A student drilled a hole into a six-sided die and filled it with a lead weight, then proceeded to roll the die 200 times here are the observed frequencies 27 31 42 40 28 and 32 use a 0. 05 significance level to test the claim that the outcomes are not equally likely find the test statistic x^2 and critical value for the goodness-of-fit needed to test the claim
Answers
To test the claim that the outcomes of rolling the modified die are not equally likely, we can use a chi-square goodness-of-fit test. We will use a significance level of 0.05.
The null hypothesis is that the outcomes are equally likely. The alternative hypothesis is that the outcomes are not equally likely.
First, we need to calculate the expected frequencies assuming that the outcomes are equally likely.
Since the die has six sides, each outcome has a probability of 1/6. Therefore, the expected frequency for each outcome is 200/6 = 33.33.
To calculate the test statistic \(x^2\), we can use the formula:
\(x^2 = Σ (observed frequency - expected frequency)^2 / expected frequency\)
where Σ is the sum over all outcomes.
Using the observed and expected frequencies given in the problem, we get:
\(x^2 = (27 - 33.33)^2 / 33.33 + (31 - 33.33)^2 / 33.33 + (42 - 33.33)^2 / 33.33 + (40 - 33.33)^2 / 33.33 + (28 - 33.33)^2 / 33.33 + (32 - 33.33)^2 / 33.33\)
\(x^2 = 3.02\)
The degrees of freedom for this test is 6 - 1 = 5 (since there are 6 sides on the die).
Using a chi-square distribution table (or calculator), we can find the critical value for a significance level of 0.05 and 5 degrees of freedom to be 11.070.
Since the test statistic x^2 = 3.02 is less than the critical value of 11.070, we fail to reject the null hypothesis.
Therefore, we do not have enough evidence to conclude that the outcomes of rolling the modified die are not equally likely.
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Related Questions
how much did she spend on food for the party?
Answers
Answer:
Step-by-step explanation:
You can write and equation for this problem.
as 20.27-2.01x= The left money for food.
x: is two.
SO applying the number to the equation:
20.27-4.02= Food money
$16.25 is the answer
The translation shown in the graph moves the figure to the right. What kind of translation is shown?
Answers
the figure go to the left
If point Q is between endpoints P and R on a segment, PQ = 4x - 12, QR = 2x + 7, and PR = 31, then find the value of x.
Answers
Answer:
x = 6
Step-by-step explanation:
Here it's sayin that Q is a point in between the end-points P & R. If we join P & R , it forms a line segment & Q is in the line segment PR. Hence PQ & QR are also line segments which combine to form line segment PR. So ,
PR = PQ + QR
Putting the given values of PQ ,QR & PR
=> 4x - 12 + 2x + 7 = 31
=> 6x - 5 = 31
=> 6x = 31 + 5
= 36
=> x = 36/6 = 6
solve for u, show all work
Answers
Answer:
u = 2\(\sqrt{3}\)
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin60° = \(\frac{\sqrt{3} }{2}\) , then
sin60° = \(\frac{opposite}{hypotenuse}\) = \(\frac{u}{4}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )
2u = 4\(\sqrt{3}\) ( divide both sides by 2 )
u = 2\(\sqrt{3}\)
The following are the last 10 run scores colin got in cricket: 16, 11, 25, 27, 11, 25, 20, 26, 29, 35 a) work out colin's mean score. b) colin plays cricket again on sunday. he gets 6 runs. what is his new mean score? give your answers as decimals.
Answers
Colin's new mean score, after getting 6 runs on Sunday, is approximately 20.09.
To calculate Colin's mean score, we need to sum up all his scores and divide by the number of scores.
a) Mean score:
16 + 11 + 25 + 27 + 11 + 25 + 20 + 26 + 29 + 35 = 215
Total scores: 10
Mean score = 215 / 10 = 21.5
Colin's mean score is 21.5.
b) To calculate his new mean score after getting 6 runs on Sunday, we need to add the new score to the previous total and divide by the new number of scores.
New total scores = 215 + 6 = 221
New number of scores = 10 + 1 = 11
New mean score = 221 / 11 = 20.09 (rounded to two decimal places)
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-help me write an equation!!!
Answers
The absolute value function for this problem is given as follows:
g(x) = |x - 1| - 2.
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
In which a is the leading coefficient.
The coordinates of the vertex for this problem are given as follows:
(1, -2).
As the slope of the line is of 1, the leading coefficient is given as follows:
a = 1.
Hence the absolute value function for this problem is given as follows:
g(x) = |x - 1| - 2.
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The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
f(x) = 4(x2 + 12x) + 10
(twelve-halves) squared = 36
What is the function written in vertex form?
f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154
Answers
The function written in vertex form is:
f(x) = 4(x + 6)² - 26
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4(x² + 12x) + 10
Now,
f(x) = 4(x² + 12x) + 10
f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10
f(x) = 4(x + 6)² - 26
Thus,
f(x) = 4(x + 6)² - 26 is the function in vertex form.
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Answer:
B is correct
Step-by-step explanation:
Create x and y vectors from -5 to +5 with a spacing of 0.1. Use the meshgrid function to map x and y onto two new two-dimensional matrices called X and Y. Use your new matrices to calculate vector 2, with magnitude Z = sin x2 + y2 Title and label all axes. Include code and graphs. (a) Use the mesh plotting function to create a three-dimensional plot of Z. [5 Marks] (b) Use the surf plotting function to create a three-dimensional plot of Z. Compare the results you obtain with a single input (Z) with those obtained with inputs for all three dimensions (X, Y, Z). (5 Marks] (c) (d) Modify your surface plot with interpolated shading. Try using different colormaps. [2 marks] Generate a contour plot of Z. [3 Marks] Set up manually a colormap for parts (c) and (d), by determining the limits of the colorbar based on the plotted function and use a different colour for each range of values on the colorbar. (5 Marks] Generate a combination surface and contour plot of Z. (5 Marks)
Answers
The (a) and (b) parts show the 3D plot of Z using different functions (plot_surface and surf).
In part (c), the plot is modified to have interpolated shading using the plot_surface function with a different colormap (coolwarm).
In part (d), a contour plot of Z is created using the contour function, and a custom colormap is set up based on the limits of the function.
Finally, in part (e), a combination of the surface and contour plot is generated using the plot_surface and contour functions together.
What is Python?
Python is a general-purpose language, meaning that it can be used to create a number of different programs and is not specialized for any particular problem. Advertisement Brainly User Response: Python is a computer programming language often used to create websites and software, automate tasks, and perform data analysis.
Here's the code to generate the plots you described using Python and the Matplotlib library:
import numpy as np
import matplotlib.pyplot as plt
# Create x and y vectors
x = np.arange(-5, 5.1, 0.1)
y = np.arange(-5, 5.1, 0.1)
# Create matrices X and Y using meshgrid
X, Y = np.meshgrid(x, y)
# Calculate vector 2, Z = sin(x^2 + y^2)
Z = np.sin(X**2 + Y**2)
(a) Create a 3D plot using mesh plotting function
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.title('3D Plot of Z')
plt.show()
(b) Create a 3D plot using surf plotting function
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap='viridis')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.title('3D Plot of Z using surf')
plt.show()
(c) Modify the surface plot with interpolated shading and different colormaps
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap='coolwarm', rstride=1, cstride=1, linewidth=0, antialiased=False)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.title('Modified 3D Plot with Interpolated Shading')
plt.show()
(d) Generate a contour plot of Z
plt.contour(X, Y, Z, cmap='rainbow')
plt.xlabel('X')
plt.ylabel('Y')
plt.title('Contour Plot of Z')
plt.colorbar(label='Z')
plt.show()
# Set up a custom colormap for parts (c) and (d)
cmap = plt.cm.get_cmap('coolwarm')
norm = plt.Normalize(vmin=-1, vmax=1) # Set the limits of the colorbar
sm = plt.cm.ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])
# Generate a combination surface and contour plot of Z
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot_surface(X, Y, Z, cmap=cmap, rstride=1, cstride=1, linewidth=0, antialiased=False)
ax.contour(X, Y, Z, zdir='z', offset=-1, cmap=cmap)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.title('Combination Surface and Contour Plot of Z')
plt.colorbar(sm, label='Z')
plt.show()
This code will generate the requested plots.
The (a) and (b) parts show the 3D plot of Z using different functions (plot_surface and surf).
In part (c), the plot is modified to have interpolated shading using the plot_surface function with a different colormap (coolwarm).
In part (d), a contour plot of Z is created using the contour function, and a custom colormap is set up based on the limits of the function.
Finally, in part (e), a combination of the surface and contour plot is generated using the plot_surface and contour functions together.
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Rewrite the equation for x, 3/-2x-4=20
Answers
The rewritten form of the equation as required to be determined for x is; x = 0.5 (-77/20).
What is the rewritten form of the given equation for x?It follows from the task content that the given equation is to be rewritten for variable x as required.
Given; 3 / (-2x - 4) = 20
3/20 = -2x - 4
2x + 4 = 3/20
2x = 3/20 - 4
x = 0.5 (-77/20)
Ultimately, the rewritten equation for variable x is; x = 0.5 (-77/20).
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Without finding the product, what is the sign of this product?(-4)(-1)(-2)(-6)(-3)(-5)(-2)(-2)
Answers
Answer:
positive (+)
Step-by-step explanation:
- × - = +
+ × - = -
+ × + = +
Answer:
there are 8 numbers, all are negetive and they are multiplied with each-other
we know, (-negative)(-nagative) = positive number
so even quantity of negative numbers multiplied with each-other makes a positive number.
so the sign of the product is +
Step-by-step explanation:
\(9x^2-4\)
please simplify!
Answers
Answer:
(3x+2)(3x−2)
Step-by-step explanation:
Simplify: (x + 7)(x-4)
A. 2r +3
B. 12-28
C. x2-3x - 28
D. x2 + 3x - 28
Answers
Answer:
(x + 7)(x - 4) = x2 - 4x + 7x - 28 = x2 + 3x - 28
how many are 2 raised to 2 ???
Answers
Answer:
Step-by-step explanation: 2 raised to 2 or 2^2
is the same as saying 2*2 so 2 raised to 2 or 2^2 is 4
Answer:
The answer is 4
Step-by-step explanation:
Juan's Garage charges $60 per hour plus an evulatation fee of $30. The function to represent the charges f(x)=60x+30, where x represents the number of hours the repairs take. Evaluate f(5.5). Please show you work if you'd would like brainliest!
Answers
Answer:
f(5.5) = 360Step-by-step explanation:
function; f(x)=60x+30
where x = 5.5 as a number of hours the repairs take.
find f(5.5)
plugin value of x=5.5 back into the equation:
f(x) = 60x + 30
f(5.5) = 60(5.5) + 30
f(5.5) = 330 + 30
f(5.5) = 360
Step-by-step explanation:
hope this will help you.
What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Answers
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
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5/4 as a percentage
;-;
Answers
Answer:
125%
Step-by-step explanation:
What will you see on the next line? >>> alist = [9, 2, 3.5, 7] >>> alist.sort() >>> alist
Answers
>>> alist = [2, 3.5, 7, 9]. It can be find out by using concept of sorting and basic knowledge of programming.
What is sorting?
A sorting algorithm in computer science is a method for organising the items on a list. The most frequently utilised ordering systems are lexicographical and numerical, both in ascending and descending order. The effectiveness of other algorithms (like search as well as merge algorithms) which require input data being in sorted lists must be maximised, so efficient sorting is crucial. Additionally, canonicalizing data and creating output that is readable by humans both benefit from sorting.
i.e. either in ascending or descending order.
Here , sort() is a function that is used to sort the given list "alist".
By default sort() arranges in ascending order.
Given elements of list = 9, 2, 3.5, 7
So, ascending order = 2, 3.5, 7, 9
So, >>>alist = [2, 3.5, 7, 9]
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what is the 8th term in the following sequence? 27, 39, 51, 63
Answers
Answer:
the 8th term = 111Step-by-step explanation:
39-27=12
51-39=12
63-51=12
It’s clear that ,in this sequence we add 12 each time to a term to get the next term.
This means that this is an arithmetic sequence with a common difference of 12.
Therefore,
Term1 = 27 ; Term2 = 39 ; Term3 = 51 ; Term4 = 63
Term5 = 75
Term6 = 87
Term7 = 99
Term8 = 111
Method 2 :
Un = U1 + (n-1)r
r is the common difference = 12
U1 = 27 is the first term
Then
U8 = 27 + (8-1)×12
= 27 + 7×12
= 27 + 84
= 111
Solve for the angles in the triangle below.
A
70
B.
C
Blank #1 - what is angle y (where B is)?
Blank #2 - what is angle x (where C is)?
Answers
Answer:
y=70°(base angle of isosceles triangle)
in triangle ABC
70°+x°+y°=180°{sum of interior angle triangle}
70+x+70=180
x=180-140=40°
Step-by-step explanation:
x=40
y=70
Is x•y is a whole number?
Always true
Never true
sometimes true
Answers
Answer: Always true
Step-by-step explanation:
The total length of these planks is 92 metres. Work out the number of planks of length 2 metres in Ben workshop.
Answers
Answer: 13
Step-by-step explanation:
a baker made 260 cupcakes last week of 55% were chocolate how many cupcakes were chocolate
Answers
Fifty five percent times two hundred and sixty equal one hundred and forty three
There is 1/3 of a pie shared equally between 5 children. How much of the pie does each child receive?
1/9 pie
1/15 pie
1/18 pie
1/20 pie
Answers
Answer:
1/15 pie
Step-by-step explanation:
An easy way to do this is instead of dividing, multiply the denominator by 5. You get 15. You can say Im just making a coincidence, but try it yourself!
(1/3)/5 is basically multiplication. You may have heard the saying, "division with fractions is multiplication". Thats true. Turn 5 into 5/1 and multiply. 5/1x1/3.
you get 1/15. Hope it helps
Also you have to flip 5/1 to 1/5 and then multiply hehe. thats how you get 1/15
Answer:
Its B, 1/15 hope this helps
Step-by-step explanation:
A rectangle has an area of 18cm
the lengths of the sides are whole numbers.
how long could the sides of the rectangle be?
give all the examples you can think of.
Answers
Answer:
1cm long, 18cm wide
2cm long, 9cm wide
3cm long, 6cm wide
6cm long, 3cm wide
9cm long, 2cm wide
18cm long, 1cm wide
Step-by-step explanation:
All examples given will equal to 18cm2
Plz help. Only answer if you know.
Find the length of each side of the triangle to determine the classification. A(1,0), B(1,8), C(5,4).
1. AB =
2. BC =
3. AC =
4. Type of triangle ____________________
Answers
If the temperature increases and the amount of water vapor in the air remains unchanged, how has the RH (relative humidity) changed?
Answers
When the temperature increases and the water vapor content in the air stays the same, the relative humidity decreases. This is because warmer air can hold more moisture than colder air, and therefore the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor that the air can hold decreases as the air temperature increases.
Relative humidity depends on two factors: the amount of water vapor present in the air and the maximum amount of water vapor that the air can hold at a given temperature. As the temperature rises, so does the amount of water vapor that the air can hold, since warm air has more energy to hold the water molecules in vapor form. This reduces the ratio of the actual amount of water vapor in the air to the maximum amount of water vapor the air can hold, resulting in lower relative humidity.
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Geometric mean
Pls help thank u
Answers
Answer:
Step-by-step explanation:
1). Geometric mean of a and b = \(\sqrt{a\times b}\)
Therefore, geometric mean of 2 and 50 = \(\sqrt{2\times 50}\)
= 10
2). By geometric mean theorem,
\(\frac{JM}{KM}=\frac{KM}{ML}\)
\(\frac{6}{e}=\frac{e}{24}\)
e² = 6 × 24
e = √144
e = 12
Similarly, \(\frac{JL}{KJ}=\frac{KJ}{JM}\)
\(\frac{6+24}{d}=\frac{d}{6}\)
d² = 6 × 30
d = √180
d = 6√5
And \(\frac{JL}{KL}=\frac{KL}{ML}\)
\(\frac{6+24}{c}=\frac{c}{24}\)
c² = 30 × 24
c = √720
c = 12√5
2(5m-8)+3(m+2)=12+4(2m-1)
Answers
Answer:
3.6
Step-by-step explanation:
2(5m-8)+3(m+2)=12+4(2m-1)
10m - 16 + 3m + 6 = 12 + 8m -4
13m - 10 = 8 + 8m
13m = 18 + 8m
5m = 18
m = 3.6
m = 3 3/5
Step-by-step explanation:Hi there !
2(5m - 8) + 3(m + 2) = 12 + 4(2m - 1)
10m - 16 + 3m + 6 = 12 + 8m - 4
10m + 3m - 8m = 12 - 4 + 16 - 6
5m = 18
m = 18/5
m = 3 3/5
Good luck !
solve: log∨(2x-4)(216) = 3
Answers
Answer:
5
Step-by-step explanation:
since the base of the log is 2x-4 we can bring up 2x-4 to be (2x-4)^3=216
2x-4=216^(1/3)
2x-4=6
x=5
hope that help :)
4. construct a geometric figure that illustrates why a line in lr2 not through the origin is not closed under vector addition.
Answers
In LR2 (two-dimensional Euclidean space), a line passing through the origin is closed under vector addition, meaning that if you take any two vectors on that line, their sum will also lie on the same line.
However, a line not passing through the origin is not closed under vector addition.
To illustrate this, let's consider a line L in LR2 that does not pass through the origin. We can represent this line as a straight line segment starting from a point A and ending at a point B. The line segment AB represents the line L.
Now, consider two vectors represented by two line segments starting from the origin O and ending at points C and D, respectively. These vectors can be represented as OC and OD. Since the line L does not pass through the origin, OC and OD will not lie on line L.
If we try to add these two vectors, we construct the parallelogram OBCD, where BC represents the vector addition OC + OD. Since OC and OD do not lie on line L, their sum BC will also not lie on line L. This violates the closure property, where the sum of two vectors on a line should also be on the same line.
the geometric figure, in this case, would consist of a line L not passing through the origin, two vectors OC and OD not lying on line L, and the resulting vector BC (sum of OC and OD) not lying on line L. This figure demonstrates that a line in LR2 not passing through the origin is not closed under vector addition.
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