When testing the differences between means, the research hypothesis suggests that population means are not equal. (Option B)
Hypothesis refers to a concept or explanation for a trend that is based on known facts but has not yet been proved. A research hypothesis, also known as scientific hypothesis, is a statement about the expected result of a study. It is the proposed answer to the research question and generally includes an explanation (e.g., x affect y because …). It introduces a research question and proposes an expected result. It illustrates the relationship between two variables - an independent and dependent variable. Hence, when testing the difference between means, the hypothesis that suggests that population means are not equal is a research hypothesis.
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Mercury orbits the Sun 3 times in 264 days.
a. How many times does Mercury orbit the Sun in 440 days?
Mercury orbits the Sun__________ times in 440 days.
Question 2
b. How many days does it take Mercury to orbit the Sun 8 times?
It takes Mercury_________ days to orbit the Sun 8 times.
Answer:
a. 15 days
b. 704 days
Step-by-step explanation:
a.264+88+88=440
b.It takes mercury 264 days to orbit the sun 3 times which means all you have to do is
264+264=528+264=792-88=704
3 + 3 = 6 + 3 = 9- 1 = 8
Which criteria for triangle congruence allows you to immediately conclude that the triangles.
We may determine that the triangles are congruent based on the (B) HL criterion right away.
What are HL criteria?According to the HL Postulate, a right triangle's hypotenuse and leg are congruent if they are also congruent with the hypotenuse and leg of another right triangle.
So, we can see from the accompanying figure that these two triangles share a center line that is parallel to the base.
The two triangles are therefore right-angled triangles.
The hypotenuse of two triangles being congruent is then mentioned as a further argument.
Triangle congruence according to the HL criterion allows for a quick determination of congruence.
Therefore, we may determine that the triangles are congruent based on the (B) HL criterion right away.
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Complete question:
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?
A) SAS
B) HL
C) AAS
D) none
Find the value of so that the graph of the equation has the given y-intercept
Y= -1/3x + 5/6k; b= -10
The value of 'k' will be;
⇒ k = - 12
What is Equation of line?
The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph of the equation has the given y-intercept are;
⇒ Y= -1/3x + 5/6k; b= -10
Now,
Since, The equation of line in point-slope form will be;
⇒ y = mx + b
Here, The equation is,
⇒ Y= -1/3x + 5/6k
Hence, The y - intercept (b) = 5/6k
But here, b = - 10
So, We get;
⇒ 5/6 k = - 10
Solve for k as;
⇒ 5k = - 10 × 6
⇒ 5k = - 60
⇒ k = - 12
Thus, The value of 'k' will be;
⇒ k = - 12
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1. Claude can do 120 jumping jacks in 2 minutes.
Write an equation to represent how many jumping
jacks Claude can complete in 5 minutes.
A drummer and a guitarist each wrote songs for their band. The guitarist wrote 10 fewer than twice the number of songs that the drummer wrote. They wrote a total of 50 songs. Write the system of equations that models this situation if the drummer wrote d songs and the guitarist wrote g songs.
Answer:
Step-by-step explanation:
no
Please help asap now !!!!!
Answer:
220.25
Step-by-step explanation:
881 divided by 4 is 220.25
two polygons are similar, and the ratio s1/s2? of their corresponding sides is 8/7. find the ratio of their areas, a1/a2.
Two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.
In the given question, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7.
We have to find the ratio of their areas, a1/a2.
As we know that, the measurement of the area that a polygon encloses serves as its definition. The area of a polygon is the space that it takes up in a two-dimensional plane since polygons are closed plane structures.
As given that, two polygons are similar.
The ratio of their corresponding sides are
s1/s2 = 8/7
According to properties of similar polygon, the ratio of the areas of the two polygons is the square of the ratio of the sides. Hence,
a1/a2 = (s1/s2)^2
a1/a2 = (8/7)^2
a1/a2 = 64/49
Hence, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.
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to sample the class you split the class into guys and girls. you then select at random 3 guys and 3 girls. what type of sampling did you do?
The type of sampling used to sample the class split into girls and boys is stratified sampling.
As given in the question,
Sample the class to split into guys and girls
Select at random 3 guys and 3 girls.
Types of sampling :
A simple random : Chances of selection is equally likely. Randomly choose the data.
False
B systematic: Samples are collected from large data so that it can systematically arranged.
False
C convenience : In this sample or data collection is done as per convenience.
False
D cluster : It divides the group into multiple group or clusters.
False
E stratified : This represents the division of heterogeneous group into fairly homogeneous group in form of strata.
True.
Therefore, the stratified sampling represents the splitting of class into guys and girls.
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What is the equation of this line in slope intercept form?
−x −5y=10
A y=−1/5x+10y
B y=5x−2y
C y=−1/5x−2y
D y=1/5x+10
C
Step-by-step explanation:
add x on both sides
-5y=10+x
divide both sides by -5
y=-1/5x-2
Determine whether or not each of the following have the well-ordering property (i.e. whether "WOP(A;)" holds/is true or if is fails/is false). If for a set Ai, WOP(Ai) fails, then give a nonempty subset Eị of the set Aj which has no least element, i.e. give a subset that serves as a counterexample to "WOP(A;)", in other words give a witness that shows that the well- ordering property fails. 1 (iv) A4 = {5i +į lien} = {} \}} (v) A5 ne Z\ {0} n (vi) A6 = {-5, 7, 10, 13}
(iv) set A₄ holds well ordering property.
(v) set A₅ does not hold well ordering property.
(vi) set A₆ holds well ordering property.
(iv) A₄ = {5i+1/i I i ∈ N}
= { 5(1) + 1/1, 2(2)+1/2, 5(3)+1/3, 5(4)+1/4, .....}
= {5+1, 10+1/2, 15+1/3, 20+1/4, ....}
Elements of the set A₄ are distinct and increasing and 6 is the least elements of A₄.
set A₄ holds well ordering property.
(v) A₅ = { 1/n I n ∈ ZI }
= {1,1/2,1/3,1/4,1/5,....}
A₅ does not hold well ordering property.
(vi) A₆ = {-5,7,10,13}
A₆ is the finite set and all elements are distinct .
For any sub sets of A₆ there exists a dense elements.
A₆ holds well deseriving property.
Hence we get the required answer.
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tasmanian automobile licence plates consist of three capital letters (a through z) followed by three digits (0 through 9). how many different tasmanian license plates are possible?
tasmanian license plates are 8,000,000 combinations possible
In probability, what do combination and permutation mean?
Combinations and permutations may appear to be synonyms. However, they are defined differently in probability theory. Combinations: The sequence of results is irrelevant. Permutations: The sequence of events matters.
If an event is made up of numerous other events (i.e., when it is a list), we may calculate the probability that it will occur with the help of permutations and combinations. If the sequence of the events doesn't matter, we have a combination; if it does, we have a permutation. A permutation can be defined as an ordered combination.
An ordered combination is what is meant by a permutation.
The number of permutations of n objects, taken r at a time, is calculated using the formula below:
P(n,r)=n!(n-r)!
The following formula calculates the number of combinations of n objects taken r at a time: C(n,r)=n!/(n-r)!r!
there are 26^3 combinations of letters. And 10^3 combinations of numbers.
So the total combinations is 26^3 x 10^3 = 17,576,000
Many license plates don’t allow vowels a,e,i,o,u,and y which would accidentally form some awkward words…
Then you’d have 20^3 x 10^3 = 8,000,000 combinations.
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The annual cost C (in thousands of dollars) and revenue R (in thousands of dollars) for a company each
year from 2010 through 2016 can be approximated by the models = 254 − 9 + 1. 12 and = 341 +
3. 2 where t is the year.
Write a function P that represents the annual profit of the company.
(Profit = Revenue − Cost)
A function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
Describe the term Function?Function: A relationship between two variables, one of which is dependent on the other and the other of which is independent, is represented by an expression.The overall cost incurred by a business (or organization) for one employee over the course of a year is known as the annual cost.We provided Cost C. ( in thousand of dollar)
And a company's revenue R (in thousands of dollars).
C is the cost function.
C = 254 - 9t + (1.1)t²Revenue function R = 341 - 3.2t where t time in year .The value t = 9 is 9 years.
If P is the Annual profit. Then,
Profit = Revenue − Cost
P = R - C
P = 341 - (3.2)t - 254 - 9t + (1.1)t²
= (1.1)t² - (12.2)t + 87
Thus, a function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .
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Complete Question:
The annual cost C in thousands of dollars and revenue R in thousands of dollars for a company each year from 2010 through 2016 can be approximated by the models C = 254 − 9t + 1.1t2 and R = 341 + 3.2t where t is the year, with t = 10 corresponding to 2010.
(a) Write a function P that represents the annual profit of the company.
The parking garage at the airport has 625 parking spaces. 92% of the spaces are empty. How
many empty spaces are there in the parking garage?
Answer:
575 empty spaces
Step-by-step explanation:
If 625 --> 100% then
X --> 92%
X= (625 * 92)/100
X= 575
Please answer! Another math prob!
Gavin worked 7 hours tutoring and 3 hours landscaping.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Gavin is working for making $14 per hour tutoring and $13 per hour landscaping.
And, Last week Gavin worked a total 10 hours and earned $137.
Now,
Let number of hour for tutoring = x
And, Number of hour for landscaping = y
Since, Gavin is working for making $14 per hour tutoring and $13 per hour landscaping and earned $137.
So, We can formulate;
⇒ 14x + 13y = 137 ..(i)
And, Last week Gavin worked a total 10 hours.
So, We get;
⇒ x + y = 10 ..(ii)
Multiply by 13 in equation (ii) and subtract from (i0, we get;
⇒ 14x + 13y - 13x - 13y = 137 - 130
⇒ x = 7
And, x + y = 10
⇒ 7 + y = 10
⇒ y = 10 - 7
⇒ y = 3
Thus, Gavin worked 7 hours tutoring and 3 hours landscaping.
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let $s$ be the set of the 2005 smallest positive multiples of 4, and let $t$ be the set of the 2005 smallest positive multiples of 6. how many elements are common to $s$ and $t$? (a) 166 (b) 333 (c) 500 (d) 668 (e) 1001
The number of elements that are common to S and T are 668 elements ,
the correct option is (d) .
In the question ,
it is given that ,
the set S is the set of 2005 positive multiple of 4
that is S = {4,8,12,16,....}
and the set T is the set of 2005 positive multiple of 6
that is T = {6,12,18,24,....}
and since the least common multiple , LCM of 4 and 6 is = 12,
So , elements that are common to set S and T must be multiples of 12.
Since, 4 × 2005 = 8020 and 6 × 2005 = 12030,
the several multiples of 12 that are in set T won't be in set S,
but all multiples of 12 that are in set S will be in set T.
So we have to find the number of multiples of 12 that are in set S.
and since 4 × 3 = 12, that means every 3rd element of set S will be a multiple of 12.
which is = 2005/3 = 668 .
Therefore , there are 668 elements that are common .
The given question is incomplete , the complete question is
Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. how many elements are common to S and T ?
(a) 166 (b) 333 (c) 500 (d) 668 (e) 1001
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if sam has 100 apples and Jante steals 36 from sam how many does sam have left
Answer:
the answer to that is 65.
Step-by-step explanation:
maths
Point 8 in the graph below is reflected through the line y=-x.
Iy
++
-6-4-2
6-
2-
-2.
-6
B.
2 46. x
I
What are the coordinates of Point B', the image of Point B?
Answer:
[tex](-4,-5)[/tex]
Step-by-step explanation:
When reflecting over [tex]y=-x[/tex], [tex](x,y) \longrightarrow (-y, -x)[/tex].
explain how the is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers.
Nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
What is birth weight?
The body weight of a newborn is referred to as birth weight. Infants of European descent typically weigh between 2.5 and 4.5 kilogrammes at birth, with an average of 3.5 kilograms. South Asian and Chinese babies weigh about 3.26 kilogrammes on average.
Babies born to nonsmokers typically weighed between 1,000 and 5,000 grammes. Babies born to smokers often ranged in weight from 500 to 4500 grammes.
However, we also notice some significant variations between the two groups' normal ranges of birth weights. With fewer infants in the lower weight ranges, nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.
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there are 38 different time periods during which classes at a university can be scheduled. if there are 677 different classes, what is the minimum number of different rooms that will be needed?
The minimum number of different rooms that will be needed = 18
We know that the Pigeonhole Principle states that if N objects are placed into k boxes, then at least one box contains at least N/k objects.
In this question, we have been given there are 38 different time periods during which classes at a university can be scheduled.
if there are 677 different classes, we need to find the minimum number of different rooms that will be needed.
There exists a time period will have at least 677/38 = 18 classes during
it.
Therefore, 18 different rooms will be needed.
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length
Quantity
amount of substance
luminous intensity
US Customary Units
inch (in), foot (ft), yard (yd), mile (mi)
ounce (oz), pound (lb), ton (tn)
fluid ounce (fl oz), pint (pt), quart (qt),
gallon (gal)
second (sec), minute (min), hour (hr)
degrees Fahrenheit ("F)
SI Units
kilometer (km), meter (m), centimeter
(cm), millimeter (mm)
second (s)
Kelvin (K)
kilogram (kg), gram (g), milligram (mg)
ampere (A). milliampere (mA)
mole (mol)
candela (cd)
Answer:
Step-by-step explanation:
All units of a physical measure are linked via a conversion factor. On this web page for every unit you can find the conversion factor compared to the base unit (SI unit).
To do a conversion (or equivalent) you must multiply the value to be converted by the conversion factor of the start unit and then divide the result by the conversion factor of the destination unit.
For example, we want to know how many centimeters equals 12 yards?
# convert the units in meters (which is the SI base unit for the lengths)
# 1 yard = 0.9144 meters
# 1 centimeters = 0.01 meters
# derive the conversion factor between the yard and centimeters by dividing the factors found
# 0.9144/0.01 = 91.44
# 1 yd = 91.44 cm
# now we multiply the amount to be converted by the conversion factor found
# 12 * 91.44 = 1097.28
# result: 12 yd equals 1097.28 cm
Unit conversion tool implements this simple algorithm.
find the probability if two dice are rolled. (enter the value of probability in decimals. round the answer to three decimal places.)
The probability of getting a total of 8 when two dice are rolled is 0.139.
Probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be represented by proportions on a 0–1 scale.
A single die will have six sides with the numbers: 1, 2, 3, 4, 5, and 6. Each of these events is equally likely to occur if the dice are rolled fairly. So the probability of getting any side of the number is 1/6. Therefore, the probability of getting 1 in dice is 1/6, 2 is 1/6, and so on.
Therefore, the total possible outcomes are the multiplication of the total possible outcomes on dice 1 and dice 2, which is 36.
This possible outcome of rolling two dice is given by,
[tex]\left\{\begin{array}{ccccccc}(1, 1)&(1, 2)& (1, 3)&(1, 4)&(1, 5)&(1, 6)\\(2, 1)&(2, 2)&(2, 3)&(2, 4)&(2, 5)&(2, 6)\\(3, 1)&(3, 2)&(3, 3)&(3, 4)&(3, 5)&(3, 6)\\(4, 1)&(4, 2)&(4, 3)&(4, 4)&(4, 5)&(4, 6)\\(5, 1)&(5, 2)&(5, 3)&(5, 4)&(5, 5)&(5, 6)\\(6, 1)&(6, 2)&(6, 3)&(6, 4)&(6, 5)&(6, 6)\end{array}\right\}[/tex]
The probability of getting a total of 8 from both dice is given by, (2, 6) (3, 5) (4, 4) (5, 3) (6, 2). So the number of favorable outcomes is 5 and the total outcome is 36. The probability is P(getting a total of 8 from both dices)=5/36= 0.139.
The answer is 0.139.
The complete question is -
Consider rolling dice and getting a total of 8. Find the probability of two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places).
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Equivalent Ratios: Liam practiced piano 24 times in 4 weeks. His brother practiced 12 times in 2 weeks. Are the rates at which each brother practiced equivalent?
(1): Yes, they are equivalent.
(2): No, they are not equivalent.
Answer:
The rates are equivalent.
Step-by-step explanation:
Liam practiced piano 24 times in 4 weeks. 1 week = 7 days. 4 weeks = 28 days.
A company that makes hair-care products had 8000 people try a new shampoo. Of the 8000 people, 48 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
0.6% of the people had a mild allergic reaction
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A company that makes hair-care products had 8000 people try a new shampoo.
In the 8000 people, 48 had a mild allergic reaction.
We need to find the percent of the people had a mild allergic reaction
We have to find what is 48 percent in 8000.
x×8000=48
Divide both sides by 8000
x=48/8000
x=0.006
Now we need to multiply by 100 as it is a hundredth part.
0.006×100
0.6
Hence, 0.6% of the people had a mild allergic reaction
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using the following information. coefficients intercept −12.8094 independent variable 2.1794 anova df ss ms f regression 1 12,323.56 12,323.56 90.0481 residual 8 1,094.842 136.8553 total 9 13,418.4 what is the standard error of the estimate? multiple choice 136.8552 1,094.842 11.6985 13,418.4
The Standard error of the estimate is 11.6985
The standard error of estimate is the measure of variation of an observation made around around the regression line
Simply, It is used to check the accuracy of prediction made with the regression line. A standard deviation which measures the variation in the set of data from its mean, the standard error of estimate also measured the variation in actual values of Y from the computed values of Y on the regression line.
Given in the question,
coefficient of y-intercept = -12.8094
Coefficient of x = 2.1794
N-1 = 9
=> N = 10
SSE = 1094.842
Standard error of estimate = √SSE(N-2)
where , SSE is sum of square of error
S.E = √(1094.842)/ (10-2)
=> √(1094.842)/8
=> √136,855
=> 11.6985 is standard error
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What number is 150% of 90
Answer: 135
Step-by-step explanation:
Answer: 145
Step-by-step explanation:
100% of 90 is, welll 90, and 50% of 90 is 45, so 150% of 90 is 145
first, we form a riemann sum with n rectangles (or subintervals). (i) what is the width of each rectangle? (ii) list the right-hand endpoints of each rectangle. (iii) list the heights of each rectangle. (iv) list the areas of each rectangle. (v) what is the riemann sum with n rectangles? you may use summation notation, but you do not need to.
The Reimann sum with n rectangle will be given as [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]
Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].
The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:
“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up
(i ) The width of each rectangle will be denoted as Δx
Δx = b-a/n,
where , a is lower bound
b is upper bound of the integral
(ii) The right-hand endpoints of each rectangle are refer as [tex]x_i[/tex] and we can find the right endpoints by [tex]x_i[/tex] = a + Δx.i
(iii) The height of each rectangle is the value of the function at the upper point of the interval.
a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on
(iv) The area of the each rectangle will be
Area = Width × height
=> A = (b-a)/2 × a + i(b-a)/2
(v) The Riemann sum with n rectangles is
Area of rectangle = [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]
Which is also known as Reimann sum
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a researcher developing a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3). educational status is a dummy variable with 0
36% of the variability equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).
Given:
Correlation value: 0.6
The amount of variation in the dependent variable that can be predicted from the independent variable is shown by the coefficient of determination.
The correlation coefficient is equal to;
Since the correlation in this instance is equal to 0.6, our coefficient is 0.36. Therefore, the age of the home can account for 36% of the variation in equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).
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tion for y: 2x + 3y = -6. Then, answer the questions that follow.
formed equation, what is the slope of the linear equation 2x + 3y = -6?
to find solutions to the linear equation.
x
Lesson 17 Problem Se
Transformed Linear Equation:
y
Answer:
The slope is -2/3
Step-by-step explanation:
2x + 3y = -6
We want to find the slope, so we need to get the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept
Subtract 2x from each side
3y = -2x+6
Divide each side by 3
y = -2/3x +2
The slope is -2/3
two boats leave a dock at the same time. one boat travels south at and the other travels east at . after half an hour, how fast is the distance between the boats increasing?
After half an hour the two boats will be at a distance of 68 mph
Given,
Both boats are moving in a direction that creates a right angle triangle. The lengths of the triangle's legs are the distances that both boats travelled going straight south and straight east. The hypotenuse of a right angle triangle is the distance between them after t hours.
Let x stand for the length of the triangle's shorter south leg.
Let y stand for the length of the right angle triangle's longer (east) leg.
Assume that z is the hypotenuse.
Using the Pythagorean theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
We would discriminate with regard to t in order to ascertain the speed of the distances' alterations.
It develops,
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Therefore,
The distance between the boats after half an hour is 68 mph
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Completed question is given below with missing parts.
Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60 mi divided by hr60 mi/hr. After half an hour, how fast is the distance between the boats increasing?
ar chie and bijan share some money in the ratio 7 : 11. bijan gets £132. how much money does archie get?
Archie will get $84.
We have given that,
archie and bijjan share some money in the ratio 7:11 and bijjan get $132.
We have to find how much money will archie get.
Let us consider x as a money
i.e. 7x:11x
bijjan gets $132
means 11x = 132
x = [tex]\frac{132}{11}[/tex]
x = 12
Therefore archie's money,
7x=7(12) = 84
Hence archie get $84.
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. The concept of ratio defines us to compare two quantities while the proportion is an equation that shows that two ratios are equivalent.
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