The probability that the mean completion time of 4 projects falls between 16 and 19 months is approximately 0.6568 or 65.68%.
The Central Limit Theorem states that for a sufficiently large sample size, the distribution of sample means will approach a normal distribution regardless of the shape of the population distribution.
Specifically, if we have a random sample of n observations drawn from a population with mean μ and standard deviation σ, then the distribution of the sample means will have a mean equal to the population mean μ and a standard deviation equal to the population standard deviation σ divided by the square root of the sample size n.
In this case, the average time taken to complete a project in the real estate company is 18 months, with a standard deviation of 3 months.
Assuming that the project completion time approximately follows a normal distribution, we can use the Central Limit Theorem to find the probability that the mean completion time of 4 such projects falls between 16 and 19 months.
First, we need to calculate the standard deviation of the sample mean. Since we have 4 projects, the sample size is n = 4.
Therefore, the standard deviation of the sample mean is σ/√n = 3/√4 = 3/2 = 1.5 months.
Next, we can standardize the values of 16 and 19 months using the formula z = (x - μ) / (σ/√n), where x is the value, μ is the population mean, σ is the population standard deviation, and n is the sample size.
For 16 months: z1 = (16 - 18) / (1.5) = -2/1.5 = -1.33
For 19 months: z2 = (19 - 18) / (1.5) = 1/1.5 = 0.67
Using a standard normal distribution table, we can look up the probabilities corresponding to the z-scores -1.33 and 0.67.
The table provides the cumulative probabilities for values up to a certain z-score.
For -1.33, the cumulative probability is approximately 0.0918.
For 0.67, the cumulative probability is approximately 0.7486.
To find the probability between these two z-scores, we subtract the cumulative probability associated with -1.33 from the cumulative probability associated with 0.67:
P(-1.33 < Z < 0.67) = 0.7486 - 0.0918 = 0.6568
Therefore, the probability that the mean completion time of 4 projects falls between 16 and 19 months is approximately 0.6568 or 65.68%.
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Evaluate the algebraic expression5m + 4n – 3 whenm=3 and n=4. Show your work.
Answer:
Given, m = 3 and n = 4
5×3 + 4×4 – 3
15 + 16 - 3
31 - 3
28
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¿can you help me, please?
Find the volume of the con round you answer to the nearest tenth
Answer:
16.76 inch³
Step-by-step explanation:
volume of cone is 1/3 πr²h
h=4
r=2
then 1/3* 22/7* 2*2 *4
=352/21
=16.76
a) give stating reasons five other angles each equal to x
b) prove that AECF is a parallelogram
Simple Proof:
a) In the image, we know that ABCD is a parallelogram and that means opposite angel measures should be the same. We know that angel DCB is made up by angel 1 and 2, and angel DAB and DCB are equal and angel DAB is made up by angel 1 and x. So now we can conclude that angel x is equal to angel 2.
b) According to the definitions of a parallelogram, opposite angel measures have to be the same, while AECF have angle 1 to angel 1 and angel 2 to angel 1. We can conclude that AECF is NOT a parallelogram. (Sorry, you didn't give me the full question so some information remains unclear. )
Which shows a correct way to determine the volume of the right rectangular prism?
Answer:
the last answer
Step-by-step explanation:
[tex]V=l*w*h\\l=8\\w=9\\h=1\\V=8*9*1\\V=72[/tex]
1.13 UNIT TEST GRAPH OF SINUSOIDAL FUNCTION PART 1
What is the equation of the midline for the function f(x)?
f(x) =1/2 sin(x)+6
Answer:
The equation of the midline for the function [tex]f(x)[/tex] is [tex]y = 6[/tex].
Step-by-step explanation:
The sinusoidal function of the form [tex]y = A_{o}+A\cdot \sin x[/tex] is a periodic function whose range is bounded between [tex]A_{o}-A[/tex] (minimum) and [tex]A_{o}+A[/tex] (maximum). The equation of the midline is a line paralel to the x-axis, that is:
[tex]y = c,\forall\, c\in \mathbb{R}[/tex] (1)
Where [tex]c[/tex] is mean of the upper and lower bounds of the sinusoidal function, that is:
[tex]c = \frac{(A_{o}+A+A_{o}-A)}{2}[/tex]
[tex]c = A_{o}[/tex] (2)
If we know that [tex]y = \frac{1}{2}\cdot \sin x + 6[/tex], then the equation of the midline for the function [tex]y[/tex] is:
[tex]c = A_{0} = 6[/tex]
[tex]y = 6[/tex]
The equation of the midline for the function [tex]f(x)[/tex] is [tex]y = 6[/tex].
2 Which expressions can be used to find the volume of the rectangular prism?
3 ft
5 ft
7 ft
apply.
5
35 + 5
35 x 3
(7 + 5) x3
7+3+5
35 + 35 + 35
Answer:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Create a real-world application and its complete solution that requires concepts of linear algebra.
Real-World Application: Image Compression: Image compression is a fundamental concept in the field of computer graphics and image processing.
Linear algebra plays a crucial role in various image compression techniques. Let's consider a complete solution for image compression using concepts of linear algebra.
Image Representation:Linear algebra concepts, such as matrix operations and transformations, are fundamental to every step of the image compression process outlined above. By applying these techniques, we can achieve efficient storage and transmission of images while balancing the trade-off between image quality and compression ratio.
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How far apart are - 7 and |-7| on a number
line?
Answer:
the answer is 7. :)
Step-by-step explanation:
A kindergarten teacher asked the students' parents to send their child to school with two fruits (apples and/or oranges). Below are the combinations of fruits brought to class the next day.
Fruit
2 Apples : 9 students
1 Apple and 1 Orange : 4 students
2 Oranges : 8 students
What is the frequency of oranges in the classroom? Round your answer to 4 decimal places.
The frequency of oranges in the classroom can be calculated as follows:Frequency of oranges in the classroom = Total number of oranges / Total number of fruits= 16/42 = 0.3809 (rounded to 4 decimal places)Thus, the frequency of oranges in the classroom is approximately 0.3809.
To determine the frequency of oranges in the classroom, we need to calculate the proportion of students who brought oranges out of the total number of students.
First, let's calculate the total number of students:
Total students = Number of students with 2 apples + Number of students with 1 apple and 1 orange + Number of students with 2 oranges
Total students = 9 + 4 + 8 = 21
Next, let's calculate the number of students who brought oranges:
Number of students with oranges = Number of students with 1 apple and 1 orange + Number of students with 2 oranges
Number of students with oranges = 4 + 8 = 12
Finally, we can calculate the frequency of oranges:
Frequency of oranges = Number of students with oranges / Total students
Frequency of oranges = 12 / 21 ≈ 0.5714 (rounded to 4 decimal places)
Therefore, the frequency of oranges in the classroom is approximately 0.5714.
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To determine the frequency of oranges in the classroom, it is important to add up the total number of fruits brought to the classroom. The given information is as follows:
2 Apples: 9 students
1 Apple and 1 Orange: 4 students
2 Oranges: 8 students
Thus, the frequency of oranges in the classroom is approximately 0.2105.
Total number of fruits = 2(9) + 1(4) + 2(8)
= 18 + 4 + 16
= 38 fruit in total
So, total number fruits are 38.
Frequency of oranges = Number of oranges / Total number of fruits
There are 8 oranges brought to class, so the frequency of oranges is:
8 / 38 ≈ 0.2105 (rounded to 4 decimal places)
Hence, the frequency of oranges in the classroom is approximately 0.2105.
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5. Calculate the area.
9ft
4
11 ft.
ООО
40
44
о
396
[tex]area = b \times h \\ = 11 \times 4 \\ = 44[/tex]
A rotating lawn sprinkler sprays water in a circular area of grass, as shown in the
picture. The diameter of the circular area of grass is 16 ft. what is the closest measurement to the area in square feet ?
Answer:
Area of the lawn = 64π square feet
Step-by-step explanation:
Area of the circular lawn = πd²/4
d is the diameter of the lawn = 16ft
Substitute the given value into the formula
Area = π(16)²/4
Arrea of the lawn = 256π/4
Area of the lawn = 64π square feet
9 ft =_________in. How many inches????
108 inches
hope this helped <3
Write a Matlab code to solve the following problems. 1-use Bisection Method x3 + 4x2 - 10 = 0 for x = [0,5] x3 - 6x2 + 10x - 4 = 0 for xe [0,4] 2-Use Newton Method x3 + 3x + 1 = 0 for x = (-2,0] 3-Use fixed point Method x3 - 2x - 1 = 0 for x E (1.5,2] 4-Use secant Method 1-2e -* - sin(x) = 0 for x € (0,4] 2-x3 + 4x2 - 10 = 0 for x € [0,4]
a) Bisection Method MATLAB code for equation [tex]x^3 + 4x^2 - 10 = 0[/tex] in the interval [0,5]:
function root = bisection_method()
f = [tex]x^3 + 4*x^2 - 10[/tex];
a = 0;
b = 5;
tol = 1e - 6;
while (b - a) > tol
c = (a + b) / 2;
if f(c) == 0
break;
elseif f(a) * f(c) < 0
b = c;
else
a = c;
end
end
root = (a + b) / 2;
end
b) Bisection Method MATLAB code for equation [tex]x^3 - 6x^2 + 10x - 4 = 0[/tex] in the interval [0,4]:
function root = bisection_method()
f = [tex]x^3 - 6*x^2 + 10*x - 4[/tex];
a = 0;
b = 4;
tol = 1e-6;
while (b - a) > tol
c = (a + b) / 2;
if f(c) == 0
break;
elseif f(a) * f(c) < 0
b = c;
else
a = c;
end
end
root = (a + b) / 2;
end
c) Newton's Method MATLAB code for equation [tex]x^3 + 3x + 1 = 0[/tex] in the interval (-2,0]:
function root = newton_method()
f = [tex]x^3 + 3*x + 1[/tex];
df = [tex]3*x^2 + 3[/tex];
[tex]x_0[/tex] = -1;
tol = 1e-6;
while abs(f([tex]x_0[/tex])) > tol
[tex]x_0 = x_0 - f(x_0) / df(x_0)[/tex];
end
root = [tex]x_0[/tex];
end
d) Fixed-Point Method MATLAB code for equation [tex]x^3 - 2x - 1 = 0[/tex] in the interval (1.5,2]:
function root = fixed_point_method()
g = [tex](x^3 - 1) / 2[/tex];
[tex]x_0 = 2[/tex];
tol = 1e-6;
while abs([tex]g(x_0) - x_0[/tex]) > tol
[tex]x_0 = g(x_0)[/tex];
end
root = [tex]x_0[/tex];
end
e) Secant Method MATLAB code for equation 1 - 2*exp(-x) - sin(x) = 0 in the interval (0,4]:
function root = secant_method()
f = 1 - 2*exp(-x) - sin(x);
[tex]x_0[/tex] = 0;
[tex]x_1[/tex] = 1;
tol = 1e-6;
while abs(f([tex]x_1[/tex])) > tol
[tex]x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))[/tex];
[tex]x_0 = x_1[/tex];
[tex]x_1 = x_2[/tex];
end
root = [tex]x_1[/tex];
end
f) Secant Method MATLAB code for equation [tex]2 - x^3 + 4*x^2 - 10 = 0[/tex] in the interval [0,4]:
function root = secant_method()
f = [tex]2 - x^3 + 4*x^2 - 10[/tex];
[tex]x_0 = 0[/tex];
[tex]x_1 = 1[/tex];
tol = 1e-6;
while abs(f([tex]x_1[/tex])) > tol
[tex]x_2 = x_1 - f(x_1) * (x_1 - x_0) / (f(x_1) - f(x_0))[/tex];
[tex]x_0 = x_1[/tex];
[tex]x_1 = x_2[/tex];
end
root = [tex]x_1[/tex];
end
How to find the MATLAB code be used to solve different equations numerically?MATLAB provides several numerical methods for solving equations. In this case, we have used the Bisection Method, Newton's Method, Fixed-Point Method, and Secant Method to solve different equations.
The Bisection Method starts with an interval and iteratively narrows it down until the root is found within a specified tolerance. It relies on the intermediate value theorem.
Newton's Method, also known as Newton-Raphson Method, approximates the root using the tangent line at an initial guess. It iteratively refines the guess until the desired accuracy is achieved.
The Fixed-Point Method transforms the equation into an equivalent fixed-point iteration form. It repeatedly applies a function to an initial guess until convergence.
The Secant Method is a modification of the Newton's Method that uses a numerical approximation of the derivative. It does not require the derivative function explicitly.
By implementing these methods in MATLAB, we can numerically solve various equations and find their roots within specified intervals.
These numerical methods are powerful tools for solving equations when analytical solutions are not feasible or not known.
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If the mode of the data 2,3,3,5,7,7,6,5, x and 8 is 3. Then what is the value of 'x'.
Answer:
x = 3
Step-by-step explanation:
Given that,
The mode of the data 2,3,3,5,7,7,6,5, x and 8 is 3.
We need to find the value of x.
We know that, Mode is the number in a data with Max frequency. x can be 3 or 7. If x = 7, mode becomes 7 and if x = 3, mode equals 3.
Hence, the value of x is equal to 3.
Nick is curious about which cell phone provider is most used by his neighbors. He asks several neighbors about their provider and draws a conclusion based on the answers he received. What kind of statistical study did Nick conduct? A. survey B. experiment C. observational study D. theoretical study
Answer:
A. Survey
Step-by-step explanation:
Answer:
Option A. Survey
Step-by-step explanation:
What is survey?
Survey is defined as the act of examining a process or questioning a selected sample of individuals to obtain data about a service, product, or process.
Nick collected samples and then concluded his answer which is a survey he conducted.
Correct answer is Option A.
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What is the perimeter of AOJL?
3
Ρ 2
K
M
9
Answer:
dunno.
Step-by-step explanation:
duno
If x=(y+2)^2 and y= -7 then what is the value of x
Answer:
25
Step-by-step explanation:
(y+2)^2=x
(-7+2)^2=x
(-5)^2=x
(-5)(-5)=x
25=x
Hope that helps :)
Answer:
x=25
Step-by-step explanation:
Plug it innnn plug it innnn
Euler's formula, v − e + f = 2, relates the number of vertices (v), the number of edges (e), and the number of faces (f) of a polyhedron. Solve Euler's formula for v.
a) v = e + f + 2
b) v = e + f - 2
c) v = e - f - 2
d) v = e - f + 2
Euler's formula, v − e + f = 2, relates the number of vertices (v), the number of edges (e), and the number of faces (f) of a polyhedron.
Therefore, the correct option is (d) v = e - f + 2.
To solve Euler's formula for v, we'll have to isolate v on one side of the equation. The first step is to add e to both sides of the equation:
v − e + f + e = 2 + e
v + f = e + 2
Now subtract f from both sides of the equation:
v + f - f = e + 2 - f
v = e + 2 - f
Hence, the solution for Euler's formula for v is:
v = e + 2 - f
Therefore, the correct option is (d) v = e - f + 2.
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at traget a 5 pack of gaterade cost 8.78 how much would 21 packs of gatorade cost
Answer:
21 packs of gatorade would cost $36.88.
Step-by-step explanation:
Mathematically:
8.78 / 5 = 1.756
1.756 * 21 = 36.876 ~= $36.88
"Marty purchased a car. The car cost him $16,500 and it depreciates in value at a rate of 4.3% per year. How much will the car be worth in 12 years?"
Answer:
"Marty purchased a car. The car cost him $16,500 and it depreciates in value at a rate of 4.3% per year. How much will the car be worth in 12 years?"
Step-by-step explanation:
Please help I’ll give brainliest if you answer all :)
Step-by-step explanation:
a^2 +b^2 = c^2
b^2 = c^2 - a^2
3 - solving for h
A = bh
h = A ÷h
4 - solving for r
I = prt
r = I÷ pt
5- solving for b
A= 1/2 bh
can rewrite as
A = bh ÷2
b = 2A ÷ h
An electrician bent a section of copper wire into a partial circle as shown. The dimensions are
given in feet (ft).
2.5 f
880
2.5
ft
What is the length of the section of wire to the nearest hundredth of a foot?
Answer:
Length = 3.84 feets (nearest hundredth)
Step-by-step explanation:
The length of section of wire can be obtyaiejd using the length of of a arc formular :
Length of arc = θ/360° * 2πr
Radius, r = 2.5 feets
Length of arc = (88/360) *2πr
Length of arc = (88/360) * 2π*2.5
Length of arc = 0.244444 * 15.707963
Length of arc = 3.8397
Length = 3.84 feets (nearest hundredth)
Answer:
Step-by-step explanation:
3.84
What is the value of 3^2? (3^2 means 3 raised to the second power.)
Answer:
9
Step-by-step explanation:
From a survey taken by Survey 'R Us, 243 respondents out of the 1523 cat owners surveyed claim that their cats speak to them.
A.) With an 85% confidence level, provide the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them: use all three notations Set notation, interval notation, +/- notation
B.) Do the same as you did for 1a, but use a 95% confidence level instead Set Notation, Interval Notation, +/- notation
C.) Describe the differences between the ranges given for 1a and 1b. Why are the ranges different D.) Provide an interpretation for the interval given in 1b.
The interpretation of the interval in 1b (95% confidence level) is that we can be 95% confident that the true proportion of the population that hears their cats talking to them falls within the range of 0.1241 to 0.2137.
A.) With an 85% confidence level, the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them is [0.1459, 0.1919] in set notation, (0.1459, 0.1919) in interval notation, and +/- 0.023 in +/- notation.
B.) With a 95% confidence level, the confidence interval that could be used to estimate the proportion of the population that hears their cats talking to them is [0.1241, 0.2137] in set notation, (0.1241, 0.2137) in interval notation, and +/- 0.045 in +/- notation.
C.) The ranges for 1a and 1b are different because the confidence level affects the width of the interval. A higher confidence level requires a wider interval to provide a more reliable estimate. In this case, the 95% confidence level has a wider range compared to the 85% confidence level.
This means that if we were to repeat the survey multiple times, approximately 95% of the intervals calculated would contain the true proportion.
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a) The 85% confidence interval is given as follows: (0.146, 0.174).
b) The 95% confidence interval is given as follows: (0.142, 0.178).
c) The interval for item a is narrower than the interval for item b, as the lower confidence level leads to a lower critical value and a lower margin of error.
d) We are 95% sure that the true population proportion is between the two bounds found in item b.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.For the confidence level of 85%, the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.85}{2} = 0.925[/tex], so the critical value is z = 1.44.
For the confidence level of 95%, the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for the confidence interval are given as follows:
[tex]n = 1523, \pi = \frac{243}{1523} = 0.16[/tex]
Hence the bounds of the 85% confidence interval are given as follows:
[tex]0.16 - 1.44\sqrt{\frac{0.16(0.84)}{1523}} = 0.146[/tex][tex]0.16 + 1.44\sqrt{\frac{0.16(0.84)}{1523}} = 0.174[/tex]The bounds of the 95% confidence interval are given as follows:
[tex]0.16 - 1.96\sqrt{\frac{0.16(0.84)}{1523}} = 0.142[/tex][tex]0.16 + 1.96\sqrt{\frac{0.16(0.84)}{1523}} = 0.178[/tex]More can be learned about the z-distribution at https://brainly.com/question/25890103
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plssssssss help solve
Answer:
cosine = adjacent/hypotenuse
cos A = 20/29 (choice: yellow)
Step-by-step explanation:
Answer:
yellow
Step-by-step explanation:
Mrs. Canales has 1,248 student pictures to displayaround the school. She plans to put them on 24 poster boards with the same amountof pictures on each poster board. How many student pictures will Mrs.Canales place on each poster board?
Answer:
52
Step-by-step explanation:
Its simple, its just division because she is asking how many for EACH(key word) so 1,248/24 equals 52 giving your answer.
mark brainliesttt??
Algebra 2 PLEASE HELP
Answer:
[tex]\frac{x+20}{x+4}[/tex]
Step-by-step explanation:
Can't cancel out terms like that
need to factor out the top and bottom
[tex]\frac{x^{2} +16x-80}{x^{2} -16}[/tex] = [tex]\frac{(x+20)(x-4)}{(x-4)(x+4)}[/tex] now cancel out the (x-4) from the top and bottom
= [tex]\frac{x+20}{x+4}[/tex]
Answer & Explanation:
Error: individual terms in an equation in a fraction cannot be directly canceled out.
Correction:
the easy way (solve the quadratic equation in the numerator and complete the square in the denominator):
(x^2 + 16x - 80) / (x^2 - 16)
(x+20)(x-4) / (x+4)(x-4)
x+20 / x+4
the complicated way (manipulate the exponents and common factors):
(x^2 + 16x - 80) / (x^2 - 16)
(x^2 - 4x + 20x - 80) / x^2 - 2^4
x(x^2-1 - 2^2)+4*5(x - 2^4-2) / (x - 2^2)(x + 2^2)
x(x-4)+20(x-4) / (x-4)(x+4)
x(x-4)+(2^2 (5))(x-4) / (x-4)(x+4)
(x-4)(x + 2^2 (5)) / (x-4)(x+4)
(x-4)(x+20) / (x-4)(x+4)
x+20 / x+4
multiply
12 times 1/3?
Answer:
4
Step-by-step explanation:
12(1/3)
so it is just 12/3 which is 4
Hope that helps :)
In 2005, there are 705 cable users in the small town of Whoville. The number of users
increases by 56% each year after 2005. Find the number of users to the nearest whole in 2020.
Answer:2008
Step-by-step explanation: