Find the ordered pair solution for the
system of equations.
f(x) = x² + 4
f(x) = 4x
([? ], 1)
Enter the smallest x first.

Answer:

$11.8

Step-by-step explanation:

Probability of winning = 1/50

Probability of not winning = 1 - 1/50 = 49 / 50

Amount won = 590

X : ____ 590 ___ 0

P(X) : __ 1/50 __ 49/50

Expected payoff :

ΣX * p(x)

(590 * 1/50) + (0 * 49/50)

0.02 * 590 + 0

11.8 + 0

= $11.8

Based on the fact that there are 8 sports drinks and 6 peach flavored drinks, the probability that all 4 drinks picked by Malia would be peach flavored is 0.2143.

The probability that all 4 drinks will be peach flavored can be found as:

= Probability of first drink being peach x Probability of second drink being peach + Probability of third drink being peach + Probability of fourth drink being peach

The probability of the drinks being peach flavored is:

= 6/8 x 5/7 x 4/6 x 3/5

= 0.2143

In conclusion, the probability that all the drinks are peach flavored is 0.2143.

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About 3 full cones of water are needed to be added to the cylinder to completely fill it.

The radius of the right circular cone is 3cm and the slant height is 5 cm.

The height of the cone can be found as,

H = √(5)²- (3)²

H = 4cm

The volume of the cone is given by,

V = πR²H/3

R is the radius and H is the height of the cone,

Putting values,

v = π x 5 x 5 x 4/3

v = 104.71 cm³

Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.

The volume of the cylinder is given as,

V = πr²h

V = π x 4 x 4 x 6

V = 301.59

Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,

nv = V

Putting values,

n104.71 = 301.59

n = 2.85

So, we have to add roughly three full cones of water to completely fill the cylinder.

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The measure of the missing angle is 80 degrees.

The shape of the object formed by GEF is a triangle. A triangle is a polygon that has three sides. The sum of angles in a triangle is 180. A triangle has three vertices.

<EGF = 180 - (28 + 58)

180 - 80

100

<EGF+ <FGT = 180 degrees

This is because angle on straight line is equal to 180 degrees

<FGT = 180 - 100 = 80 degrees

Alternatively, <FGT is equal to80  (28 + 58). This is because the sum of the two interior opposite angles in equal to the exterior angle.

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The probability that the student will finish her trip in 60 minutes or less is 0.4

To find the probability that the student will finish her trip in 60 minutes or less, we need to find the proportion of the total area under the uniform distribution curve that lies to the left of 60 minutes.

Since the travel time is uniformly distributed between 40 and 90 minutes, the probability density function is

f(x) = 1/(90-40) = 1/50, for 40 ≤ x ≤ 90

The probability of finishing the trip in 60 minutes or less is therefore

P(X ≤ 60) = ∫[40, 60] f(x) dx

= (60-40)/50

Do the arithmetic operations

= 0.4

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Answer:

$22.60

Step-by-step explanation:

$20 * 1.13 = $22.60

The problem provides a decay law for the radioactive element polonium, where the amount of the element left after time t is given by Q(t) = Q0 · 2-(t/140), where Q0 is the initial amount.

The question asks us to find the initial amount of polonium present given that 10 mg of the element is left after 700 days. To solve this problem, we can substitute the given values into the decay law and solve for Q0. We can write the equation as 10 = Q0 · 2^(-700/140), and then simplify to 10 = Q0 · 2^(-5), or Q0 = 10 · 2^5 = 320 mg.

In summary, the problem provides a decay law for polonium and asks us to find the initial amount of the element given the amount left after a certain amount of time. By substituting the given values into the decay law and solving for Q0, we find that the initial amount of polonium present was 320 mg.

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Chronic obstructive pulmonary disease (COPD) is a disease characterized by permanent airflow obstruction and extended periods of disability and restricted activity.

Chronic obstructive pulmonary disease (COPD) is a chronic respiratory condition that affects the lungs and airways. It is primarily caused by long-term exposure to harmful substances such as cigarette smoke, air pollution, and occupational hazards.

COPD is characterized by permanent airflow obstruction, which means that the airways become narrowed and it becomes difficult for air to flow in and out of the lungs. This obstruction leads to symptoms such as shortness of breath, persistent coughing, wheezing, and frequent respiratory infections.

The disease is progressive and can result in extended periods of disability and restricted activity, as the individual's lung function gradually declines over time. COPD requires long-term management and treatment to improve symptoms and prevent further deterioration of lung function.

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Answer:

v = k\(\sqrt{E}\)

Step-by-step explanation:

Given v is proportional to \(\sqrt{E}\) then the equation relating them is

v = k\(\sqrt{E}\) ← k is the constant of proportion

Answer:

v = k√E

Step-by-step explanation:

v is proportional to square root of E means:

v ϱ √E

the general formula for variation is y=kx

as y is proportional to x

P(|X-Y|≤1) = P(X=Y) + P(|X-Y| = 1) = 6/25 + 6/25 = 12/25 Answer: a) c=1/25; b) P(X=0 and Y=2)=2/25;

a) The probability mass function (PMF) is given as;f X,Y
​
(x,y)={ c∣x+y∣
0
​
if x,y∈{−2,−1,0,1,2}
otherwise. ​
For a joint PMF, the sum of probabilities across all x and y must be equal to 1. Therefore;∑∑f X,Y
​
(x,y)=1
The sum of the probabilities when (x,y) is not an element of {−2,−1,0,1,2} is zero, and there are 25 other possibilities. When |x+y| = 0, there are four possibilities: (0, 0), (−1, 1), (1, −1) and (2, −2).∑∑f X,Y
​
(x,y)=4c+4c+4c+3c+4c+3c+2c+2c+2c+1c+1c+0+1c+2c+3c+4c+3c+4c+4c+4c+0+4c+4c+4c=25

c=1
Hence, the value of the constant c is; c=1/25
b) For P(X = 0 and Y = 2), there is only one possibility, and that is when X = 0 and Y = 2. Therefore;P(X = 0 and Y = 2) = f X,Y
​
(0,2) = c|0+2| = c×2 = 2/25
c) The marginal distribution of X is given as;f X
​
(x)=∑yf X,Y
​
(x,y)
The possible values of X are -2, -1, 0, 1, 2. The probabilities are as follows:

For x = -2, f X
​
(-2) = (0+0+0+0+1)c = c
For x = -1, f X
​
(-1) = (0+0+0+1+2)c = 3c
For x = 0, f X
​
(0) = (0+0+1+2+1)c = 4c
For x = 1, f X
​
(1) = (0+1+2+1+0)c = 4c
For x = 2, f X
​
(2) = (1+2+1+0+0)c = 4c
Hence, the marginal distribution of the random variable X is given by;f X
​
(-2) = 1/25, f X
​
(-1) = 3/25, f X
​
(0) = 4/25, f X
​
(1) = 4/25, f X
​
(2) = 4/25
d) To evaluate P(|X-Y|≤1), we consider the cases where |X-Y| = 0 or 1. When |X-Y| = 0, this means that X = Y. Therefore;P(X = Y) = ∑xP(X = x and Y = x) = f X,Y
​
(−2,−2)+f X,Y
​
(−1,−1)+f X,Y
​
(0,0)+f X,Y
​
(1,1)+f X,Y
​
(2,2)
= (1+2+1+1+1)c = 6c = 6/25
When |X-Y| = 1, there are four possible pairs; (−1,0), (0,−1), (0,1) and (1,0).P(|X-Y| = 1) = ∑i∑jP(X = i and Y = j) where i and j are any two of −1, 0, 1
= f X,Y
​
(−1,0)+f X,Y
​
(0,−1)+f X,Y
​
(0,1)+f X,Y
​
(1,0)
= (0+0+2+2+2)c = 6c = 6/25

c) The marginal distribution of X is given by; f X
​
(-2) = 1/25, f X
​
(-1) = 3/25, f X
​
(0) = 4/25, f X
​
(1) = 4/25, f X
​
(2) = 4/25; d) P(|X-Y|≤1)=12/25

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This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.

​​​​​​​This is the program in C++ demonstrating the above classes.

#include<iostream>

using namespace std;

class shapes

{

public:

   string name;

   string color;

   virtual void getAttributes()=0;

};

class Circle: public shapes

{

public:

   float radius;

   Circle(string n,string c, float r)

   {

       name=n;

       color=c;

       radius=r;

   }

   float getPerimeter()

   {

       return(2*(3.142)*radius);

   }

   float getArea()

   {

       return((3.142)*(radius*radius));

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Square:public shapes

{

public:

   float side;

   Square(string n,string c, float s)

   {

       name=n;

       color=c;

       side=s;

   }

   float getPerimeter()

   {

       return(4*side);

   }

   float getArea()

   {

       return(side*side);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Triangle:public shapes

{

public:

   float base;

   float height;

   float side1;

   float side2;

   float side3;

   Triangle(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter side1\n";

       cin>>side1;

       cout<<"Enter side2\n";

       cin>>side2;

       cout<<"Enter side3\n";

       cin>>side3;

       return(side1+side2+side3);

   }

   float getArea()

   {

       cout<<"Enter base\n";

       cin>>base;

       cout<<"Enter height\n";

       cin>>height;

       return((0.5)*base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rectangle:public shapes

{

public:

   float length;

   float breadth;

   Rectangle(string n,string c, float l,float b)

   {

       name=n;

       color=c;

       length=l;

       breadth=b;

   }

   float getPerimeter()

   {

       return(2*(length+breadth));

   }

   float getArea()

   {

       return(length*breadth);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Rhombus:public shapes

{

public:

   float diagonal1;

   float diagonal2;

   float side;

   Rhombus(string n,string c)

   {

       name=n;

       color=c;

   }

   float getPerimeter()

   {

       cout<<"Enter Side\n";

       cin>>side;

       return(4*side);

   }

   float getArea()

   {

       cout<<"Enter diagonal 1\n";

       cin>>diagonal1;

       cout<<"Enter diagonal 2\n";

       cin>>diagonal2;

       return((0.5)*diagonal1*diagonal2);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

class Parallelogram:public shapes

{

public:

   float base;

   float height;

   Parallelogram(string n,string c, float b,float h)

   {

       name=n;

       color=c;

       base=b;

       height=h;

   }

   float getPerimeter()

   {

       return(2*(base+height));

   }

   float getArea()

   {

       return(base*height);

   }

   void getAttributes()

   {

       cout<<"Name  :"<<name<<endl;

       cout<<"Color :"<<color<<endl;

   }

};

int main()

{

   int choice;

   while(1)

   {

       cout<<"\n\nEnter your choice :";

       cout<<"\n1 for Circle\n";

       cout<<"2 for Square\n";

       cout<<"3 for Triangle\n";

       cout<<"4 for Rectangle\n";

       cout<<"5 for Rhombus\n";

       cout<<"6 for Parallelogram\n";

       cin>>choice;

       system("cls");

       switch(choice)

       {

       case 1:

           {

               float r;

               cout<<"Enter radius\n";

               cin>>r;

               Circle c("Circle","Yellow",r);

               c.getAttributes();

               cout<<"Perimeter : "<<c.getPerimeter()<<endl;

               cout<<"Area : "<<c.getArea()<<endl;

           }break;

       case 2:

           {

               float side;

               cout<<"Enter side\n";

               cin>>side;

               Square s("Square","Red",side);

               s.getAttributes();

               cout<<"Perimeter : "<<s.getPerimeter()<<endl;

               cout<<"Area : "<<s.getArea()<<endl;

           }break;

       case 3:

           {

               Triangle t("Triangle","Green");

               t.getAttributes();

               cout<<"Perimeter : "<<t.getPerimeter()<<endl;

               cout<<"Area : "<<t.getArea()<<endl;

           }break;

       case 4:

           {

               float l,b;

               cout<<"Enter Length and breadth\n";

               cin>>l>>b;

               Rectangle r("Rectangle","Blue",l,b);

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 5:

           {

               Rhombus r("Rhombus","Purple");

               r.getAttributes();

               cout<<"Perimeter : "<<r.getPerimeter()<<endl;

               cout<<"Area : "<<r.getArea()<<endl;

           }break;

       case 6:

           {

               float b,h;

               cout<<"Enter base\n";

               cin>>b;

               cout<<"Enter height\n";

               cin>>h;

               Parallelogram p("Parallelogram","Pink",b,h);

               p.getAttributes();

               cout<<"Perimeter : "<<p.getPerimeter()<<endl;

               cout<<"Area : "<<p.getArea()<<endl;

           }break;

       }

   }

}

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To solve the exercise you can first take the equation of the given line to its slope-intercept form, that is,

To take the equation of the given line to its slope-intercept form, you can solve for y, like this

Now, two lines are perpendicular if their slopes satisfy the equation

So, in this case, you have

Therefore, the equation that represents a line that is perpendicular to the line 5x + 2y = 12 is

Answer:

I think the answer is 1 3/4 cups

Step-by-step explanation:

Hope this helps! <3

Answer:

100d / (s+2h)

Step-by-step explanation:

The most appropriate test statistic for constructing confidence intervals for the population mean when the population is normally distributed, but the variance is unknown, is the t-statistic.

The t-statistic is used when the sample size is small (typically less than 30) and the population standard deviation is unknown. It takes into account the uncertainty introduced by estimating the population standard deviation from the sample.

To construct a confidence interval using the t-statistic, follow these steps:

Take a random sample from the population.
Calculate the sample mean and sample standard deviation.
Determine the desired level of confidence, often expressed as a percentage (e.g., 95% confidence).
Look up the appropriate critical value from the t-distribution table based on the sample size and desired level of confidence.
Calculate the margin of error by multiplying the critical value by the standard error of the sample mean.
Construct the confidence interval by adding and subtracting the margin of error from the sample mean.
Write the conclusion, stating the confidence interval and interpreting it in the context of the problem.

The t-statistic is the most appropriate test statistic for constructing confidence intervals when the population is normally distributed but the variance is unknown. The t-statistic takes into account the uncertainty introduced by estimating the population standard deviation from the sample.

The steps to construct a confidence interval using the t-statistic include calculating the sample mean and sample standard deviation, determining the desired level of confidence, looking up the appropriate critical value, calculating the margin of error, and constructing the confidence interval.

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Answer:

the scale factor is 25, 3000/125 scaled down,

Step-by-step explanation:

you can also explain this with a 25:1 ratio, 25 inches from the original scaled to 1 inch for the photo copy.

Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months. To calculate how much Derek must give the bank to pay off his car loan after 11 months, we need to consider the principal amount borrowed, the interest rate, the loan term, and the number of payments made.

Derek borrows $30,924.00 to buy a car, and he will make monthly payments for 6 years. The interest rate is 5.89%.

First, we need to calculate the monthly interest rate. We divide the annual interest rate by 12 (number of months in a year) and convert it to a decimal:

Monthly interest rate = 5.89% / 12 = 0.4908%

Next, we calculate the number of payments made up to the point when Derek decides to pay off the loan. In this case, he makes payments for 11 months.

Now, let's calculate the remaining balance on the car loan using the formula for the remaining balance on an amortizing loan:

Remaining balance = Principal * [(1 + r)^n - (1 + r)^p] / [(1 + r)^n - 1]

Where:

Principal = $30,924.00 (initial loan amount)

r = Monthly interest rate (0.004908)

n = Total number of payments (6 years * 12 months per year = 72 payments)

p = Payments made (11 payments already)

Substituting the values into the formula, we have:

Remaining balance = $30,924.00 * [(1 + 0.004908)^72 - (1 + 0.004908)^11] / [(1 + 0.004908)^72 - 1]

Using a calculator, we can evaluate this expression:

Remaining balance ≈ $30,924.00 * [1.4042 - 1.0552] / [1.4042 - 1] ≈ $30,924.00 * 0.3490 / 0.4042 ≈ $26,695.78

Therefore, Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months.

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Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

pls give me brainlyist

Answer:

Substitute x = 11 to x + 4, you get,

11 + 4 = 15

Thanks

\(x+4\) when x is equal to 11

Evaluate:

\((11)+4\)

\(=15\)

Answer:

1.00 meter.

Step-by-step explanation:

For the first day, she dug eighteen twentieth of a meter = \(\frac{18}{20}\) x 1 meter

                                                                        = \(\frac{9}{10}\) meters

The second day, she dug nine twentieth of a mater = \(\frac{9}{20}\) x 1 meter

                                                                        = \(\frac{9}{20}\) meters

Total length of the trench = \(\frac{9}{10}\) + \(\frac{9}{20}\)

                                          = \(\frac{18 + 9}{20}\)

                                          = \(\frac{27}{20}\)

                                          = 1\(\frac{7}{20}\)

                                          = 1.35 meters

Total length of the trench is 1.35 meters.

A reasonable estimate of the total length of the trench is 1.00 meter.

Answer:

It is 1 and 1 half. or C

Step-by-step explanation:

It is 18/20 + 9/20. 18 + 9 = 27, and there is (number)/20. since it is 20 it will get 1 whole. now there is just 7, and 7 you round up to 1 half because 5 and over round up, while 4 and under round down.

Can I have brainlist?

Answer:

x=75

The measures of the polygon are 75, 105, 70 and 110.

Step-by-step explanation:

Since the sum of the angles is 360, we can set up an equation, where all the angles add up to 360:

(x-5)+(x+35)+(1.4x)+(x)=360

x-5+x+35+1.4x+x=360

4.4x+30=360

4.4x=330

x=75

Now, to find the angles, all you have to do is plug in 75 for x in every angle:

First angle: 75

Second angle: 1.4*75=105

Third angle: 75-5=70

Fourth angle: 75+35=110

Answer:

3/8

Step-by-step explanation:

the answer is 3/8 because u are muliplying 1/2 and 3/4 and 1×3 is 3 and 2×4 is 8 3/8

Answer:

Meters

Step-by-step explanation:

The position of an object is its location at a given time. Which is subjected to change with respect to time, especially for any object which has potential energy.

In the standard unit of measurements (SI unit), it is required that distance which is a measure of length is recorded in meters. Thus, the best unit of measurement to use when recording a change in the position of an object is meters.

A website randomly generates an initial password for new users, which consists of five letters. The password cannot contain numbers or special characters, and each letter can only be used once. To create such a password, you would follow these steps:

1. Start with an empty password string.
2. Generate a random letter.
3. Check if the generated letter is already in the password string.
4. If the letter is not in the password string, add it to the string.
5. Repeat steps 2-4 until the password string contains five unique letters.
6. Use the final password string as the initial password for the user's account.

By following these steps, the website can ensure that each user is assigned a unique initial password consisting of five letters, without any numbers or special characters.

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The equilibrium quantity can be found by setting the demand equal to the supply and solving for x.

This gives x = 2716. The producer surplus at the equilibrium quantity can be found by calculating the area between the supply curve and the equilibrium price (which is found by substituting x=2716 into either the demand or supply function). This gives a producer surplus of $3285.64.
The equilibrium quantity occurs when the demand function, d(x), equals the supply function, s(x). Therefore, we can set d(x) = s(x):
2312/√x = 2√x
To solve for x, multiply both sides by √x, which gives:
2312 = 2x
Now, divide both sides by 2:
x = 1156 items
To find the producer surplus at the equilibrium quantity, we need the difference between the total revenue and the total cost. The total revenue can be found by multiplying the equilibrium quantity (x) by the supply function, s(x):
Total revenue = 1156 * 2√1156 = $4612
The total cost can be found by integrating the supply function:
Total cost = ∫2√x dx from 0 to 1156 = (4/3)x^(3/2) evaluated from 0 to 1156 = $3468
The producer surplus is the difference between the total revenue and the total cost:
Producer surplus = $4612 - $3468 = $1144

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The equation of the locus of P is y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.

Consider a point P(x, y) on the locus of P, which is equidistant from point A(3, k) and the straight line L: y = -3.

The perpendicular distance from a point (x, y) to a straight line Ax + By + C = 0 is given by |Ax + By + C|/√(A² + B²).

The perpendicular distance from point P(x, y) to the line L: y = -3 is given by |y + 3|/√(1² + 0²) = |y + 3|.

The perpendicular distance from point P(x, y) to point A(3, k) is given by √[(x - 3)² + (y - k)²].

Now, as per the given problem, the point P(x, y) is equidistant from point A(3, k) and the straight line L: y = -3.

So, |y + 3| = √[(x - 3)² + (y - k)²].

Squaring on both sides, we get:

y² + 6y + 9 = x² - 6x + 9 + y² - 2ky + k²

Simplifying further, we have:

y² - x² + 6x - 2xy + y² - 2ky = k² + 2k - 9

Combining like terms, we get:

y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0

Hence, the required equation of the locus of P is given by:

y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.

Thus, The equation of the locus of P is y² - 2xy + (k² + 2k - 18)x + (k² + 4k) - 9 = 0.

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You need to mix 60 liters of the 40% alcohol solution with 60 liters of the 60% solution to get a 50% solution.

Let's solve the problem step by step:

Step 1: Define the variables:

Let x be the number of liters of the 40% alcohol solution that needs to be mixed.

Step 2: Write the equation based on the alcohol content:

In the final mixture, the amount of alcohol from the 40% solution and the amount of alcohol from the 60% solution should be equal.

Alcohol from the 40% solution + Alcohol from the 60% solution = Total alcohol in the mixture

0.40x + 0.60(60) = 0.50(x + 60)

Step 3: Solve the equation for x:

0.40x + 0.60(60) = 0.50x + 0.50(60)

0.40x + 36 = 0.50x + 30

0.10x = 6

x = 6 / 0.10

x = 60

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Answer:

d. $6

Step-by-step explanation:

From the given set S, the only integer that makes the inequality m - 5 + 3 false is m = -24.

To determine which integer(s) from the set S: (-24, 2, 20, 35) will make the inequality m - 5 + 3 false, we need to substitute each integer from the set into the inequality and check if the inequality becomes false.

The inequality is:

m - 5 + 3 < 0

Substituting each integer from the set S into the inequality:

For m = -24:

(-24) - 5 + 3 < 0

-26 + 3 < 0

-23 < 0 (True)

For m = 2:

2 - 5 + 3 < 0

0 < 0 (False)

For m = 20:

20 - 5 + 3 < 0

18 < 0 (False)

For m = 35:

35 - 5 + 3 < 0

33 < 0 (False)

From the given set S, the only integer that makes the inequality m - 5 + 3 false is m = -24.

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