When the following code section runs, the value of the variable y will be -2.
Given that,
We have to find when the following code section runs, what value will the variable y have? Assume the following input values:
The code mentioned above is explained in the section below.
Here, x=5, n=0, and the input values are 1–6.
So, x>3 is true.
Control will go to second if block and input y and z.
Now y=1 and z=2 and n=1
Next control goes to if(x) since x>0 which is true.
Now z=3 and x=4 and y=0 and n=0
Her n==0 so r=z- ++x => 3- (5) =>-2.
Hence r=-2
Therefore, the variable r=-2 is the output for the code.
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What’s a pattern for determining 10% of a number?
To take 10% of something, move the decimal point one spot to the left
Examples:
10% of 12.3 is 1.2310% of 567.89 is 56.789Stock Market Worksheet 1
You need to show your work in order to receive full credit.
Business Organization
1. James invests $10,000 in a partnership with 3 other people. One of those people also invested
$10,000 and the other two invested $90,000 each. What percent of the business does James
own?
I would give whoever answers this all my 330 points please help
The percentage of the business that James owns, given the amount he invested into the partnership, is 5 %
How to find the percentage owned ?To find the percentage of the business that James owns, you first need to find the total amount invested into the business by all the partners. That amount is :
= 10, 000 + 10, 000 + 90, 000 + 90, 000
= $ 200, 000
The percentage of the business owned by James is :
= Amount invested by James / Total amount invested by partnership
= 10, 000 / 200, 000
= 5 %
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Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
The inequality is: h less than equal to 2 That is the Numbers written in order from least to greatest going across
To find:
The values that make the given inequality true.
We have,
h less than equal to 2
It means the value of h must be less than or equal to 2.
In the given options, the list of numbers which are less than or equal to 2 is
-6, -3, -1, 1, 1.9, 1.99, 1.999, 2
The list of numbers which are greater than 2 is
2.001, 2.01, 2.1, 3, 5, 7, 10
Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
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code a function definition for a function named shiftdiagonal which does the following: 1) accepts an x coordinate, y coordinate and amount to shift them by. 2) increments the x and y coordinates by the amount.
As per the condition for defining the function with name shiftdiagonal , we need to define the function with two parameter (x,y,z). Then the function ultimately increments the values in x and y by z and returns the updated values of x, y.
What is a function in programming?Simply said, a function is a "block" of code that you may reuse again rather than having to write it out several times. Programmers can divide an issue into smaller, more manageable parts, each of which can carry out a specific job, using functions. The specifics of how a function operates can virtually be forgotten once it has been built. By abstracting the specifics, the programmer may concentrate on the broad picture.
How do we define a function in python?In Python 'def' keyword is used to define functions.
for example:- def function_name( ):
The code for a function definition to fulfill the conditions put by the question(using python) is given below:
def shiftdiagonal(x , y, z):
x = x + z
y = y + z
return x,y
In the above code z is supposed to be the amount to shift x and y by.
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x y . (b) are x y and x y independent studysoup
If x and y be i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.
Yes, x y are x y independent studysoup.
Here x and y be i.i.d. unif(0, 1)
The i.i.d stands for independent and identically distributed
unif means that the uniformly distributed
Here x and y are i.i.d unif (0,1)
The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable
Here we have to find the covariance of x + y and x - y
According to the properties of covariance
Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0
Because Cov(x, x) = Cov (y, y)
Cov(y, x) = Cov(x, y)
Therefore, the covariance of x+y and x - y is 0.
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The following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation = 17.49 + 1.0334x. For these data SSE = 1541.4. Click on the webfile logo to reference the data. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).
$ ______
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).
($_____, $_____)
c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
($_____, $_____)
The estimated regression equation for the given data is y = 17.49 + 1.0334x.Create a 95% confidence interval for the median entertainment spending for all cities with $89/day room rates.
a. Estimate the amount of money that will be spent on entertainment in a city with a $89 daily hotel fee (to 2 decimals).
$106.55
b. Create a 95% confidence interval for the average entertainment spending for all cities with $89 daily room rates (to 2 decimals).
($102.61, $110.49)
c. A hotel in Chicago costs $128 on average per night. Create a 95% prediction interval for Chicago's entertainment spending (to 2 decimals).
($132.42, $143.75)
The estimated regression equation for the given data is y = 17.49 + 1.0334x. For a particular city that has a daily room rate of $89, the predicted amount spent on entertainment is $106.55. The 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 is ($102.61, $110.49). For Chicago, which has an average room rate of $128, the 95% prediction interval for the amount spent on entertainment is ($132.42, $143.75).
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7
The Spinner is a ride that straps people to the edge of a circle
and spins. If riders are traveling 25 mph and the radius of the
wheel is 15 feet, find the angular speed in rpm.
To find the angular speed in rpm, we need to use the formula for tangential speed, which is the speed at which an object moves along a circular path. The formula for tangential speed is:
v = r * omega
where v is the tangential speed, r is the radius of the circle, and omega is the angular speed.
In this case, we are given that v = 25 mph and r = 15 feet. We can solve for omega by dividing both sides of the equation by r:
omega = v / r
Substituting the given values, we get:
omega = 25 mph / 15 feet
To convert the units of speed from mph to feet per second, we need to use the conversion factor that 1 mph is equal to 5280/3600 feet per second. We can use this conversion factor to rewrite the expression for omega in terms of feet per second:
omega = (25 mph * (5280/3600)) / 15 feet
This simplifies to:
omega = 0.7222 feet/second
Next, we need to convert the angular speed from feet per second to rpm. To do this, we need to use the formula for converting from linear speed to angular speed, which is:
omega = (v * 60) / (2 * pi * r)
where v is the linear speed, r is the radius of the circle, and omega is the angular speed in rpm.
In this case, we are given that v = 0.7222 feet/second and r = 15 feet. We can solve for omega by plugging these values into the formula and simplifying:
omega = (0.7222 feet/second * 60) / (2 * pi * 15 feet)
= 0.7222 feet/second * 60 / (2 * pi * 15 feet)
= 0.7222 * 60 / (2 * pi * 15)
= 4.3332 / (2 * pi * 15)
= 0.2821 / (pi * 15)
Therefore, the angular speed in rpm is 0.2821 / (pi * 15), or approximately 0.0046 rp
help please
In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
The value of c in the triangle is 14.
How to angles of triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
In the triangle LMN, m ∠L = (3c + 66)°. The exterior angle to ∠L measures 72 degrees.
Therefore, let's find c.
Hence, the sum of the exterior angle and the interior angle is 180 degrees.
Therefore,
72 + 3c + 66 = 180
3c = 180 - 66 - 72
3c = 42
divide both sides by 3
c = 42 / 3
Therefore,
c = 14
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1. A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability. a) Write down the stochastic matrix M that describes, given a probability vector, the probability that the woman will be at each of the places during the next hour. (b) Find the steady state vector. (This is a probability vector [positive entries that add up to 11 satisfying Mu- [Hint: you should simply assume that λ-1 is an eigenvalue for M (this is guaranteed for all stochastic matrices) and find the corresponding eigenspace. Divide by a suitable constant to get the steady state vector (c) After many hours pass, what are the probabilities that the woman will be at A? B? C? D? (These are recorded in the steady state vector.)
The resulting probability is 100%
How to calculate probability?
The general formula to calculate the probability is
=> P(B) = (n(B)/N(S)
where,
P(B) is the probability of an event 'B'.
n(B) is the number of favorable outcomes of an event 'B'.
n(S) is the total number of events occurring in a sample space.
Given,
A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability.
Here we have given that,
Number of places = 4 (A, B, C, D)
Initial point = A
Point D probability = 100%
For Point B to A probability = 100%
For point C to A or B probability = 50%
For point D to B and C probability = 50%
Now, here we need to find the probabilities that the woman will be at.
Like the women will spend three hours of travelling in the point A, B and C, then the probability of the points are calculated as,
=> 1 + 0.5 + 0.5 - 1
=> 2 - 1 = 1
Therefore, the resulting probability is 100%.
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Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.)
y = 5 - x2
(1) units (width)
(2) units (height)
The length of the rectangle is 1.054 units and the width of the rectangle is 4.72 units.
Length times width equals the area of a rectangle. Let's assume that x represents length and y represents width. To determine the dimensions of the rectangle, we must apply y values to the area formula, differentiate with respect to x, and then set differentiate to zero.
Parabola: [tex]y=5-x^{2}[/tex]
The equation of parabola indicates that it opens down and the axis of symmetry is x=0. So we can take the vertices of the rectangle on the x-axis as [tex]A=(-x,0)[/tex] and [tex]D=(x,0)[/tex]). The other two vertices above the x-axis on the parabola will be [tex]B=(-x, 5-x^{2} )[/tex] and [tex]C=(x,5-x^{2} )[/tex]
Dimensions of the rectangle will be,
[tex]x-(-x)=2x[/tex] and [tex](5-x^{2} )[/tex]
Area of the rectangle (A) = [tex]2x(5-x^{2} )[/tex]
Area function when differentiated (A′) = [tex]2x(-2x)+(5-x^{2} )(2)[/tex]
A′= [tex]-4x^{2} + 10 -2x^{2}[/tex]
A′= [tex]-6x^{2} +10[/tex]
Critical points for maxima and minima ⟹ [tex]-6x^{2} +10=0[/tex]
⟹ [tex]10=6x^{2}[/tex]
⟹ [tex]x^{2} = \frac{10}{6}[/tex]
⟹ [tex]x= \sqrt \frac{10}{6}[/tex]
⟹ [tex]x=[/tex] ±[tex]0.527[/tex]
Maximum area of 2X2 rectangle(square)
A= [tex]2*0.527(5- 0.527^{2} )[/tex] = [tex]4.97[/tex] [tex]units^{2}[/tex]
Length = 2x = 1.054 units
Width = [tex](5-x^{2} )[/tex] = 4.72 units
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Find the length of an arc on a circle whose radius is 10 cm and whose central angle subtends a central angle of 20º
anova 7. a large marketing firm uses many photocopying machines, several of each of four different models. during the last six months, the office manager has tabulated for each machine the average number of minutes per week that it is out of service due to repairs, resulting in the following data: model g: 56 61 68 42 82 model h: model k: 74 77 92 63 54 25 36 29 56 44 model m: 78 105 89 112 61 perform an analysis of variance to decide whether the difference among the means of the four samples can be attributed to chance.state the conclusion.
The null and alternative hypothesis of the number models are
H₀ : There is no difference among the means of four samples models.
H₁ : There is difference among the means of four samples models.
Given that,
Many photocopiers are used by a large marketing company, several of each of the four models. The office manager calculated for each machine the typical amount of minutes per week that it is out of commission due to repairs over the previous six months, yielding the following information:
Model g: 56 61 68 42 82
Model h: 74 77 92 63 54
Model k: 25 36 29 56 44
Model m: 78 105 89 112 61
We have to find the null and alternative hypothesis.
We know that,
So,
H₀ : There is no difference among the means of four samples models.
H₁ : There is difference among the means of four samples models.
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Write a function that takes as arguments: the data frame you generated above from importing the Walmart dataset a state abbreviaton (e.g. AR) and, then, the function returns a pandas Data Frame with 2 columns: 1) a column called date that contains the date (note that date must be properly ordered) 2) a column called cumsum that contains the cumulative (i.e. running) sum of the number of stores over time opened in that state Please tell how to use cumsum function for number of stores and then another column that has respective dates.
The cumsum function returns the cumulative sum of an array whose size is not 1 from the dataset that is imported from Walmart.
Create an array of the number of stores in each state along with the date opened. You can then use the cumsum option to find the total number of stores Walmart has over the states.
For instance, to find cumulative sum of integers 1 to 6, we have
A = 1:6;
B = cumsum(A)
It yields the output:
1, 3, 6, 10, 15, 21
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Express the number as a product of two fractions 2/5
The number as a product of two fractions is 4/2 * 1/5
How to express the number as a product?From the question, we have the following parameters that can be used in our computation:
Fractions = 2/5
To express it as a product of two fractions, we start with the following equation (first split)
Fractions = 2/1 * 1/5
Express 2 as 4/2
So, we have the following representation
Fractions = 4/2 * 1/5
Hence, the fraction products is 4/2 * 1/5
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Given the following linear function, sketch the graph of the function and find the domain and range.
2
f(x)=²x-3
The domain and range of the given function is a set of al real numbers and as such;
Domain : (-∞,∞)
Range : (-∞,∞)
What is the domain and range of the Linear Function?We are given the function as f(x)= -3x+7.
In order for us to sketch the graph of this given function, we need to make a function table
Lets assume some random number for x and find out f(x)
x f(x) = -3x + 7
-2 -3(-2) + 7 = 13
-1 -3(-1) + 7 = 10
0 -3(0) + 7 = 7
1 -3(1) + 7 = 4
We now plot the points as shown in the graph attached
Domain is defined as the set of all x values for which the function is defined while Range is defined as the set of all y values for which the function is defined
In this case, there is no restriction for x and y and as such the domain and range is a set of all real numbers
Domain : (-∞,∞)
Range : (-∞,∞)
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Complete question is;
Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7
can someone help me figure out how to solve this problem
Answer:
[tex]r = \frac{3}{4}[/tex]
Step-by-step explanation:
Geometric sequence formula: [tex]a_n = a_1 r^{n-1}[/tex]
From the provided sequence, we know that the first term is -4
The second term is -3
Inserting to value to the formula
( n = 2, since we are using the value of the second term)
[tex]a_2 = -4 * r^{2-1}\\[/tex]
[tex]-3 = -4 * r[/tex]
[tex]r = \frac{-3}{-4}[/tex]
[tex]r = \frac{3}{4}[/tex]
[(b-3)/(b^2+2b)]+[b/(4b+8)] simplify
The simplified expression of [(b - 3)/(b² + 2b)] + [b/(4b + 8)] is (b² - 12 + 4b)/[(4b)(b + 2)]
How to simplify the expression?From the question, we have the following parameters that can be used in our computation:
[(b-3)/(b^2+2b)]+[b/(4b+8)]
Rewrite the exponents
[(b - 3)/(b² + 2b)] + [b/(4b + 8)]
So, we have
(b - 3)/(b² + 2b) + b/(4b + 8)
Factor out b and 4
(b - 3)/b(b + 2) + b/4(b + 2)
Factor out 1/(b + 2)
1/(b + 2) * ((b - 3)/b + b/4)
So, we have
1/(b + 2) * (4(b - 3) + b²)/(4b)
This gives
1/(b + 2) * (4b - 12 + b²)/(4b)
Rewrite as
1/(b + 2) * (b² - 12 + 4b)/(4b)
Lastly, we have
(b² - 12 + 4b)/[(4b)(b + 2)]
Hence, the solution is (b² - 12 + 4b)/[(4b)(b + 2)]
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On a number line, the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the
directed line segment from Q to S in a 3:5 ratio.
Which expression correctly uses the formula
x; to find the location of point R?
To get the coordinate of point R partitioned by the ratio 3:5, the required
What is partition
To divide (something, as a country) into two or more territorial pieces with distinct political standing is to divide it into parts or shares. to divide or separate by a partition (such as a wall), frequently used with off.
formula will be given as [tex]M(x, y)=\left(\frac{a x_1+b x_2}{a+b}, \frac{a y_1+y_2}{a+b}\right)[/tex]M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)
The midpoint rule
From the given statement, we have the following information
Point Q = (-14, 0)
Point S = (2, 0)
R = (x, y)
To get the coordinate of point R partitioned by the ratio 3:5, the required formula will be given as M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)
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Which design? The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.
(a) You want to estimate the average age of your store’s customers.
(b) You do an SRS survey of your customers every year. One of the questions on the survey asks about customer satisfaction on a seven-point scale with the response 1 indicating "very dissatisfied" and 7 indicating "very satisfied." You want to see if the mean customer satisfaction has improved from last year.
(c) You ask an SRS of customers their opinions on each of two new floor plans for your store.
As per the sampling, the resulting values of
(a) Single sample design
(b) two independent samples
(c) matched pairs
What is meant by sampling?
In math, sampling is the process of selecting the group that you will actually collect data from in your research.
Here we have find in Which design the following situations all require inference about a mean or means.
By looking into the given statement, (a) You want to estimate the average age of your store’s customers.
Here this is a single sample design and the only sample we need here is the store’s customers.
Where as (b) You do an SRS survey of your customers every year. One of the questions on the survey asks about customer satisfaction on a seven-point scale with the response 1 indicating “very dissatisfied’’ and 7 indicating “very satisfied.’’ You want to see if the mean customer satisfaction has improved from last year.
In this is the two independent samples design. Because in this case we compare the customer satisfaction of two groups of customers. And the first group is the customers from last year and the other is the group from this year.
Finally, (c) You ask an SRS of customers their opinions on each of two new floor plans for your store.
Here we have a matched-pair design in this case because one group of people gave opinions on two new floor plans.
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Find the derivative a. by evaluating the integral and differentiating the result b. by differentiating the integral directly. d/dx sin t dt a. Evaluate the integral and differentiate the result to find the derivative, d/dx sin t dt = (Simplify your answer.) b. Differentiate the integral directly to find the derivative. d/dx sin t dt = (Simplify your answer.)
The result of derivative by evaluating the integral and differentiating is 2sinx.
What is derivative?The function itself is the derivative of a function's integral. But only in the case of indefinite integrals is this always the case. Only when the lower limit of the integral is a constant and the higher limit is the variable we are differentiating with, is the derivative of a defined integral of a function the function itself.
The function itself is the derivative of an indefinite integral of a function. Specifically, d/dx f(x) dx = f (x)
d/dx ∫x -x (sin t) dt
⇒ d/dx [- cos t] x -x
⇒ - d/dx [cos x - cos (-x)]
⇒ - d/dx [ 2 cos x]
⇒ -2 d/dx [cos x]
⇒ -2 [- sin x]
⇒ 2 sin x
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i need help??!!!!!!!
Answer:
Triangle RST rises 4 units and runs 8 units.
Triangle XYZ rises 3 units and runs 6 units.
The slope of line b is 1/2.
Step-by-step explanation:
Triangle RST rises 4 units and runs 8 units.
Triangle XYZ rises 3 units and runs 6 units.
The slope of line b is 1/2.
(2, 0) and (8, 3)
m = 3-0/8-2
m = 3/6
m = 1/2
solve the inequality 11x > 4(1+3x). record your answer in interval notation
Answer:
(-∞, -4)
Step-by-step explanation:
11x > 4(1+3x)
11x > 4*1+4*3x ==> distribute 4 to 1 and 3x using the distribution property
11x > 4 + 12x ==> simplify
11x-12x > 4 + 12x-12x ==> isolate x by subtracting 12x on both sides
-x > 4
x < -4 ==> when dividing by a negative number, switch the inequality sign
x < -4 can also be written as -∞ < x < -4
This is because x is greater than -∞ but can never equal -∞.
-∞ < x < -4 ==> (-∞, -4)
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Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis ________.
A. should not be rejected
B. must be rejected
C. may or may not be rejected depending on the square root of the sample size
D. is the same as the alternative hypothesis
Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis should not be rejected.
What is null hypothesis?The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
What is alternative hypothesis?An assertion used in statistical inference experiments is known as the alternative hypothesis. It is indicated by Ha or H1 and runs counter to the null hypothesis. Another way to put it is that it is only a different option from the null. An alternative theory in hypothesis testing is a claim that the researcher is testing.
One less than the confidence level, or 0.01, is the test's level of significance. The null hypothesis is not rejected since the p-value of 0.05 exceeds the level of significance of 0.01.
Therefore, the null hypothesis should not be rejected.
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use the given information, determine weather you can prove each pair of triangles congruent…
Both triangles are congruent by the SAS congruence theorem.
The congruence statement is, ΔBDC ≅ ΔBDA.
How to Prove that Two Triangles are Congruent by the SAS?The SAS stands for side-angle-side theorem, which means that if we can show that two triangles have two corresponding congruent sides and one pair of corresponding congruent included angle, then both triangles are congruent.
From the information given, we can state the following:
AB ≅ CB, which is one pair of corresponding congruent sides [given]
Angle ABD ≅ angle CBD, which is one pair of corresponding included congruent angles [given]
BD ≅ BD, also one pair of corresponding congruent sides [reflexive property of congruence]
Therefore, we can conclude based on the above information that:
ΔBDC ≅ ΔBDA by the SAS congruence theorem.
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A mining company wants to test a claim concerning the mean weight of their silver nuggets. They are testing the null hypothesis that the true mean is 3 ounces against the alternative that the mean is less than 3 ounces. The p-value for the hypothesis test was determined to be 0.002. Which of the following is a correct interpretation of this p-value?
a. The null hypothesis would not be rejected at either the 0.05 or 0.01 level b. The null hypothesis would be rejected at a 0.01 level but not at a 0.05 level. c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels. d. The null hypothesis would be rejected at a 0.05 level but not at a 0.01 level
The correct answer is c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels.
A p-value is a probability of obtaining a result that is at least as extreme as the one observed in the sample data, given that the null hypothesis is true. The smaller the p-value, the less likely it is that the observed result occurred by chance, and the more likely it is that the null hypothesis is false.
In this case, the p-value of 0.002 is less than both the 0.05 and 0.01 significance levels, which means that it is highly unlikely that the observed result occurred by chance if the null hypothesis is true. Therefore, the null hypothesis should be rejected at both the 0.05 and 0.01 levels.
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Find the 3rd order Taylor polynomial of the function f(x)= √x centered at 4 and then use this polynomial to approximate √14.03. Show at least 8 decimal places in your answer.
The 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is expressed as f(x) ≈ P3(x) = a₀ + a₁(x - 4) + a₂(x - 4)² + a₃(x - 4)³.
Here, a₀, a₁, a₂, and a₃ are the coefficients that need to be calculated. To find these coefficients, we must use the Taylor series formula and the derivatives of f(x) evaluated at 4.
The Taylor series formula is Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!) (x-a)² + (f'''(a)/3!) (x-a)³ + ... +[tex](f^(n)(a)/n!) (x-a)^n[/tex].
The derivatives of f(x) evaluated at 4 are f'(4) = 1/2, f''(4) = -1/8, f'''(4) = -1/16.
Using these values, the coefficients of the 3rd-order Taylor polynomial can be calculated as a₀ = 2, a₁ = 1/2, a₂ = -1/8, and a₃ = -1/16.
Therefore, the 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is P3(x) = 2 + (1/2)(x - 4) - (1/8)(x - 4)² - (1/16)(x - 4)³.
Using this polynomial to approximate √14.03, we have P3(14.03) = 2 + (1/2)(14.03 - 4) - (1/8)(14.03 - 4)² - (1/16)(14.03 - 4)³ ≈ 3.76401097.
Therefore, the approximation of √14.03 using the 3rd-order Taylor polynomial is 3.76401097 to 8 decimal places.
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What is the simplified form of each expression?
The simplified form of an expression is the expression written in its simplest form, usually achieved by combining like terms and removing unnecessary parentheses.
The 20-cm-diameter disk in the figure can rotate on an axle through its center.
What is the net torque about the axle?
If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94
As we can see here,
20N force which is passing through the center O will not produce any torque about point O
For 30N force which is acting at 45 angles with the x−axis, its x−component will pass through the origin, hence its horizontal component will also not cause any torque about O
Hence, torque because of 20N force which is acting in a tangential direction :
τ1=r⊥F=0.1×30=3N-m
Torque produced by y component of 30N force acting at angle 45:
τ2=r⊥F=0.05×30sin45∘
=0.05×30×1/√2=1.5/√2Nm⨀
Torque produced by 20N force acting in negative y direction:
τ3=r⊥×F=0.05×20
τ=1Nm⨀
Hence, the Net torque produced on O
τnet=τ1+τ2+τ3
τnet=−3+(1.5/√2)+1
τnet=−0.94Nm
or
|τnet|=0.94Nm
So If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94
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if two dice are rolled one time, find the probability of getting these results a sum of greater than or equal to 11
for two dices, there are 36 possible combinations, the probability of getting these results a sum of greater than or equal to 11 is 3/36 = 12
What is probability and example?
Example: toss a coin 100 times, how many Heads will come up? Probability says that heads have a ½ chance, so we can expect 50 Heads. But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.
The only way to get 11 or more is getting 5 with one dice and 6 with another or getting 6 with both dices.
Therefore, there are only three combinations that satisfy this condition: (5,6), (6,5), and (6,6).
Since, for two dices, there are 36 possible combinations, the probability is 3/36 = 12
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A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a through d? Explain. (Round to two decimal places as needed.) (Round to two decimal places as needed.) (Round to two decimal places as needed.) d. (ID) (Round to two decimal places as needed.) e. Choose the correct answer below. O A. No, since the sample sizes are large in 2 30), the condition guarantees that the sampling distribution of x is approximately normal. O B . No, since the confidence level is at least 90%, the underlying distribution need not be normal. OC. No, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal. OD. Yes, the underlying distribution must be normal for the validity of these confidence intervals O E. No, since the sample sizes are large in 230) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal.
As per the 95% confidence interval for the population mean is (31.042, 42.958).
What is meant by confidence interval?
In math, A normal distribution with a mean, μ and standard deviation, σ is used to estimate the confidence interval for the unknown population mean.
Here we have given that the random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations.
And we need to find the 95% confidence interval for ju for each of these situations.
Here we are given the following data:
• Sample size, n=70
• Sample mean, ¯x=37
• Population standard deviation, σ=20
Then the 95% confidence interval for the population mean is defined as:
=> x±z0.01/2×σ√n
Here by applying Excel function for the confidence coefficient:
=> NORM.INV(0.01/2,0,1)
Then we get,
=> 37±2.58×20√75(31.042, 42.958)
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