The Central Limit Theorem. During each day, the probability that your computer's operating system crashes at least once is 5%, independent of every other day. You are interested in the probability of at least 45 crash-free days out of the next 50 days. (a) Find the probability of interest using the normal approximation. (b) Find the probability of interest using the Poisson approximation. (c) Calculate the exact probability of at least 45 crash-free days. Compare the normal approximation and the Poisson approximation. Which one is more accurate? Can you explain why?
Answers
To find the probability using the normal approximation, we can consider the number of crash-free days as a binomial distribution with parameters n = 50 (number of trials) and p = 0.95 (probability of a crash-free day).
The mean of the binomial distribution is μ = np = 50 * 0.95 = 47.5, and the standard deviation is σ = √(np(1-p)) = √(50 * 0.95 * 0.05) ≈ 3.08.
We can approximate this binomial distribution with a normal distribution with mean μ and standard deviation σ. The probability of at least 45 crash-free days can be approximated by finding the cumulative probability up to 45. Using the normal distribution, we calculate:
P(X ≥ 45) ≈ P(Z ≥ (45 - μ) / σ)
where Z is a standard normal random variable. Substituting the values, we have:
P(X ≥ 45) ≈ P(Z ≥ (45 - 47.5) / 3.08)
Calculating this probability using a standard normal distribution table or a calculator, we can find the approximate probability.
(b) To find the probability using the Poisson approximation, we can use the Poisson distribution with parameter λ, where λ is the mean number of crash-free days. In this case, λ = 47.5. We want to find the probability of at least 45 crash-free days, which can be calculated as:
P(X ≥ 45) = 1 - P(X ≤ 44)
Using the Poisson distribution, we can calculate this probability directly.
(c) To calculate the exact probability of at least 45 crash-free days, we need to use the binomial distribution directly. We sum up the probabilities of having 45, 46, 47, 48, 49, or 50 crash-free days. This requires evaluating multiple terms in the binomial probability formula.
Comparing the normal approximation and the Poisson approximation, we can determine which one is more accurate by comparing the results to the exact probability. Generally, the Poisson approximation is better when the mean is small, and the normal approximation is better when the mean is large. In this case, with a mean of 47.5, both approximations should provide reasonable results. However, the exact probability calculation will give the most accurate result.
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Related Questions
3/4 - 1/8 how much is it? help me please
Answers
Answer:5/8
Step-by-step explanation:
\(\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}\)
Therefore, the result of this subtraction of fractions is five eighths.
How to subtract unlike fractions:
Heterogeneous fractions are fractions that have different denominators.
To subtract heterogeneous fractions we follow these steps:
We find the common denominator, which is the least common multiple of the denominators. We divide the common denominator by the other denominator and multiply by the numerator.We will write the above results as numerators with the subtraction sign between them.We subtract the numerators.We simplify the result if possible.The Alpha.Complete the point-slope equation of the line through (-8,-8) and (-7,9).
Use exact numbers.
Answers
Step-by-step explanation:
m=Y2-Y1/X2-X1
m=9--8/-7--8= 16/15
y-b=m(x-a)
y--8=16/15(x--8)
y+8=16/15(x+8)
15y+120=16(x+8)
15y+120=16x+128
15y=16x+8
y=16/15x+8/15
can cut paper animals with scissors, something she couldn't accomplish at age 3. how did her dexterity improve?
Answers
Her dexterity improved due to Increased myelination of the central nervous system.
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if f(x) = 10x, what is the equation for generating x, given the random number r?
Answers
The equation for generating x, given the random number r, can be found by rearranging the equation f(x) = 10x to solve for x. The equation would be x = f⁻¹(r/10), where f⁻¹ is the inverse function of f.
In this case, the inverse function of f(x) = 10x is f⁻¹(x) = x/10. Therefore, to generate x from a random number r, we can use the equation x = r/10. This is because when a random number between 0 and 1 is multiplied by 10, it gives a number between 0 and 10, which is the range of x in this case. So, dividing the random number r by 10 will give a value for x in the same range as the original function f(x). This equation can be used in various simulations and mathematical models where a random value for x is needed.
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13. Julio is evaluating the expression below.
6+2(9-4) -3 x5
Which operation should be performed first
according to the order of operations?
a. Add 6 and 2.
b. Multiply 2 by 9.
c. Subtract 4 from 9. d. Multiply 3 by 5.
Answers
The operation that should be performed first, in Julio's expression 6+2(9-4) -3 x5, according to the order of operations, is c. Subtract 4 from 9.
What is the order of operations?The order of mathematical operations is known as PEMDAS.
PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
Julio's expression = 6+2(9-4) -3 x5
The first operation is to tackle what is in parenthesis, (9 -4).
Thus, the correct option for evaluating Julio's expression is Option C.
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If the simple interest on 5,000 for 2 years is $500, then what is the interest rate?
Answers
Answer:
5%
Step-by-step explanation:
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given:
I = $500P = $5,000t = 2 yearsSubstitute the given values into the simple interest formula and solve for r:
\(\implies 500=5000 \cdot r \cdot 2\)
\(\implies 500=10000r\)
\(\implies r=\dfrac{500}{10000}\)
\(\implies r=0.05\)
\(\implies r=5\%\)
Therefore, the interest rate is 5%.
Answer:
Interest rate = 5% (or) 0.05
Step-by-step explanation:
Now we have to,
→ find the required interest rate.
Formula we use,
→ I = P × R × T
→ PRT = I
→ R = I/PT
Then the interest rate will be,
→ R = I/PT
→ R = $500 ÷ ($5000 × 2 years)
→ R = 500/(5000 × 2)
→ R = 500/10000
→ R = 0.05 × (100)
→ [ R = 5% ]
Hence, the interest rate is 5%.
which one best matches the graph?
A)y=x+6
B)y=-x+6
C)y=6x+6
D)y=-6x-6
Answers
The answer is C because 6x and 6 are both in the line
What equation, in point-slope form, matches the graphed line shown?
Question 3 options:
y−5=−23(x+9)
y−6=45(x−2)
y−2=−34(x−6)
y+6=45(x+3)
Answers
Answer:
Here’s the graph
Step-by-step explanation:
The equation of the line in point-slope form that matches the graph passing through the points (6, 2) and (10, -1) is:
y = (-3/4)x + 13/2
The correct answer is: Option C: y - 2 = -3/4(x - 6).
Here, we have to find the equation of the line in point-slope form that matches the graph passing through the points (6, 2) and (10, -1), we first need to find the slope (m) of the line using the formula:
\(m = (y_2 - y_1) / (x_2 - x_1)\)
where \((x_1, y_1) = (6, 2) ; (x_2, y_2) = (10, -1)\).
m = (-1 - 2) / (10 - 6)
m = (-3) / 4
Now that we have the slope (m), we can use the point-slope form of the equation of a line:
\(y - y_1 = m(x - x_1)\)
Using the point (6, 2):
y - 2 = (-3/4)(x - 6)
Now, simplify the equation:
y - 2 = (-3/4)x + 9/2
Finally, move -2 to the other side to get the equation in the point-slope form (y = mx + b):
y = (-3/4)x + 9/2 + 2
y = (-3/4)x + 9/2 + 4/2
y = (-3/4)x + 13/2
So, the equation of the line in point-slope form that matches the graph passing through the points (6, 2) and (10, -1) is:
y = (-3/4)x + 13/2
The correct answer is: Option C: y - 2 = -3/4(x - 6).
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complete question:
missing graph is attached:
Use the following box plot on TV Time per night (in minutes) to answer the
following question:
0 15
60
110
225
Use the outlier rule to determine if the 225 minutes of TV watching time is
an outlier.
O Yes, because 225 minutes is greater than 205 minutes.
O No, because 225 is not greater than 252.5 minutes.
O Yes, because it is more than twice as much time as the 110 minutes.
O Yes, because it is more than 95 minutes away from the upper quartile.
Answers
Yes, because 225 minutes is greater than 205 minutes.
what is outlier rule?Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset. Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly. Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling. Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.In this question answer is
Yes, because 225 minutes is greater than 205 minutes.
This can be determined by using the outlier rule
which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.
The IQR is calculated as Q3 - Q1,
which in this case is
110 - 15 = 95. Therefore,
1.5 times the IQR is 95 x 1.5 = 142.5.
The upper quartile (Q3) is 110,
so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.
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Yes, because 225 minutes is greater than 205 minutes.
what is outlier rule?Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset.
Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly.
Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling.
Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.
In this question answer is
Yes, because 225 minutes is greater than 205 minutes.
This can be determined by using the outlier rule
which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.
The IQR is calculated as Q3 - Q1,
which in this case is
110 - 15 = 95. Therefore,
1.5 times the IQR is 95 x 1.5 = 142.5.
The upper quartile (Q3) is 110,
so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.
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There are 30 drips in 1 minute and have already found out how many drips are in 1 day. I found out the answers for how many gallons the drips are and how many cups, but I need to show my work in order to get the points but don't know how to. Please help me figure out a way to show my work, I am new to this new math subject.
Answers
I estimate that the amount of water wasted by the leaky faucet over the course of 1 day is closer to 1 gallon.
What is a leaky faucet?
Leaky faucets are a common issue that can cause significant water waste. A faucet is said to be leaking when it is dripping from the spout when it is not in use. This is usually caused by a worn-out washer, O-ring, or packing nut. Leaky faucets can also be caused by high water pressure or a defective valve seat. A leaky faucet can be a nuisance and an unnecessary expense as it wastes a significant amount of water over time.
With the provided conversion ratios, it can be seen that 15,140 drips is equal to 1 gallon. Since the faucet is leaking 30 drips per minute, it would take 15,140/30 = 505 minutes for 1 gallon of water to be wasted.
Hence, there are 1440 minutes in 1 day, 505 minutes is equal to
(505/1440) x 100 = 35.2% of 1 day. Therefore, it is closer to 1 gallon.
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There has been a person on here posting the same link to many answers, can you please delete their account? Thanks.
Answers
Yeah... they should.
Identify the correct property of equality to solve each equation.
3 + x = 27
addition property of equality with 3
subtraction property of equality with 3
multiplication property of equality with 3
division property of equality with 3
Answers
Answer:
24
Step-by-step explanation:
because it's just a addition so my answer must be right and it's not wrong I swear to God
Answer:
3 + x = 27
✔ subtraction property of equality with 3
x over 6 = 5
✔ multiplication property of equality with 6
I need to learn for the 6th grade georgia milestone
Answers
Answer:
math
In your math class right now what type of stuff are you learning? Geometry, algebra, or what?
I'm not in class right now I needed to study for my final exam
Yea but i need to know the type of stuff you’ve been focusing on. It’s been years since I’ve taken a 6th grade class
well mostly division
But even though everyone hates it IXL is a good place to study once you find ones that have the things you’re not that great at. And Kahn academy has helped me a lot
ok I will try it thank you
Also for the majority of the Georgia milestone that involve division you are allowed to have a calculator just so you don’t get that stressed over it
ok thank you
Step-by-step explanation:
2 questions to answer. Solve each of the following inequalities, 1. \(\frac{10q+9}{2}\) ≤ \frac{3}{8}\) 2. \(\frac{5(-5s-1)}{6}\) > - \(\frac{9}{5}\) ( negative 9 over 5) representing each solution on a number line.
Answers
Answer:
To solve the inequality ≤ \frac{3}{8}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x ≤ \frac{3}{8}
To graph the solution on a number line, we can use an open circle at \frac{3}{8} to indicate that the value is not included in the solution. So the solution set is: (-∞,3/8)
To solve the inequality > -\frac{9}{5}, we need to find all the values of x that will make the inequality true. We can start by setting the inequality equal to zero and solving for x.
x > -\frac{9}{5}
To graph the solution on a number line, we can use an open circle at -\frac{9}{5} to indicate that the value is not included in the solution. So the solution set is: (-9/5, ∞)
Step-by-step explanation:
The function f(x) = –x2 – 4x + 5 is shown on the graph.
On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0).
Which statement about the function is true?
The domain of the function is all real numbers less than or equal to −2.
The domain of the function is all real numbers less than or equal to 9.
The range of the function is all real numbers less than or equal to −2.
The range of the function is all real numbers less than or equal to 9.
Answers
Answer:
the last one : the range of the function is all real numbers less than our equal to 9.
Step-by-step explanation:
it is a parabola that opens up only down. that means all the calculated y-values go deeper and deeper into lower and negative values the more right or left we go on the x-axis.
the maximum y-value we have at the vertex with y=9. no other x-value can generate a bigger y-value.
that's why the last answer option is right.
Which value of x makes the equation 0.1x - 2.5 = 1.0 true
A 10
B 15
C 20
D 35
Answers
Answer:
D 35
Step-by-step explanation:
When figuring this out you can just plug in your answers if you want to take it the easier way by just putting in the 35 in places of x and multiplying 0.1 times 35 gets you 3.5 so 3.5 minus 2.5 is 1
Answer:
xDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD.........................................................D :D
distributive law
4 ( 32+9x)
9x (2+8x)
12(x-y)
2(21x)
Answers
Find the area of the parallelogram.
a. 70cm
b. 80 cm
c. 224 cm
d. 60 cm
Answers
Answer:
c. 80 cm
Step-by-step explanation:
Area of a parallelogram = base × height
A = 16 cm × 5 cm
A = 80 cm
Answer:
b. 80 cmStep-by-step explanation:
\(Base =16\\Height =5\\Area = Base\times Height\\= 16 \times 5\\= 80cm\)
Please help
A ferry that carries passengers and vehicles across a channel charges a base rate of $30 per vehicle. The first two passengers are included in this price, but each additional passenger is charged $5. Additionally, the ferry charges more for vehicles over 4,000 pounds. The rate for excess weight is $10 per 500 pounds.
-Write an equation for this situation.
-Find the cost of a truck that weighs 5,000 pounds with three passengers.
Answers
The cost of the truck with 3 passengers is A = $ 45
Given data ,
Let's denote the number of passengers as P and the weight of the truck in pounds as W.
For the base rate of $30 per vehicle, the equation can be written as:
Cost = $30
For additional passengers beyond the first two, the equation can be written as:
Cost += ($5) * (P - 2)
For excess weight over 4,000 pounds, the equation can be written as:
Cost += ($10) * (W - 4000) / 500
To find the cost of a truck that weighs 5,000 pounds with three passengers, we substitute the values into the equation:
Cost = $30 + ($5) * (3 - 2) + ($10) * (5000 - 4000) / 500
Simplifying the equation:
Cost = $30 + $5 + $10
Cost = $45
Hence , the cost of a truck that weighs 5,000 pounds with three passengers would be $45
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Solve for n.
(72)4 = n8
n =
The 2 4 and 8 are squared
Answers
Step-by-step explanation:
(72)4=n8
72×4=n8
288=n8
n=288÷8
n=36
please help me with this question
In engineering, equilateral triangles can support the most weight and so are commonly found in the design of bridges and buildings. Equilateral triangles are triangles with three congruent sides and three congruent angles. What are the measures of the angles of an equilateral triangle?
Answers
Answer:
Hey mate....
Step-by-step explanation:
This is your answer....
Yes, because a equilateral triangle has 3 equal angles. The 3 angles of a triangle equal 180°. So if the angles are all equal in an equilateral triangle, we do 60 times 3 which equals 180°.
hope it helps you,
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A shipping container is in the shape of a right rectangular prism with a length of 7.5
feet, a width of 1.5 feet, and a height of 6.5 feet. The container is completely filled
with contents that weigh, on average, 0.34 pound per cubic foot. What is the weight
of the contents in the container, to the nearest pound?
Answers
Answer:
3
Step-by-step explanation:
because two plus two
20 points! Which graph represents two functions that are decreasing on all points across the domain that is common to both functions?
Answers
D(x) is decreasing
Answer:
Its C or D, I would say C tho
Step-by-step explanation:
I took the test and both A and B are wrong
converting measures 48ft= yd
Answers
Answer:
48 Feet (ft) 16.000 Yards (yd)
1 ft = 0.333333 yd 1 yd = 3.000000 ft
Step-by-step explanation:
A cylindrical soup can has a radius of 1.8 in. and is 6.7 in. tall. Find the volume of the can.
Answers
Volume = base area x tall
base area = π x (1.8in)²
base area = 10.179 in²
Volume = 10.179 in² x 6.7 in
Volume = 68.198 in³
Answerthe volume is 68.198 in³
se Euler's formula to show that the product ofstudent submitted image, transcription available belowcan be used to derive the trigonometric identities
student submitted image, transcription available below
student submitted image, transcription available below
Answers
Euler's formula can be used to derive the trigonometric identities.
How does Euler's formula relate to the derivation of trigonometric identities?Euler's formula states that for any real number x, the complex exponential function can be represented as follows:
\(\[e^{ix} = \cos(x) + i\sin(x)\]\)
where \(e\) is the base of the natural logarithm, \(i\) is the imaginary unit, \(\cos(x)\) represents the cosine function, and \(\sin(x)\) represents the sine function. This formula provides a powerful connection between exponential functions and trigonometric functions.
To derive trigonometric identities using Euler's formula, we can start with the exponential form of Euler's formula and manipulate it algebraically. Let's consider the complex exponential function for two angles, \(x\) and \(y\):
\(\[e^{ix} \cdot e^{iy}\]\)
Using the properties of exponents, we can simplify this expression:
\(\[e^{ix} \cdot e^{iy} = e^{i(x + y)}\]\)
Now, applying Euler's formula to both sides, we get:
\(\[\cos(x) + i\sin(x) \cdot \cos(y) + i\sin(y) = \cos(x + y) + i\sin(x + y)\]\)
By comparing the real and imaginary parts of this equation, we obtain the sum and product formulas for cosine and sine:
\(\[\cos(x) \cdot \cos(y) - \sin(x) \cdot \sin(y) = \cos(x + y)\]\[\sin(x) \cdot \cos(y) + \cos(x) \cdot \sin(y) = \sin(x + y)\]\)
These are known as the angle addition formulas, and they form the basis for deriving other trigonometric identities. By manipulating and applying these formulas, we can establish relationships such as double-angle formulas, half-angle formulas, and more.
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Great make greatest 5 digit number 4 2 and 0
Answers
To create the greatest 5-digit number using the digits 4, 2, and 0, we need to place the highest value digit in the leftmost position. Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
By arranging the digits in this order, you ensure that you have the largest possible value while still using only the given digits 4, 2, and 0. In this case, the digit 4 is the highest value digit. So we place it in the ten-thousands place. This gives us 40,000. Now we need to fill in the remaining four digits. Since we want to create the greatest possible number, we need to use the next highest digit, which is 2, in the thousands place. This gives us 42,000. We can then use the remaining digit, which is 0, in the hundreds, tens, and ones places. to create the greatest 5-digit number, we need to start with the highest value digit and place it in the leftmost position. Then, we fill in the remaining digits with the next highest value digits in descending order. This ensures that we create the greatest possible number.
The greatest 5-digit number using the digits 4, 2, and 0, you can repeat the digits as needed. Place the largest digit (4) in the leftmost position to maximize the value, and then fill in the remaining positions with the next largest digit (2), followed by the smallest digit (0).
Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
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-4x - 5 > 19 algebra answer
Answers
Answer:
x < -6
Step-by-step explanation:
-4x - 5 > 19
+5 +5
-------------------
-4x > 24
/-4 /-4
-------------------
x < -6
Answer:
x < -6 is x's value
The nth term of a sequence is 12n -5. Work out the numbers in the sequence that have two digits and are not prime. Your final line must say Not Prime and list only the numbers that are not prime
Answers
Answer:
55 and 91 are not prime.
Step-by-step explanation:
\(12(1) -5=7\\12(2) -5=19\\12(3) -5=31\\ 12(4) -5=43\\12(5) -5=55\\12(6) -5=67\\12(7) -5=79\\12(8) -5=91\\12(9) -5=103\)
The two digits numbers in the sequence that are not prime: 55 and 91
What is sequence?"It is a list of numbers in particular order."
What is a prime number?"A natural number that are divisible by only 1 and the number itself."
For given example,
The nth term of a sequence is 12n -5.
The numbers in the sequence that have two digits and are not prime.
The two digit numbers have range: [10, 99]
Assuming n be a positive natural number,
⇒ 10 ≤ 12n - 5 ≤ 99
⇒ 10 + 5 ≤ 12n - 5 + 5 ≤ 99 + 5
⇒ 15 ≤ 12n ≤ 104
⇒ 15/12 ≤ 12n/12 ≤ 104/12
⇒ 1.25 ≤ n ≤ 8.67
This means, 'n' can take values 2, 3, 4, 5, 6, 7, and 8
For n = 2,
12n -5
= 12(2) - 5
= 19 which is a prime number.
For n = 3,
12n -5
= 12(3) - 5
= 31 which is a prime number.
For n = 4,
⇒ 12n -5
= 12(4) - 5
= 43 which is a prime number.
For n = 5,
⇒ 12n -5
= 12(5) - 5
= 55 which is not prime.
For n = 6,
⇒ 12n -5
= 12(6) - 5
= 67 which is a prime number.
For n = 7,
⇒ 12n -5
= 12(7) - 5
= 79 which is a prime number.
For n = 8,
⇒ 12n -5
= 12(8) - 5
= 91 which is not prime.
From above, the two digits numbers in the sequence that are not prime: 55 and 91
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Is the relation below a function?
x
-2 -1
0
1
2
у
4
1
0
1
4
No, it is not a fonction
Yes, it is a function
Answers
Answer:
not a function
Step-by-step explanation:
the ratios of y/x are not equal