Based on the observations, the maximum likelihood estimate of λ is 11/5.
What is probability?Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.
The probability mass function (PMF) of a Poisson distribution with parameter λ is given by:
P(X = k) = [tex](e^{(-\lambda)} * \lambda^k)[/tex] / k!
The likelihood function for a sample of size n from a is given by:
L(λ) = P(X1 = x1, X2 = x2, ..., Xn = xn) = ∏[i=1 to n] [tex]( e^{(-\lambda)} * \lambda^{xi})[/tex] / xi!
The log-likelihood function is then:
ln L(λ) = ln ∏[i=1 to n] [tex](e^{(-\lambda)} * \lambda^{xi})[/tex] / xi! = ∑[i=1 to n] [tex](ln e^{(-\lambda)} * \lambda^{xi})[/tex] - ∑[i=1 to n] ln(xi!)
Simplifying further, we get:
ln L(λ) = (-nλ) + (∑[i=1 to n] xi)ln(λ) - ∑[i=1 to n] ln(xi!)
To find the maximum likelihood estimate (MLE) of λ, we need to differentiate the log-likelihood function with respect to λ, set the derivative to zero, and solve for λ.
d/dλ ln L(λ) = -n + (∑[i=1 to n] xi)/λ = 0
Solving for λ, we get:
λ = (∑[i=1 to n] xi) / n
Substituting the given values, we get:
λ = (2 + 5 + 2 + 1 + 1) / 5 = 11 / 5
Therefore, the maximum likelihood estimate of λ, based on the given observations, is 11/5.
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For a confidence level of 99%, find the critical value, Round to two decimal places Enter an integrar decimal number (more..]
To find the critical value for a 99% confidence level, you will need to use the z-table, which lists the z-scores for different confidence levels. Here's a step-by-step explanation:
1. Identify the confidence level: In this case, it's 99%.
2. Calculate the area under the curve: Since the confidence level is 99%, the area under the curve would be 0.99 or 99%. The remaining 1% is split between the two tails of the distribution.
3. Determine the area in one tail: Divide the remaining area by 2 (1% ÷ 2 = 0.005 or 0.5%). This is the area in one tail of the distribution.
4. Use the z-table to find the critical value: Look for the closest value to 0.995 (0.990 + 0.005) in the z-table. This value corresponds to a z-score of 2.576.
5. Round the critical value: Since the question asks for the critical value rounded to two decimal places, the answer would be 2.58. So, the critical value for a 99% confidence level is 2.58.
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Kevin drew a double number line diagram and stated of 24 is 15. Is he correct?
Yes Kevin's comparison in the number line is correct because 10.9 is less than 11.5.
What is Number line?A number line is described as a picture of a graduated straight line that serves as visual representation of the real numbers.
We can agree with Kevin after referencing the decimal value chart or decimal comparisons below.
o t h
10 9
11 5
A number line can also be referred to as a pictorial representation of numbers on a straight line that is used for comparing and ordering numbers.
The complete question is attached in the image.
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What is equal in the value to 27%?
F. 2. 7
G. 0. 027
H. 0. 270
J. 0. 27
H. 0.270 is equal in value to 27% in the given case. Option 3 is correct
A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is the percent sign (%).
To convert a percentage to a decimal, we divide the percentage by 100. For example, 50% is equal to 0.50 as a decimal.
To convert a percentage to a decimal, we divide the percentage by 100.
So to convert 27% to a decimal, we divide 27 by 100:
27/100 = 0.27
Therefore, 27% is equal to 0.27 as a decimal.
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A cooler is filled with 4 1/2 gallons of water
A Total of 144 small cups can be filled with the water from the cooler before it's empty.
The cooler has 4 1/2 gallons of water, which can be written as 9/2 gallons. Each small cup holds 1/32 gallon. To find the number of small cups that can be filled with the water from the cooler, we need to divide the total amount of water by the amount of water in each cup.
9/2 ÷ 1/32 = (9/2) * (32/1) = 144 small cups.
Therefore, 144 small cups can be filled with the water from the cooler before it's empty.
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Complete Question:
A cooler is filled with 4 1/2 gallons of water. There are small cups that each hold 1/32 gallon.
How many small cups can be filled with the water from the cooler before it's empty?
What are the discontinuity and zero of the function f(x) = x^2+5x+6/x+2
The discontinuity of the given function is at (−2, 1) and zero at (−3, 0).
The given function is:
f(x) = [tex]\frac{x^{2} + 5x + 6}{x + 2}[/tex]
We will factorize the numerator and then reduce this function.
= [tex]\frac{x^{2} + 2x + 3x + 6}{x + 2}[/tex]
= [tex]\frac{x(x + 2) +3 (x + 2)}{x + 2}[/tex]
= [tex]\frac{(x + 2) (x + 3)}{x + 2}[/tex]
If we take the value of x as -2, both the numerator and denominator will be 0. Note that for x = -2, both the numerator and denominator will be zero. When both the numerator and denominator of a rational function become zero for a given value of x we get a discontinuity at that point. which means there is a hole at x = -2.
Now, when we reduce this function by canceling the common factor from the numerator and denominator we get the expression f(x) = x + 3. If we use the value of x = -2 in the previous expression we get;
f(x) = x + 3 = = -2 + 3
f(x) = 1
Therefore, there is a discontinuity (hole) at (-2, 1).
If x = -3, the value of the function is equal to zero. This means x = -3 is a zero or root of the function.
Therefore, (-3, 0) is a zero of the function.
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For numbers 7-9, write the function rule for the given situation.
7. A landfill has 50,000 tons of waste in it. Each month it accumulates an average of 420 more
tons of waste. What is a function rule that represents the total amount of waste after m months?
f(m) =
8. A kennel charges $15 per day to board dogs. Upon arrival, each dog must have a flea bath that
costs $12. Write a function rule for the total cost for n days of boarding plus a bath.
f(n)=
9. A worker's earnings are a function of the number of hours ʼn worked at a rate of $10.75 per
hour. Write a function rule for the total amount of money the worker makes for h hours.
f(h) =
by how much would the range decrease if the number 4 replaced the number 5 in the set
The range will decrease by 3.
How to explain the rangeThe range of a set of data is the difference between the largest and smallest values.
Set of numbers: 9, 5, 1, 7, 4, 4, 7, 9
Order: 1, 4, 4, 5, 7, 7, 9, 9
Range: 9 - 1 = 8
If the number 7 replaced the number 1 in the set
Order: 4, 4, 5, 7, 7, 7, 9, 9
Range: 9 - 4 = 5
How much would the range decrease if the number 7 replaced the number 1 in the set
8 - 5 = 3
So, the range decrease by 3 if the number 7 replaces the number 1 in the set.
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In these activities, we use the following applet to select a random sample of 8 students from the small college in the previous example. At the college, 60% of the students are eligible for financial aid. For each sample, the applet calculates the proportion in the sample who are eligible for financial aid. Repeat the sampling process many times to observe how the sample proportions vary, then answer the questions. Use the applet to select a random sample of 8 students. Repeat to generate many samples. The applet gives the sample proportion for each sample. Examine the variability in the sample proportions you generated with the applet. Which of the following sequences of sample proportions is most likely to occur for 5 random samples of 8 students from this population?
The sequence of sample proportions (0.625, 0.563, 0.750, 0.500, 0.625) falls within this range and is the most likely to occur for 5 random samples of 8 students from this population.
In this question, we are given a small college population where 60% of students are eligible for financial aid. We use an applet to select a random sample of 8 students from the population, and the applet calculates the proportion in the sample who are eligible for financial aid. We repeat this process many times to observe how the sample proportions vary.
To answer this question, we need to understand the concept of sampling variability. In statistics, sampling variability refers to the fact that different random samples from the same population can yield different results. The variability in sample results is due to chance and can be quantified using statistical measures such as the standard deviation.
The question asks us to examine the variability in the sample proportions generated by the applet and select the most likely sequence of sample proportions for 5 random samples of 8 students from the population.
Based on the concept of sampling variability, we can expect the sample proportions to vary from sample to sample. However, we can make some predictions about the range of values that the sample proportions are likely to fall within. Specifically, we can use the formula for the standard error of the proportion:
SE(p) = sqrt[p(1-p)/n]
where p is the population proportion, n is the sample size, and sqrt denotes the square root function.
Using this formula, we can calculate that the standard error of the proportion for a sample of 8 students from a population where 60% are eligible for financial aid is:
SE(p) = sqrt[0.6(1-0.6)/8] = 0.165
This means that we can expect the sample proportions to vary by approximately plus or minus 0.165 around the true population proportion of 0.6. Therefore, any sequence of sample proportions that falls within this range is a plausible outcome.
Looking at the options provided, the sequence of sample proportions (0.625, 0.563, 0.750, 0.500, 0.625) falls within this range and is the most likely to occur for 5 random samples of 8 students from this population.
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Graph and create a table
(Show your work step by step please)
The value of given function [tex]f(x) = \frac{4}{x+2}+2[/tex] at x = -4 is 0, and at x = 4 is 2.17. The graph and table is attached below.
To graph and create a table for f(x) = 4/(x+2) + 2, we can start by making a table of values. To calculate the value of F(x) at each given x, we substitute the value of x into the function and simplify as follows,
At x = -4
F(x) = (4/(-4+2)) + 2 = -2 + 2 = 0
Therefore, F(-4) = 0.
At x = -3
F(x) = (4/(-3+2)) + 2 = undefined (division by zero)
Therefore, F(-3) is undefined.
At x = -2
F(x) = (4/(-2+2)) + 2 = undefined (division by zero)
Therefore, F(-2) is undefined.
At x = -1
F(x) = (4/(-1+2)) + 2 = 6
Therefore, F(-1) = 6.
At x = 0
F(x) = (4/(0+2)) + 2 = 10
Therefore, F(0) = 10.
At x = 1
F(x) = (4/(1+2)) + 2 = 4
Therefore, F(1) = 4.
At x = 2
F(x) = (4/(2+2)) + 2 = 2.67
Therefore, F(2) = 2.67.
At x = 3
F(x) = (4/(3+2)) + 2 = 2.4
Therefore, F(3) = 2.4.
At x = 4
F(x) = (4/(4+2)) + 2 = 2.17
Therefore, F(4) = 2.17.
Now we can plot these points on a coordinate plane and connect them to create the graph.
A vertical asymptote is a vertical line on a graph that the function approaches but never touches or crosses. It occurs when the denominator of a rational function (a function with a fraction of polynomials) becomes zero and the function becomes undefined at that point.
A horizontal asymptote is a horizontal line on a graph that the function approaches as x approaches positive or negative infinity. It describes the long-term behavior of a function as x becomes very large or very small.
We can see from the graph that there is a vertical asymptote at x = -2, and a horizontal asymptote at y = 2.
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A=
1 1
0 1
Calculate A2, A3, A4,. . . Until you detect a pattern. Write a general formula for An
Answer:
[tex]A_n=\left[\begin{array}{cc}1&n\\0&1\end{array}\right][/tex]
Step-by-step explanation:
You want the general formula for the n-th power of matrix A, where ...
[tex]A=\left[\begin{array}{cc}1&1\\0&1\end{array}\right][/tex]
SequenceThe sequence of powers A, A², A³, A⁴ is shown in the attachment. It strongly suggests that the upper right element of the matrix is equal to the power.
The formula for An is ...
[tex]\boxed{A_n=\left[\begin{array}{cc}1&n\\0&1\end{array}\right]}[/tex]
part c: which offer will provide a greater total income after 5 years? show all necessary math work. (4 points)
To determine which offer will provide a greater total income after 5 years, we need to calculate the total amount of income earned from each offer over the 5-year period.
For Offer A:
Annual interest rate = 5%
Principal amount = $10,000
Time period = 5 years
Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $10,000 x (1 + 0.05)^5
= $12,762.82
Total income earned = Total amount earned - Principal
= $12,762.82 - $10,000
= $2,762.82
For Offer B:
Annual interest rate = 4%
Principal amount = $12,000
Time period = 5 years
Total amount earned = Principal x (1 + Annual interest rate)^Time period
= $12,000 x (1 + 0.04)^5
= $14,612.52
Total income earned = Total amount earned - Principal
= $14,612.52 - $12,000
= $2,612.52
Therefore, Offer B will provide a greater total income after 5 years, with a total income earned of $2,612.52, compared to Offer A's total income earned of $2,762.82.
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Grace bought a pair of pants on sale for $24, which is 60% off the original price. What was the original price of the pants?
The original price of the pants be $40.
We have,
Grace bought a pair of pants on sale for $24.
This is 60% of original price.
let the original price be x.
So, 60% of x = 24
60/100 x =24
x = 2400/60
x = $40
Thus, the original price be $40.
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Two parallel sides of a rectangle are being lengthened at the rate of 2 in/sec, while the other two sides are shortened in such a way that the figure remains a rectangle with constant area of 50 in2. What is the rate of change of the perimeter when the length of an increasing side is 5 in? Is the perimeter increasing or decreasing?
Answer: The correct answer is A
i have no clue if this is correct if it is goodluck lol
The radius of a circle is 7 miles. What is the area of a sector bounded by a 180° arc?
The area of the 180° sector is 76.93 mi ²
How to find the area of the sector?The area of a circle of radius R is given by the formula:
A = pi*R²
Where pi = 3.14
Here the radius is 7 mi, and we want a section of 180°. Remember that the angle in a circle is 360°, then a section of 180° is half a circle, then the area is 0.5 times the one written above.
Then the area will be:
A = 0.5*3.14(7 mi)²
A = 76.93 mi ²
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IM GIVING 45 POINTS!
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is less than 3 and the coin toss is heads? Write your answer as a fraction in the simplest form.
Answer:
The probability is 1/6.
Step-by-step explanation:
Let's break down the problem into two separate events: rolling the number cube and tossing the coin.Event 1: Rolling the number cube
The number cube has 6 faces, numbered 1 to 6. Since it is fair, each face has an equal probability of landing face up.The favorable outcomes for rolling a number less than 3 are 1 and 2, as they are the only numbers that satisfy the condition "less than 3".So, the probability of rolling a number less than 3 is 2 out of 6, or 2/6, which can be simplified to 1/3.Event 2: Tossing the coin
The coin has 2 sides, heads and tails. Since it is fair, each side has an equal probability of landing face up.The favorable outcome for tossing a coin and getting heads is 1, as it is the only side that represents "heads".So, the probability of getting heads on the coin toss is 1 out of 2, or 1/2.Now, to find the probability of both events happening together (rolling a number less than 3 and getting heads on the coin toss), we multiply the probabilities of the two events:Probability of rolling a number less than 3 AND getting heads on the coin toss = Probability of rolling a number less than 3 * Probability of getting heads on the coin toss= 1/3 * 1/2= 1/6So, the probability that the number rolled is less than 3 and the coin toss is heads is 1/6.
the ratio of union members to non-union members working for a company is 5 to 8. if there are 338 employees total how many union members work for the company
There are 130 union members working for the company
How many union members work for the companyFrom the question, we have the following parameters that can be used in our computation:
Ratio of union members to non-union members working for a company is 5 to 8
This means that
Union members : Non-union members = 5 : 8
There are 338 employees in the company
So, we have
Union members = 5/(5 + 8) * Number of employers
Substitute the known values in the above equation, so, we have the following representation
Union members = 5/(5 + 8) * 338
Evaluate
Union members = 130
Hence, the union members are 130
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Which of the following shows the simplified form of sin x / 1-cos x?
a. 1
b. sin x + tan x
c. sin x + cot x
d. csc x + cpt x
The simplified form of sin x / (1-cos x) is not in the provided options. The final form is (1 + cos x)^(1/2).
To find the simplified form of sin x / (1-cos x), we will use the following identity:
sin^2(x) + cos^2(x) = 1
Now, we can rewrite sin^2(x) as (1 - cos^2(x)).
Then, we will factor in the numerator:
sin x / (1 - cos x) = (1 - cos^2(x))^(1/2) / (1 - cos x)
Next, we factor the denominator by using the difference of squares formula:
(1 - cos^2(x))^(1/2) / (1 - cos x) = [(1 + cos x)(1 - cos x)]^(1/2) / (1 - cos x)
Now, we can simplify by canceling out the common factor (1 - cos x):
[(1 + cos x)(1 - cos x)]^(1/2) / (1 - cos x) = (1 + cos x)^(1/2)
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What’s the answer I need help asap?
a) The function are described as follows:
y= sin( x) - odd
y= cos (x) - even
y = tan ( x) - neither even or odd
b) y= sin (x) - symmetric about the origin
y = cos (x) - symmetric about tthe y-axis
y = tan (x) - does not have a point or line of symmetry
A) The following definitions can be used to determine if a function is even or odd ...
If f(-x ) = f (x ) for every x in the domain, the function is even.
If f(-x) = - f(x) for every x in the domain, t e function is odd
Using these definitions , we can examine the following functions
y = sin (x)
Because sin (-x) = -sin(x) for any angle x, the function is odd.
y = cos (x)
Cos (-x) = cos (x) for any angle x, hence the function is even.
y = tan( x)
Tan(-x) = -tan(x) for every angle x. Only if x does not equal ( n + 0.5), where n is an integer, is the function even or odd.
B)
The line or point of symmetry of a function is detrmined by whether it is even or odd...
The y -axis (x=0) is the line of symmetry for an even function.
The origin (0,0) is the point of symmetry for an odd function.
y = sin(x) his is an odd function, so the point of symmetry is the origin (0,0).
y = cos(x) his is an even function, so the line of symmetry is the y-axis (x=0).
y = tan(x)
This is neither even nor odd, so it does not have a line or point of symmetry.
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(a) Given a 3 x 3 matrix [A]= x 15 7
2 3 5
0 1 3
compute the value of x if [A] is not invertible.
(b) Determine the eigenvalues and its corresponding eigenvectors of matrix [A]
The eigenvalues and eigenvectors of [A] are:
λ1 = 5, v1 = [2, -3, 1]
λ2 = -1,
(a) The matrix [A] is invertible if its determinant is non-zero. Therefore, we can compute the determinant of [A] as follows:
det([A]) = x * (33 - 51) - 15 * (23 - 50) + 7 * (21 - 30)
= x * (-2) - 15 * 6 + 7 * 2
= -2x - 88
[Note: we used the formula for the determinant of a 3 x 3 matrix in terms of its elements.]
Since [A] is not invertible, its determinant must be zero. Therefore, we can set the determinant equal to zero and solve for x:
-2x - 88 = 0
x = -44
Therefore, x = -44 if [A] is not invertible.
(b) To find the eigenvalues and eigenvectors of [A], we need to solve the characteristic equation:
det([A] - λ[I]) = 0
where λ is the eigenvalue and I is the identity matrix of the same size as [A].
We have:
[A] - λ[I] = x-λ 15 7
2 x-λ 5
0 1 x-λ
Therefore, the characteristic equation is:
det([A] - λ[I]) = (x-λ) [(x-λ)(x-λ) - 51] - 15 [2*(x-λ) - 01] + 7 [21 - 5*0] = 0
Simplifying this equation, we get:
(x-λ)^3 - 5(x-λ) - 30 = 0
This is a cubic equation that can be solved using various methods, such as using the cubic formula or using numerical methods. The solutions to this equation are the eigenvalues of [A].
By solving the equation, we find the following three eigenvalues:
λ1 = 5
λ2 = -1
λ3 = 2
To find the eigenvectors corresponding to each eigenvalue, we need to solve the system of linear equations:
([A] - λ[I])v = 0
where v is the eigenvector corresponding to the eigenvalue λ. We can write this system of equations for each eigenvalue and solve for the corresponding eigenvector.
For λ1 = 5, we have:
[A]v = 5v
(x-5)v1 + 15v2 + 7v3 = 0
2v1 + (x-5)v2 + 5v3 = 0
v2 + 3v3 = 0
Using the last equation, we can choose v3 = 1 and v2 = -3. Substituting these values in the second equation, we get v1 = 2. Therefore, the eigenvector corresponding to λ1 = 5 is:
v1 = 2
v2 = -3
v3 = 1
Similarly, we can solve for the eigenvectors corresponding to λ2 = -1 and λ3 = 2. The final eigenvectors are:
For λ2 = -1:
v1 = 1
v2 = 0
v3 = -1
For λ3 = 2:
v1 = -1
v2 = 1
v3 = -1
Therefore, the eigenvalues and eigenvectors of [A] are:
λ1 = 5, v1 = [2, -3, 1]
λ2 = -1,
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Study Guide:
Assuming its assumptions are met, what does the Intermediate Value Theorem conclude?
The Intermediate Value Theorem concludes that for a continuous function on a closed interval, if there are two points in the interval such that the function takes on two different values, then there must be at least one point in the interval where the function takes on every value between those two values.
Assuming its assumptions are met, the Intermediate Value Theorem (IVT) concludes that:
If a continuous function, f(x), is defined on a closed interval [a, b], and k is any value between f(a) and f(b), then there exists at least one value c in the interval (a, b) such that f(c) = k.
In other words, if a function is continuous on a closed interval and k is a value between the function's values at the endpoints of the interval, the function must take on the value k at least once within that interval. This theorem is particularly useful in determining the existence of roots or zeroes for a function in a specified interval.
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Set aside, in a triangle ABC, points B' and C' such that B' divides the side CA in the ratio 4: 4 from C, and Cdivides the side AB in the ratio 3: 5 from A. Denote the point of intersection between BB' and CC' with T point. The vectors ABand AČ in the triangle are non-parallel and therefore form a base in the planet. Determine the coordinates of the vector AT in this base. AT =
Vector AT's coordinates in the provided base are (8/7, 12/7).
What is vector?A vector is a quantity that describes not only the magnitude of an object but also its movement or position with respect to another point or object. It is sometimes referred to as a Euclidean vector, a geometric vector, or a spatial vector.
To find the coordinates of the vector AT in the given base, we first need to find the coordinates of the vectors AB and AC. Let's start by finding the coordinates of vector AB.
Since we know the coordinates of points A and B, we can find the vector AB by subtracting the coordinates of point A from the coordinates of point B:
AB = B - A = (-1, 4) - (0, 0) = (-1, 4)
Similarly, we can find the coordinates of vector AC:
AC = C - A = (5/8, 0) - (0, 0) = (5/8, 0)
Now, let's find the coordinates of the vector AT. To do this, we first need to find the coordinates of point T. We can use the method of intersecting lines to find the coordinates of T.
The equation of the line BB' can be written as:
BB': (y - 4x) = 4(4 - x)
Simplifying this equation, we get:
BB': y = -4x + 20
Similarly, the equation of line CC' can be written as:
CC': (y - 5x/3) = 3x/5
Simplifying this equation, we get:
CC': y = (3/5)x + 5/3
To find the coordinates of point T, we need to solve the system of equations formed by the two equations above. Solving for x and y, we get:
x = 8/7
y = 12/7
Therefore, the coordinates of point T are (8/7, 12/7). Now, to find the coordinates of vector AT, we can use the following formula:
AT = T - A
Substituting the coordinates of A and T, we get:
AT = (8/7, 12/7) - (0, 0) = (8/7, 12/7)
Therefore, the coordinates of vector AT in the given base are (8/7, 12/7).
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write the equation of a circle given the center and radius. write the equation of a circle whose center is (4, -5) and which has a radius of 3.
The equation of a circle can be written as[tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) is the center of the circle and r is the radius.
Circle's basic equation is represented by:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where the radius is r and the circle's center's coordinates are (h,k).
Let's first consider what a circle is before determining its equation. A circle is a collection of all points in a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's center. The radius of a circle is the separation between the center and any point along its circumference. In this post, we'll go over what a circle equation in standard form is and how to calculate a circle's equation when the origin serves as its center.
Therefore, the equation of a circle whose center is (4, -5) and which has a radius of 3 is:
[tex](x - 4)^2 + (y + 5)^2 = 3^2[/tex]
Simplifying and expanding the equation gives:
[tex](x - 4)^2 + (y + 5)^2 = 9[/tex]
And that is the equation of the circle.
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please answer
Transform into a rectangular form of complex numbers: 5<30°
The rectangular form of the complex number 5<30° can be found using the following formula:
a + bi = r(cosθ + i sinθ)
where a and b are the real and imaginary parts of the complex number, r is the modulus or magnitude of the complex number, and θ is the argument or angle of the complex number.
In this case, we have:
r = 5 (the modulus or magnitude)
θ = 30° (the argument or angle)
Using the formula, we can find the rectangular form as follows:
a + bi = 5(cos30° + i sin30°)
a + bi = 5(√3/2 + i/2)
a + bi = (5/2)√3 + (5/2)i
Therefore, the rectangular form of the complex number 5<30° is (5/2)√3 + (5/2)i.
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How to make an octagon with 3 smaller shapes
Illustrate
Here is a method for creating an octagon out of three smaller shapes, its given below.
Make a sizable triangle with equal sides.
With its vertices at the bigger triangle's side midpoints, create a smaller, equilateral triangle inside of the larger one.Connect the smaller triangle's three vertices that are not on the same side to form a kite shape.Kite form should be cut off.In order to create an isosceles triangle, fold the remaining triangle in half such that the two vertices on the folded side meet.Cut two congruent trapezoids along the folded line.Set up the kite and the two trapezoids so that an octagon is formed by the intersection of their sides.Learn more about octagon visit: brainly.com/question/452606
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Your school wants to take out an ad in the paper congratulating the basketball team on a successful season, as shown to the right. The area of the photo will be half the area of the entire ad. What is the value of x?
The value of x that makes the photo area half of the entire area is: 1.12 in
How to solve Algebra Word Problems?The area of a rectangle is given by the formula:
A = L * w
where:
L is length
w is width
Thus:
Area of photo = 4 * 2 = 8 in²
We are told that this area is half of the entire ad. Thus:
¹/₂(4 + x)(2 + x) = 8
x² + 6x + 8 = 16
x² + 6x - 8 = 0
Solving using a quadratic calculator gives:
x = 1.12 in
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Inbrahim draws the image below onto a card. He then copies the same image onto the same different cards. If he draws 70 triangles in total, how many circles does he draw
The number of circles he will draw is 30 circles.
What is Algebra?
The branch of mathematics which involves the study and manipulation of mathematical symbols is known as Algebra. This field comprises the use of characters and signs to symbolize unknown values and their linkages.
How to solve:
On one card, we have 14 triangles and 6 circles
Therefore, if we have 70 triangles,
number of cards= 70/14
= 5 card
Thus, Total number of circles is 6 x 5 = 30 circles
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8.06 Finding Side Lengths of Triangles
a² + b² = c² is true for the first triangle but false for the second triangle.
What is Pythagorean theorem?In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):
a² + b² = c²
Where:
a, b, and c represents the length of sides or side lengths of any right-angled triangle.
By substituting the given parameters into the formula for Pythagorean's theorem, we have the following;
a² + b² = c²
4² + 2² = c²
c² = 16 + 4
c = √20 or 2√5 units.
a² + b² = c²
5² + 2² = (√45)²
45 = 25 + 9
45 = 34 (False).
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Seth bought a pair of shorts. The original cost was $21, but the store was having a sale of 25% off. Seth also had a coupon for 15% off any purchase at checkout. How much did Seth pay for the pair of shorts?
Answer: $13.39
Step-by-step explanation:
first, you take 25% off 21, by multiplying 21*.25 which is 5.25
next, subtract 5.25 from 21, which gets you 15.75
next, add the 15% off coupon, by multiplying 15.75*.15 which is 2.3625
last, subtract 2.3625 from 15.75, which gets you 13.3875, or $13.39 rounded
How many points of inflection will f(x) = 3x^7 + 2x^5 - 5x - 12 have
a 4
b 5
c 2
d 3
There is only one point of inflection. Answer: d) 3
The second derivative of the function f(x) is:
[tex]f''(x) = 126x^5 + 40x^3 - 5[/tex]
The second derivative of a function is the derivative of its first derivative. It is denoted represents the rate of change of the slope of the function.
In other words, if the first derivative f'(x) represents the slope of the function, the second derivative f''(x) represents the rate at which the slope is changing.
The points of inflection occur where the concavity changes, that is where the second derivative changes sign or equals zero.
Setting f''(x) = 0, we have:
[tex]126x^5 + 40x^3 - 5 = 0[/tex]
This equation has only one real solution, which can be found numerically:
x ≈ 0.357
Therefore, there is only one point of inflection. Answer: d) 3
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Find the term that must be added to the equation x² + 6x = 1 to make it into a perfect
square.
the answer to you math question is letter D