Answer:
D. 11 weeksStep-by-step explanation:
Let the number of weeks Riley need to work is x.
She has $200.39 and will save $75.26 for x weeks to get $1028.25 total.
Set this as equation:
75.26x + 200.39 = 1028.25Solve it for x:
75.26x = 1028.25 - 220.3975.26x = 807.86x = 807.86/75.26x = 10.73 ≈ 11 (rounded to whole number)Correct choice is D
Answer:
d) 11
Step-by-step explanation:
Forming the equation,
→ 75.26w + 220.39 = 1028.25
Now the value of w will be,
→ 75.26w + 220.39 = 1028.25
→ 75.26w = 1028.25 - 220.39
→ 75.26w = 807.86
→ w = 807.86/75.26
→ w = 10.73425
→ [ w = 11 weeks ]
Hence, the answer is 11 weeks.
Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1400 grams, how long would it be until the mass of the sample reached 800 grams, to the nearest tenth of a year? please help
It would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.
To determine how long it would take for the mass of the sample of Element X to reach 800 grams, we can use the information provided about its rate of decay.
Given:
Initial mass (M₀) = 1400 grams
Decay rate: The mass decreases by half every 30 years.
To solve this problem, we need to find the time it takes for the mass to decrease from 1400 grams to 800 grams.
Let's set up an equation to represent the decay of the mass:
M(t) = [tex]M\circ * (1/2)^(t/30)[/tex]
Here, M(t) represents the mass at time t in years, M₀ is the initial mass, and t is the time in years.
We need to find the value of t when M(t) = 800 grams:
800 = [tex]1400 * (1/2)^(t/30)[/tex]
To solve for t, we can take the logarithm of both sides of the equation (base 1/2) to isolate t:
[tex]log\base1/2(800/1400) = t/30[/tex]
Using logarithmic properties, we can simplify further:
[tex]log\base1/2(4/7) = t/30[/tex]
Now, we can solve for t by multiplying both sides of the equation by 30:
[tex]t = 30 * log\base1/2(4/7)[/tex]
Using a calculator or logarithmic tables, we find:
t ≈ 14.1 years
Therefore, it would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.
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select the expression that shows the distributive property applied to 5(6 + 8)
A.5 ⋅ 6 + 8
B.5 ⋅ 6 + 6 ⋅ 8
C.5 ⋅ 6 + 5 ⋅ 8
D.5(8+6)
urgent
Please help me do these two!! I don’t understand what to do with the arc(sin,cos,tan) in these problems. I’ll mark branliest!!
Answer:
See below=====================
Use identities:
sin (x + y) = sin x cos y + cos x sin ytan (x - y) = (tan x - tan y)/(1 + tan x tan y)sin (sin⁻¹ x) = xcos (cos ⁻¹ x) = xtan (tan⁻¹ x) = xsin (cos⁻¹ x) = √ (1 - x²)cos (sin⁻¹ x) = √ (1 - x²)Question 11sin (sin⁻¹ 4x + cos⁻¹ x) = sin (sin⁻¹ 4x) cos (cos⁻¹ x) + cos (sin⁻¹ 4x) sin(cos⁻¹ x) = 4x*x + √ (1 - (4x)²) * √ (1 - x²) = 4x² + √(1 - x²)(1 - 16x²)Question 12tan (tan ⁻¹ 1 - tan ⁻¹ √x) = [tan (tan ⁻¹ 1) - tan (tan ⁻¹ √x)] / [1 + tan (tan ⁻¹ 1) tan (tan ⁻¹ √x)] =(1 - √x) / (1 + 1*√x) = (1 - √x) / (1 + √x)Answer:
[tex]\textsf{11.} \quad 4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}[/tex]
[tex]\textsf{12.} \quad \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}[/tex]
Step-by-step explanation:
Question 11[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Double Angle Identity}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Inverse Trigonometric Identities}\\\\$\sin(\cos^{-1}x)=\sqrt{1-x^2}$\\\\$\cos(\sin^{-1}x)=\sqrt{1-x^2}$\\\end{minipage}}[/tex]
Given trigonometric expression:
[tex]\sin ( \sin^{-1} 4x + \cos^{-1} x)[/tex]
Using the Sine Double Angle Identity:
[tex]\textsf{Let $A=\sin^{-1}4x$}[/tex][tex]\textsf{Let $B=\cos^{-1}x$}[/tex]Therefore:
[tex]\begin{aligned}\sin ( \sin^{-1} 4x + \cos^{-1} x)&=\sin(\sin^{-1}4x) \cos (\cos^{-1}x)+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x \cdot x+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \sqrt{1-(4x)^2}\sqrt{1-x^2}\\&=4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}\end{aligned}[/tex]
Question 12[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan Double Angle Identity}\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given trigonometric expression:
[tex]\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})[/tex]
Using the Tan Double Angle Identity:
[tex]\textsf{Let $A=\tan^{-1}1$}[/tex][tex]\textsf{Let $B=\tan^{-1}\sqrt{x}$}[/tex]Therefore:
[tex]\begin{aligned}\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})&=\dfrac{\tan (\tan^{-1}1) - \tan (\tan^{-1}\sqrt{x})}{1 + \tan (\tan^{-1}1) \tan (\tan^{-1}\sqrt{x})}\\\\&=\dfrac{1 - \sqrt{x}}{1 + 1 \sqrt{x}}\\\\&=\dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}\\\\\end{aligned}[/tex]
Beatrice makes a jar of dry soup mix. The ingredients are:
1\frac {3}{4}
4
3
= \frac {7}{4}
4
7
cups uncooked rice
\frac {1}{2}
2
1
cup dry lentils
1\frac {2}{3}
3
2
= \frac{5}{3}
3
5
cups uncooked pasta
\large \frac {1}{3}
3
1
cup beef bouillon
\frac {1}{4}
4
1
cup dried onion flakes
\frac {1}{2}
2
1
cup dried peas
How much soup mix does this recipe make?
Answer the questions to find out.
The sum \frac {7}{4}
4
7
+ \frac {1}{2}
2
1
+ \frac{5}{3}
3
5
+ \large \frac {1}{3}
3
1
+ \frac {1}{4}
4
1
+ \frac {1}{2}
2
1
gives the amount of mix.
1. Which property could you use to change the order of the addends? (2 points)
2. Which property could you use to change the grouping of the addends? (2 points)
3. Use these properties to rewrite \frac {7}{4}
4
7
+ \frac {1}{2}
2
1
+ \frac{5}{3}
3
5
+ \large \frac {1}{3}
3
1
+ \frac {1}{4}
4
1
+ \frac {1}{2}
2
1
in a way that makes the addition easier. Explain how your changes simplify the addition. (3 points)
4. Simplify your sum to find the total amount of soup mix. Show your work. (3 points)
error analysis correct the error in the following equation explain the mistake 5x + 5(-2x - 12) = 130 5x + -10x - 60 = 130 =65x = 130 x = -2
Answer:
Step-by-step explanation:
The given error full solution is
5x+5(-2x-12)=130
5x+-10x-60=130
65x=130x=-2.
Correct answer is given as
5x+5(-2x-12)=130.
We solve this question using Bodmas rule. So first we remove the parenthesis.
5x+5(-2x-12)=130
5x+5(-2x)+5(-12)=130
5x-10x-60=130
-5x=130+60
-5x=190
dividing both side by by (-5). We, get
x=190/(-5)
x=-38
Hence, the correct answer is x=-5
Over which interval is this function continually decreasing?
The given function is continuously decreasing for x = (-∝, 1).
Given function,
f(x) = | 4(x - 1) | + 2
⇒ f(x) = |4||x-1| + 2
⇒ f(x) = 4|x - 1| + 2
If x ≥ 1, |x - 1| = x - 1
⇒ f(x) = 4(x - 1) + 2 = 4x - 4 + 2
⇒ f(x) = 4x - 2
On differentiating on both sides:
f'(x) = 4 > 0
⇒ Function is continuously increasing for x ≥ 1.
If x < 1, |x - 1| = -(x - 1) = 1 - x
⇒ f(x) = 4(1 - x) + 2 = 4 - 4x + 2
⇒ f(x) = 6 - 4x
On differentiating on both sides:
f'(x) = -4 > 0
⇒ Function is continuously decreasing for x < 1.
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Values = [ 14, 10, 8, 19, 7.13] print the interger at index 2 of values and print the integer at index -2 of values, both on one line.
Therefore, the final code would be:values = [ 14, 10, 8, 19, 7.13] print(values[2], values[-2])This code would print the following output:8 19
What is meant by indices?Indices, also known as exponents or powers, are mathematical symbols that express the repeated multiplication of a number. These numbers show how many times the base number has been multiplied by itself. For example, the index of 2 in the formula 23 is 3, which indicates that 2 is multiplied by itself three times to provide the value 8. Indices are often written as little numbers to the right and above the base number, with the latter enclosed in parentheses or brackets. Indices are often used to indicate the size or quantity of a number in mathematical model, but they may also be used to represent the degree of a polynomial function or the order of a derivative in calculus.
How to solve?
To print the integer at index 2 of the values list, we can use the following code: print(values[2])
To print the integer at index -2 of the values list, we can use the following code: print(values[-2])
Here, the index -2 refers to the second-to-last element in the list, which is the integer 19.
Therefore, the final code would be:
values = [ 14, 10, 8, 19, 7.13]
print(values[2], values[-2])
This code would print the following output:
8 19
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participants should be selected by chance for an experimental or control group so each has equal probability of being assigned to any of the groups. this is done by
The instance in question was chosen at random assignment.
Given statement;
Participants should be selected by chance for an experimental or control group so each has an equal probability of being assigned to any of the groups.
The given case is done by Random assignment.
In Mathematical experiments, random assignment refers to the use of chance processes to ensure that each participant has an equal chance of being assigned to any particular group. Participants in studies are divided into several groups at random, such as the experimental group or the treatment group.
It is known as random assignment.
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suppose braking distance for the new system is normally distributed with s 5 10. let x denote the sample average braking distance for a random sample of 36 observations. which values of x are more contradictory to h0 than 117.2, what is the p-value in this case, and what conclusion is appropriate if a 5 .10?
The x value that more contradictory to h0 than 117.2 is the value less than 117.2 and p-value is 0.0465 and the conclusion is we reject h0.
How to calculate p-value?μ = mean = 120
x = 117.2
σ = standard deviation = 10
n = random sample = 36
Lets take the z test,
z = [tex]\frac{x-\mu }{\sigma / \sqrt{n}}[/tex]
= [tex]\frac{117.2 - 120}{10/\sqrt{36}}[/tex]
= [tex]\frac{-2.8}{1.667}[/tex]
= -1.68
From the test, we know test is left tailed and the rejection area is negative. So, the less x than 117.2 the more contradictory to h0.
For p-value use z-score table and we get 0.0465. Because the p-value is less than the appropriate α, which is 0.1, it can be concluded that h0 is rejected.
Thus, the less x value than 117.2 the more contradictory to h0 and we rejected h0 because p-value is lower than appropriate α.
Your question is incomplete, but most probably your full question was (image attached)
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Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each . The total cost C, of all the 2- liter sodas will be proportional to the number of 2- liter sodas, S, that she buys . Which equation represents the relationship between C and S
The total cost of all the 2- liter sodas will be proportional to the number of 2- liter sodas that Sue buys is c = 1.25s
How to explain the equation that represents the relationship between the cost and soda?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each.
Let the number of soda be s.
The total cost will be:
c = 1.25 × s
c = 1.25s
The cost is 1.25s.
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48 tens divided 6 tens
Answer:
The answer is 8.
Step-by-step explanation:
Since 48 10s, equals 480, and 6 tens equal 60, we do 480/60 which equals 8.
Find the perimeter and area of the rectangle with vertices (1, 7), (1, -2), (-3, -2), and (-3, 7).
Check the picture below.
1/2(x+2) = -1/3 (x+3)
Answer:
[tex]X=-2\frac{2}{5}[/tex]
Step-by-step explanation:
1/2(x+2)=-1/3(x+3)
1/2x+1=-1/3x-1
+1/3x
5/6x+1=-1
-1. -1
5/6x=-2
/5/6. /5/6
x=-2*6/5
x=-12/5
x= -2 2/5
Hopes this helps please mark brainliest
so lets say you have to do 257+102+51+41 which is 451 right?
so what would it be if someone took 30% of that 451 like tax what would you be left with? first person to answer CORRECTLY ill give u thanks
First we are supposed to find 30% of 451
30/100×451 = 135.3
So, 451 - 136= 315.7
Therefore I would be left with 315.7
Answer:
$315.70
Step-by-step explanation:
the sum of these is 451 so to find 30 percent we multiply 451 by 30 percent
First turn 30 percent into a decimal by moving the decimal point to places to the left
0.30 and now we multiply
0.3x451
135.30 is 30% of 451 and since someone is taking it we subtract it by 451
451-135.30
315.70 is what you are left with
But if it was tax you would add this to the total amount you are spending
Hopes this helps please mark brainliest
What is the end behavior of the function f(x) = 5/4x²,
As x→ ∞o. f(x) → -∞
O As x-00. f(x) → ∞0
As X→ ∞o, f(x) → -∞
O As x-00, f(x) → -∞0
As x→
O As x →
∞o. f(x) → ∞0
∞0. f(x) → -∞
The end behavior of function is positive non decreasing.
What is meant by function ?A function is a relationship between a set of inputs and a set of allowable outputs in mathematics. The feature of functions is that each input corresponds to exactly one output. For example, in the function f(x)=x², any x input will result in only one output.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
How to solve?Given function f(x) = 5/4x²
as the function is square of x hence we can clearly see function is positive
Hence end behavior of function is positive non decreasing.
The complete question is : What is the end behavior of the function f(x)=5/4x2?
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Subtract (3x-4x+2) from (7x-10x-8x) then divide the difference by -2x
Answer: -6
Step-by-step explanation:
Answer:
5 + (1/x)
Step-by-step explanation:
(3x - 4x + 2) - (7x - 10x - 8x)
3x - 4x + 2 - 7x + 10x + 8x
(3x - 4x - 7x + 10x + 8x) = 10x
10x + 2
10x + 2 10x 2 1
---------- = ------- + ------- = 5 + ------
2x 2x 2x x
I hope this helps!
Mariam ue 12 gallon of ga to drive 259. 2 mile in her car. Find the rate of change
The rate of change is 21.6 mpg.
The rate of change determines how one variable changes because of another variable. This rate value can be either positive or negative. Considering x as an independent variable and y as a dependent variable, the rate of change for these two variable is given by,
[tex]\text{rate of change}= \frac{\text{change in y}}{\text{change in x}}=\frac{\Delta y}{\Delta x}[/tex]
From the given value, miles traveled is a dependent variable because it depends on the amount of gas. So the amount of gas is the independent variable.
Therefore, the rate of change is,
[tex]\begin{aligned}\text{rate of change}&=\frac{\Delta y}{\Delta x}\\&=\frac{\mathrm{259.2\;miles}}{1\mathrm{2\;gallons}}\\&=\mathrm{21.6\;mpg}\end{aligned}[/tex]
Therefore, the rate of change is 21.6 miles per gallon.
This formula is also used to calculate gas mileage.
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The complete question is -
Mariam uses 12 gallons of gas to drive 259.2 miles in her car. Find the rate of change.
Subtract 8x10 from x² - 2x.
Answer:(4 x 103) x (2 x 107) = ( 4 x 2 ) x ( 103 + 7 ) = 8 x 10 10.
Step-by-step explanation:
The obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Is given expression is, Subtract 8x¹⁰ from x² - 2x.
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
=8x¹⁰-x²+2x
=8(x²)⁵-x²+2x
=x²(8x⁴-1)+2x
Thus, the obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
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Manuel is using a table to calculate information for an upcoming business trip. Based on the table, for every 60 miles traveled, the number of gallons of fuel he uses increases by approximately how many gallons?
120 6
180 9
240 12
300 15
360 18
A. 3 gallons
B. 6 gallons
C. 12 gallons
D. 18 gallons
For every 60 miles traveled 3 gallons of fuel usage is increasing approximately.
Given,
Manuel is using a table to calculate information for an upcoming business trip.
We have to find the number of gallons of fuel he uses increases by approximately for every 60 miles traveled.
Here,
Distance in miles ;- 120, 180, 240, 300, 360
Fuel used in gallons;- 6, 9, 12, 15, 18
Then,
For 120 miles 6 gallons of fuel is usedFor 180 miles; 9 - 6 = 33 gallons of fuel is used
Lets check for this to all;-
For 240 miles; 12 - 9 = 3For 300 miles;- 15 - 12 = 3For 360 miles;- 18 - 15 = 3That is,
For every 60 miles traveled 3 gallons of fuel usage is increasing approximately.
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Based on the triangle shown, what is the approximate value of Cos(20)?
Use exact fractions. To receive credit for this question, you must show your work.
3
5
e
The value of cos 2θ will be;
⇒ cos 2θ = 7/25
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;
The sides of triangle are 3 , 5, 4
Now,
Since, In a triangle;
cos 2θ = 2cos²θ - 1 .....(i)
And, cos θ = Base / Hypotenuse
Substitute all the values, we get;
cos θ = Base / Hypotenuse
cos θ = 4 / 5
Substitute above value in equation (i), we get;
cos 2θ = 2cos²θ - 1
cos 2θ = 2(4/5)² - 1
cos 2θ = 32/25 - 1
cos 2θ = 7/25
Thus, The value of cos 2θ will be;
⇒ cos 2θ = 7/25
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How many gallons of a 35% solution should be mixed with 7 gallons of a 60% solution to create a 50% solution?
From the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.
As given in the question,
Quantity of 60% solution in making 50% solution is = 7 gallons
Let us consider y gallons be the quantity of 35% solution to make 50% solution.
Quantity used to make 50% solution is (7 + y)
Required equation is:
(y × 35%) + (7× 60%) = (7+y) 50%
⇒(35y/100) + (420/100) = (350 + 50y)/100
⇒35y + 420 = 350 + 50y
⇒50y - 35y = 420 -350
⇒15y = 70
⇒y = 4.666..
⇒y = 4.7 gallons ( approximately)
Therefore, from the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.
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GCF of 21 and -24x PLS I NEED HELP IN THESE THERES SO MANY
Answer: 3
Step-by-step explanation:
Jordan and her grandmother are making a quilt. They will cut square pieces from
fabric to make their quilt. They have already purchased three lengths of fabric. The
lengths are 30 inches 48 inches and 60 inches what is the largest length each
square can be in order to have the least amount of waste from the fabric
The largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.
What is a square?It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
It is given that, Jordan and her grandma are creating a quilt as a result. To make their quilt, they will cut square pieces of cloth. They have already bought three fabric lengths. 30 inches, 48 inches, and 60 inches are the lengths.
The total length of the fabric is,
=30+48+60
=138 inches
The perimeter of a square is,
P = 4a
138 = 4a
a=138/4
a=34.5 inches
Thus, the largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.
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According to the WHO MONICA Project the mean blood preure for people in China i 128 mmHg with a tandard deviation of 23 mmHg. Aume that blood preure i normally ditributed
0.0088 is standard deviation of blood presure is normally distributed.
What is standard deviation simple terms?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.Blood pressure in china
= P( x> 182.6 )
= P( x> 182.6 - 128/23)
= P( Z > 2.3739 )
= 0.0088
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Work out the trapezium below
Answer:
A = 40 cm^2
Step-by-step explanation:
A = (3+13)/2 * 5
A = 16/2 * 5
A = 8 * 5
A = 40 cm^2
Allie and Roman attempted to graph the blue line.
Allie's equation was y = 2x - 8
Roman's equation was y = − 2x + 8
Who had the correct equation and why? Explain your an-
swer in 1 to 2 complete sentences.
Roman's equation is correct.
What is an equation?
An equation is composed of two expressions joined by an equals sign. The phrases on each side of the equals sign are referred to as the equation's "bottom left" and "top part." The right hemisphere of an equation is frequently considered to be zero. Assuming that this does not limit the generality, it is possible to implement this by subtracting the right-hand side from both sides. The most frequent sort of equation is a polynomial equation, which has two polynomial sides. A scale into which weights are inserted is akin to an equation. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal.
given equations,
Allie's equation is y = 2x - 8
Roman's equation is y = -2x + 8
Roman's equation matches the given graph, so his equation is correct.
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I am stuck on this question, help please!
Answer:
y= -1x + 4 or y= -x + 4
Step-by-step explanation:
Find X and Y so that the Quadrilateral is a Parallelogram. Answer below and show work.
The values of x and y are given by 8 and 9 respectively.
Since the quadrilateral is a parallelogram. So the opposite sides should be equal and parallel.
So,
4x-17 = 2x-1
4x-2x = 17-1
2x = 16
x = 8
Again the angles (3y+5) and (5y-13) are alternating angles with respect to parallel opposite sides of parallelogram and diagonal as transversal. So they are equal.
3y+5 = 5y-13
5y-3y = 13+5
2y = 18
y = 18/2
y = 9
So the values are, x=8 and y=9.
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how is the slope coefficient interpreted in a log-linear model, where the independent variable is in logarithms but the dependent variable is not? in a linear-log model? in a log-log model?
Interpret the coefficient as the percent increase in the dependent variable for every 1% increase in the independent variable.
What is log-linear model?Log-linear models specify how the cell counts depend on the levels of categorical variables, going beyond simple summary statistics. They simulate the relationships and interactions between categorical variables. For Poisson, Multinomial, and Product-Multinomial sampling, the log-linear model makes sense. Log-linear models specify how the cell counts depend on the levels of categorical variables, going beyond simple summary statistics. They simulate the relationships and interactions between categorical variables. For Poisson, Multinomial, and Product-Multinomial sampling, the log-linear model makes sense.
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