We treat the estimated intercept and slope coefficients from the sample regression as normally distributed because of Central Limit Theorem .
The Central Limit Theorem is the reason is the estimated intercept and slope coefficients from a sample regression as normally distributed.
In the Regression Analysis, the intercept and slope coefficients are estimated using a sample of data, instead of the entire population.
The Central Limit Theorem states that ; as sample size increases, the distribution of the sample mean approaches a normal distribution.
In the context of regression analysis, it means that, as sample size increases, distribution of estimated coefficients approaches a normal distribution.
The given question is incomplete , the complete question is
We treat the estimated intercept and slope coefficients from the sample regression as normally distributed because of _____ .
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You have a combination lock with 3 secret digits. Find the 3 correct digits using the following clues and enter your answer below.
Based on the clues, it can be concluded the correct digits for the lock are 564.
What are the correct digits?This password can be solved by using logic and the information provided in the clues as it follows:
The fourth clue says all digits are false which means 2, 3, and 8 are not in the number.The fifth clue says one digit is right but in the wrong place and this number is 5.The third clue says two digits are right but in the wrong place based on this, we can know 5 should go in the first place.It can be inferred that the digit that is right and in its place is 4 in the first clue.Finally, it can be inferred the missing number is 6.Learn more about combinations in https://brainly.com/question/19692242
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Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $0.20 and that the retail price per gallon has a bell-shaped distribution. (a) What percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon? % (b) What percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon? % (c) What percentage of regular grade gasoline sold for more than $3.85 per gallon? %
The required percentage of regular grade gasoline are;
a) 34%
b) 95.5%
c)4.5%
How we determine the percentage of regular grade gasoline?(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.
$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.
Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.
Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.
(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.
$3.85$ is $1.5$ standard deviations above the mean.
Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.
Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.
(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.
Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.
Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.
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A graphed line has a slope of -2 and passes through the point (7,-4). Which equation represents the line?
Answer:
C
Step-by-step explanation:
if you put the point value in the equation you get
-4 - (-2×7) = n
-4 + 14 = n
10 = n
Consider two investments, one earning simple interest and one earning compound interest. If both start with the same initial deposit (and you make no other deposits or withdrawals) and earn the same annual interest rate, how will the balance in the simple interest account compare to that of the compound interest?
A. The account with simple interest will have the same balance as the account with compound interest because the annual interest rates are equal.
B. The account with simple interest will have the same balance as the account with compound interest because the initial deposits are equal.
C.The account with simple interest will have a greater balance than the account with compound interest because compound interest is interest paid only on the original investment.
D.The account with simple interest will have a smaller balance than the account with compound interest because the more times interest is applied to an investment, the smaller the balance.
E. The account with simple interest will have a smaller balance than the account with compound interest because compound interest is interest paid both on the original investment and on all interest that has been added to the original investment.
The account with simple interest will have a smaller balance than the account with compound interest because compound interest is interest paid both on the original investment and on all interest that has been added to the original investment. (option F)
What is simple and compound interest?An account that earns a simple interest grows at a linear rate while an account that earns a compound interest grows at an exponential rate.
Let us assume the following:
Amount invested = $1000
Interest rate = 5%
Number of years = 5 years
Future value of the account that earns a simple interest in 5 years = amount invested + simple interest
Simple interest = amount invested x time x interest rate
$1000 x 0.05 x 5 = $250
Future value in 5 years = $1000 + $250 = $1250
Future value of the account that earns a compound interest :
Future value = amount invested x (1 + interest rate)^number of years
= 1000 x (1 + 0.05)^5
= 1000 x 1.05^5
= 1,276.28
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there are 200 cookies in a bag. 15% for which are wrapped. if 80% of the cookies are oatmeal, what is the smallest number of wrapped oatmeal cookies that could be in the bag
15% wrapped = 30
20% not oatmeal = 40
30 wrapped could all be not oatmeal.
there are 200 pieces of cookies in a bag.
15% are wrapped.
this means that .15 * 200 = 30 are wrapped.
80% of the cookies are oatmeal.
this means that .8 * 200 = 160 are oatmeal.
this also means that .2 * 200 = 40 are not oatmeal.
Unless I'm misreading the situation, it is entirely possible that none of the wrapped cookies are oatmeal as there are more than 30 cookies that are not oatmeal and 30 are wrapped.
It would be a different situation if cookies were chosen at random and then wrapped.
Without even glancing at the cookies, you would choose 30 for wrapping.
The likelihood that you would choose an oatmeal cookie is.
.8 given that oats make up 80% of the batch of cookies.
the likelihood that you would choose an oatmeal-free cookie. 2 since just 20% of the batch's cookies contains oats.
The likelihood of it happening if you pick at random is: The fewest number of oatmeal cookies that are wrapped would still be 0, and the probability of that happening is:
c(40,30) / c(200,30) = 2.069..... * 10^-27
bottom line is that it is possible to get 0 oatmeal cookies wrapped if you pick cookies out of the batch randomly, but the probability that they will all not be oatmeal is extremely small.
the probability that all the wrapped cookies are not oatmeal when you pick the cookies out of the batch randomly is 2.06907098 * 10^-27
that's a very small probability.
it's so small that if you rounded the answer to 26 decimal digits, it would be equal to 0.
but it's not zero, and therefore it is possible that you could get zero wrapped cookies that are oatmeal if you picked them out of the batch randomly without looking at them.
if you looked, and you could tell the difference, then there's no question that you could pick 30 cookies to be wrapped that are not oatmeal since you would have 40 to pick from.
that's my take.
but it's not zero, and therefore it is possible that you could get zero wrapped cookies that are oatmeal if you picked them out of the batch randomaly without looking at them.
if you looked, and you could tell the difference, then there's no question that you could pick 30 cookies to be wrapped that are not oatmeal since you would have 40 to pick from.
that's my take.
but it's not zero, and therefore it is possible that you could get zero-wrapped cookies that are oatmeal if you picked them out of the batch randomly without looking at them.
if you looked, and you could tell the difference, then there's no question that you could pick 30 cookies to be wrapped that are not oatmeal since you would have 40 to pick from.
that's my take.
15% wrapped = 30
20% not oatmeal = 40
30 wrapped could all be not oatmeal.
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PLEASE HELP!!!
For the figure below, what is the total sum degrees of the exterior angles? How do you know?
Answer:
360°
Step-by-step explanation:
The sum of all exterior angles for a polygon is always 360 degrees
Malcolm and his father want to build a frame for their favorite poster. What strategy could they use to find out how much framing material they will need?
The strategy to use to find out how much framing material they will need is d. Cover the poster with square-inch grid paper to find the area
Why is Option D correct?Cover the poster with square-inch grid paper to find the area - This method would give the total number of square inches of the poster and would be a good starting point for determining the size of the frame required.
The recommended strategy would be to measure the poster in inches with a ruler to determine the dimensions, then use that information to calculate the total area. This would be a good starting point for determining the size of the frame required.
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Round to the nearest tenth. This is a multi-step problem so do not round until the final answer.
The segment drawn from the apex to the edge of the circular base is ___ units.
The segment drawn from the apex to the edge of the circular base is 24.19 units.
How to determine the slant heightFrom the question, we have the following parameters that can be used in our computation:
Volume = 72π
Diameter = 6
The volume of a cone is
V = 1/3πr^2h
Where
r = 6/2 = 3
So, we have
1/3π * 3^2h = 72π
This gives
3h = 72
Divide by 3
h = 24
The slant height is then calculated as
l = √(h² + r²)
So, we have
l = √(24² + 3²)
Evaluate
l = 24.19
Hence, the slant height is 24.19 units
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HELP ASAP, 100 POINTS, WILL GIVE BRAINLIEST TO FIRST ANSWER,
How should a writer address opposing views in an argument?
The writer should ignore opposing views so as to not bring attention to conflicting information.
The writer should mention opposing views to point out the flaws of the people who believe in them.
The writer should include an explanation and evidence as to why the counterclaim is incorrect.
The writer should give equal attention and value to opposing views, including using evidence.
Answer:
The writer should give equal attention and value to opposing views, including using evidence. This helps to strengthen the argument by acknowledging and refuting counterarguments. It also demonstrates to the reader that the writer has considered multiple perspectives and is able to effectively argue their position. By giving equal attention to opposing views, the writer shows that their argument is well-reasoned and credible.
Step-by-step explanation:
When making an argument, it's important to consider and address any opposing views that exist. Giving equal attention to opposing views means acknowledging the validity of these views and providing evidence to refute them. This helps to strengthen the argument by showing that the writer has considered multiple perspectives and has a solid understanding of the issue at hand. It also demonstrates to the reader that the argument is well-reasoned, credible, and based on evidence.
On the other hand, ignoring opposing views, or attacking those who believe in them, weakens the argument and undermines the writer's credibility. If a counterargument is not addressed, the reader may assume that the writer is not aware of it or cannot effectively defend their position. By giving equal attention to opposing views and refuting them with evidence, the writer is able to make a stronger argument and persuade the reader of their point of view.
Answer:
The writer should use facts that can be verified to address and disprove opposing viewpoints.
Step-by-step explanation:
Hope it helps long time no seen
Montana decided to start his ball from the second diamond from the left along the bottom rail. He is planning to aim at the third diamond from the top right. If he hits the ball sufficiently hard, will the ball eventually reach a pocket? If so, show the path of the ball. Explain the steps used to solve the problem and write a concluding statement
Answer:
To determine whether the ball will eventually reach a pocket, we need to determine if the ball will collide with any other balls or obstacles on the way to its target. If there are no obstacles, and the ball has enough force and the correct trajectory, it will reach the target pocket.
To show the path of the ball, we can draw a straight line connecting the starting position and the target pocket. This line represents the trajectory of the ball if it is not obstructed by any other balls or obstacles.
In conclusion, without any obstacles in the way, if Montana hits the ball with enough force and the correct trajectory, the ball will reach the target pocket. It is important to consider any potential obstacles or interference when planning a shot in billiards.
A souvenir shop sells standard-sized decks of cards and mini-decks of cards. A card in the standard deck is a rectangle that has a length of 3.5 inches and a width of 2.5 inches. The perimeter of a card in the mini deck is 6 inches. What is the area of a card in the mini deck?
The required area of a card in the mini deck is 2.1875 inch².
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
Perimeter of the card in a standard deck = 2 [3.5 + 2.5] = 12 inch
Scale factor = perimeter of the mini deck / standard deck = 6 / 12 = 1/2
Now,
Dimensions of mini-deck,
length = SF × length of large card
length = 1/2 × 3.5
length = 1.75 inch
Similarly,
Width = 1.25
Now,
Area of the mini cards = 1.75 × 1.25 = 2.1875 inch².
Thus, the required area of a card in the mini deck is 2.1875 inch².
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if n and r are positive integers such that 1<=r<=n, show that [tex]^nC_{r} + 2[^nC_{r-1}] + ^nC_{r-2} = ^n^+^2 C_{r}[/tex]
correct answer :- instant brainliest
Answer:
AnCr+AnCr - 1 = n!/(n - r)!r! + n/(n - r + 1)!(r -
|1)! = n!(n - r+ 1)/(n -r+ 1)!r! + n!r/(n - r + 1)!r!
F n!/(n - r+ 1)!r!(n - r+1 +r) = (n +.
I’m order to measure the height of a large tree, Adam measures the tree’s shadow and immediately measures the length of his shadow. I’d Adam is 4ft 6in. with a shadow of 3ft and the same time the tree’s shadow is 57ft 10in, what is the height of the tree? Round to the nearest tenth of a foot.
The height of the tree is 86.745 feet.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that Adam measures the tree’s shadow and immediately measures the length of his shadow.
Adam is 4ft 6in. with a shadow of 3ft
4ft 6 inches =4.5 feet.
The tree’s shadow is 57ft 10in, we need to find the height of the tree.
57 ft 10 inches=57.83 feet
Let x be the height of the tree.
4.5/3=x/57.83
Apply cross multiplication
4.5(57.83)=3x
260.235=3x
Divide both sides by 3
x=86.745
Hence, the height of the tree is 86.745 feet.
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: (17, -12) and (12, 8)
Answer:
What is the question?
Step-by-step explanation:
The following data represent the test scores of a math class.
Make a frequency table using six classes.
26 29 37 37 46 62 64 68 71 73 74 80 86 92 94 97 100
The frequency table using the six classes have been done below
How to draw the frequency tableClass interval Frequency
20 - 35 2
36 - 50 0
51 - 65 2
66 - 80 5
81 - 95 5
96 - 110 5
Note: The class intervals were created as follows: 20-35, 36-50, 51-65, 66-80, 81-95, and 96-110. The frequency is the number of data values that fall into each class interval.
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Choose the correct response.
A. Yes. Every unique input has a unique output.
B. Yes. Every input maps to more than one output.
C. No. Not every input maps to an output.
D. No. Not every unique input maps to only one unique output.
Answer:
The answer would be C: not every input maps to an output.
The time it takes to travel to a location varies inversely to the speed traveled. It takes 4 hours driving at an average speed of 55 miles per hour to reach a location. To the nearest tenth of an hour, how long will it take to reach the same location driving at an average speed of 50 miles per hour?
Time it will take to reach the same location driving at an average speed of 50 miles per hour, 4.4 hour
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
The time it takes to travel to a location varies inversely to the speed traveled,
Time = 4 hours
Average speed = 55 miles per hour
If average speed = 50 miles per hour
then time = ?
First, it is required to calculate distance covered,
Distance = Time × Speed
= 4 x 55
= 220 miles
Now, when average speed is 50 miles per hour,
Distance = Time × Speed
Speed = Distance/Time
= 220/50
= 4.4 hour
Thus, the required time is 4.4 hour
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Methods used that summarize or describe characteristics of data are called?
Methods used that summarize or describe characteristics of data are called Descriptive statistics
Descriptive statistic is defined as the method fro summarizing data and information to partition them into a section of meaningful data.It contains descriptive coefficients that defined the meaningfulness of the data .
Variability and central tendency are the part of descriptive statistics that describe the spread and central point of the data respectively.
Other options are incorrect because overall statistics measure complete components ,average statistics take mean of complete statistic data and inferential statistic is based on random data sample.
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the blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 0.8 years. the company is willing to have a warranty that replaces at most 6% of their blenders sold. what is the longest a blender can last and still be in the lowest 6% of life spans?
The longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.
The longest a blender can last and still be in the lowest 6% of life spans is calculated by using the inverse normal distribution formula. This formula is P(X ≤ x) = 1 - P(X > x). The X is the longest a blender can last and P(X ≤ x) is 6%. First, we need to calculate the z-score for 6%. This can be done by P(X ≤ x) = 0.06 and using the z-score formula z = (x - μ) / σ , where μ is the mean and σ is the standard deviation. Substituting the values into the equation, we get z = 0.06 = (x - 8.2) / 0.8. Solving for x gives us x = 7.96. Therefore, the longest a blender can last and still be in the lowest 6% of life spans is 7.96 years.
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Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.
PLEASE HELP ASAP I HAVE 3 MINS LEFT!!!
PLEASE ANSWER THE PICTURE I SENT YOU BECAUSE IT HAS TO DO WITH THE QUESTION.
JUST DO NUMBER 2
Peter is right and Nadia is wrong.
What are equivalent fractions?Equivalent fractions are fractions that represent the same value, even though they look different.
Given is that Peter says 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says while 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.
{ 1 } -
3/4 = (3 x 2)/(4 x 2) = 6/8
Peter is right.
Now -
3/4 = 6/8
So it could not represent two different quantities. So, Nadia is wrong.
{ 2 } -
3/4 = 6/8 = 9/12 = 12/15
These all represent the same quantity. Division of all the expressions will result in same value.
Therefore, Peter is right and Nadia is wrong.
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You and your friend just got new puppies. Your puppy, Max, currently weighs 5 pounds and is expected to gain 1 pound per week. Your friend's puppy, Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week. After how many weeks will the puppies weigh
Two puppy's Max and Ruby will have equal weight after 6 weeks
What is an arithmetic sequence?In the arithmetic sequence the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
Given that,
Two puppy's
Max, currently weighs 5 pounds and is expected to gain 1 pound per week,
Ruby, currently weighs 8 pounds and is expected to gain 0.5 pounds per week
The number of weeks when both will have equal weight = ?
Suppose, it number of weeks = n
It can be solved by using concept of arithmetic sequence,
a₁ = 5 pounds
d₁ = 1 pound per week
Tₙ = 5 + 1xn = 5 + n
a₂ = 8 pounds
d₂ = 0.5 pounds per week
Tₙ = 8 + 0.5xn = 8 + 0.5n
Both should be equal,
5 + n = 8 + 0.5n
0.5n = 8 - 5
n = 6
Hence, after 6 weeks they will have same weight
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which of the following is true regarding trendlines in a scatter chart in excel? group of answer choices excel can add only linear trendlines to data in a scatter chart. excel can output the r square value for a trendline in excel for scatter charts of 3 or more variables. for simple linear regression models, the trendline in excel will give a different equation than the data analysis toolpak regression tool. none of these are true.
Out of the following, the statement Excel can add only linear trendlines to data in a scatter chart is true regarding trendlines in scatter chart in excel.This means that the trendline in Excel will be a straight line that will best fit the data points in the scatter chart.
It will not be able to fit any other type of trendline, such as a polynomial or exponential trendline. Additionally, Excel cannot output the R Square value for a trendline in Excel for scatter charts of 3 or more variables. This is because the R Square value is a statistical measure that can only be calculated for linear regression models.
Finally, for simple linear regression models, the trendline in Excel will give the same equation as the data analysis toolpak regression tool. This means that the equation of the trendline in Excel will be the same as the equation of the regression line calculated by the data analysis.
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WILL MARK BRAINLIEST!
A) On a school trip the ratio of adults to students is 1: 10.
All of the students are in year 10 or year 11.
The ratio of year 10 to year 11 is 1: 4.
What fraction of all the people on the trip are year 11 students?
(b)
In a cinema the ratio of adults to children is 2: 3.
The children are either boys or girls.
The ratio of boys to girls is 5: 2.
What fraction of all the people in the cinema are girls?
Answer:
A) 2/5
B) 4/15
Step-by-step explanation:
A)
adults : students
1 : 10
year 10 : year 11
1 : 4
fraction of all the people on the trip are year 11 students =
4 : 10
4 / 10
2 / 5
B)
adults : children
2 : 3 _____________(1)
boys : girls
5 : 2 _____________(2)
multiplying ratio (1) with 5
adults : children
10 : 15
multiplying ratio (2) with 2
boys : girls
10 : 4
fraction of all the people in the cinema are girls
4 : 15
4 / 15
The ages of the people at two tables in a restaurant are shown in the chart. Which statement about the ranges of the data sets is true?
Answer:
Where is the data ?
Step-by-step explanation:
Need the data set
HELP pls will mark you the brainliest. Please show your work too.
An ordered pair which is a solution of the linear system of equations include the following: A. (-3, -1/2)
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 1/2 x + 1 ......equation 1.
y = 3x/2 + 4 ......equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant III and it is given by the ordered pair (-3, -1/2).
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Acellus Geometry Question in Picture. Helpppp BRAINLIEST FOR CORRECT ANSWER
Rotation clockwise about the origin 90 degrees , then reflect over the x axis
What is transformation?A transformation is a mapping or a function that changes the position, size, or shape of an object or image. In mathematics, transformations can refer to a variety of operations such as
translation, rotation, reflection, dilationThe transformation involved in the image is 90 degrees counterclockwise rotation and reflection over the x axis.
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A cylinder has a height of 9 yards and a diameter of 34 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the cylinder is given by the equation V = 8,167.14 yards³
What is a Cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is
Volume of Cylinder = πr²h
Surface area of cylinder = 2πr ( r + h )
where r is the radius of the cylinder
h is the height of the cylinder
Given data ,
Let the volume of the cylinder be represented as V
Now , the equation will be
The height of the cylinder h = 9 yards
The diameter of the cylinder d = 34 yards
So , the radius of the cylinder r = d/2 = 17 yards
And , Volume of Cylinder = πr²h
Substituting the values in the equation , we get
Volume of Cylinder = ( 3.14 ) x ( 17 )² x 9
On simplifying the equation , we get
Volume of Cylinder = ( 3.14 ) x 2,601
Volume of Cylinder = 8,167.14 yards³
Hence , the volume of cylinder is 8,167.14 yards³
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if the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?
The new length and width of the living room would be 20% greater than the original length and width.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used.
A percentage is a number with no dimensions; it has no unit of measurement.
To increase the length and width of a room by 20%,
We need to add 20% of the original length and width to the original values.
If the original length and width of the living room are L and W respectively, the new dimensions would be:
New length = L + 0.20 * L = 1.20 * L
New width = W + 0.20 * W = 1.20 * W
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Question
How should this model be completed to represent 1,881 ÷ 33?
Enter your answers in the boxes.
The completed entries is added as an attachment
How to determine the entries in the boxFrom the question, we have the following parameters that can be used in our computation:
1,881 ÷ 33
Express 1881 as 1650 + 231
So, we have the following representation
1,881 ÷ 33 = (1650 + 231) ÷ 33
Expand the expression
So, we have the following representation
1,881 ÷ 33 = 1650 ÷ 33 + 231 ÷ 33
Evaluate the quotients
1,881 ÷ 33 = 50 + 7
Next, we complete the blanks (see attachment) for the completed entries
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BRAINLIEST MARKED FOR EXPLANATION - HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Figure 1 is vertical, through the cone's topmost point
Figure 2 is horizontal
Figure 3 is diagonal
Explanation:
The easiest way to think about this is that you have a cone-shaped cake and you are cutting it.