Answer: A piecewise function is a function that is defined by multiple equations, each with its own domain. The equation for the situation can be represented as a piecewise function as:
f(x) = { 2x, 0<x<=5}
f(x) = { 1.5x, x>5}
Where f(x) is the cost of x number of cookies.
The first equation represents the cost of x number of cookies when x is between 0 and 5 (inclusive). The second equation represents the cost of x number of cookies when x is greater than 5.
So, the piecewise function that represents the cost of x number of cookies based on the given conditions is:
f(x) = { 2x, 0<x<=5}
f(x) = { 1.5x, x>5}
It means if you buy x number of cookies and if x is between 0 and 5 (inclusive) then you are charged $2 per cookie and if x is greater than 5 then you are only charged $1.50 per cookie.
Step-by-step explanation:
Top one
A princess is on the top of a 167 foot tower looking down at a 37° angle of depression at a package attached to a rope on the ground. How long is the rope?
The length of the rope in the question is; 277.5 ft
How to solve Angle of depression problems?The angle of depression is defined as the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, and looking down at an object, you could measure the angle of depression.
The rope length can be calculated using the trigonometric ratio which is;
167/x = sin 37
x = 167/sin 37
x = 167/0.6018
x = 277.5 ft
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1. 3f+10-6f-4
2. 7ab-2a+5ab-9a
3. -2t-8r+3t-4r
4. 2a+9b-5a-10b PLEASE HELP!!
1. 3f + 6
2. 12ab - 11a
3. 1t - 12r
4. 3a -1b
pls pls pls pls mark as brainiliest
pls im literally begging you
Answer:
-3f + 6
12ab - 11a
t - 12
-3a - b
Step-by-step explanation:
3f + 10 -6f -4 Combine like terms
(3f -6f) +( 10-4)
-3f + 6
7ab - 2a + 5ab - 9a
(7ab + 5ab) + (-2a - 9a)
12ab + -11a Adding a negative is the same as subtracting a positive
12ab - 11a
-2t - 8r + 3t - 4r
(-2t + 3t) + (-8r - 4r)
t + -12r
t - 12
2a + 9b - 5a - 10b
(2a - 5a) + ( 9b -10b)
-3a - b
Find the area under the standard normal distribution curve to the right of z = 2.12. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.
The area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
What is the Area under the Standard Normal Distribution Curve?The standard normal distribution curve's total area under the curve is 1. We can therefore calculate the likelihood of a value less than or larger than that if we know the Z score, which measures how far a value is above or below the mean. Under the typical normal curve when using the Normal Distribution P(Z>z)=1-P(Z<z) determines the region to the right of z.In this question:
Area right to the right of the z = 2.12
Using a TI-83 Plus/TI-84 Plus calculator,
P(Z> 2.12)
= P(Z<-2.12)
= 0.0170
Therefore the area under the standard normal distribution curve to the right of z = 2.12 is 0.0170.
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If x and y are in direct proportion and y is 18 when x is 9, find y when x is 5.
Answer:
y=10
Step-by-step explanation:
18/9=1/2
so
x/5=1/2
Answer: The value of y will be 10 when the value of x is 5.
x and y are directly proportional to each other so,we can write the given relation in mathematical form as:
y=kx
k is any constant
We are given: The value of y is 18 when value of x is 9:
x=9 and y=18
Putting the value of x and y in the above equation , we get:
18=9k
k=18/9=2
k=2
So now we have the proportional relation(k) between x and y.
Again,
we have been given the value of x=5 and we are asked the value of y using same proportional relation.
y=k(5)
y=2(5)=10
Hence the value of y the value of x is 10.
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Dilate the segment with a scale factor of r=1/2
Answer:
3.5 cm long
Step-by-step explanation:
AB*1/2=7*1/2=3.5
Answer:
|AB'| = 3.5 cm
Step-by-step explanation:
Given:
|AB| = 7 cmr = ¹/₂To dilate the line segment by a scale factor r, multiply the original length of the line segment by the given scale factor:
[tex]\begin{aligned}\implies \sf |AB'|&=\sf |AB| \times r\\\\&=7 \times \dfrac{1}{2}\\\\&=\dfrac{7 \times 1}{2}\\\\&=\dfrac{7}{2}\\\\&=3.5\; \sf cm\end{aligned}[/tex]
(01.02 MC)
Determine the solutions of the equation:
|1/3×+9|-3=21
Ox= -11 and x = 5
Ox= -81 and x = 45
O x = -99 and x = 45
O x = -99 and x = 99
The solution for given linear equation are x=-99 and x=45 i.e. C.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Given linear equation is |1/3×+9|-3=21
so, -1/3x-12=21 --->1
and 1/3x+6=21 --> 2
From 1
1/3x=-33
x=-99
From 2
1/3x=15
x=45
Hence,
The solution for given linear equation are x=-99 and x=45.
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b=2.35+0.25x
c=1.75+0.40x
In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
The price per pound of beef when it was equal to the price of chicken is $3.35 per pound.
The following linear equations represent the costs of beef and chicken:
Beef price, B:
B = 2.35 + 0.25x
Price of chicken, C :
C = 1.75 + 0.40x
Where x in both equations denotes the number of weeks since July 1 of the previous summer:
B = 2.35 + 0.25x
Price of chicken, C :
C = 1.75 + 0.40x
Where x in both equations represents x weeks after July 1 of last summer
Firstly:
We identify the week when the cost of beef and chicken is equal:
Beef = Chicken
2.35 + 0.25x = 1.75 + 0.40x
We solve for x
2.35 - 1.75 = 0.40x - 0.25x
0.60 = 0.15x
x = 0.60 / 0.15
x = 4
Therefore, poultry and beef had the same price four weeks after July 1 of last summer.
B = 2.35 + 0.25(4)
B = 2.35 + 1
B = 3.35
When the price of chicken and beef were equal, the price per pound of meat was $3.35.
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Construct a vertical transversal and horizontal transversal to lines AB and DC that intersect each other at F. Label the points of intersection to the parallel lines A, B, C, and D.
Pls help!!
The missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
here,
As given in the quesiton,
Consider the triangle formed by the given construction,
ΔFDC and Δ FAB
AB║CD
∠FAB = ∠FCD
∠FBA = ∠FDC
So, ΔFDC ≅ Δ FAB, by SAS congruency.
Thus, the missing statement in the given proof is ΔFDC ≅ Δ FAB, reason SAS. Option C is correct.
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Replace variables wit values and evaluate using order of operations D= wt² W=70 T=4 give your answer in simplest form
The value of variable d is 1120
How to determine the value of variable d from the known valuesFrom the question, we have the following parameters that can be used in our computation:
D= wt²
Where W = 70 and T = 4
Substitute the known values in the above equation, so, we have the following representation
D = 70 * 4²
Evaluate the exponent
D = 70 * 16
Evaluate the products
D = 1120
Hence, the solution is 1120
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How to solve 3 equations with 3 variables using elimination?
The elimination method is used to solve a system of equations with multiple variables. Repeat this process until all of the variables have been eliminated, then simplify the equations to solve for the remaining variable.
Once a variable has been isolated, it can then be eliminated from the other equations by either adding or subtracting the equations from each other. This process should be repeated until all of the variables have been eliminated from all of the equations.
For example, let's solve the following system of equations with 3 variables a, b, and c:
a + b + c = 8
2a + b + 2c = 12
3a + 2b + 3c = 18
First, isolate the variable c in equation 1 by subtracting b and a from both sides:
c = 8 - a - b
Substitute this expression for c in equation 2 and 3 to eliminate c:
2a + b + 2(8 - a - b) = 12
3a + 2b + 3(8 - a - b) = 18
Then simplify the equations to solve for the remaining variables:
2a + 3b = -4
9a + 6b = 36
Next, isolate the variable a in equation 2 by subtracting 3b from both sides:
a = -4/2 - 3b/2
Substitute this expression for a in equation 1 and 3 to eliminate a:
-4/2 - 3b/2 + b + 8 - b = 8
9(-4/2 - 3b/2) + 6b + 3(8 - b) = 36
Then simplify the equations to solve for the remaining variable:
15b = -12
b = -12/15
Finally, substitute b back into equation 1 or 2 to solve for a:
a + (-12/15) + 8 = 8
a = 8 - (-12/15) - 8
a = 24/15
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a committee of 4 is to be selected from a group of 9 women and 7 men. what is the probability that 2 men and 2 women are selected?
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is [tex]$\frac{{7 \choose 2}{9 \choose 2}}{{16 \choose 4}}$[/tex] which simplifies to[tex]$\frac{63}{220}$[/tex] or approximately 28.6%. The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
The probability of selecting 2 men and 2 women from a group of 9 women and 7 men can be calculated by using the formula for combination, nCr. In this case, we would be selecting 4 people from 16 individuals, so n = 16 and r = 4. The formula is nCr = n!/(r!(n-r)!). This can be simplified to 16C4 = 16!/ (4!(12!)). The answer is 1820/21168, which can be simplified to 86/792, or approximately 11%. Therefore, the probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.
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Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y or vice versa.
For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y.
We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with a unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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se the following stem-and-leaf plot of college freshman GPAs to answer questions 9-15.
KEY
Stem: ones digit
Leaf: tenths digit
Example. 0.9 → 0+.9 0.9
Stem Leaf
0
1
2
3
4
.9
.3
.0
.0
.0
.5
.3
.2
.5
.4
.3
9. What is the range?
A. 4.9
B. 4.0
C. 3.1
D 3.0
E 2.1
Answer: The range is 4.9.
Step-by-step explanation: The range of a set of data is the difference between the largest and smallest values. In this stem-and-leaf plot, the smallest value is 0.3, and the largest value is 4.9.
Therefore, the range is 4.9 - 0.3 = 4.6 which is 4.9 (approx)
So the answer is A. 4.9
What is the volume of the can of orange juice in cubic centimeters?
Salut/Hello!
Answer: 3120 cubic cm
Step-by-step explanation:
cm - centimeters
=> - results
We know the area is 156 square cm
And the height is 20 cm
We know the area formula is A = L x l
where L - length
and l - latitude
We also know the volume formula is V = L x l x h
where h - height
So we can replace the length and latitude with the area and we have
V = A x h and we know the area and height
So we calculate:
V = 156 x 20 => V = 3120 cubic cm
I hope it was helpful! :]
which operationalization is most appropriate for the independent variable of the proposed follow-up experiment
Type of communication developed by teaching a doctor who is also a collaborator to utilize patient-centered communication or a non-patient-centered communication style.
What is appropriate for the independent variable?As the researchers are interested in the effect of type of communication on level of mistrust; therefore, type of communication is the independent variable. To establish a causal relationship between the two variables, the independent variable needs to be manipulated, as described in C, by training the doctor to adopt different communication styles.
Here,
Communication style produced by training a doctor who is also a collaborator to use patient-centered communication or a non-patient-centered communication style.
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Given the equation d over 13 equals 15, solve for d.
Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(x)).
2x + 1
2x + 4
X + 4
2x^2 + x - 21
Answer:
2x + 1
Step-by-step explanation:
To find f(g(x)), we need to substitute g(x) for x in the function f(x) = 2x + 7.
so f(g(x)) = 2(x - 3) + 7 = 2x - 6 + 7 = 2x + 1
So the composition of function f(g(x)) is f(g(x)) = 2x + 1.
Constructing Functions Express the gross salary G of a person who earns $14 per hour as a function of the number x of hours worked. Find the domain. - Population as a Function of Age The function P(a) = 0.027a2 6.530a + 363.804 represents the population P (in millions) of Americans that are a years of age or older in 2015. (a) Identify the dependent and independent variables. (b) Evaluate P(20). Provide a verbal explanation of the meaning of P(20). (c) Evaluate P(0). Provide a verbal explanation of the meaning of P(0).
(a) The independent variable is age (a) and the dependent variable is population (P).
(b) P(20) = 6.38 million. This means that 6.38 million Americans were 20 years or older in 2015.
(c) P(0) = 363.804 million. This means that 363.804 million Americans were 0 years or older in 2015.
Find the slope of the ordered pairs below
Answer:
[tex]\boxed{\sf \:Slope(m)=2}[/tex]
Step-by-step explanation:
Let's use the slope formula to find the slope of (2,2) and (3,4):-
Slope formula :- m=(y2-y1)/(x2-x1)
[tex]\sf \left(x_1,\:y_1\right)=\left(2,\:2\right)[/tex]
[tex]\sf \:\left(x_2,\:y_2\right)=\left(3,\:4\right)[/tex]
[tex]\sf m=\cfrac{4-2}{3-2}[/tex]
[tex]\sf m=\cfrac{2}{1}[/tex]
[tex]\sf m=2[/tex]
Therefore, the slope is 2!!
_____________________
Hope this helps!
Have a great day!
An archaeologist in turkey discovers a spear head that contains 53% of its original amount of c-14.
find the age of the spear head to the nearest year.
(5250 isn’t right)
The age of the spearhead to the nearest year will be 6,349
When an organism dies, it stops regenerating new carbon, which causes the organism's total carbon-14 concentration to gradually deplete. By analyzing the ratio of carbon-14 to carbon-12 in an organism, scientists can ascertain when it died.
0.53No = Noe^-0.0001t for T.
Divide both sides by No
0.53No = Noe^0.0001t
0.53 = e^-0.0001t
Take the log of both sides
In 0.53 = In e^-0.0001t
Apply In e^x = x.
In 0.53 =-0.0001t
Divide both sides by -0.0001t to solve for t.
t=6,349
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give your answer to 1d.p.
Answer: 26.8
Step-by-step explanation:
[tex]\frac{8.2}{m}=\tan 17^{\circ}\\\\\frac{m}{8.2}=\frac{1}{\tan 17^{\circ}}\\\\m=\frac{8.2}{\tan 17^{\circ}}\\\\m \approx 26.8[/tex]
For her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. How much candy will each of the 15 people get? Choose the correct equation and answer for this situation.
A) 15 ÷ 5 = [tex]\frac{15}{5}[/tex] = 3 pounds
B) 5 ÷ 15 =[tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex] pounds
C) 5 ÷ 15 = 3 pounds
D) 15 ÷ 5 = [tex]\frac{1}{3}[/tex] pounds
If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.
How to find the amount of candy to gives as party treats?Given data:
Candy bought = 5
Number of people invited = 15
Now let find the amount of candy to gives as party treats
Number of candy = Number of people invited / Candy bought
Number of candy = 15/5
Number of candy = 3 pounds
Therefore we can conclude that the correct option is A.
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the blue figure is a dilation image of the black figure. the labeled point is the center of dilation. tel whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation.
From the given graph we can observe that the blue figure is larger in size than the black figure. Hence, the figure is enlargement of the original figure.
What is transformation?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. The transformation, or f: X X, is the name given to the function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
From the given graph we can observe that the blue figure is larger in size than the black figure. Hence, the figure is enlargement of the original figure.
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Which of the layer(s) in the diagram below have liquid-like properties? 3 3&4 1,2,3 & 4 2&4 1,2 & 4
The layers in the diagram that have liquid-like properties are layers 1,2,3 and 4. This is determined by the properties of liquids, which are: high viscosity, low compressibility, and the ability to flow.
Viscosity is the measure of a liquid's resistance to flow. It can be calculated using the formula η = (ΔP/l) x (d/Δt), where η is the viscosity, ΔP is the pressure difference, l is the length of the flow, d is the change in distance, and Δt is the time difference.
Compressibility is the measure of how a liquid responds to pressure or volume change. It is calculated using the formula β = -1/V (dV/dP), where β is the compressibility, V is the volume, and dV/dP is the change in volume over the change in pressure.
The ability to flow is the measure of how a liquid can move from one place to another. It is calculated using the formula Q = A x v, where Q is the flow, A is the area of the cross-section of the flow, and v is the velocity.
By using these formulas and calculations, it can be determined that layers 1,2,3, and 4 have liquid-like properties.
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Forgotten how to do this
Explanation to please
Answer:
We can use the trigonometric function sine to calculate the length of AB in a right-angled triangle.
The sine function relates the ratio of the side opposite an angle (in this case, AB) to the hypotenuse (AC) with the angle in question (in this case, angle C):
sin(C) = AB/AC
In this case, we know that angle C is 29 degrees and the hypotenuse AC is 5cm, so we can substitute these values into the equation to find AB:
sin(29) = AB/5
To solve for AB, we can multiply both sides of the equation by 5:
AB = 5sin(29)
AB=2.42cm
Use the teams data frame from the lahmanrbroom package. fit a multivariate linear regression model to obtain the effects of bb and hr on runs () in 1971. use the tidy() function in the package to obtain the results in a data frame.1) what is the estimate for the effect of bb on runs? what is the estimate for the effect of hr on runs?2) fit a linear model on the results from question to determine the effect of year on the impact of bb. for each additional year, by what value does the impact of bb on runs change?3) what is the p-value for this effect?
1) library(lahmanrbroom)
model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))
tidy(model)
2) model2 <- lm(bb ~ year, data = tidy(model))
3) The p-value for this effect is significantly different from zero.
The teams data frame from the lahmanrbroom package1) To obtain the effects of bb (walks) and hr (homers) on runs in 1971 using the teams data frame from the lahmanrbroom package and the tidy() function, the following code can be used:
library(lahmanrbroom)
model <- lm(runs ~ bb + hr, data = teams %>% filter(yearID == 1971))
tidy(model)
The estimate for the effect of bb on runs can be found in the 'Estimate' column for the variable 'bb', and the estimate for the effect of hr on runs can be found in the 'Estimate' column for the variable 'hr'.
2) To determine the effect of year on the impact of bb, a linear model can be fit on the results from the previous question. The following code can be used:
model2 <- lm(bb ~ year, data = tidy(model))
The coefficient for the variable 'year' in this model represents the change in the impact of bb on runs for each additional year.
3) The p-value for this effect can be found in the 'p.value' column of the output of the summary() function applied on the model2, which tests if the coefficient for the variable 'year' is significantly different from zero.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
12y would be the answer
Step-by-step explanation:
To simplify, you first need to combine like terms
6y + 6y =12y
-10x+11x=x
x+12y+8 would be the simplified result
Answer:
x+12y+8
Step-by-step explanation:
8+6y-10x+6y+11x
8+6y+6y-10x+11x.......................collecting like term
8+12y+x = x+12y+8
Determine if the columns of the matrix A span R2. A = 2 1 0 1 Arlo -3 -1 )-The columns span R2. -The columns do not span R2.
The columns of the matrix A span R2.
In order to determine if the columns of the matrix A span R2, we need to check if the columns of A can be used to generate all possible linear combinations of the form a1v1 + a2v2, where a1 and a2 are scalars and v1 and v2 are the columns of A.
A = [2 1]
[0 1]
[-3 -1]
The columns of A are [2, 0, -3] and [1, 1, -1]. To check if these columns span R2, we need to see if we can create any vector in R2 by taking linear combinations of the columns. We can see that by taking linear combinations of the columns, we can create any vector of the form (a, b) in R2.
For example, by taking a = 2, b = 1, we can generate the vector (2, 1) by taking
a[2, 0, -3] + b[1, 1]
And by taking a = 3, b = -1, we can generate the vector (3, -1) by taking
a[2,0,-3] + b[1,1,-1].
So the answer would be: The columns of the matrix A span R2.
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Suppose that rob and big both raise animals and sell them. Because rob and big have different talents, they have varying abilities to raise these animals. In 1 day, rob can produce either 10 cows or 20 pigs. In 1 day, big can produce either 9 cows or 36 pigs.
If Rob can produce either 10 cows or 20 pigs and Big can produce either 9 cows or 36 pigs per day then the person that have comparative advantage in production of Cows is Rob and in production of Pigs is Big .
For Rob :
in 1 day , the number of cows produced is = 10 cows ,
the number of pigs produced is = 20 pigs ;
For Big :
in 1 day , the number of cows produced is = 9 cows ,
the number of pigs produced is = 36 pigs ;
On comparing ,we get that Rob produces more number of Cows than Big;
and also Big produces more number of Pigs than Rob .
Therefore , Rob has advantage in production of Cows and Big has advantage in production of pigs .
The given question is incomplete , the complete question is
Suppose that Rob and Big both raise animals and sell them. Because Rob and Big have different talents, they have varying abilities to raise these animals. In 1 day, Rob can produce either 10 cows or 20 pigs. In 1 day, Big can produce either 9 cows or 36 pigs.
Find who has the comparative advantage in the production of cows and pigs .
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Subtract 1/2 and 2/4 using fraction strips
Answer:
0
Step-by-step explanation:
1/2 = 2/4
1/2-2/4 = 0
