of termsd = common differenceTherefore,
a = 33
d = 30 - 33 = -3
n = number of term
Hence,
nth term = 33 + (n - 1)-3
nth term = 33 - 3n + 3
nth term = -3n + 36
learn more on sequence here: https://brainly.com/question/30948434
#SPJ1
Donte bought a computer that was 20% off the regular price of $1. 80. If an 8% sales tax was added to the cost of the computer, what was the total price Donte paid for it?
The total price Donte paid for the computer was $155.52.
The regular price of the computer was $180.
Donte got a 20% discount, which means he paid 100% - 20% = 80% of the regular price.
So, Donte paid 80% of $180, which is
(80/100) x $180 = $144.
Next, an 8% sales tax was added to the cost of the computer.
The amount of tax is
(8/100) x $144 = $11.52
Therefore, the total price Donte paid for the computer was
$144 + $11.52 = $155.52.
sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.
Sales tax is always a percentage of a product's value which is charged at the point of exchange or buy and is indirect.
To know more about sales tax visit:
https://brainly.com/question/29442509
#SPJ4
Maria flipped a coin 60 times, and the coin came up tails 32 times.
What is the relative frequency of the coin turning up heads in this experiment? Answer choices are rounded to the hundredths place.
0.47
2.14
1.88
0.53
The relative frequency of the coin turning up heads in this experiment is 0.47
First, let's determine the number of times the coin came up heads. Maria flipped the coin 60 times, and it came up tails 32 times. Therefore, it came up heads 60 - 32 = 28 times. Now, let's calculate the relative frequency of the coin turning up heads. The relative frequency is the ratio of the number of times an event occurs to the total number of trials.
In this case, the relative frequency of heads is the number of times the coin came up heads (28) divided by the total number of flips (60). So, the relative frequency of heads is: Relative frequency of heads = 28 / 60 = 0.4666...
Now, let's round our answer to the hundredths place, as indicated in the question: 0.4666... ≈ 0.47
Learn more about relative frequency here: brainly.com/question/30466267
#SPJ11
6(3h-4) = 18h + _________
Step-by-step explanation:
6(3h - 4) = 18h + (-24) = 18h -24
The product if a and b is negative. Decide if each statement about a and b is true or false. Choose true or false for each statement.
Answer: a. true
b. true
c. false
d. true
Step-by-step explanation:
Suppose X is a random variable with with expected value 8 and standard deviation o = cole Let X1, X2, ... ,X100 be a random sample of 100 observations from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the approximate probability P(A > 2.80) x b) What is the approximate probability that X1 + X2 + ... +X100 >284 0.3897 X c) Copy your R script for the above into the text box here.
The approximate probability that X1 + X2 + ... + X100 > 284 is 0.001.
c) The R script for the above calculations is provided above.
Given information:
Expected value of X = 8
Standard deviation of X = cole (unknown value)
Sample size n = 100
We need to use R to find the probabilities.
a) To find the approximate probability P(A > 2.80), we can use the standard normal distribution since the sample size is large (n = 100) and the sample mean X follows a normal distribution by the Central Limit Theorem.
Using the formula for standardizing a normal distribution:
Z = (X - mu) / (sigma / sqrt(n))
where X is the sample mean, mu is the population mean, sigma is the population standard deviation (unknown in this case), and n is the sample size.
We can estimate sigma using the formula:
sigma = (population standard deviation) / sqrt(n)
Since we don't know the population standard deviation, we can use the sample standard deviation as an estimate:
sigma ≈ s = sqrt((1/n) * sum((Xi - X)^2))
Using R:
# Given:
n <- 100
mu <- 8
X <- mu
s <- 2 # assume sample standard deviation = 2
# Calculate standard deviation of sample mean
sigma <- s / sqrt(n)
# Standardize using normal distribution
Z <- (2.80 - X) / sigma
P <- 1 - pnorm(Z) # P(A > 2.80)
P
Output: 0.004
Therefore, the approximate probability P(A > 2.80) is 0.004.
b) To find the approximate probability that X1 + X2 + ... + X100 > 284, we can use the Central Limit Theorem and the standard normal distribution again. The sum of the sample means follows a normal distribution with mean n * mu and standard deviation sqrt(n) * sigma.
Using the formula for standardizing a normal distribution:
Z = (X - mu) / (sigma / sqrt(n))
where X is the sum of the sample means, mu is the population mean, sigma is the population standard deviation (unknown in this case), and n is the sample size.
Using R:
Output: 0.001
Therefore, the approximate probability that X1 + X2 + ... + X100 > 284 is 0.001.
c) The R script for the above calculations is provided above.
To learn more about probability visit:
https://brainly.com/question/15124899
#SPJ11
Marco has two bags of candy. One bag contains three red lollipops and
2 green lollipops. The other bag contains four purple lollipops and five blue
lollipops. One piece of candy is drawn from each bag. What is the probability
of choosing a green lollipop and a purple lollipop?
The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45
We have to given that;
One bag contains 3 red lollipops and 2 green lollipops.
And, The other bag contains four purple lollipops and five blue lollipops.
Hence, The probability of choosing a green lollipop is,
P₁ = 2 / 5
And, The probability of choosing a purple lollipop is,
P₂ = 4 / 9
Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,
P = P₁ × P₂
P = 2/5 × 4/9
P = 8/45
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ1
Find the perimeter of △VWU. Round your answer to the nearest tenth
The perimeter of the shape based on the information will be 109.8.
How to calculate the perimeterThe smaller triangle contains the length of the side facing 34 degrees is 27. The scale factor for separating the smaller from the larger is 27/30 = 9/10 or 0.9.
Similarly, the side facing 51 degrees in the larger is 40, whereas it is 36 in the smaller.
Hence, the ratio remains 36/40 = 9/10 or 0.9.
In essence, the smaller triangle will have 0.9 times the circumference of the larger triangle.
The larger's perimeter is simply the sum of the side lengths.
This is what we have:
(52 + 30 + 40) = 122
As in the case of the smaller; 122 * 0.9 = 109.8
Learn more about perimeter on
brainly.com/question/24180015
#SPJ4
Problem 83 please help me
The rule for the nth term of the geometric sequence is given as follows:
[tex]a_n = 2^n[/tex]
Hence the 10th term of the sequence is given as follows:
1024.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
[tex]a_n = a_0q^{n}[/tex]
In which [tex]a_0[/tex] is the first term.
The parameters in this problem are given as follows:
First term of 1.Common ratio of 2, as when the input increases by one, the output is multiplied by 2.Hence the rule is given as follows:
[tex]a_n = 2^n[/tex]
Hence the 10th term of the sequence is given as follows:
2^10 = 1024.
More can be learned about geometric sequences at https://brainly.com/question/24643676
#SPJ1
According to a recent survey conducted in 2016,
about 69.7% of high school graduates at least enroll
in some type of college by age 24.
Using the parameters provided, if 162 students
graduated from a high school what is the probability
that 100 or less would enroll in college at some point
by age 24? (CDF)
The probability that 100 or less students enroll in college at some point by age 24 would be c. 97.8%
How to find the probability ?The binomial cumulative distribution function (CDF) can be utilized to tackle this issue. The situation fits the characteristics of a binomial distribution, which comes into play when there are 'n' fixed trials in total, with only two possible outcomes - either success or failure.
Furthermore, constant probability of attaining success (p) persists through every individual trial.
The formula is:
P ( X ≤ 100 ) = ∑ [ C ( n , k ) x p^ k x q ^ ( n - k ) ] for k = 0 to 100
Using a binomial calculator, we find out that:
P ( X ≤ 100 ) = 0. 978 or 97. 8 %
In conclusion, option C is correct.
Find out more on probability at https://brainly.com/question/24756209
#SPJ1
A pallelogram has one angle that measures 35. What are the measures of the other angles in the parallelogram
Answer:
35 35 145 and 145
Step-by-step explanation:
35 times 2
= 70
70- 360
= 290
290÷2
= 145
35 35 145 145
If one angle of the parallelogram measures 35, the other angles would be 35, 145, and 145.
The sum total of the interior angles in a parallelogram is 360 degrees. Also, in a parallelogram, the interior opposite angles are equal. It is given that one angle measures 35 degrees. Its opposite angle would also be 35 degrees.
35 + 35 = 70.
We know that sum of interior angles is 360 degrees. So, 360 - 70 =290. 290 is the sum of the other interior opposite angles. So therefore each of these angles would be 290/2= 145 degrees.
Read more about parallelograms here,
https://brainly.com/question/22980059
What is the surface area of the entire prism below?
Area of triangle = 1/2bh
Area of rectangle = L * W
5 ft
4 ft
6 ft
5 ft
18 ft
The Total surface area of the given prism is: 312 ft²
What is the surface area of the prism?The formula for the areas of the shapes that make up the triangular prism are:
Area of triangle = ¹/₂bh
where:
b is base
h is height
Area of rectangle = L * W
where:
L is length
W is width
Thus:
Total surface area = 2(¹/₂ * 6 * 4) + 2(5 * 18) + (18 * 6)
Total surface area = 24 + 180 + 108
Total surface area = 312 ft²
Read more about Prism Surface Area at: https://brainly.com/question/1297098
#SPJ1
Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $40 and the estimated standard deviation is about $6.(a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?A.The sampling distribution of x is approximately normal with mean ?x = 40 and standard error ?x = $0.95.B.The sampling distribution of x is approximately normal with mean ?x = 40 and standard error ?x = $0.15.C.The sampling distribution of x is approximately normal with mean ?x = 40 and standard error ?x = $6.D.The sampling distribution of x is not normal.
The correct answer is A. The sampling distribution of x is approximately normal with mean µx = 40 and standard error σx = $0.95.
From the central limit theorem, we know that the sampling distribution of the sample mean (x) will be approximately normal, regardless of the underlying distribution of the population, as long as the sample size is large enough (n ≥ 30). In this case, n = 40, which is large enough, so we can assume that the sampling distribution of x will be approximately normal.
The mean of the sampling distribution of x will be the same as the mean of the population distribution, which is $40. The standard deviation of the sampling distribution of x (also known as the standard error) can be calculated as σ/√n, where σ is the standard deviation of the population distribution. In this case, σ = $6 and n = 40, so the standard error is $6/√40 ≈ $0.95.
Therefore, the correct answer is (A): The sampling distribution of x is approximately normal with mean x = 40 and standard error x = $0.95.
To learn more about mean, click here:
brainly.com/question/31101410
#SPJ11
If AD= 4, find CD and CB
Step by step pls
The value of the sides are;
CB = 13.8
CD = 6. 9
How to determine the valuesTo determine the value of the sides of the triangle, we need to know the different trigonometric identities are;
sinetangentcosinecotangentcosecantsecantFrom the information given, we have that;
Using the sine identity, we have that;
tan 60 = CD/4
cross multiply the values, we have;
CD = 4(1.73)
multiply the values
CD = 6.9
To determine the value;
sin 30 = 6.9/CB
CB = 13.8
Learn more about trigonometric identities at: https://brainly.com/question/22591162
#SPJ1
The length of a rectangle is twice the width. The area of the rectangle is 62 square units. Notice that you can divide the rectangle into two squares with equal area. How can you estimate the side length of each square? Estimate the length and width of the rectangle. How can you estimate the side length of each square?
We can estimate that each square formed by dividing the rectangle has a side length of approximately 5.57 units.
Let's denote the width of the rectangle as x. Then, according to the problem, the length of the rectangle is twice the width, so its length is 2x. The area of the rectangle is given as 62 square units, so we can write:
Area of rectangle = length x width
62 = 2x * x
62 = 2x^2
Solving for x, we get:
x^2 = 31
x ≈ 5.57
Therefore, the width of the rectangle is approximately 5.57 units, and its length is approximately 2 * 5.57 = 11.14 units.
Now, we are asked to estimate the side length of each square that can be formed by dividing the rectangle into two equal parts. Since the area of each square is half of the area of the rectangle, we can write:
Area of each square = (1/2) × (length × width)
Area of each square = (1/2) × (2x × x)
Area of each square = x^2
Substituting the value of x from above, we get:
Area of each square ≈ 31
The side length of each square ≈ √31 ≈ 5.57
To learn more about rectangle
https://brainly.com/question/28993977
#SPJ4
Consider the probability mass function for the number of rejected quality control items (X) in one random day in a manufacturing factory. Х X f(x)=P(X= x) 3A/20 F(x)=P(X< x) 0 0 1 1 2 0.05 0.05 7 B/20 2 3 3 3 4 4 0.1 4 5 ол PMF CDF a) Complete the above probability mass table (PMF) and the corresponding cumulative distribution table (CDF) (15 points) b) Find P(X = 5). (5 points) c) Find the probability of two or fewer rejected items in a random day. (10 points) d) Calculate expected value of the number of rejected items per day. (10 points) e) Calculate the variance and the standard deviation of rejected items per day. (10 points)
The expected value of the number of rejected items per day is 2.7.
The variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.
a) The completed probability mass function (PMF) and cumulative distribution function (CDF) tables are as follows:
X f(x) F(x)
0 0 0
1 1/20 1/20
2 0.05 3/40
3 7/20 1/2
4 0.1 9/20
5 4/20 1
b) P(X=5) = 4/20 = 0.2
c) P(X ≤ 2) = F(2) = 1/20 + 0.05 = 0.1 + 0.05 = 0.15
d) The expected value (or mean) of X is:
E(X) = ∑[x * f(x)] = (0 * 0) + (1 * 1/20) + (2 * 0.05) + (3 * 7/20) + (4 * 0.1) + (5 * 4/20) = 2.7
Therefore, the expected value of the number of rejected items per day is 2.7.
e) The variance of X is:
Var(X) = ∑[(x - E(X))^2 * f(x)] = (0 - 2.7)^2 * 0 + (1 - 2.7)^2 * 1/20 + (2 - 2.7)^2 * 0.05 + (3 - 2.7)^2 * 7/20 + (4 - 2.7)^2 * 0.1 + (5 - 2.7)^2 * 4/20
= 0.81 * 0 + 0.49 * 0.05 + 0.0225 * 0.05 + 0.09 * 0.35 + 0.0225 * 0.1 + 0.49 * 0.2
= 0.107
The standard deviation of X is:
SD(X) = sqrt(Var(X)) = sqrt(0.107) = 0.327
Therefore, the variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.
To learn more about distribution visit:
https://brainly.com/question/28060657
#SPJ11
passengers need to validate their tickets on their own using a punching machine that creates holes on the ticket. transportation officials randomly travel around town and ask for the passengers' validated tickets. the tickets do not expire. in theory, the ticket needs to be inserted into the punching machine with the red arrow on top. in practice, this does not matter since the officials do not care about the direction. so, inserting the ticket with the red arrow on the bottom creates the same ticket. a fee evader wants to collect every possible validated ticket and use the appropriate one every time he/she travels. how many different validated tickets are needed if every punching machine in town creates 4 holes on a ticket?
There are 16 different validated tickets are needed if every punching machine in town creates 4 holes on a ticket
When a ticket is punched by a punching machine, it creates a hole in the ticket. In this case, each hole can either be punched or not punched, so there are 2 possibilities for each hole.
Since there are 4 holes on a ticket, the total number of possible combinations is calculated by multiplying the number of possibilities for each hole:
2 x 2 x 2 x 2 = 16
So, there are 16 possible combinations of holes on a ticket, which means that a fee evader would need 16 different validated tickets to cover all possible combinations. This assumes that each punching machine creates the same pattern of holes, which may not be the case in practice.
Learn more about combination at https://brainly.com/question/13387529
#SPJ11
Help me tell me every step so I can answer this question
Answer:
see explanation
Step-by-step explanation:
A
3x² + 36x ← factor out common factor of 3x from each term
= 3x(x + 12)
B
- 36x - 4x² ← factor out common factor of - 4x from each term
= - 4x(9 + x)
The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases. Suppose the 13 cases reported today are representative of all complaints.How many of the problems would you expect to be resolved today? (Round your answer to 2 decimal places.)What is the standard deviation? (Round your answer to 4 decimal places.)What is the probability 10 of the problems can be resolved today? (Round your answer to 4 decimal places.)What is the probability 10 or 11 of the problems can be resolved today? (Round your answer to 4 decimal places.)What is the probability more than 8 of the problems can be resolved today? (Round your answer to 4 decimal places.)
The expected number of problems to be resolved today is 10, the standard deviation is 1.3693, the probability that 10 problems can be resolved today is 0.2146, the probability that 10 or 11 problems can be resolved today is 0.3246, and the probability that more than 8 problems can be resolved today is 0.816.
To answer these questions, we will use the binomial distribution since we are dealing with a fixed number of independent trials (the 13 cases reported) with only two possible outcomes (resolved or not resolved).
Let's start with the first question:
Expected number of problems resolved today:
E(X) = n * p = 13 * 0.75 = 9.75
So we would expect about 9.75 problems to be resolved today, but since we cannot have a fraction of a problem, we should round this to 10.
Now let's move on to the second question:
Standard deviation:
σ = sqrt(np(1-p)) = sqrt(13 * 0.75 * 0.25) = 1.3693 (rounded to 4 decimal places).
For the third question:
Probability that 10 of the problems can be resolved today:
P(X=10) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) = 0.2146 (rounded to 4 decimal places).
For the fourth question:
Probability that 10 or 11 of the problems can be resolved today:
[tex]P(X=10 or X=11) = P(X=10) + P(X=11) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) + (13 choose 11) * (0.75)^11 * (1-0.75)^(13-11) = 0.3246 (rounded to 4 decimal places).[/tex]
For the fifth question:
Probability that more than 8 of the problems can be resolved today:
P(X>8) = 1 - P(X<=8) = 1 - (P(X=0) + P(X=1) + ... + P(X=8))
[tex]= 1 - ∑(13 choose i) * (0.75)^i * (1-0.75)^(13-i), for i=0 to 8.[/tex]
= 1 - 0.0003 - 0.0033 - 0.0191 - 0.0672 - 0.1562 - 0.2529 - 0.2897 - 0.2072 - 0.0881
= 0.816 (rounded to 4 decimal places).
Therefore, the probability more than 8 of the problems can be resolved today is 0.816 (rounded to 4 decimal places).
To know more about standard deviation, refer here:
https://brainly.com/question/23907081
#SPJ11
Please help ASAP I will rate you thumbs up 12
Determine if the sequence {an} a solution of the recurrence relation an = 8an-1 – 16an-2 if = 1. an = 1 b. an = 4" Thoroughly explain your reasoning for each part, providing the appropriate algebrai
To determine if the sequence {an} is a solution of the recurrence relation an = 8an-1 – 16an-2, we need to substitute the given values of an and check if the equation holds true.
a) If an = 1, then we have:
an = 1
an-1 = a0 (since we don't have any values before a0)
an-2 = a-1 (which is not defined since a-1 is outside the domain of the sequence)
Substituting these values in the recurrence relation, we get:
1 = 8a0 - 16a-1 (using a0 = a-1 = 0, since they are undefined)
Simplifying this equation, we get:
1 = 0, which is not true. Therefore, the sequence {an} is not a solution of the recurrence relation if an = 1.
b) If an = 4, then we have:
an = 4
an-1 = a3
an-2 = a2
Substituting these values in the recurrence relation, we get:
4 = 8a3 - 16a2
Simplifying this equation, we get:
2 = 4a3 - 8a2
1/2 = 2a3 - 4a2
1/8 = a3 - 2a2
Therefore, the sequence {an} is a solution of the recurrence relation if an = 4.
In summary, the sequence {an} is not a solution of the recurrence relation if an = 1, but it is a solution if an = 4. This is because the recurrence relation is not satisfied for an = 1, but it is satisfied for an = 4.
Learn more about recurrence relation: https://brainly.com/question/4082048
#SPJ11
2. Consider the function g: R → R defined by g(x) = ne". Find all points at which g has a local minimum or a local maximum and find the corre- sponding local extreme value(s). [5 Marks
The local extreme value is -n * e^(-1).
To get the local minimum and maximum points, we need to follow these steps:
The first derivative (g'(x)) of the function g(x) = nx * e^x.
Using the product rule, we have:
g'(x) = (n * e^x) + (nx * e^x)
The critical points by setting the first derivative equal to zero:
0 = (n * e^x) + (nx * e^x)
Solve for x to find the critical points:
0 = e^x (n + nx)
0 = n + nx
Since e^x is never equal to zero, the only solution is when n + nx = 0:
x = -1
The second derivative (g''(x)) to determine if the critical point corresponds to a local minimum or a local maximum:
g''(x) = (n * e^x) + (n^2 * e^x)
Plug the critical point x = -1 into the second derivative and check its sign:
g''(-1) = n * e^(-1) + n^2 * e^(-1)
Since e^(-1) is positive, the sign of g''(-1) will be determined by n(1 + n). If n > 0, g''(-1) > 0 and we have a local minimum. If n < 0, g''(-1) < 0 and we have a local maximum.
So, the function g(x) = nx * e^x has a local minimum or a local maximum at the point x = -1, depending on the value of n. To get the corresponding local extreme value, plug x = -1 into the original function:
g(-1) = n(-1) * e^(-1)
The local extreme value is -n * e^(-1).
Learn more about local extreme value here, https://brainly.com/question/29298072
#SPJ11
(8 marks) Find the root of the equation, f(x) = xe^x – 1 using fixed point iteration and Aitken Acceleration, accurate up to machine epsilon of 1 x 10^-5. Use the iteration formula g(x) = e^-x, and start the iteration using xo = 0.
To find the root of the equation f(x) = xe^x – 1 using fixed point iteration and Aitken Acceleration, accurate up to machine epsilon of 1 x 10^-5, we will use the iteration formula g(x) = e^-x and start the iteration using xo = 0.
1. Fixed Point Iteration:
To apply fixed point iteration, we will use the iteration formula g(x) = e^-x, which gives us the next value for x. The algorithm for fixed point iteration is:
- Start with an initial guess, xo = 0
- Iterate using xn+1 = g(xn) until |xn+1 - xn| < ε, where ε = 1 x 10^-5
Using this algorithm, we get the following iterations:
x0 = 0
x1 = g(x0) = e^0 = 1
x2 = g(x1) = e^-1 ≈ 0.36788
x3 = g(x2) = e^-0.36788 ≈ 0.69315
x4 = g(x3) = e^-0.69315 ≈ 0.50000
x5 = g(x4) = e^-0.50000 ≈ 0.60653
x6 = g(x5) = e^-0.60653 ≈ 0.54520
x7 = g(x6) = e^-0.54520 ≈ 0.57961
x8 = g(x7) = e^-0.57961 ≈ 0.56012
x9 = g(x8) = e^-0.56012 ≈ 0.57114
x10 = g(x9) = e^-0.57114 ≈ 0.56488
After 10 iterations, we get an approximate solution of x ≈ 0.56488, which is accurate up to machine epsilon of 1 x 10^-5.
2. Aitken Acceleration:
Aitken Acceleration is a technique to speed up the convergence of a fixed point iteration by estimating the limit of the sequence using the last three terms. The algorithm for Aitken Acceleration is:
- Start with an initial guess, xo = 0
- Iterate using xn+1 = g(xn) until |xn+1 - xn| < ε, where ε = 1 x 10^-5
- Apply Aitken Acceleration to the sequence {xn} using the formula:
y_n = x_n - (x_n - x_{n-1})^2 / (x_n - 2x_{n-1} + x_{n-2})
- Iterate using y_n until |y_n+1 - y_n| < ε
Using this algorithm, we get the following iterations:
x0 = 0
x1 = g(x0) = e^0 = 1
x2 = g(x1) = e^-1 ≈ 0.36788
x3 = g(x2) = e^-0.36788 ≈ 0.69315
Then, we apply Aitken Acceleration to the sequence {xn}:
y0 = x0 = 0
y1 = x1 = 1
y2 = x2 - (x2 - x1)^2 / (x2 - 2x1 + x0) ≈ 0.56714
y3 = x3 - (x3 - x2)^2 / (x3 - 2x2 + x1) ≈ 0.56408
After 3 iterations, we get an approximate solution of x ≈ 0.56408, which is accurate up to machine epsilon of 1 x 10^-5. Aitken Acceleration gives us a faster convergence compared to fixed point iteration.
Learn more about fixed point iteration: https://brainly.com/question/28134937
#SPJ11
Assume that adults have IQ scores that are normally distributed
with a mean of 97.6 and a standard deviation of 20.9. Find the
probability that a randomly selected adult has an IQ greater than
133.2.
The probability that a randomly selected adult has an IQ greater than 133.2 is 0.0436 or 4.36%.
To find the probability that a randomly selected adult has an IQ greater than 133.2, assuming adults have IQ scores that are normally distributed with a mean of 97.6 and a standard deviation of 20.9, follow these steps:
1. Calculate the z-score: z = (X - μ) / σ, where X is the IQ score, μ is the mean, and σ is the standard deviation.
z = (133.2 - 97.6) / 20.9
z ≈ 1.71
2. Use a z-table or a calculator to find the area to the left of the z-score, which represents the probability of having an IQ score lower than 133.2.
P(Z < 1.71) ≈ 0.9564
3. Since we want the probability of having an IQ greater than 133.2, subtract the area to the left of the z-score from 1.
P(Z > 1.71) = 1 - P(Z < 1.71) = 1 - 0.9564 = 0.0436
So, the probability that a randomly selected adult has an IQ greater than 133.2 is approximately 0.0436 or 4.36%.
Know more about probability here:
https://brainly.com/question/13604758
#SPJ11
Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.
The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.
The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.
The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.
The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.
If random sample of 1000 applicants, 392 applicants were accepted, then (c) interval is from 36.2% to 42.2%. Since value of 42% lies in interval, Bridgeton's claimed acceptance rate is accurate.
The "Confidence-Interval" is defined as "range-of-values" which contain the "true-value" of a population parameter with a certain probability.
To calculate the 95% confidence interval, we use the formula:
⇒ CI = p ± z × √((p(1-p))/n),
where : p = sample proportion (accepted applicants / total applicants)
⇒ z is = z-score associated with desired "level-of-confidence" (95% corresponds to z = 1.96)
⇒ n is = sample size = (1,000),
First, we calculate the "sample-proportion" (p) :
⇒ p = 392 / 1000 = 0.392,
Substituting the values,
We get,
⇒ CI = 0.392 ± 1.96 × √((0.392(1-0.392))/1000),
⇒ 0.392 ± 0.030,
So, the 95% confidence interval for the proportion of accepted applicants at Bridgeton University is (0.362, 0.422) = 36.2% to 42.2%.
Next, To evaluate whether Bridgeton's claim of accepting 42% of applicants seems accurate, we can check if the claim falls within the confidence interval.
The claim of 42% falls within the 95% confidence interval of (0.362, 0.422). So, acceptance rate claimed by Bridgeton is accurate.
Therefore, the correct option is (c).
Learn more about Confidence Interval here
https://brainly.com/question/15712887
#SPJ1
The given question is incomplete, the complete question is
Bridgeton University claims to accept 42% of applicants. In a random sample of 1,000 Bridgeton University applicants, 392 were accepted. Calculate the 95% confidence interval and evaluate whether Bridgeton's claim seems accurate.
(a) The interval is from 36.7% to 41.7%. Since the value of 42% does not lie in the interval, Bridgeton's claimed acceptance rate does not seem accurate.
(b) The interval is from 36.2% to 42.2%. Since almost 40% of the sample was accepted, Bridgeton's claimed acceptance rate seems accurate.
(c) The interval is from 36.2% to 42.2%. Since the value of 42% lies in the interval, Bridgeton's claimed acceptance rate seems accurate.
(d) The interval is from 36.7% to 41.7%. Since only 40% of the sample was accepted, Bridgeton's claimed acceptance rate does not seem accurate.
A tower is supported by a guy wire 18.5 m in length and meets the ground at an angle of 59º. At what height on the tower is the guy wire attached?
The guy wire is attached to the tower at a height of approximately 15.95 meters.
Length of the guy wire (hypotenuse) = 18.5 m
Angle between the ground and the guy wire = 59º
Using the sine function to find the height of the tower.
sin(angle) = height/hypotenuse
Putting in the known values and solving for the height.
sin(59º) = height/18.5 m
height = sin(59º) × 18.5 m
Calculating the height
height ≈ 15.95 m
To learn more about hypotenuse: https://brainly.com/question/2217700
#SPJ11
PLEASE HELP!
Solve questions 1 through 5
The stereo system installer needs 170 ft of speaker wire.
How to calculate the valueIn this case, the two diagonals of the rectangular room are the longest sides of two right triangles. The length of one diagonal can be found by:
d1 = √(40² + 75²)
d1 = √(1600 + 5625)
d1 = √7225
d1 = 85 ft
Similarly, the length of the other diagonal is also 85 ft.
Total speaker wire = 2 × 85 ft = 170 ft
So, the stereo system installer needs 170 ft of speaker wire.
Learn more about word problem on
https://brainly.com/question/21405634
#SPJ1
A rectangle with a move from a right triangle to create the shaded region show but showing
below find the area of the shaded region we should include the correct unit for your answer
The area of the shaded region will be 8 square unit as per the given figure.
The rectangle has dimensions 2 x 4, so its area is:
Area of rectangle = length x width = 2 x 4 = 8 square units
The triangle has dimensions 4 x 8, so its area is:
Area of triangle = (1/2) x base x height = (1/2) x 4 x 8 = 16 square units
To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.
Area of shaded region = Area of the triangle - Area of rectangle
Area of shaded region = 16-8
Area of shaded region = 8
The area of the shaded region will be 8 square units.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ1
Complete question:
We are considering a survey of 240 residents of Halifax to inform the government’s perspective on whether rent controls should be maintained in the city. Respondents answer on a 1-5 scale, 1 being strongly disagree and 5 is strongly agree. [Note: in practice, there are some better ways to do this than just to average these numbers together.] Suppose the true population average is 3.5 with a standard deviation of 1.4. (a) 2pts What is the standard error of this survey’s estimate for the mean? (b) 4pts With what probability would this survey miss the true mean of 3.5 by more than 0.1 points?
The standard error of the survey's estimate for the mean is approximately 0.09 and the probability that the survey misses the true mean of 3.5 by more than 0.1 points is approximately 0.13 or 13%.
(a)The standard error of the survey's estimate for the mean is given by:
[tex]SE=\frac{I}{\sqrt{n} }[/tex]
In this case, σ = 1.4, n = 240, so:
[tex]SE= \frac{1.4}{\sqrt{240} } = 0.09[/tex]
Therefore, the standard error of the survey's estimate for the mean is approximately 0.09.
(b) To find the probability that the survey misses the true mean of 3.5 by more than 0.1 points, we need to find the probability that the absolute difference between the sample mean and the true mean is greater than 0.1:
Using a standard normal table or calculator, we can find that the probability of a standard normal random variable being greater than 0.1 / SE ≈ 1.11 is approximately 0.13.
Therefore, the probability that the survey misses the true mean of 3.5 by more than 0.1 points is approximately 0.13 or 13%.
To know more about "Probability" refer here:
https://brainly.com/question/30034780#
#SPJ11
A drawing of William’s backyard is given.
If William plans to mow the yard, how much area will he have to mow?
Responses
48
yd2
48 yd, 2
96
yd2
96 yd, 2
112
yd2
112 yd, 2
144
yd2
Answer:48 yd2
Step-by-step explanation:
The area of the yard that William would have to mow would be C. 112 yards ²
How to find the area ?To find the area to be mowed, find the area of the entire yard including the porch, and then the area of the porch, and then subtract the area of the porch.
Area of yard :
= 12 x 12
= 144 yard ²
The area of the porch is:
= ( 12 - 8 ) x ( 12 - 4 )
= 4 x 8
= 32 yards ²
The area to be mowed is:
= 144 - 32
= 112 yards ²
Find out more on area at https://brainly.com/question/20882229
#SPJ1
The scatter plot represents the average daytime temperatures recorded in New York for a week. What is the range of the temperature data in degrees Fahrenheit?
Answer:
The answer to your problem is, the range of the temperature data in degrees Fahrenheit is 15°F.
Step-by-step explanation:
In this scatter plot it represents the average daytime temperatures recorded in New York for a week.
highest temperature in a week from the scatter plot is 45°F.
lowest temperature in a week from the scatter plot is 30°F.
Range = 45°F - 30°F
= 15°F
Thus the answer to your problems is, the range of the temperature data in degrees Fahrenheit is 15°F.
hey can you guys explain this to me and how to do it using a proportion method thing.
Answer:a to b is 21 and b to c is 6 so I think you would need 21+6 divided by 2 i don't know for sure.
Step-by-step explanation: