A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.
In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent a function.By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:
g(x) = f(x - 5) - 7
g(x) = 1/(x - 5) - 7
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Kristen works for Lincoln Canning Company. She wants to make labels for several cans like the one shown below, only covering the lateral surface area. She is going to cut them from a sheet of plastic film that has an area of 2,265 square inches.
6 inches . 5 inches
What is the maximum number of labels she could make assuming there is minimal film wasted?
the x vector component of a displacement vector has a magnitude of 118 m and points along the negative x axis. the y vector component has a magnitude of 198 m and points along the negative y axis. find (a) the magnitude and (b) direction of . specify the direction as a positive angle with respect to the negative x axis.
The magnitude and direction of the displacement vector are 253.4 m and 60.3°, respectively.
The magnitude of a displacement vector can be calculated using the Pythagorean Theorem, where the magnitude is equal to the square root of the sum of the squares of the x and y components of the vector. In this case, the magnitude is equal to the square root of (118)2+(198)2=253.4 m.
To find the direction, we can use the trigonometric inverse tangent function. The angle must be measured counterclockwise from the negative x axis. We can calculate the angle θ using the equation θ=tan-1(y/x). In this case, θ=tan-1(198/118)=60.3°. Therefore, the magnitude and direction of the displacement vector are 253.4 m and 60.3°, respectively.
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Is 3X +6 equivalent to 3( X +2)
answer
the answer is yes they are equvalent
Answer:
Yes
Step-by-step explanation:
If you multiply 3 and x you get 3x
If you multiply 3 and 2 you get 6. Which means the answer is [tex]3x + 6\\[/tex]
3 · x = 3x
3 · 2 = 6
3x + 6
Need help urgent please
The correct statement regarding the difference of sample means is given as follows:
The difference of sample means is statistically significant if it falls outside the 5% significance level.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.Missing InforamtionThe problem is incomplete, hence the answer was given in general terms.
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The function of y=(x+4)^4 is a transformation of the graph of the parent function y=x^4. How is zero the parent function affected by the transformation?
We have a translation of 4 units to the left, then the new zero will be at (-4, 0)
How is zero the parent function affected by the transformation?Here we have the parent function:
y = x^4
With a zero at (0, 0).
Remember that for any function f(x), we define a horizontal translation of N units as:
g(x) = f(x + N)
If N > 0, the translation is to the left.
if N < 0, the translation is to the right.
So here:
y=(x+4)^4
We have a translation of 4 units to the left, then the new zero is at x = -4
y = (-4 + 4)^4 = 0
So the new zero is at (-4, 0)
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Round to 2 decimal places. 8 of the company’s trucks from their pool of 37 trucks needed brake maintenance. What percent of the truck pool needed brake maintenance?
The percent of the truck pool that needed brake maintenance is 21.62%.
What percent of the truck pool needed brake maintenance?Percentage can be described as a fraction of an amount that is expressed as a number out of hundred. The sign that represents percentage is %. In order to convert a number to percentage, multiply the number by 100.
Percent of trucks that need maintenance = (number of trucks that need maintenance / total number of trucks) x 100
= (8/37) x 100 = 21.62%
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from 1975 to 1986, the general social survey asked its participants if they favored or opposed capital punishment. a least squares regression line was calculated to predict the percent that favored the death penalty based on the year. the least squares regression equation is yhat
The y-intercept for this equation makes no sense for this model.
The given expression is
y=-1912.49+1.003x.
This linear regression expresses a line in its explicit form: y=mx+c
Where y=-1912.49 represents the y-interception.
This element of the linear regression represents the initial condition of the modeled problem, that is, in this case, the initial year.
So, it doesn't make sense that the initial year is -1912.49 because years are whole numbers, they are not represented as decimals. Additionally, years cannot be negative numbers, because it won't make sense, time cannot go backward.
Therefore, the y-interception is not appropriate to model this problem.
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Consider the line 4x+ 8y = -9.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
The slope of a line perpendicular to this line is 2.
The slope of a line parallel to this line is (-1/2)
What is the slope of a line perpendicular to another line?The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
The slope-intercept form of a straight line is:
y = mx + c,
where m is the slope and c is the y-intercept
Let's rewrite the given equation 4x+ 8y = -9
4x+ 8y = -9
8y = -4x - 9
y = (-4/8)x - 9/8
y = (-1/2)x - 9/8
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ * m₂ = -1
where m₁ and m₂ represent the slope of the lines
The slope of a line perpendicular to this line will be:
m₁ * m₂ = -1
(-1/2) * m₂ = -1
m₂ = 2
When the two lines are parallel, they have the same slope. That is:
m₁ = m₂
The slope of a line parallel to this line will be:
m₂ = (-1/2)
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if a and b represent two outcomes that are not disjoint, what is the probability that at least one of them occurs?
The probability that at least one of the two outcomes occurs is equal to the sum of the individual probabilities minus the overlap between them.
The probability that at least one of two outcomes, represented by a and b, occurs is given by the union of the two events, represented by
P(a U b)
This probability is calculated as the sum of the individual probabilities of the two events, minus the probability of their intersection, represented by
P(a ∩ b)
This is because the intersection represents the overlap between the two events and is counted twice in the sum of the individual probabilities.
Mathematically, the probability of the union of two events can be expressed as:
P(a U b) = P(a) + P(b) - P(a ∩ b)
Therefore, the probability that at least one of the two outcomes occurs is equal to the sum of the individual probabilities minus the overlap between them. This calculation takes into account the fact that the overlap represents the probability of both outcomes occurring together, which is counted twice in the sum of the individual probabilities.
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Sari makes an investment with the goal of having $20,000 after 30 years. If the growth factor is 1.12, how much money will she need to invest to reach her goal?
The yearly investment she needs to make to reach her goal is $667.558
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given that Sari makes an investment with the goal of having $20,000 after 30 years,
total amount = $20,000
time period = 30 years
let the investment she made is compounded annually,
for growth rate = 1.12
the amount for CI is given by,
A = p[tex](1 + i)^{t}[/tex]
where 1 + i = growth rate = 1.12
so p = A/[tex](1 + i)^{t}[/tex]
p = 20000/(1.12)³⁰
p = $667.558
Hence she needs to invest $667.558 yearly.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Answer:
Hi!
Step-by-step explanation:
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3).
listed below are blood platelet counts (1000 cells/l) randomly selected from adults in the united states. why does it not make sense to construct a histogram for this data set?
In order to simply construct a histogram, we require additional data and the range is excessive here.
The lowest and highest valleys for this set of data are 191 and 646, respectively. Therefore, the range is excessive here. However, the total number of data, in this case, is only 2468, or ten numbers. Therefore, only N is 10 is provided. That indicates that the question contains 10 data. Therefore, we are unable to create a histogram for this data.
In the given number of data, which is too little and too close to causing a disaster. He still possesses him. Therefore, in order to simply construct a histogram, we require additional data. But with these 10 pieces of data, this is impossible. Additionally, the range is extremely wide, allowing us to construct a histogram for this question.
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Complete Question:
Listed below are blood platelet counts (1000 cells/ uL ) randomly selected from adults in the United States. Why does it not make sense to construct a histogram for this data set?
191 286 263 193 193 215 162 646 250 386
The price of a share of one stock fell from $8.75 to $8.54. Find the percent change.
Answer: 2.5%
Step-by-step explanation:
8.54 / 8.75 =0.975
1 - 0.975 = 0.025
0.025 x 100% ( and nearest thenth)
=2.5%
At a berry farm, Clayton picks 1
1/4cups of blackberries and twice as many raspberries. He takes the berries home and uses them to make mixed-berry muffins. If Clayton needs
3/4of a cup of mixed berries for each batch of muffins, how many batches can he make?
The number of batches of muffins she can make will be 5.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other features.
Clayton picks two times as many raspberries and 11/4 cups of blackberries at a berry farm. He brings the berries home and makes mixed-berry muffins with them.
The number of the batches of muffins can be calculated as:-
Number = ( 1¹/₄ + 2 x 1 ¹/₄ ) / ( 3 / 4 )
Number = [ ( 5 / 4 ) + ( 5 / 2 ) ] / ( 3 / 4 )
Number = [ ( 15 / 4 ) / ( 3 / 4 ) ]
Number = 5
Therefore, the number of batches of muffins will be 5.
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in the diagram, four circles of radius 1 with centers $p$, $q$, $r$, and $s$ are tangent to one another and to the sides of $\triangle abc$, as shown.
The answer is 8 + 8√2 = 12 + 4√2, which is closest to answer choice (A), so the answer is (A).
Since the circles have radius 1, the sides of the triangle that are tangent to the circles are equal to 2. The sum of the sides of the triangle is equal to the perimeter of the triangle, so if we add up the sides that are tangent to the circles, we can find the perimeter.
There are four sides of the triangle that are tangent to the circles, so the sum of these sides is
4 * 2 = 8
To find the perimeter, we simply add 8 to the remaining sides of the triangle.
Since the triangle is isosceles, it has two equal sides that are equal to 4√2, and one side equal to the diameter of the circles, which is equal to 4. The perimeter is then equal to :
8 + 4 + 4√2 * 2 = 8 + 4 + 8√2.
The answer is 8 + 8√2 = 12 + 4√2, which is closest to answer choice (A), so the answer is (A).
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The complete question is :
In the diagram, four circles of radius 1 with centers P, Q, R and S are tangent to one another and sides of △ABC . Find the perimeter of △ABC
(A) 12+4√2
(B) 12+4√3
(C) 12+6√2
(D) 12+6√3
(E) 24
The integer that represents the temperature after a drop of 11° from 3° below zero
3(2x+11) and (3c+15)(2) equivalent
Step-by-step explanation:
3(2x+11)=(3c+15)(2)
6x+33=6c+30
6c-6x=30-33
6c-6x=3
6c=3-6x
3(3-6x)+33=6(3-6x)+30
9-18x+33=18-36x+30
24-18x=12-36x
-18x=-12
x=4/6
6(4/6)+33=(3c+15)(2)
4+33=6c+30
37-30=6c
7/6=c
The expressions 3(2x + 11) and (3c + 15)(2) are not equivalent, as they are different when they are simplified the most.
What are equivalent expressions?Equivalent expressions are expressions that are simplified to the same expression.
The first expression is simplified applying the distributive property as follows:
3(2x + 11) = 6x + 33.
The second expression is also simplified applying the distributive property as follows:
(3c + 15) x 2 = 2(3c + 15) = 6c + 30.
Different expressions, due to different variables (x and c) and constants (33 and 30), hence they are not equivalent.
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2. The national average utility cost is $236.24 per month. If the average electric bill is 38% the total
amount and the average utility cost for Tolleson, AZ is $192.40, what would be the cost of a typical
Tolleson electric bill and how would that compare with the national average? How much lower is
Tolleson's average compared to the national average?
Answer:To find the cost of a typical Tolleson electric bill, we need to calculate what portion of the total average utility cost is for electricity. If the average electric bill is 38% of the total amount, we can multiply the total average utility cost in Tolleson by 0.38:
$192.40 * 0.38 = $72.90
So the cost of a typical Tolleson electric bill is $72.90.
To compare Tolleson's electric bill cost with the national average, we can subtract the national average from Tolleson's average:
$236.24 - $72.90 = $163.34
So the national average is $163.34 higher than Tolleson's average electric bill cost.
Therefore, Tolleson's average electric bill cost is lower than the national average by $163.34.
Step-by-step explanation:
What system of inequalities is shown by each graph?
The system of inequalities is shown by each graph are;
y ≤ 0.5x - 4 and y < -2x + 0
How to interpret Inequality Graphs?An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
From the given graph, the y-intercept of the solid line is y = -4.
The slope is gotten as; m = (0 - (-4))/(8 - 0)
m = 4/8 = 0.5
Thus inequality is;
y ≤ 0.5x - 4
Similarly, the y-intercept for the dashed line ins y = 0
(-2, 4), (-4, 8)
The slope is gotten as; m = (8 - 4)/(-4 - (-2))
m = 4/-2
m = -2
Thus, the equation is;
y < -2x + 0
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in cell d7 return the statistic that correspond to the city and statistics chosen by the user in cells c6 and c7. your formula should use a combination of the vlookup and match functions. you should also employ error handling using the ifna function in case the lookup returns invalid data. note: if you use relative and absolute references appropriately, you can reuse your formula to complete the next task.
Return desired statistic from city and statistic chosen by user in cells C6 and C7 using VLOOKUP and MATCH functions with error handling using IFNA.
To solve this problem, you need to use the combination of the VLOOKUP and MATCH functions in cell D7. The VLOOKUP function is used to search for a value in a table and return the corresponding value from a specified column. The MATCH function is used to find the position of a value in a range.
Assuming the data is in a table called "Data" with columns A and B representing the city and statistics, respectively, the formula in cell D7 would be:
=IFNA(VLOOKUP(C6,Data,MATCH(C7,Data[1],0),FALSE),"Invalid Data")
The IFNA function is used to handle any errors that might occur during the lookup. If the lookup returns an error, it will return the text "Invalid Data".
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enrollment date is to be stored to include the month, day and year. it is expected to vary from jan 1, 1980 to latest of dec 31, 2350. which of the following would be the most suitable data type? date day, month, year datetime smalldatetime time
The most suitable data type for storing the enrollment date is Datetime.
'Datetime' is a data type in SQL that can store the date and time value, with the highest precision up to fractions of a second. This data type can store dates between January 1, 1753, and December 31, 9999, which makes it suitable for storing the enrollment date that ranges from January 1, 1980, to December 31, 2350.
'The smalldatetime' data type is also an option, but it has a lower precision and only stores the date and time with minutes accuracy. The 'date', 'day', 'month', 'year', and 'time' data types are not suitable for storing the enrollment date as they only store either the date or time component and not both.
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What is the measure of 2HPL?
H
(12x - 15)"
(8x + 33)
The measure of <HPL is 129 degrees
How to determine the measure of <HPL?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
(12x - 15) = (8x + 33)
This is so because they are alternate angles
So, we have
12x - 15 = 8x + 33
Evaluate the like terms
4x = 48
Divide by 4
x = 12
Recall that
HPL = 12x - 15
So, we have
HPL = 12 * 12 - 15
Evaluate
HPL = 129
Hence, the angle is 129 degrees
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I NEED HELP!!!!! Please I have no clue what to do!
The lengths in the geometric system are UW = 20√2, TU = 60√2 and TW = 80.
How to calculate the missing lengths of a geometric system
In this problem we find the case of a geometric system formed by two right triangles: UWV, UTW. All missing lengths can be determined by means of Pythagorean theorem, whose formulae are shown below:
UV² = UW² + WV²
TU² = TW² + UW²
Where:
UV, TU - HypotenusesUW, TW, WV - LegsIn addition, both triangles are proportional since they are similar. The proportion formula is:
UV / TV = WV / UV = UW / TU
First, determine the length of side UW:
UW = √(UV² - WV²)
UW = √(30² - 10²)
UW = 20√2
Second, determine the length of side TV:
UV / TV = WV / UV
TV = UV² / WV
TV = 30² / 10
TV = 90
Third, determine the length of side TW:
TW = TV - WV
TW = 90 - 10
TW = 80
Fourth, calculate the length of side TU:
TU = √(TV² - UV²)
TU = √(90² - 30²)
TU = 60√2
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A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month. If M represents the number of movies that the user rents, and C represents the user's total charge for the month, find the relationship between M and C.
The relationship between M and C can be given by the equation C= 6M + 12
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month.
Now M represents the number of movies and C represents the user's total charge for the month
Thus C= 6M + 12
where 6M is the total cost due to renting some number of movies M
Hence, The relationship between M and C can be given by the equation C= 6M + 12
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Canceling common factors and evaluating the limit, we can finally conclude that the velocity of the ball at t = 2 is as follows. v(2) = lim (-160 + 17)(t - 2) t-2 t2 lim (-160 + 17] t2 = -16 + 17 =
The velocity of the ball at t = 2 is 1 m/s.
To calculate the velocity of a ball at a certain time, we can use the following formula:
[tex]v(t) = lim (F(t) - F(t0)) / (t - t0)[/tex]
where F(t) is the position of the ball at time t, and t0 is the starting time. In this example, we are trying to find the velocity of the ball at t = 2, so t0 = 0. Substituting these values into the equation, we get:
[tex]v(2) = lim (F(2) - F(0)) / (2 - 0)[/tex]
F(2) is the position of the ball at time 2, which is given as -160 + 17t. Plugging this into the equation, we get:
[tex]v(2) = lim (-160 + 17t - 0) / (2 - 0)[/tex]
We can simplify this equation by canceling out the common factors and evaluating the limit, which gives us:
[tex]v(2) = lim (-160 + 17)(t - 2) / (t - 2)[/tex]
Canceling the common factors, we get:
[tex]v(2) = lim (-160 + 17) / 1[/tex]
Finally, evaluating the limit, we get the velocity of the ball at t = 2:
[tex]v(2) = -160 + 17 = -16 + 17 = 1 m/s[/tex]
The velocity of the ball at t = 2 is 1 m/s.
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What is the surface of the triangular pyramid below? 818.1 . 453.6. 762.5. 465.75
The surface area of the triangular pyramid is 465. 75 m². Option D
How to determine the surface area of the triangular pyramidThe formula for calculating the surface area of a trIangular pyramid is expressed with the equation;
S = 1/2 b× a + 3/2 b× s
Given that the parameters are;
S is the surface area of the triangular pyramidb is the base of the pyramida is the height of the pyramids is the side length of the pyramidNow, substitute the values into the formula, we get;
Surface area = 1/2 × 16. 2 × 14. 0 + 3/2 × 16. 2 × 14.5
Multiply the values
Surface area = 113. 4 + 352. 35
Surface area = 465. 75 m²
Hence, the value is 465. 75 m²
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The HR manager at a large company wents to estimate the percentage of employees who would support a change to the promotion policies at the company. In this company, 30% of the employees are relatively new (have been with the company less than 4 years) while 70% are experienced (have worked at least 4 years at the company). The HR menager rendomly samples 17 new employees and 41 experienced employees. (a) Which sempling design is being used by the HR manager? • Stratified random sample O Cluster sample O Simple random sample O Systematic sample
The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum.
The HR manager is using a stratified random sample, which is a technique of dividing the population into multiple strata (groups) and then randomly selecting from each stratum. In this case, the population is divided into two strata, new employees (30%) and experienced employees (70%). The HR manager then randomly selects 17 new employees and 41 experienced employees. This technique ensures that each stratum is represented in the sample, making it more representative of the population. Furthermore, it increases the precision of the sample by focusing on the subgroups that may have different characteristics and opinions on the matter, rather than relying on a simple random sample. The advantage of this sampling design is that it allows the HR manager to make more accurate estimates of the population's opinion on the change in promotion policies.
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A triangle has vertices at (5, 4), (−2, 3), and (−2, 2). What are the coordinates of the vertices of the image after the translation (x, y) arrow right (x + 4, y − 2)?
Answer:
c below
Step-by-step explanation:
(5, 4), (−2, 3), and (−2, 2) became
(9, 2), (2, 1), and (2, 0).
they got moved 4 units to the right & 2 down
the ratio of working-age population to the elderly in the united states (including projections after 2000) is given by the function below, with t
The decline of the ratio of greatest on interval (in year), We get
[t=15,t=35]=[2010,2030]
we have
[tex]f(t) =\left \{ {{4.1, 0 < t < 5} \atop {-0.03t+4.25, 5 < t < 15}} \atop {-0.075t4.925, 15 < t < 35}} \right.[/tex]
a)
The graph of f(t),
b)
the ratio begging of 2003 (t = 8),
f(t) = = -0.03t + 4.25
put t = 8,
f(8) = -0.03(8) + 4.25
f(8) = 4.01
The answer,
2003 : 4.01 ..................i)
and the ratio begging of 2027 (t = 32),
f(t)=-0.075t+4.925
put t = 32,
f(32) = -0.075(32) + 4.925
f(32)=2.525
The answer,
2027 : 2.525 ..........................ii)
c)
The ratio is constant on interval (in year)
[t=0, t=5]=[1995,2000]
d)
The decline of the ratio of greatest on interval (in year)
[t=15,t=35]=[2010,2030]
A graph is a mathematical representation of a set of objects in which some pairs of the objects are connected by links. The objects are called vertices or nodes and the links are called edges. Graphs can be used to model a wide range of real-world situations such as networks of roads, social relationships, and computer networks.
There are two main types of graphs: directed and undirected. In a directed graph, the edges have a direction, while in an undirected graph, the edges do not have a direction. Additionally, there are weighted and unweighted graphs. In a weighted graph, the edges have a weight or cost associated with them, while in an unweighted graph, the edges do not have any weight. Graphs are widely used in computer science, operations research, and various other fields for modeling and solving problems.
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Complete Question: -
The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by the function below, with t = 0 corresponding to the beginning of 1995. 4.1 if 0<t<5 f(t) = -0.03t +4.25 if 5<t <15 -0.075 +4.925 if 15 <t <35 (a) Sketch the graph of the function f. When sketching the function, make sure you pay attention to whether each section of the graph starts and ends with open or closed circle. Graph Layers << After you add an object to the graph you can use Graph Layers to view and edit its properties. Fill No Solution Lelo WebAssign. Graphing Tool (b) What was the ratio at the beginning of 2003? At the beginning of 2027? 2003 2027 (c) Over what years is the ratio constant? O [5, 15] O [0, 5] O [2000, 2010] O [2010, 2030] O [1995, 2000] (d) Over what years is the decline of the ratio greatest? O [1995, 2000] O [2000, 2010] O [15, 35] O [5, 15] O [2010, 2030]
A little league team hits the ball appropriately 15 times in 5 innings . Write an equation that could be used to predict the number of hits, h, the team has after n innings.
Answer:
h=3n
Step-by-step explanation:
well based off the numbers given, you can assume that you hit the ball 3 times in 1 inning. Therefore, it is a 3:1 ratio from hits to innings, concluding that h=3n.