The value of lim F(t) for F(t) if F is a solution to the logistic differential equation dF/dt is 10 in option (c).
Finding through differential equation
[tex]\small \text{Consider the differential equation}\\ \frac{\mathrm{d} F}{\mathrm{d} t}=0.2\left ( 5F-\frac{F^2}{2} \right ),\quad F(0)=47\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{0.2}{2}\left ( 10F-F^2 \right )\\ \frac{\mathrm{d} F}{\mathrm{d} t}=\frac{F}{10}\left ( 10-F \right )\\[/tex]
[tex]\text{Separable the variables of F and t on both sides}\\ \int \frac{1}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{10}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \frac{1}{10}\int \frac{(10-F)+F}{F(10-F)}\: dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{10F}dF-\int \frac{1}{10\left(F-10\right)}dF=\frac{1}{10}\int \: dt\\ \int \frac{1}{F}dF-\int \frac{1}{\left(F-10\right)}dF= \int \: dt\\[/tex]
[tex]\small \ln \left|F\right|- \ln \left|F-10\right|=t+\ln C\\ \ln \left|\frac{F}{F-10}\right| =\ln \left |Ce^{t} \right |\\ \frac{F}{F-10}=Ce^{t}\\ F(0)=47\Rightarrow \frac{47}{47-10}=C\Rightarrow C=\frac{47}{37}\\ \text{Therefore,}\\ \frac{F}{F-10}=\frac{47}{37}e^{t}\\ F=\frac{47}{37}e^{t}(F-10)\\ F=\frac{47}{37}e^{t} F-\frac{470}{37}e^{t}\\ F\left ( \frac{47}{37}e^{t}-1 \right ) =\frac{470}{37}e^{t}\\ =\frac{\frac{470}{37}e^{t}}{\left ( \frac{47}{37}e^{t}-1 \right )}\\[/tex]
[tex]\small F(t) =\frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ \lim_{t\rightarrow \infty }F(t)=\lim_{t\rightarrow \infty } \frac{\frac{470}{37}}{\left ( \frac{47}{37}-e^{-t} \right )}\\ = \frac{\frac{470}{37}}{\left ( \frac{47}{37}-0 \right )}\\ = \frac{\frac{470}{37}}{\frac{47}{37}}\\ =\frac{470}{47}\\ =10\\[/tex]
If F is a solution to the logistic differential equation then dF/dt is 10 in option (c).
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How to get
The midpoint of GH is M(-6,-3). One endpoint is H (-4,4). Find the coordinates of endpoint G
The coordinates of point G are (-8, -10)
What is the midpoint of a line?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments
The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
midpoint(M) = (-6, -3)
H = (-4, 4)
let the coordinates of G be (p,q)
taking the x coordinates for M, G and H
-6 = p -4/2
cross multiply
p -4 = -12
p = -12 + 4
p = -8
taking y-coordinates
-3 = q +4/2
q + 4 = -6
q = -6 -4
q = -10
coordinates of G (-8, -10)
in conclusion the coordinates of G is ( -8, -10)
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Compute the surface integral ∫ ∫S F⋅dS, where F = , over the plane
33x−19y+z=1,0≤x,y≤1, oriented by the upward-pointing normal.
The surface area is 131 square units.
What is Surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies
An upward point normal to the plane 33x−19y+z=1,0≤x,y≤1 is is
N=<33,−19,1>
Therefore F⋅N=33y−19z+x
Since the plane is defined by the equation z=1+19y-33x
the dot product becomes 33x−(33y−19z+x)+x=628x-328y-19
The limits of integration are given as 0≤x≤1, 0≤y≤1
Therefore the surface integral becomes
∫ ∫S F⋅dS= [tex]\int\limits^1_0 \int\limits^1_0{(628x-328y-19)dy} \, dx[/tex]
=[tex]\int\limits^1_0{(628x-183)} \, dx[/tex]
=314x²-183x|₀¹
=131
Hence, the surface area is 131 square units.
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a baseball coach uses a pitching machine to simulate pop flies during practice. the quadratic function f(x)
The time taken by the baseball in the air if the ball is not caught is 4.513 seconds.
Here we have to find the time taken by the baseball.
Given data:
The quadratic function is given:
f(x) = 16x² + 70x + 10
To find the value of x we have to formula:
x = ±b [tex]\sqrt{b^{2} - 4ac}[/tex] / 2a
from the equation we get the value of a, b, and c as:
a = -16
b = 70
c = -10
now putting in the equation we have:
x = -70 ±[tex]\sqrt{70^{2} -4(-16)(10)}[/tex] / 2(-16)
= -70 ±[tex]\sqrt{4900 + 640}[/tex] / -32
= -70 ± √5540 / -32
= - 70 ± 74.43 / -32
By calculating this we get two values:
x = -0.138 and 4.513
Time can never be negative so.
x = 4.513
Therefore the time taken is 4.513 seconds.
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a hypothesis test was performed to decide whether houses are more prone to being lost to fire than condominiums are. the researcher looked at 1500 randomly selected houses and 1200 randomly selected condominiums over a ten year period. then, since over 30 of each were in the sample, the researcher can use a z-test for the difference between two proportions.
o False
o True
It is false, the researcher cannot use a z-test for the difference between two proportions.
A hypothesis test was performed to decide whether houses are more prone to being lost to fire than condominiums are. the researcher looked at 1500 randomly selected houses and 1200 randomly selected condominiums over a ten year period. then, since over 30 of each were in the sample, the researcher cannot use a z-test for the difference between two proportions.
z = (X - mean)/(SD/√n)
Where SD is the standard deviation and n is the number of observations.
Here, the required value is not provided. So, we cannot use the z - test.
Therefore, the researcher cannot use a z-test for the difference between two proportions, so the given statement is false.
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for each of the three plots, identify the strength of the relationship (e.g. weak, moderate, or strong) in the data and whether fitting a linear model would be reasonable.
These following answers are correct
We are given residual plots
In given(a) plot there is weak relationship between scatter points
we see curved relationship in this residual plot therefore model is unreasonable .
Note - This model is reasonable when this plot should look approximately normal and scatterplot of residuals should show random
scatter. In these plots we see weak relationship and line as model is unreasonable
2)We are given residual plot.
Given 2nd (c) plot there is strong relationship between scatter points we see positive straigh line relationship in this plot therefore model is resonable.
Also these model look approximately normal land scatterplot of residuals show random scatter.
In these plot we see strong relationship and linear model is reasonable
Therefore, these statements are correct.
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5-55.
Additional Challenge: At the beginning of 1990, oil prices were $20 a barrel. Some oil investors predicted that the price
of oil would increase by $2.25 a barrel per year.
In the beginning of 2005, the price of oil was $30 a barrel. With increasing demand for oll around the world, oil investors in
2005 predicted that the price of oil would increase by $5.00 a barrel each year.
DILOIL
a. Let a represent the number of years since 2005. Write an equation that predicts the price of oil, y, using the information available in 2005.
b. Investors in 1990 did not have the benefit of the 2005 information. Write an equation that represents the prediction made in 1990, using the same variables as in
part (a). Remember that a represents the number of years since 2005.
c. Use the equations you wrote in parts (a) and (b) to determine when the cost of a barrel of oil would be the same for both price predictions.
d. In the spring of 2011, a barrel of oil was selling for about $112. Which prediction was closer? Was it a pretty good prediction?
a) The linear function for the 2005 estimate is given as follows: y = 30 + 5x.
b) The linear function for the 1990 estimate is given as follows: y = 53.75 + 2.25x.
c) They would be predicted to have the same cost in the year of 2013.
d) The 1990 prediction was closer, however it still had a large residual, hence neither was good enough.
How to define the linear functions?The linear functions are defined in the slope-intercept format, given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change for the price.b is the y-intercept, representing the initial cost in the reference year.Taking 2005 as the estimate, the function is given as follows:
y = 30 + 5x.
Taking 1990 as the estimate, the equation would be of:
y = 20 + 2.25x.
The estimate for 2005 would be of:
y = 20 + 2.25(15) = 53.75.
Hence the equation taking 2005 as the estimate would be of:
y = 53.75 + 2.25x.
The costs would be the same when:
30 + 5x = 53.75 + 2.25x.
2.75x = 23.75
x = 23.75/2.75
x = 8.63 -> + 2005 -> year of 2013.
The estimates for 2011(6 years after 2005) are given as follows:
y = 30 + 5x = 30 + 5(6) = $60.y = 53.75 + 2.25(6) = $67.25. (better estimate but not good enough).More can be learned about linear functions at https://brainly.com/question/24808124
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$6,000 for six years at 8½% compounded daily will grow to:
Multiple Choice
$9,060.00
$9,788.81
$9,991.15
It will grow to $9991.15
How do you teach regrouping to 2nd graders?
Answer:Pass out the pennies and the dimes to your students. Write a couple of problems on the board that will use regrouping. As you write them, write “ones” over the ones column. Write “tens” over the tens column. Have students take out their coins for each problem.
Step-by-step explanation:
Which of the following are solutions to the inequality below? Select all that apply.
4>q/23
q = 138
q = 46
q = 69
q = 92
For the functions f(t) = 5t and g(t) = sin(t) defined on 0≤t<[infinity], compute f * g in two different ways.a. By directly evaluating the integral in the definition of f * g.b. By computing L−1{F(s)G(s)} where F(s)=L{f(t)} and G(s)=L{g(t)}.
The laplace inverse transformation L−1{F(s)G(s)} = 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is
L−1{F(s)} = f(t). (1)
The inverse transform L−1is a linear operator:
L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)
andL−1{cF(s)} = cL−1{F(s)}, (3)
for any constant c
given functions are
f(t) =5t ,g(t) = sin(t)
L(f(t)) = F(s)
L{F(s)*G(s)} = L^-1{5tsin(t)}
=5L^-1{tsin(t)}
=5L^-1{[tex]\frac{d}{ds}[/tex] tsin(t)}
= 5 [tex]\frac{2s}{s^{2} + 1^{2} }[/tex]
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A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles. In how many hours (at a constant speed)
The required time to travel 30 miles is given as 45 minutes and 3/4 hours.
Given that,
A car that travels 20 miles in 1/2 hour at constant speed is traveling at the same speed as a car that travels 30 miles.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Speed = Distance/time
Speed = 20 / [1/2]
Speed = 40 miles per hour,
Time = Distance / Speed
Time = 30 / 40
Time = 3 / 4 hour
Thus, the required time to travel 30 miles is given as 45 minutes and 3/4 hours.
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Question 1 of 10
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The corresponding sides of the triangles are congruent.
B. The triangles have the same shape.
C. The corresponding angles of the triangles are congruent.
D. The triangles have the same size.
Answer:
b c and d
Step-by-step explanation:
At the time of her grandson's birth, a grandmother deposits 14000 in an account that pays 9.5% compounded monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawals are made during this period?
The value of the account at the child's twenty-first birthday is 102125.44
How to determine the value of the account at the child's twenty-first birthday?We can use the compound interest formula to determine the value of the account (A) on the child's twenty-first birthday:
A = P (1 + r/n)^(nt)
Where:
P is the initial amount of money deposited in the account
r is the interest rate
n is the number of times the interest is compounded per year
t is the number of years
Given: P = 14000, r = 9.5% = 0.095, t = 21, n = 12 (i.e. 12 months per year)
Substitututing into A = P (1 + r/n)^(nt):
A = 14000 (1 + 0.095/12)^(12×21)
A = 14000 (1 + 0.095/12)^(252)
A = 102125.44
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a popular brand of pen is available in 5 colors and 4 writing tips. how many different choices of pens do you have with this brand?
If a popular brand of pen is available in 5 colors and 4 writing tips. The number of different choices of pens do you have with this brand is: 20 choices.
How to find the number of different choices of pen?Using this formula to find the number of different choices of pen
Number of different choices of pen = Number of color × Number of writing tips
Where:
Number of color = 5
Number of writing tips = 4
Let plug in the formula
Number of different choices of pen = 5 × 4
Number of different choices of pen = 20 choices
Therefore the number of different choices of pen is 20 choices.
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Which of the following can be a representation of a function?
All of the above can be a representation of a function:
A graph can be used to visualize a function.A table can be used to show input and output values.An equation can be used to express the relationships between the inputs and the outputs.Which of the following can be a representation of a function?Option D. All of the aboveA function can be represented in a variety of ways, such as:
A graph is a useful tool for visualizing the relationship between inputs and outputs of a function. A table can be used to represent the inputs and outputs of a function.An equation can be used to express the relationship between the inputs and outputs.All of these methods are valid representations of a function and can be used to explore and better understand the function.
Since the question is not complete, here's the full task:Which of the following can be a representation of a function?
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PLEASEEE HELP THIS IS 3 GRAFE LEVELS ABOVE ME!
Check your answer to problem 4 by solving it using a different strategy Show your work.
Answer:
you are right
n=1
Step-by-step explanation:
1/2(-3/2n+1)=3/4-n
-3/4n+1/2=3/4-n
-3/4n+2/4=3/4-4/4n
+3/4n +3/4n
2/4=3/4-1/4n
-3/4. -3/4
-1/4= -1/4n
/-1/4. /-1/4
1=n
to check i normally just pop in the value (i know no other way in all my years of school)
1/2(-3/2(1)+1)=3/4-1
1/2(-3/2+1=3/4-1
1/2(-1/2)=-1/4
-1/4= -1/4
hopes this helps please mark brainliest
hese are curves obtained by the intersection of right circular cone and a plane.
a. Parabola
b. Ellipse
c. Hyperbola
d. Conic sections
Answer: conic sections
Step-by-step explanation: the other options are a part of conic sections that are named depending on the angle of the plane relative to the cone, and the intersection.
The domestic price of shoes is $80. After trade the price of a pair of shoes is $60. After trade this country will import
The trade this country will import is given by the option (C) 300 pair of shoes.
The number of shoes exported will be calculated by the formula -
Import = quantity demanded - quantity supplied. The formula is based on the concept that the import of shoes will be carried out once the manufacturing is more than the demand.
The graph indicates the quantity demanded is 1000 and the quantity supplied is 1300. Keep the values in formula to find imports.
Imports = 1300 - 1000
Performing subtraction on Right Hand Side of the equation
Imports = 300
Hence, the import is 300.
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The complete question is attached in figure.
the area of a rectangle is square feet. determine the length and width if the length is times the width.
According to the given area of rectangle, the length and width of the rectangle is 7 and 21 respectively.
Area of rectangle
The standard form of calculating the area of the rectangle is written as,
A = l x w
where l refers the length and w refers the width of the rectangle.
Given,
Here we have given that the area of a rectangle is 147 square feet. And we need to determine the length and width if the length is three times the width.
Let us consider length of rectangle is n,
Then the width of rectangle is 3n.
Here we have to remember that the area of a rectangle is
=> A = n x 3n = 3n²
Here we are told that the area,
=> 3n²=147
Then the value of n² = 49
Therefore, the length is 7 and the width is 21.
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PLEASE HELP! I'LL MARK YOU AS THE BRAINIEST AND I'LL GIVE YOU A LOT OF POINTS!
Answer:
B) -2x+y=8
Step-by-step explanation:
First I looked at the graph and found the y-intercept and slope.
Y-intercept = 8
I found that because the point was the on the y-axis line like (0,8)
To find the slope I identified the next point. From the Y-intercept (0,8), you have to go down 8 units. Then I saw the point go left 4 units which makes it negative.
Slope = -8/4, which is also -2
Slope Intercept Equation (y=mx+b) would be: y=-2x+8
Then I compared it to the options and that's what I got.
• For which of the following equations is (3, - 1) not a solution?
Therefore , x +3 =y is the equation which is not the solution of point (3,-1)
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. It is demonstrated that the expressions on the left and right are equivalent to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations.
Here,
The given equations are ( a) x-4= y (b) 2x -7 =y (c ) x +3 =y ( d) x/3 = -y
Thus from the given equation
We put, values in each of equation to find that values satisfy the equation or not
Thus, we found x +3 =y does not satisfy the point (3,-1)
Therefore , x +3 =y is the equation which is not the solution of point (3,-1)
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The correct question is -
For which of the following equations is (3, - 1) not a solution?
Group of answer choices - y=x-1, -3x=4y-6, 2y-3x=0, 5x+2y=-16
Multiply (2+3i)(13 – 6i) .
Answer:
44+27i
Step-by-step explanation:
Multiply using the FOIL method, then combine the real and imaginary parts of the expression.
Can someone help me with this, please?
π√π÷√π is an irrational number. So option (a) is required answer.
What is irrational number?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number 2. Any irrational number, such as p/q, where p and q are integers, q, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
Examples of irrational number: √3, ∛2, π
π is an irrational because it is neither ending nor recurrent.
Solving each part of options, we get
π√π÷√π = π
√25 = 5
√π÷π = 1
2√2 ÷ √2 = 2
As most of the option give rational number only one option gives irrational number which is π
We get π from option (a)
So, option (a) is correct option.
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What is ? x 5 = 9 for 5th grade
Answer:
The answer is 1.8
Step-by-step explanation:
Let the number be y
So,
y × 5 = 9
5y = 9
Divide both side by 5
5y/5 = 9/5
y = 9/5 = 1.8
Thus, The value of y is 1.8
Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $615. Otherwise, you have to pay your friend $37.
Step 2 of 2 :
If this same bet is made 621 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
If this same bet is made 621 times,then we expect to lose of $4514670
Probability
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The bet is done 621 times then expected value is that we may have a loss of $4514670.if the bet is that is heart comes we will get $615 and lose $37 if not comes.
$615 if hearts come and lose $37 when not comes and bet is made 621 times. Calculate the expected win after 621 times.
There are 578 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 578/52*577/51
=333,506/2652
=125.75
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-125.75
=124.75
When bet is made only 1 time expected value will be 125.75*615-124.75*37
=77,336.25 - 4,615.75
=-72720.5 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -72720*621= 4514670.
Then the expected value when bet is made 621 times is that we will lose $4514670 .
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which option proves the following statement by contradiction? for all real numbers r and s, if r is rational and s is irrational, then r 2s is irrational. proof (by contradiction): suppose not. that is, suppose there are real numbers r and s such that r is rational and s is irrational and r 2s is rational. [we must show that this supposition leads logically to a contradiction.] by definition of rational,
Any whole number, fraction, or decimal that terminates or repeats is a rational number. Any number that cannot be divided into a fraction and hence does not meet the concept of a rational number is said to be irrational.
When it comes to rationality, we have
r + 2s = c/d and r = a/b.
The result of the substitution is a/b + 2s = c/d
2s= c/d-a/b=(bc-ad)/bd
s = (bc-ad)/2bd
Now that both (bc - ad) and (bd) are integers, bd is not equal to 0
As a result, the integer s is a quotient of the two integers (bc - ad) where bd is not equal to 0. So, s is rational according to the definition. This disproves the idea that s is irrational.
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Which of the following is an identity?
A. csc²x + cot²x = 1
B. (cscx + cotx)2 = 1
C. sin²x-cos²x = 1
D. sin²x sec²x + 1 = tan²x csc²x
Answer:
Step-by-step explanation:
it is D as
L.H.S.=sin²x sec²x+1
[tex]\frac{sin^2x}{cos^2x} +1\\=\frac{sin^2x+cos^2x}{cos^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
again
[tex]R.H.S.=tan^2x csc^2x\\=\frac{sin^2x}{cos^2x} \times \frac{1}{sin^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
L.H.S.=R.H.S.
Order the answers of these following expressions from least to greatest. -13 + 12= . -3 - (-2) + 3= . -3 + 9= . 9 + (-15)= . 13 - (-13)= .
The answers of the given expressions ordered from least to greatest is
-6, -1, 2, 6, 26
Ordering the answers of expressions from least to greatestFrom the question, we are to order the answers of the given expressions from the least to greatest
To do this, we will evaluate the expressions
Evaluating -13 + 12 =-13 + 12 = -1
Evaluating -3 - (-2) + 3-3 - (-2) + 3
-3 + 2 + 3 = 2
Evaluating -3 + 9 =-3 + 9 = 6
Evaluating 9 + (-15)9 + (-15)
9 - 15 = -6
Evaluating 13 - (-13)13 - (-13)
13 + 13 = 26
Hence, ordering the answers from least to greatest, we get
-6, -1, 2, 6, 26
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In a simple random sample of 144 households in a city in Kentucky, the average number of children in these households was 1.12 children. The standard deviation from this sample was
2.40 children. A 90 percent confidence interval for the mean number of children in all
households in this city is:
Select one:
O a. 1.12 ± 0.2.
O b. 2.40 ± 0.2.
c. It is impossible to tell without a census.
O d. 1.12 ± 2.40.
O e. 1.12 ± 0.328.
A 90% confidence interval for the mean number of children in all household in this city is 1.12 ± 0.328, using formula for confidence interval.
What are mean and standard deviation ?
The standard deviation is a summary measure of the differences of each observation from the mean.
Formula to calculate confidence interval using mean and deviation:
mean ± Z*(std deviation/√n)
where n = sample size,
Given that :
mean = 1.12
deviation = 2.40
n = 144
We know Z is fixed for 90% confidence i.e. 1.64
So, the confidence interval = 1.12 ± 1.64*(2.4/√144)
= 1.12 ± 1.64 * .2
= 1.12 ± .328
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Jada has $260 to spend on flowers for school celebration. She decides that the only flower that she wants to buy are roses and carnations. Roses cost $1.50 each and carnations cost $0.65 each. Jada buys enough roses so that each of the 75 people attending the event can take home at least one rose. Let x be the number of roses and y be the number of carnations.
a. Write an inequity to represent the constant “that every person takes home at least one rose”
b. Write an inequality to represent the cost constraints?
R ≥75 will be the inequality to symbolize the need that each individual bring home at least one rose, and for the cost requirement, it will be, 1.45R + 0.65C ≤ 200.
What is inequality?
A connection that compares two numbers or other mathematical expressions unequally is known as an inequality in mathematics. Most frequently applied when comparing two numbers on the number line that differ in size.
Given:
Jada has $200 she can use to buy flowers. Each carnation costs $0.65 and a rose costs $1.45, so 75 guests may leave with at least one rose.
Jada has a total of $200.
Let R be the number of roses Jada bought.
There will be 75 persons in all present at the event.
As a result, the cost of R roses at $1.45 each is 1.45R.
Combined with roses C: Jada bought carnations.
Currently, each carnation costs $0.65.
Cost of C carnations at $0.65 per flower, then, equals 0.65C.
Inequality will serve as a restraint that requires everyone to bring home at least one rose,
[tex]R \geq 75[/tex]
There will be inequality that represents the cost limitation.
[tex]1.45R + 0.65C \leq 200[/tex]
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