this question is for the southern hemisphere. for each direction (n, s, e, or w), pick the drawing that best describes how the stars appear to move above that point on the horizon.
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The drawings that best describe the way the stars appear to move in the Southern Hemisphere on the horizon is:
North - DSouth - A East - E West - F What direction do the stars appear to move ?When in the Southern Hemisphere, the drawings would appear to move upwards when moving North. The stars would also appear to move down when moving to the South as shown in A.
The East would show drawings moving towards the right as shown in E and the West would show stars appearing to move to the left which is shown with Drawing F.
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Related Questions
Maria has 12 gallons of lemonade. She wants to give each of her friends 1/3 gallon of lemonade. How many friends can receive 1/3 gallon of lemonade?
Answers
which point best represents √10
Answers
Answer: Q is the answer.
Step-by-step explanation:
the shape is a rectangular prism. find the lateral surface area of the shape. then enter your answer without units below.
Answers
The lateral surface area of a rectangular prism is 2(l + w)h sq units.
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).
All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. The lateral surface area of a rectangular prism is the sum of the surface area of all its faces without the base of the rectangular prism. The lateral surface area of any right rectangular prism is equivalent to the perimeter of the base times the height of the prism.The lateral surface area of a rectangular prism is given by
2(l + w)h sq unitsWhere l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.
Without these values, it is not possible to determine the lateral surface area of the rectangular prism.
Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.
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I need help with this someone exponents and exponential functions portfolio task 2 and task 3 for task 1 I have Growth Rate=5. A.The number of bacteria after 24 hours would be approximately 11 quadrillion.B. This table represents exponential growth because as the number gets bigger, so does the total number overall.C. Any non-zero number raised to a power of zero is equal to one becauseall the numbers that are raised to the zero power are equivalent and areequal to one. Also 0⁰is undefined.D. My rule for this table would be B x 5h+1+1E. If I started with 100 bacteria I would change my rule by cutting my hourly growth rate in half
Answers
The correct statement regarding the exponential function in this problem is given as follows:
B. This table represents exponential growth because as the number gets bigger, so does the total number overall.
How to model the situation?The situation is modeled with an increasing exponential function, which has the format presented as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The rate of change for this problem is given as follows:
b = 5.
As the absolute value of the rate of change is greater than 1, the exponential function is a growth function.
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true/false. in a regular tetrahedron the centers of the four faces are the vertices of a smaller tetrahedron. the ratio of the volume of the smaller tetrahedron to that of the larger is , where and are relatively prime positive integers. find .
Answers
The percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base will be ~43.30%
Given that the normal tetrahedron's (Vt) side-S volume,
Vt = S3/(6*(square(2))
Considering a regular tetrahedron with side S and the radius (r) of a sphere,
the proportion of the total volume of four identical spheres stacked in a tetrahedral pattern with a triangular base
r = (S) / (2 + (2*sqrt(6))
S =[tex](2 + 2(sqrt(6)*r)[/tex]
S = r times 6.898979486
for S = 1
r = ~0.144948974
Sphere volume = (4*pi*r3)/3
Vsphere = 0.012756574 (Vs).
Vs = [tex]((2+(2*sqrt(6)/(2+(2*sqrt(6)3/3[/tex]
Vs equals 0.012756574 when S = 1.
4 spheres' volume equals 0.051026296.
Tetrahedron volume = Vt = S3/(6*(sqrt(2))
When S = 1, Vt equals 0.11785113.
4Vs/Vt = ~0.432972475
4Vs/Vt = ~43.30%
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The complete question:
What is the percentage of the combined volume of 4 equal spheres stacked in a tetrahedral arrangement with a triangular base, inscribed within a regular tetrahedron, to the volume of the tetrahedron?
Can anyone help me?
Answers
Due to length restrictions, we kindly invite to check the explanation for further detail on how to complete a maze with trigonometric functions.
How to complete sucessfully a trigonometric maze
In this question we must go through a maze formed by 16 squares, fifteen of them with cases of right triangles, we must apply trigonometric functions to complete the maze. To complete this task, we need to use the following trigonometric function:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
Where:
x - Adjacent legy - Opposite legNow we proceed to show how deal with the maze:
Step 1:
x = 19 · cos 28°
x = 16.78 (LEFT)
Step 2
x = 39 / tan 59°
x = 23.43 (LEFT)
Step 3:
x = 31 · sin 71°
x = 29.311 (RIGHT - DOWN)
Step 4:
x = 12 · tan 25°
x = 5.600 (RIGHT)
Step 5:
x = 27 / sin 48°
x = 36.332 (RIGHT)
Step 6:
x = 38 / cos 14°
x = 39.163 (DOWN - LEFT)
Step 7:
x = 16 · cos 54°
x = 9.405 (RIGHT)
Step 8:
x = 29 / tan 74°
x = 8.316 (DOWN)
Step 9:
x = 17 · sin 42°
x = 11.375 (LEFT)
Step 10:
x = 47 · tan 29°
x = 26.052 (LEFT)
Step 11:
x = 31 / sin 63°
x = 34.792 (LEFT)
Step 12:
x = 24 / cos 51°
x = 38.136 (UP)
Step 13:
x = 46 · tan 31°
x = 27.640 (RIGHT)
FINISH
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Bookwork code: F41 a) What is the frequency of the modal interval? b) What is the modal interval?
Answers
Modal interval is discussed below.
What is statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given is the modal interval.
Modal interval →An interval of neighboring values for a measurement variable that occur noticeably more often than the values on each side of this interval.The frequency in the class interval is the highest in a continuous quantitative distribution where the values are grouped into classes with similar dimensions. Mode is not used as a measure of central tendency for continuous quantitative variables since it is more helpful for qualitative variables.The mode can be calculated by the formula -MODE = [tex]$L + h\frac{(f_{m} -f_{1}) }{(f_{m} -f_{1} ) + (f_{m} - f_{2} )}[/tex]
Therefore, Modal interval is discussed above.
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A local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers on Saturday. There were 58 fewer
cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
Answers
The number of hamburgers sold was 275.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Hamburgers = x
Cheeseburgers = y
There were 58 fewer cheeseburgers sold than hamburgers.
This means,
y = x - 58 ______(1)
A local hamburger shop sold a combined total of 492 hamburgers and cheeseburgers on Saturday.
This means,
x + y = 492 _______(2)
Substituting (1) in (2)
x + y = 492
x + x - 58 = 492
2x = 492 + 58
2x = 550
x = 275
Thus,
275 hamburgers were sold.
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How do i solve this?
Answers
Answer:
33
Step-by-step explanation:
The highest number is 50 and the lowest number is 17.
50 - 17 = 33
state the sampling method being used.
A manufacture has to check the product being made. He decides to randomly state taking items from the finished product convener belt and after he starts he samples every 15th item off the belt
Answers
The sampling method being used is given as follows:
Systematic sampling.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence in this problem we have a systematic sample with k = 15.
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Given the following definitions:
U = {a, b, c, d, e, f, g}
A = {a, c, e, g}
B = {a, b, c, d}
Find A ∪ B'
Answers
Union of set A and set B' is A ∪ B' = {a, c, e, f, g}
What is union of sets?
Union of two or more sets is the set containing all the elements of the given sets. Union of sets can be written using the symbol “⋃”
Given sets,
U = {a, b, c, d, e, f, g}
A = {a, c, e, g}
B = {a, b, c, d}
⇒ B' = {e, f, g}
A ∪ B' = {a, c, e, g} ∪ {e, f, g}
A ∪ B' = {a, c, e, f, g}
Hence, A U B = {a, c, e, f, g} which union of both sets.
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gillan read 3,135 words in 19 minutes let w represent the number of words read each minute if gillian read the same number of words each minute how many words did she read in 1 minute?
Answers
The number of words Gillan can read in 1 minute is, 165
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Gillan read 3,135 words in 19 minutes
The number of words read each minute = w
Now, it has given,
Total words = 3135
Time taken = 19 minutes
For words per minute,
we need to take ratio of total words and total time taken,
Ratio = Total words/Time taken
= 3135/19
= 165
Hence, the number of words in 1 minute is 165
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In a triangle ABC with an orthocenter O, prove that angle AOB plus angle ACB equal to 180°. PLEASE HELP IT DEPENDS ON MY GRADE
Answers
The statement can be proved by the property of similarity and adjacent angles of a line property.
What is the orthocenter?An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle. In a triangle, it is that point where all the three altitudes of a triangle intersect.
Given here: A triangle ABC with an orthocenter O.
Now let BD and A-F be the altitudes that intersect on the sides of AC and BC
then we have in the triangles AOD and ACF we have
∠ADO=∠AFC=90 and ∠A is common and therefore ΔAOD≈ΔACF
thus ∠AOD=∠ACF=∠ACB
now ∠ACB and ∠AOB lie on a line BD thus we must have
∠ACB +∠AOB=180
Hence, The statement ∠ACB +∠AOB=180 is proved.
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41. MODELING - Wild Mustangs According to the Bureau of Land Management, the wild mustang population of Nevada in 2004 was 2515 more than six times the wild mustang population in Utah. The total number of wild mustangs in Nevada and Utah was 21,730. Determine the number of wild mustangs in each state in 2004.
Answers
The number of wild mustangs in Utah and Nevada are 2745 and 18985
respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
From the given information let the number of wild mustangs in Utah be 'x'
So, The number of wild mustangs in Nevada is 6x + 2515.
Therefore, x + 6x + 2515 = 21730.
7x = 21730 - 2515.
7x = 19215.
x = 19215/7.
x = 2745.
So, The number of wild mustangs in Utah is 2745 and hence the number of wild mustangs in Nevada is 6×2745 + 2515 = 18985.
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A three-column table is given.
Part A C D
Part 30 36 46
Whole B 54 69
What is the value of B in the table?
45
50
18
23
Answers
The value of 'B' in the table is 45.
What are the types of representing data?Data refers to the elements that make up persons, things, events, and ideas.
It could be an integer, a title, or anycast. Data must be tabulated after collection in order to study their prominent characteristics.
The presentation of data is the name given to such a configuration.
Bar Chart, Histogram, Line Graph, Pie Chart, Frequency Distribution Table.
Given, A three-column table.
Part A C D
Part 30 36 46
Whole B 54 69
In D it is 23×2 and 23×3.
Similarly, in C it is 18×2 and 18×3.
Therefore, In A it is 15×2 and 15×3 = 45.
the value of B in the table is 45.
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Let $\triangle A_0B_0C_0$ be a triangle whose angle measures are exactly $59.999^\circ$, $60^\circ$, and $60.001^\circ$. For each positive integer $n$, define $A_n$ to be the foot of the altitude from $A_{n-1}$ to line $B_{n-1}C_{n-1}$. Likewise, define $B_n$ to be the foot of the altitude from $B_{n-1}$ to line $A_{n-1}C_{n-1}$, and $C_n$ to be the foot of the altitude from $C_{n-1}$ to line $A_{n-1}B_{n-1}$. What is the least positive integer $n$ for which $\triangle A_nB_nC_n$ is obtuse?
$\textbf{(A) } 10 \qquad \textbf{(B) }11 \qquad \textbf{(C) } 13\qquad \textbf{(D) } 14 \qquad \textbf{(E) } 15$
Answers
The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.
Since the angles of[tex]$\triangle A_0B_0C_0$[/tex] are [tex]$59.999^\circ$, $60^\circ[/tex] and [tex]$60.001^\circ$[/tex], the triangle is very close to being equilateral. Therefore, each time an altitude is drawn from one of the vertices, the triangle will become more acute, and it will take many iterations before an obtuse triangle is formed. The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15. To confirm this, we can use the Law of Cosines. For [tex]$\triangle A_15B_15C_15$[/tex] , we have [tex]$A_{15}B_{15} = 90 - 60.001 = 29.999$ and $B_{15}C_{15} = 90 - 59.999 = 30.001$[/tex]. Therefore, [tex]$A_{15}C_{15}^2 = 29.999^2 + 30.001^2 - 2(29.999)(30.001)\cos \angle A_{15}B_{15}C_{15} = 899.998^2$[/tex] . Since [tex]$A_{15}C_{15}^2 > 899.997^2$, $\angle A_{15}B_{15}C_{15}$[/tex] is obtuse, and therefore the answer is (E) 15.
The least positive integer n for which [tex]$\triangle A_nB_nC_n$[/tex] is obtuse is 15.
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Fill in the blanks below with the correct units.
(a) Boris saw an elephant at the zoo. The elephant's mass was about 4000 ?
(b) In his shower, Greg used about 130 ? of water.
(c) The spacebar on the keyboard was about 11 ? long.
Answers
The respective units in the statements above are kg, L,cm
What are units?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given here: Different quantities
a) Boris saw an elephant and its mass is mentioned.
Now we know,The Metric System of Measurements uses the mass units: gram (g), kilogram (kg) and tonne (t).
Thus the mass of the elephant is 4000 kg/tonne(t)
b) Greg used some volume of liquid in the shower
Now the units of liquid primarily used daily life is liters
Thus Greg used about 130 L of water
c) "The spacebar on the keyboard " in this statement the emphasis is on length and we know the units of length are m, cm etc.
Thus the length of the spacebar on the keyboard is 11 cm long.
Hence, The respective units in the statements above are kg, L,cm
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jackson would like to explore the scientific goal of control. which of the following lines of research should jackson pursue in order to explore this goal?
Answers
Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.
One line of research Jackson could pursue to explore the scientific goal of control is control theory. Control theory is the study of how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances. Control theory uses mathematical models to describe the behavior of a system and the effects of control inputs on the system. For example, a simple linear control system can be modeled using the transfer function, which is a mathematical expression that describes how a system responds to an input signal. The transfer function can then be used to calculate the output of the system in response to different inputs. Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior.
Jackson could use control theory to explore how to design and analyze systems that are able to maintain a desired state or behavior in the face of varying environmental conditions and disturbances.
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Complete question: Which of the following lines of research should Jackson pursue in order to explore the scientific goal of control?
PLEASE HELP NOW! GRADPOINT
WHICH SYSTEM IS THE SOLUTION OF THE GRAPH?
Answers
The solution to the system of inequalities is following as y ≤ -4 ;y ≤ - x + 4
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (A), we have the system of inequality as follows:
y ≤ -4
y ≤ - x + 4
The region is above the graph, hence our inequality should be y ≤ - x + 4
The inequality sign part comes from visible the graph, the line is drawn using a dashed line, hence the line is included in the region.
Thus, this graph corresponds to a system of inequalities which is the correct answer that would be option (A).
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Peter buys 10 apples at R2.50 each. He sells each apple for R4.00. How much profit does he make if he sells 50% of his apples at full price and the rest at a 25% discount?
Answers
At full price, Peter sells 50% of the apples for R4.00, so he sells 10 * 0.5 = 5 apples at full price.
So, he makes 5 * R4.00 = R20.00 from selling the apples at full price.
He sells the rest of the apples (10 - 5 = 5 apples) at a 25% discount, so he sells them for R4.00 - (R4.00 * 25%) = R3.00 each.
So, he makes R3.00 * 5 = R15.00 from selling the rest of the apples at a discount.
Therefore, Peter's total profit is R20.00 + R15.00 = R35.00.
Answer:
R10.00
Step-by-step explanation:
Purchase:
10 apples at R2.50 each = 10 × R2.50 = R25.00
He spent R25.00 on the 10 apples.
Sales:
25% discount on R4.00 is 0.75 × R4.00 = R3.00
5 apples at R4.00 = 5 × R4.00 = R20.00
5 apples at R3.00 = 5 × R3.00 = R15.00
Total sales = R20.00 + R15.00 = R35.00
Profit:
R35.00 - R25.00 = R10.00
Select the correct solution for the expression. 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40
Answers
The correct solution of the expression is, 31/40.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
The expression is,
⇒ 2/5 + 3/8
Now, We can add the fraction as;
⇒ 2/5 + 3/8
⇒ (16 + 15) / 40
⇒ 31/40
Thus, The solution of fraction = 31/40
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Determine if the equation describes y as a function of x
xy=4
Answers
[tex]\huge\begin{array}{ccc}y=\dfrac{4}{x}&\text{for}&x\neq0\end{array}[/tex]
We have:
[tex]xy=4[/tex]
We need:
[tex]y=?[/tex]
Let's transform the equation:
[tex]xy=4\\\\\dfrac{xy}{x}=\dfrac{4}{x}\qquad\text{for}\ x\neq0\\\\\boxed{y=\dfrac{4}{x}}[/tex]
When labeling a number line, Jason begins at 3.9 and labels the next 9 tick marks to the right 3.91, 3.92, 3.93, 3.94, 3.95, 3.96, 3.97, 3.98, and 3.99. The next tick mark that Jason labels should be 3.100. True or False
Answers
Answer:
False
Step-by-step explanatio
its like saying
398
399
3100.
makes no sense
Try This question out and I’ll give you brainliest
Answers
Answer:
$168.75
Step-by-step explanation:
If you need this for 7 and a half hours, start off by multiplying 22.50 by 7.
22.50 x 7 = 157.5
Now find half of 22.50 to account for the half.
22.50/2 = 11.25
Finally, add 157.5 and 11.25, and that should be your answer. :)
157.5 + 11.25 = $168.75
I hope this helped!! :)
provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (round your answers to four decimal places.)
Answers
Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.
A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on a social networking site can be calculated using the formula for a difference in proportions:
[tex]$$\hat{p}_1 - \hat{p}_2 \pm z^* \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$$[/tex]
where [tex]$\hat{p}_1$[/tex] and [tex]$\hat{p}_2$[/tex] are the sample proportions of women and men who trust recommendations, respectively, n_1 and n_2 are the sample sizes of women and men, and z^* is the critical value from the standard normal distribution for a 95% confidence level (approximately equal to 1.96).
Since the values of [tex]\hat{p}_1, \hat{p}_2, n_1[/tex], and n_2 are not given, it is not possible to determine the exact 95% confidence interval estimate.
However, this formula can be used to calculate the estimate once the sample data is available.
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you have $8 and a $5 off coupon to buy snacks at a concession stand. Write and solve an inequality to represent the regular price of snacks. you can buy if you use the coupon
Answers
An inequality to represent the regular price of snacks, if i can buy using the coupon, x ≤ $13
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
There are two coupons available, $8 and a $5 off on buying snacks
Let's call the regular price of the snacks "x".
Since you have a $5 off coupon,
the price you would actually pay would be x - $5.
And since you only have $8, the price you pay for the snacks cannot be greater than $8:
x - $5 ≤ $8
Adding $5 to both sides:
x ≤ $13
So, the regular price of the snacks must be less than or equal to $13 if you want to use the coupon and still have enough money to pay for them.
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find the equation of the line through the point(6,7) and (2,-1). then give its x- and y- intercepts as ordered pairs
Answers
The equation of the line through the point(6,7) and (2,-1) is y = -2x + 3
How to determine the equation of a lineThe formula for the equation of a line is expressed as;
y = mx + c
Such that;
m is the slope of the liney is a point on the y -axis of the linex is a point on the x-axis of the linec is the intercept of the lineFrom the information given, the slope is expressed as;
Slope = y₂ -y₁/x₂ - x₁
Substitute the values
Slope = 8/-4 =-2
Then, substitute the values
-1 = -4 + c
collect like terms
c = 3
Hence, the equation is y = -2x + 3
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which of the following are examples of unethical statistical practices? check all that apply. representative sampling of a population accounting for all observations development of misleading graphs running multiple tests until a desired result is obtained
Answers
The receiving and giving money, gifts, and other types to get a favor from the government or from an institution or from an organization is amounts to bribe which is not an ethical practice.
The magnitude of the corruption in the form of a bribe may vary from the place of practice that is in situations where it has taken place.
This practice of taking bribe is considered to be an immoral act and it is punishable under the Foreign Corrupt Practices Act (FCPA) which became law in 1977 in the USA.
The main aim of the Act is to fight bribery and corruption from foreign countries and the US government as used by this law to control the unethical practice.
Types of bribery:
Active bribery
Passive bribery
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Solve the equation below. Show each step and check your work.
24n + 60 = 72
Answers
Answer:
n =1/2
Step-by-step explanation:
24n + 60 = 72
24n = 72 - 60
24n = 12 /24
n = 1/2
Answer:
n=1/2
Step-by-step explanation:
24n+60=72
24n=72-60
24n=12
n=12/24
n=1/2
if {xt} and {yt} are uncorrelated stationary sequences, i.e., if xr and ys are uncorrelated for every r and s, show that {xt yt} is stationary with autocovariance function equal to the sum of the autocovariance functions of {xt} and {yt}.
Answers
The [tex]& r_x(h)+r_y(h) \\[/tex] mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary.
Solution: [tex]$\left\{x_t\right\} \&\left\{y_t\right\}$[/tex] are uncorrelated stationary process i.e.[tex]$x_\gamma \& I_s$[/tex] ax uncorrelated for every r and s process [tex]$\left\{x_t+y_t\right\}$[/tex] is stationary.
The sum of the autocovariance functions of {[tex]x_{t}[/tex]} and {[tex]y_{t}[/tex]}.
The autocovariance function (ACF) is defined as the sequence of covariances of a stationary process. That is suppose that {Xt} is a stationary process with mean zero, then {c(k) : k 2 Z} is the ACF of {Xt} where c(k) = E(X0Xk). Clearly different time series give rise to different features in the ACF.
Autocovariance (auto means itself) of (xt) and (xt-1) is defined as covariance between same variable with different values.⇒Var[tex]& \left(X_t+Y_t\right)={Var}\left(X_t\right)+{Var}\left(Y_t\right) \\[/tex]
⇒[tex]& E\left(X_t+Y_t\right)=\mu_x+\mu_y \\[/tex]
⇒[tex]& r_{x+y}(h)={cov}\left(X_{t+h}+Y_{t+h}, X_t+Y_t\right) \\[/tex]
[tex]& ={cov}\left(X_{t+h}, X_t\right)+{cov}\left(Y_{t+h}, Y_t\right)+0 \\[/tex]
[tex]& =r_x(h)+r_y(h) \\[/tex]
Since, the mean and autocovariance functions are free of t , the process [tex]$\left\{X_t+Y_t\right\}$[/tex] is stationary
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