Vector equation: r(t) = <1, -1, 7> + t<6, 7, -6>
Parametric equations:
x(t) = 1 + 6t
y(t) = -1 + 7t
z(t) = 7 - 6t
The vector equation and parametric equations describe the line segment that joins the two points p and q.
The vector equation is given by r(t) = <1, -1, 7> + t<6, 7, -6>
Here, <1, -1, 7> is the vector that represents the point p, and <6, 7, -6> is the direction vector of the line segment.
The variable t is a scalar parameter that describes the position of any point on the line segment.
The parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.
These equations express the coordinates of any point on the line segment in terms of the parameter t. So we can substitute any value of t between 0 to 1 in this equation to get the coordinates of a point on the line segment.
For example, if we substitute t = 0, we get x(0) = 1, y(0) = -1, z(0) = 7
which gives us the coordinates of point p.
Similarly, if we substitute t = 1, we get x(1) = 7, y(1) = 6, z(1) = 1
which gives us the coordinates of point q.
So, the line segment is defined by the set of all points whose coordinates are given by these equations for values of t between 0 and 1.
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What is the difference between a class boundary and a class limit? (Select all that apply.)
A. Class limits specify the span of data values that fall within a class.
B. Class boundaries are values halfway between the upper-class limit of one class and the lower class limit of the next.
C. Class boundaries specify the span of data values that fall within a class.
D. Class boundaries are not possible data values.
E. Class limits are not possible data values.
F. Class limits are possible data values.
G. Class limits are values halfway between the upper-class boundary of one class and the lower-class boundary of the next.
H. Class boundaries are possible data values.
Class limits indicate the largest and smallest data values that can be included in the class. Class limits are referred to actual data values. On the other hand, class boundaries give values that remove gaps between the classes in the frequency distribution. Class boundaries are considered to be one decimal place more accurate in comparison to the data. Options A, B, D, and F correctly describe differences between a class boundary and a class limit.
Following are the potential differences between a class boundary and a class limit.
Class limits define the span of data values that fall within a class.Class boundaries are referred to the values halfway between the upper-class limit of one class and the lower-class limit of the next.Class boundaries are not possible data values.Class limits are possible data values.You can learn more about class boundary and a class limit at
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2x^4 = 50 how do you solve this using factoring?
[tex] {2x}^{4} = 50 \\ = > {x}^{4} = \frac{50}{2} \\ = > {x}^{4} = 25 \\ = > {x}^{4} - 25 = 0 \\ = > ( {x}^{2} + 5)( {x}^{2} - 5) = 0 \\ = > {x}^{2} - 5 = 0 \\ > (x - 5)(x + 5) = 0 \\ = > x = 5 \: \: and \: \: - 5[/tex]
Answer:
5, -5
Hope it helps.
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a committee of five people is to be randomly selected from a group that contains six women and three men. how many different committees can be form ed if the committee is to have at least three women?
There are a total of 126 different committees that can be formed with at least three women.
The number of different committees that can be formed with at least three women from a group of six women and three men can be calculated using the Combination formula. The Combination formula is defined as follows:
C(n,r)=n!/r!(n-r)!
where n is the total number of elements in the group and r is the number of elements to be selected from it.
In this case, n = 9 (6 women + 3 men) and r = 5 (the size of the committee).
Therefore, the number of different committees that can be formed with 3 women is:
C(9,5) = 9!/(5!*(9-5)!) = 9!/5!*4! = 126
Therefore, there are a total of 126 different committees that can be formed with at least three women.
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The following set of ordered pairs, represents a power inverse variation. Find the value of r given that k=5. ( 1/2,20)(1,5)(2,5/4) : a. r=5 b. r=2 c. r=-5 d. r=2
The correct value of r is 2.
What is the power inverse variation?
Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
The equation for a power inverse variation is y = kx^r,
where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.
We have given the set of ordered pairs,
we can find the value of r by substituting in the known values of x and y and solving for r.
(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2
So the answer is:
r = 2
Hence, the correct value of r is 2.
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2(x + 3=5x + 6 - 3x true or never true
Answer:
true
Step-by-step explanation:
2(x + 3)=5x + 6 - 3x true or never true?
2(x + 3)=5x + 6 - 3x
2x + 6 = 2x + 6
2x - 2x = 6 - 6
0 = 0
what are differences or similarities between everyday logic and mathematical logic? how can the study of mathematical logic help you in your everyday life?
Mathematics focuses on geometry, numbers, and form. For such, axioms and definitions are needed to describe the study's subjects. On the basis of those definitions and axioms, properties are proved using logic.
Mathematical logic help you in using a phone, sending a fax, or operating a vehicle and many other things.
Logic models are composed of mathematical constructs. When it comes to supporting its conclusions, mathematics employs logic. The "science" of reasoning is logic. It deals with arguments, hence learning what constitutes a strong argument is a need for becoming a logician.
Logic can also be applied in everyday conversation about non-mathematical subjects. The amount of reasoning required is typically much more for mathematical inquiries than for non-mathematical ones.
Therefore, logic is a technique that mathematicians (as well as other individuals) employ when it comes to supporting their claims. Proof involves logic.
Mathematical logic has a direct impact on our daily life now more than ever. I'm not only referring to the marks pupils receive or the number of required mathematical subjects. I'm referring to using a phone, sending a fax, or operating a vehicle. I'm referring to making a home, purchasing medication for your family, and enjoying music.
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a food corporation declared a dividend of php 1,000,000 for its common stocks.suppose there are 60,000 shares of common stocks how much is the dividend per share?
BONUS: There are 16 ounces in one pound.
a) How many pounds does a 137 ounce baby weigh?
B) Another baby weighs 9 3/8 pounds. How much heavier (in ounces) is it than the first baby?
Answer:
a) To find out how many pounds a 137 ounce baby weighs, we divide the weight in ounces by the number of ounces per pound.
137 ounces / 16 ounces/pound = 8.5625 pounds
Therefore, a 137 ounce baby weighs 8.5625 pounds.
b) To find out how much heavier the second baby is, we first convert the weight of the second baby from pounds to ounces.
We know there are 16 ounces in one pound, so we can multiply 9.375 (9 3/8) by 16 to find out how many ounces the second baby weighs.
9.375 * 16 = 150.4 ounces
Now we can subtract the weight of the first baby from the weight of the second baby to find out the difference in weight.
150.4 - 137 = 13.4 ounces
Therefore, the second baby is 13.4 ounces heavier than the first baby.
in a stem-and-leaf display, . a. a single digit is used to define each stem, and one or more digits are used to define each leaf b. one or more digits are used to define each stem, and a single digit is used to define each leaf c. a single digit is used to define each stem, and a single digit is used to define each leaf d. one or more digits are used to define each stem, and one or more digits are used to define each leaf
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
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In ΔCDE, the measure of ∠E=90°, DC = 97, CE = 72, and ED = 65. What ratio represents the sine of ∠C?
The ratio that represents the sine of angle C is 65/97
Determining the ratio of the sine of an angleFrom the given information, we are to determine the ratio that represents the sine of angle C
From SOH CAH TOA, we know that
sin(angle) = Opposite / Hypotenuse
Given triangle CDE with C as reference angle,
DE = Opposite
CD = Hypotenuse
Then,
We can write that
sin(C) = DE/CD
From the given information
DE = 65
CD = 97
Thus,
sin(C) = 65/97
Hence, the ratio is 65/97
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Find the total surface area of this cuboid.
5 cm
4 cm
6 cml
Answer: 148
Step-by-step explanation: To find the surface area, add up all the side areas. Since we know that the opposite side of one side is the same, we can do 2(4 *5) + 2(6*5) + 2(4*6). This will get 148.
Name the property of real numbers illustrated by the equation.
-2(x+4)=2x-8
A. Associative property of multiplication
B. Commutative property of addition
C. Distributive property
D. Associative property of addition
The property of real numbers illustrated by the equation -2(x+4)=-2x-8 is option C: Distributive property.
What is Distributive property?
The distributive law of multiplication and addition and subtraction is another name for the distributive property. By its very name, the procedure implies that something will be divided or distributed.
The given equation is -2(x+4)=-2x-8.
According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC.
In the equation it can be clearly seen that the form is distributive form as -
A = -2
B = x
C = 4
Therefore, the equation uses distributive property.
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How do I solve this equation
Answer: 20x
Step-by-step explanation:
Q: Find (i) The area and (ii) The perimeter of the shaded region in each of the following figures given that all arcs are either quadrant or semicircles.
(please help me solve this and tell me how to solve it properly!)
Answer:
Step-by-step explanation:
ask if you don't understand my answer
Answer:
Shaded area = 42.1 cm^2
Shaded perimeter = 44 cm
Step-by-step explanation:
See the attached worksheet. The approach is the subtract the 4 semicircle areas from the total quare area to obtain the area of the shaded region. The perimeter is calculated by the perimeter of one complete circle. Since all four semicircles are 1/4 of the full circle, the total perimeter is equivalent to one full circle.
Pls help with theseeeeeeee
Yes, you can assume both statements. In the diagram, planes W and X intersect at the line KL.
Determine whether you can assume the statement?This means that the points K, L, M, and N lie on the same plane, making them coplanar.All four points are contained within the same plane and are connected by lines, so it is clear that they all lie on the same plane.This means that statement 11 is true and statement 12 is also true.Yes, you can assume the statement in Exercises 11 and 12.The statement in Exercise 11 is true because it is shown in the diagram that Planes W and X intersect at KL.The statement in Exercise 12 is true because the points K, L, M, and N all lie on the same plane, which is Plane W.This type of reasoning is called deductive reasoning.Deductive reasoning is a logical process in which a conclusion is drawn based on the evidence that is given.In this case, the evidence is the diagram and the conclusion is the statement in the exercise.
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z is a standard normal random variable. the p(z ≥ 2.11) equals
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
To calculate the p(z ≥ 2.11), you can use a z-table to look up the z-score. This z-score falls in the area of the tail of the distribution, which means it is the area to the right of 2.11.
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
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will, tim and harry are going to have dinner together. will pays for 2 pizza costing 3.75 each. tim pays for 3 desserts costing 1.09 each. tim says I´ve paid my fair share of the total cost. Find out if Tim is correct. You must justify your answer.
Answer:
To determine if Tim is correct in stating that he has paid his fair share of the total cost, we need to calculate the total cost of the dinner and compare it to the cost of the desserts Tim paid for.
Will paid for 2 pizzas at a cost of $3.75 each, for a total of 2 * $3.75 = $7.50
Tim paid for 3 desserts at a cost of $1.09 each, for a total of 3 * $1.09 = $3.27
The total cost of the dinner is $7.50 + $3.27 = $10.77
To check if Tim has paid his fair share, we need to compare the cost of the desserts he paid for ($3.27) to the total cost of the dinner ($10.77)
$3.27 is 30.3% of $10.77, meaning Tim paid for around 30% of the dinner.
In this case, it's not fair to say that Tim has paid his fair share of the total cost, since he paid for only around 30% of the dinner, and as such, this cost should be split among the three of them.
It would be more accurate to say that Tim has paid a portion of the dinner, but not his fair share.
When 6 is added to a number, the result is 50. Which equation would help you find your solution?
Answer:
Step-by-step explanation:
the answer is 44
Draw a model that shows 5 x 3/5 = 3
The model that shows 5 * 3/5 = 3 can be shown by sketching the boxes and shading the given parts.
What are model of multiplication?The model of multiplication is a visual representation used to show multiplication without algebraic calculation. The model includes boxes and squares to indicate the multiplication.
How to draw model of multiplication?Draw 3 boxes to represent 3 groups, and then place 8 in each box to represent 8 things in each group in order to multiply 3 by 8. There are several methods to draw this model.
We deduced from the model that the unknown value (?) may be determined by dividing the number of boxes (three, which stand for three groups) by the eight items.
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Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
A(−7, — 5), B(-2, 0); 1 to 4
The coordinates of P are
The coordinates of the point P along the directed line segment AB are (-6, -4).
How to determine the coordinates of point P?In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 1 to 4.
Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(1(-2) + 4(-7))/(1 + 4)], [(1(0) + 4(-5))/(1 + 4)]
P(x, y) = [(-2 - 28)/(5)], [(0 - 20)/5]
P(x, y) = [-30/5], [(-20)/(5)]
P(x, y) = [-6, -4]
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Tuxedo Rental, first day seventy-five dollars, each additional day ten dollars.
Clyde rents a tuxedo for several days. Let d represent the number of additional days Clyde uses the tuxedo. Write an algebraic expression to represent the total cost of the rental after d additional days.
The algebraic expression representing the total cost of the rental after d additional days is 75 + 10d.
What is an algebraic expression?An algebraic expression is a combination of constants, numbers, values, and variables.
Algebraic expressions are not the same as equations because they lack the equation symbol and do not lay claim to the equality of mathematical expressions.
The rental cost on the first day = $75
The rental cost per additional day = $10
The number of additional days Clyde uses the tuxedo = d
Algebraic expression to represent the situation:
75 + 10d
Thus, an algebraic expression we can use to represent the total cost that Clyde incurred for renting the tuxedo after d additional days is 75 + 10d.
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same has 4 times as many nickels as dimes. he had 0.90 in all. how many coins of each type does he have>
The number of dimes are 2 and number of nickels are 8 according to the sum and number of coins.
Let the number of dimes be x. The number of nickels will be 4x. Also, as per the known fact, the value of dimes is 0.1 and value of nickels is 0.05. Keeping the values in formula -
0.05x + 0.1×4x = 0.90
0.05x + 0.4x = 0.90
Performing addition on Left Hand Side of the equation
0.45x = 0.9
Rewriting the equation
x = 0.9/0.45
Performing division on Right Hand Side of the equation
x = 2
Number of dimes = 2
Number of nickels = 4×2
Performing multiplication
Number of nickels = 8
Thus, there 2 dimes and 8 nickles.
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GEOMETRY/ TRIG
Anything helps! Thank you
This is an example of a triangle with two missing sides.
TrigonometryTo find the missing sides of a triangle, you can use the trigonometric ratios of sine, cosine, and tangent. All of these are based on the reference angle, which is the angle between the two known sides.For example, if the reference angle is 30°, then the trigonometric ratios are: sine of 30° is 1/2, cosine of 30° is √3/2, and tangent of 30° is √3/3.To find the missing sides of a triangle, you can use the Law of Sines and Law of Cosines. The Law of Sines states that the ratio of the lengths of the sides of a triangle to the sines of their opposite angles is the same for all three sides. The Law of Cosines states that the sum of the squares of the two sides of a triangle is equal to the square of the third side minus twice the product of the two sides multiplied by the cosine of the angle between them.Using these two laws, you can solve for the missing sides of the triangle. For example, if you know the length of two sides and the angle between them, you can use the Law of Cosines to find the length of the third side. Then, you can use the Law of Sines to find the angles of the other two sides. This method of finding the missing sides of a triangle is called trigonometry.To learn more about trigonometry refer to:
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ANDY DALTON THREW 18 TOUCHDOWn
PASSES LAST SEASON. In 2016 He
THREW 25 TOUCHDOWN PASSES. WHAT
WAS HIS PERCENT OF CHANGE?
The percentage change in the Touchdown passes is 28 %
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
Andy Dalton's throw is 18 touchdaown
In last saeson he threw 25 touchdown
So, the percentage change = (25-18)/25 * 100 = 28 %
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if 15% of adults in a certain country work from home, what is the probability that fewer than 42 out of a random sample of 350 adults will work from home?
If 15% of adults in a certain country work from home, then probability that fewer than 42 out of a random sample of 350 adults will work from home is 0.05 .
the percent of students that work from home is (p) = 15% = 0.15 ;
the number of adults in the sample is (n) = 350 ;
to find the probability , we first need to find the mean and standard deviation ;
So , mean [tex](\mu)[/tex] = [tex]n\times p = 350\times 0.15 = 52.5[/tex] ;
and Standard Deviation[tex](\sigma)[/tex] = [tex]\sqrt{np(1-p)} = \sqrt{3550\times 0.15 \times 0.85} = 6.68[/tex] ;
We need to calculate the probability that fewer than 42 out of a random sample of 350 adults will work from home ,
which means ; [tex]P(X < 42-0.5) = P(X < 41.5)[/tex] ,
So , the probability will be the p value of Z when x= 41.5 ;
we know that ; [tex]z= \frac{X-\mu}{\sigma}[/tex] ;
substituting the values of mean and standard deviation ;
⇒ [tex]Z = \frac{41.5-52.5}{6.68}[/tex] ;
On solving ,
we get ;
⇒ [tex]Z = -1.65 ;[/tex] and the p value at z = -1.65 is 0.05 .
Therefore , the required probability is 0.05 or 5% .
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Josh graphs a system of equations to determine the roots of the polynomial equation x Superscript 5 Baseline
The statement 2 is true i.e. He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.
Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.
For the equation provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.
The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.
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The correct question is:
Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x² . From the graph, he determines that there are two solutions to the equation. Which statement is true?
He is correct because the least exponent of the system is two so there must be two solutions.He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be multiplicities or complex.He is correct because the graph shows two intersection points.He is not correct because the difference of the exponents is three, so there must be three solutions, one of which is a multiplicity.if the heights of 99.7 of american men are between 5 and 7 what is the estimate of the standard deveiation of the height of american men
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
What is the empirical rule?
If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question: The height of a large population of ostriches is normally distributed.
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
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How does the us tax policy encourage long-term investments?
a. by making long-term investments tax exempt
b. by making treasury bonds tax exempt
c. by making it illegal to earn short-term gains
d. by providing a lower tax rate for long-term gains
The US tax policy encourage long-term investments by providing a lower tax rate for long-term gains.
Therefore the answer is d. by providing a lower tax rate for long-term gains.
In the United States, the tax code provides a lower tax rate for long-term capital gains, which are gains on investments held for more than one year, as a way to encourage long-term investments. This means that when an investor sells an asset that they have held for more than one year, they will pay a lower tax rate on the gain than they would if they had held the asset for less than one year. This provides an incentive for investors to hold on to their investments for a longer period of time, rather than engaging in short-term buying and selling.
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how can you identify if a function is increasing or decreasing using the derivative function of the functions
If the derivative of a function is positive, then the function is increasing. If the derivative of a function is negative, then the function is decreasing.
1. Take a function, f(x).
2. Take the derivative of the function, f'(x).
3. If f'(x) is greater than 0, then the function is increasing.
4. If f'(x) is less than 0, then the function is decreasing.
To determine if a function is increasing or decreasing, the derivative of the function must be found. The derivative of a function is written as f'(x). If the derivative is greater than 0, then the function is increasing. If the derivative is less than 0, then the function is decreasing. This is because an increasing function has a positive slope, and a decreasing function has a negative slope. The derivative is the slope of the function, so if the derivative is positive, the function is increasing, and vice versa.
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Let $f(n)$ be the sum of the positive integer divisors of $n$. If $n$ is prime and $f(f(n))$ is also prime, then call $n$ a bouncy prime. What is the smallest bouncy prime
The smallest bouncy prime is 2.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.
A number n is said to be a bouncy prime if it is prime, and the sum of the positive divisors of n (also known as the sum of divisors function, denoted f(n)) is also prime.
The smallest prime number is 2. The sum of divisors of 2 is
1+2 = 3
which is also prime, so 2 is a bouncy prime.
Since 2 is the smallest prime and it is a bouncy prime, the smallest bouncy prime is 2.
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