The product of a non-zero rational and an irrational number is always irrational number.
To prove this statement:
Let x be a rational number and y be an irrational number.
Let xy=a.
Let us assume that a is rational.
Since, a is rational it can be expressed as p/q , where p and q are integers.
Let x= m/n , where m and n are integers.
Now, xy=a
[tex]\frac{my}{n} = \frac{p}{q}[/tex]
On cross multiplying we get,
y = pn/qm
Now, pn and qm are integers.
Hence, pn/qm is a rational number.
However, y is irrational.
Hence, our assumption is incorrect.
Hence, the product of a non-zero rational and an irrational number is always an Irrational number.
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I’m stuck on this one question help
Answer:
E is a major arc
C is a minor sector
A is a major segment
Major segment is the portion (or part) of the circular region enclosed between a chord and the corresponding major arc.
Major arc is the longer arc connecting two endpoints on a circle.
A sector with a central angle less than 180° is called a minor sector.
(8)
Amelia wanted to redeem a voucher. She had only 3/5of the total number
of points needed. After she earned another 50 points, she still needed 3/10
of the total number of points. How many points were needed to
redeem the voucher?
Answer:
The number of points needed to redeem the voucher is 92.5
Step-by-step explanation:
Let x be the total number of points needed to redeem the voucher.
Amelia has [tex]\frac{3}{5}[/tex] × x points,before she earns the another 50 points,
After she earns another 50 points,
Now
she has [tex]\frac{3}{5}[/tex] × x + 50 points.
she still needs [tex]\frac{3}{10}[/tex] × x points to redeem the voucher.
Now
From above we get a equation,
[tex]\frac{3}{5}[/tex] × x + 50 = [tex]\frac{9}{10}[/tex] × x
Solving the equation we can get x,
[tex]\frac{3}{5}[/tex] × x = [tex]\frac{9}{10}[/tex] × x - 50
if we multiply both sides by 5/3, we get,
x = (9/10 × x - 50) × 5/3
After expanding the right side,
x = (9/10 × x - 50) × 5/3
x = (9x/10 - 250/3)
Now,
Subtracting 9x/10 from both sides,
0 = 250/3 - 9x/10
If we add 9x/10 to both sides,
9x/10 = 250/3
Again,
If we multiply both sides by 10/9,
x = 250/3× 10/9
x = 250 × 10 / (3 × 9)
x = 250 × 10 / 27
x = 250 × 10 / 27
x = 250 × 10 / 27
x = 250 × 10 / 27
= 250 × .37
x = 92.5
The number of points needed to redeem the voucher is 92.5
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(0) = 2 C. g(7) = -1 D. g(-4) = -11
Answer: It is not possible to determine the truth of these statements without further information about the function g. The information given only provides the domain and range of the function and the values of g at two specific points, 0 and -9. To determine the value of g at other points, we would need to know the equation for the function g.
Step-by-step explanation:
Write an inequality to represent the following: 75 less than a number x is greater than or equal to 420.
Answer: [tex]x-75\geq 420[/tex]
Step-by-step explanation:
... as it say...
Answer:
x -75 ⩾ 420
Step-by-step explanation:
we take away 75 from the value of X and compare it to 420 using the greater than or equal sign.
Serina wants to solve the following system of equations in the most efficient way. 2 x + 3 y = 18. X + 7 y = 31. She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18. Why is serina mistaken?serina should have solved for x in the second equation because it has a coefficient of 1. Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution. Serina should have solved for y in the second equation because it has the largest coefficient. Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3.
Serina is mistaken because Serina should have solved for x in the second equation because it has a coefficient of 1.
Serina is mistaken because solving for x in the first equation as her first step does not necessarily lead to the most efficient solution. While it is true that both 2 and 3 can be divided into 18, this approach may require additional steps to solve for the other variable, y, in the second equation.
In this case, it is actually more efficient to solve for x in the second equation because it has a coefficient of 1. This means that once we solve for x, we can substitute that value into the first equation and solve for y directly, without needing to perform any additional calculations.
Here's how we can solve the system of equations using this approach:
X + 7 y = 31 (solve for x)
x = 31 - 7y
Substitute x = 31 - 7y into the first equation:
2 x + 3 y = 18
2 (31 - 7y) + 3 y = 18
62 - 14 y + 3 y = 18
-11 y = -44
y = 4
Substitute y = 4 into the equation we used to solve for x:
x = 31 - 7y
x = 31 - 7(4)
x = 3
Therefore, the solution to the system of equations is x = 3, y = 4.
In summary, while it is important to consider which variable to solve for first when solving a system of equations, the most efficient approach may vary depending on the specific equations and coefficients involved. In this case, solving for x in the second equation was the most efficient approach.
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Determine the domain and range of the given
function.
The domain is
The range is
domain = all real numbers
range = y > -2
y=x²-2
range is y is -2
domain is x is
A rectangular garden has a length of 4z + 17 feet and a width of 6z feet. Which expression represents the
area of the garden in square feet?
Answer:
Step-by-step explanation:
Area of a rectangle = length times width.
Area of the garden = 6z(4z + 17)
24z² + 102z
HELP PLEASE!! SOLVE 2x=32 IS 2 DIFFERENT WAYS
i know the one way is
2x/2 = 32/2
x= 16
WHAT IS THE OTHER WAY???!!
Answer: 4x = 64 or -32/-2
Step-by-step explanation:
you could multiply both sides by 2.
4x = 64
4x/4 = 64/4
x = 16
OR
-2x or -32 to both sides
-32 = -2x
divide both sides by -2
x = -32/-2
x = 16
hope this helps
A 15.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck)if the ladder makes an angle of 53° 25' with the horizontal
d= ? m
The distance the ladder goes up the wall is approximately 12.14 meters.
What is trigonometry ?
Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
We can use trigonometry to solve this problem.
Let's call the distance the ladder goes up the wall "d". We can use the angle the ladder makes with the horizontal to find the length of the ladder that is leaning against the wall.
We know that the ladder is 15.5 m long, so we can use the sine function to find the length of the ladder that is leaning against the wall:
sin(53° 25') = d/15.5
We can solve for "d" by multiplying both sides by 15.5:
d = 15.5 * sin(53° 25')
Using a calculator, we get:
d ≈ 12.14 m
Therefore, the distance the ladder goes up the wall is approximately 12.14 meters.
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Which form or system of government gives the most power to the people of the nation?
Unitary
Autocracy
Democracy
Oligarchy
Question 3(Multiple Choice Worth 3 points)
The Leswaygo Times is a newspaper in the imaginary country Leswaygo. You read in one of its online articles that the people are unhappy with their new king. He is making changes to make Leswaygo more modern. He believes this will benefit the country, but the people do not agree. They are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to
communism
democracy
autocracy
socialism
Question 4(Multiple Choice Worth 3 points)
Which list shows forms or systems of government from the least power for the people to the most?
Oligarchy, autocracy, republic
Autocracy, oligarchy, democracy
Democracy, unitary, parliamentary
Federation, republic, unitary
Question 5(Multiple Choice Worth 3 points)
You read in the newspaper about a country that just held elections. The people voted for new representatives in their lawmaking branch of government. The members of this branch are busy meeting to discuss who will be the new prime minister. Only they, and not the voters, have a say in who will have this position. The new prime minister is part of the lawmaking branch and answers to it.
Which system of government does this represent?
Unitary
Federation
Parliamentary
Confederation
Question 6(Multiple Choice Worth 3 points)
In the early days of the United States, the central government was weak compared to the state governments. The leaders recognized there were problems with this arrangement. When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws.
Which system of government does the United States have?
Unitary
Federation
Parliamentary
Confederation
Question 7(Multiple Choice Worth 3 points)
Which of the following statements could appear in the sections labeled “B” and “D”?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
The use of force is unnecessary.
The people’s wishes are not always considered.
Local issues are heard and addressed.
Voters have a say in making decisions.
Question 8(Multiple Choice Worth 3 points)
Which of the following phrases belongs in the section labeled “A”?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
Decisions made quickly
Overlap in government services
Less waste of tax dollars
Single political party has control
Question 9(Multiple Choice Worth 3 points)
“Members can maintain power while working together on specific, shared concerns.” In which section would you place this statement?
Form or System Advantages Disadvantages
Unitary
A
Strong unity
B
Confederation
C
D
Central goverment may be too weak
Federation
E
Local governments can address local issues
F
D
B
E
C
Question 10(Multiple Choice Worth 3 points)
“Decisions take much longer because the people have a say in them.” In which section of the chart would you place this statement?
Form or System Advantages Disadvantages
Unitary
A
B
Few or none consulted when making decisions.
Oligarchy
C
Decisions can be made quickly.
D
Democracy
E
F
Difficult to get an agreement.
E
F
A
B
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The answers include the following:
The form or system of government which gives the most power to the people of the nation is Democracy.The new prime minister is part of the lawmaking branch and answers to it which means that the system of government is parliamentary.When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws which depicts Confederation.“Decisions take much longer because the people have a say in them therefore the section of the chart which you would place this statement is Democracy.What is Democracy?
This is referred to as a system of government where the citizens of a state exercise power to rule the state, either directly or through electing representatives.
Decisions take much longer because the people have a say in them through the process of voting and is therefore the reason why it was chosen as the correct choice.
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Answer:
Step-by-step explanation:The form or system of government which gives the most power to the people of the nation is Democracy.
The new prime minister is part of the lawmaking branch and answers to it which means that the system of government is parliamentary.
When they wrote the Constitution, they gave more power to the central government. The states still have authority within their borders but must follow the Constitution and its laws which depicts Confederation.
“Decisions take much longer because the people have a say in them therefore the section of the chart which you would place this statement is Democracy.
Graph this line:
y+4=3(x-6)
Click to select points on the graph.
104
-10 -8 -6
-4
-2
8
6
4
2
0
-2
4
6
-8
10
3
2
4
6
8
10
The solution is: (A) y+4=-3(x+6), is the equation of the line in point-slope form.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:
y-y1 = m (x-x1)
Given the point:
(x1,y1) = (-6, -4)
Slope, m= -3
x1 = -6,
y1 =-4
Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:
we get,
y+4=-3(x+6)
The correct option is A.
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complete question:
The graph of a line has a slope of -3 and passes through the point (-6,-4).
What is the equation of the line in point-slope form?
Oy + 4 = -3(x + 6)
y + 6 = -3(x + 4)
y-4 = -3(x-6)
y-6 = -3(x – 4)
The table shows the number of 6th grade students who prefer each kind of juice at lunch time. Draw a circle graph to display the information. 6th Grade Juice Choices: Grape Juice 8, Orange Juice 6, Fruit Punch 6, Apple Juice 20.
A circle graph representing the data presented will show half of the students prefer apple juice; while grape, orange juice, and fruit punch are preferred by a lower ratio of students.
What is a circle graph?A circle graph also known as a pie graph is a visual representation of data based on a circle and its fractions of it. In this way, if 20 out of the 40 students prefer apple juice this means in the circle graph half of it would be for students preferring apple juice.
Based on this, a possible circle graph that represents the data is shown below:
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legend has it that Isaac Newton discovered gravity when an apple feel down from a tree and hit him on the head. I a 0.2 kg apple fell 7 meters before hitting Newton, what was its change in PE during the fall?
The change in potential energy of the apple during the fall was approximately 13.72 joules.
What is the name of potential energy?One of the two types of energy is potential energy, which is the latent energy in an object at rest. Kinetic energy, on the other hand, is the energy that an item in motion expresses.
The formula: can be used to determine the change in potential energy (PE) of a mass m object that falls a distance h from the Earth's surface.
ΔPE = mgh
where g is the acceleration brought on by gravity close to Earth's surface, which is roughly 9.8 m/s^2.
In this instance, the apple weighs 0.2 kg, falls 7 metres, and accelerates by gravity at a rate of 9.8 m/s^2. So, the potential energy change is as follows:
PE is equal to (0.2 kg) times (9.8 m/s^2) times (7 m) Equals 13.72 joules (J)
As a result, the apple's potential energy changed by around 13.72 joules during the fall.
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help ASAP Thanks mwa
Answer:
3
Step-by-step explanation:
In this triangle ABC, the leg lengths are AC and BC, being x and x+7, respectively. So, the area can be listed as: 15 = (1/2) * x * (x+7). Simplifying that gets x^2 + 7x = 30 -> x^2 + 7x - 30 = (x-10)(x-3). So, x = 3 since it cannot be negative.
Write a rule for each graph below and explain it step by step
1) the rule for the graph is y=3x+3
2) the rule for the graph is y=4x+10
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
1) slope, m = change in y/change in x = 3/1 = 3
y-intercept = b = 3
A line's slope intercept form is y=mx+b
Thus, the rule for the graph is y=3x+3
2) slope, m = change in y/change in x = 4/1 = 4
y-intercept = b = 10
A line's slope intercept form is y=mx+b
Thus, the rule for the graph is y=4x+10
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The temperature in burr town starts at 21 F at midnight when H=0 for the next few hours the temperature drops 4 degrees every hour which equation represents the temperature at hour h
Answer:
t = 21 + (-4)h
Step-by-step explanation:
t = temp. at hour h
h = # of hours past midnight
t = 21° + (-4°/hr)h
Question 1
What are the coordinates of the x-intercept and y-intercept of the line
4y-4x= -16.
Find the range of each set of data.
Set 1: 1, 4, 6, 8, 10, 12
Range =
Set 2: 230, 24, 33, 22, 41
Range =
Which set of data has a wider spread of data?
The range of set 1 is 11. The range of set 2 is 208
The wider range of set 2, set 2 contains a wider spread of the given data.
What is the range of the data?The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.
The set is given in the question, as follows:
Set 1: 1, 4, 6, 8, 10, 12
The maximum value = 12
The minimum value = 1
The range of the set 1 = maximum value - minimum value
Substitute the values in the above formula,
The range of the set 1 = 12 - 1
Apply the subtraction operation to get the answer
The range of the set 1 = 11
Set 2: 230, 24, 33, 22, 41
Now, the range of the set 2 = 230 - 22 = 208
Data set 1 has a range of 11, whereas data set 2 has a range of 208.
Therefore, the wider range of set 2, set 2 contains a wider dispersion of data.
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Which two sets of values make the inequality 3(n – 2) ≤ 2n – 3 true?
A. {−2, −1, 3}
B. {−2, −1, 4}
C. {−1, 0, 3}
D. {−1, 1, 4}
E. {1, 0, 5}
Question in the picture below
Answer: $1.50 per hour
Step-by-step explanation:
Show the work steps for finding the roots of x^4-13x^2+36 algebraically
The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given polynomial is x⁴-13x²+36
Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36
= x²(x²-9)-4(x²-9)
= (x²-9)(x²-4)
= (x²-3²)(x²-2²)
By using the identity a²-b²=(a+b)(a-b)
So, (x+3)(x-3)(x+2)(x-2)
Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).
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Need help with this. Keep getting answer wrong
Answer:
[tex]\frac{-1}{5}[/tex] [tex]y^{2}[/tex] - [tex]\frac{1}{2}[/tex] y + [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
[tex]-\frac{y^3}{10} +\frac{y^2}{5} -\frac{y}{4} -\sqrt{2}[/tex]
Step-by-step explanation:
Please help me !!! I can’t find the answer
Answer:
Based on the measures of the following triangle's angles, the triangle can be classified as an obtuse triangle.
Step-by-step explanation:
In order to decide which type of triangle this is, first we must understand what an acute, right, and obtuse triangle are. Acute triangles are triangles with all three of its angles less than 90°, right triangles are triangles with one angle that is exactly 90°, and obtuse triangles are triangles with one angle that is greater than 90°. Overall, we can determine the type of this triangle by looking at its angles.
The given triangle has the angles 25°, 136°, and 19°. Now we can compare it to the rules above and see whether this triangle is acute, right, or obtuse. As the given triangle has an angle that is greater than 90°, we can conclude that the following triangle is an obtuse triangle.
Have a great day! Feel free to let me know if you have any more questions :)
Which conditions allow you to conclude that a quadrilateral is a trapezoid?
Answer:
Below
Step-by-step explanation:
It has two sides that are parallel ( the 'bases' ) and different lengths ( making the other two sides NOT parallel)
Answer:
Step-by-step explanation:
A trapezoid is a quadrilateral with at least one pair of parallel sides. In other words, a trapezoid has two opposite sides that are parallel, called the bases, and the other two sides are called the legs or lateral sides.
So, to conclude that a quadrilateral is a trapezoid, you must determine that:
1)Two of its sides are parallel.
2)The other two sides are not parallel.
If these two conditions are met, then the quadrilateral is a trapezoid.
(If a trapezoid has two pairs of parallel sides, then it is known as a parallelogram, which is a special type of trapezoid.)
write an algebraic expression for the following when a number is doubled and then decreased by 5 the result is 21
ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
First you identify your variable, for our sake lets use x:
x= number in question
Next you write the equation given in the question:
2(x-5)= x+25
Next you use the distributive property and multiply 2 by both x and negative 5 to get:
2x-10=x+25
Now you want to get all of the x's to one side so you subtract the x on the right, fro the one on the left giving you:
x-10=25
Then you simply add 10 to 25 giving you the answer of x=35
What is the y-intercept of y = x^2 - 3x + 2 by completed square form?
y-intercept(s): (0,−2)
Answer:
2
Step-by-step explanation:
The [tex]x^{2}[/tex] and x terms are made to follow the sequence:
[tex][a-b]^{2} =a^{2} -2ab + b^{2}[/tex]
Therefore the [tex]b^{2}[/tex] term has to be added to complete the [tex][a -b]^{2}[/tex] sequence, but at the same time the [tex]b^{2}[/tex] term has to be balanced as it is not originally present in the equation:
[tex]y = x^{2} - 3x + 2 = [(x)^{2} - 2(x)(\frac{3}{2}) + (\frac{3}{2})^{2}] + 2 - (\frac{3}{2})^{2}[/tex]
[tex]= [x - \frac{3}{2}]^{2} + 2 - \frac{9}{4}[/tex]
= [tex][x - \frac{3}{2}]^{2} + \frac{8}{4} - \frac{9}{4}[/tex]
= [tex][x- \frac{3}{2}]^{2} \frac{+ 8-9}{4}[/tex]
= [tex][x-\frac{3}{2}]^{2} -\frac{1}{4}[/tex]
y-intercept is the y-value obtained when x = 0 in the equation:
[tex]= [0 - \frac{3}{2}]^{2} -\frac{1}{4}[/tex]
= [tex](-\frac{3}{2})^{2} -\frac{1}{4}[/tex]
= [tex]\frac{9}{4} - \frac{1}{4}[/tex]
= [tex]\frac{8}{4}[/tex]
= 2
In a new study, Dr Matti Uhari and colleagues at the University of Oulu in Finland, randomly gave 857 healthy children in daycare centers xylitol in syrup, gum or lozenge form, or a placebo gum, syrup or lozenge in five doses per day for 3 months. According to a report in the October issue of the Journal of Pediatrics, the incidence of ear infections were reduced by 40% in children given xylitol chewing gum, 30% in those given syrup and 20% in those given lozenges when compared to children give a placebo. a) is this an observational study or a randomized experiment? b)If this is an experiment, what are the 3 criteria in this case? c) What are the explanatory and response variables? d)If it is an experiment, diagram the randomized comparative experiment.
(a) Randomized experiment, (b) There are three criteria for a randomized experiment
a) This is a randomized experiment.
b) The three criteria for a randomized experiment are:
Random assignment, the children were randomly assigned to the xylitol or placebo group.
Control group, a placebo group was used as a control.
Manipulation, the children were given different forms and doses of xylitol or placebo.
c) The explanatory variable is the form and dose of xylitol or placebo given to the children. The response variable is the incidence of ear infections.
d) Diagram of the randomized comparative experiment:
Population of healthy children in daycare centers
↓
Random assignment to xylitol or placebo group
↓
Intervention group: given xylitol in syrup, gum or lozenge form
Control group: given a placebo in gum, syrup or lozenge form
↓
Comparison of incidence of ear infections in intervention and control groups
↓
Analysis of results to determine the effectiveness of xylitol in reducing ear infections.
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Question content area top
Part 1
Find the slope of the line if it is defined.
Through (6,5) and (6,-8)
Answer:
undefined or no slope.
Step-by-step explanation:
m is slope. slope is always change of y over change of x. this mean. y2-y1 divide by x2-x1. in this case y2 is -8, y1 is 5 and x2 is 6 and x1 is 6. remember the number in front the variable are base. the answer is undefined.
In planning for a new forest road to be used for tree harvesting, planners must select the location that will minimize tractor skidding distance. In order to estimate the true mean skidding distances along a new road in a European forest, skidding distances (in meters) were measured at 20 randomly selected road sites. The data are shown in the following table.
In planning for a new forest road to be used for t
a. Calculate the mean, variance, and standard deviation of this sample.
b. Estimate the true mean skidding distance of the road with a 95% confidence interval.
c. What assumptions are needed for your inference in (b) to be valid? How would you check them?
d. A logger working on the road claims that the mean skidding distance is at least 425 meters. Do you agree? Why?
The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.
To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:
Using the formulas, we get:
Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20
= 377.5 meters
Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)
= 7007.5 meters^2
Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters
Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.
To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:
Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))
Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.
substituting the values, we get:
Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))
= 377.5 ± 37.0
Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.
The assumptions needed for this inference to be valid are:
The sample is a random sample from the population of skidding distances along the road.
The skidding distances follow a normal distribution in the population.
The sample size is large enough (at least 30) or the population standard deviation is known.
To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.
To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.
Using the formula for the t-statistic, we get:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
= (377.5 - 425) / (83.7 / sqrt(20))
= -3.61
From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.
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Margo borrows $600, agreeing to pay it back with 2% annual interest after 10 months. How much interest will she pay? Round your answer to the nearest cent, if necessary
The amount of interest paid will be $9.6.
What is simple interest?The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.
Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.
The simple interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 600 x 2 x 0.8 ) / 100
SI = 960 / 100
SI = $9.6
Therefore, $9.6 will be paid in interest.
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