The equivalent expression of the perimeter of the regular hexagon is,
⇒ 42x + 24
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A regular hexagon has six congruent sides.
And, The length of each side is represented by the expression (7x + 4).
Now, We know that;
The sum of all sides of a regular hexagon is called its perimeter.
Hence, We get;
Here, The length of each side is represented by the expression 7x + 4.
So, We get;
The perimeter of Hexagon = 6 × (7x + 4)
= 42x + 24
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the cost of a movie ticket was $10 . it increased by 15% . how much is the movie ticket now ?
Implement an efficient string matching algorithm.
That is, given a string of length N and a pattern of length k, write a program that searches for the pattern in the string with less than O(N * k) worst-case time complexity.
To implement string matching algorithm, we can use naive algorithm and write the program in C.
To conduct the string matching we can use naive algorithm. Among the pattern finding algorithms, naive pattern searching is the most basic. It looks for all characters in the main string that match the pattern.
The program in C:
---------------------------------------
#include <stdio.h>
#include <string.h>
int match(char [ ], char [ ]);
int main() {
char x[200], y[200];
int po;
printf("Write your text\n");
gets(x);
printf("Write thepattern you want to find\n");
gets(y);
pos = match(x, y);
if (pos != -1) {
printf("Found at location: %d\n", pos + 1);
}
else {
printf("No match.\n");
}
return 0;
}
int match(char text[], char pattern[]) {
int p, q, r, text_long, pattern_long, pos = -1;
text_long = strlen(text);
pattern_long = strlen(pattern);
if (pattern_long > text_long) {
return -1;
}
for (p = 0; p <= text_long - pattern_long; p++) {
pos = r = p;
for (q = 0; q < pattern_long; q++) {
if (pattern[q] == text[r]) {
r++;
}
else {
break;
}
}
if (q == pattern_long) {
return pos;
}
}
return -1;
}
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work out the area of this shape
Answer:
80
Step-by-step explanation:
96-16
suppose you buy a car with a value of 9250 each year the value of your car will depricate by 5.1 percent how much will your car be worth in 8 years
Answer: $6085.15
Step-by-step explanation:
Substituting into the exponential decay formula yields [tex]9250(1-0.051)^8 \approx \$6085.15[/tex].
The length of a picture is 2 more than the width. There is a frame of uniform width around the picture that is 3 inches wide. If the area of everything is 224 in 2 , find the dimensions of the picture.
Width = 8 inch
Length = 10 inch
This can be solved using rectangular area formula.
What is rectangular area?The area a rectangle takes up inside its four sides or limits is known as the area of the rectangle. A rectangle's sides determine how much space it has. The product of the rectangle's length and width is essentially the area formula.
By multiplying the rectangle's length by its breadth, we may get its area.
length of the picture = l inch
width of the picture = w inch
given that, length of a picture is 2 more than the width.
so, l = w + 2
There is a frame of uniform width around the picture that is 3 inches wide, now length becomes: l = w + 2 + 3
l = w + 5
and the width becomes: w = w + 3
the area of everything is 224 inch²
l × w = 224 inch²
or, (w + 5) × (w + 3) = 224 inch²
or, w² + 8w + 15 = 224
or, (w + 19) (w - 8) = 0
or, w = 8, -19
Width never be negative so w = 8 inch
Now, length = w + 2
l = 8 + 2
l = 10 inch
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The dimensions of the picture are 10 × 8 in if the area of everything is 224 in².
What is a rectangular area?The area a rectangle takes up inside its four sides or limits is known as the area of the rectangle. A rectangle's sides determine how much space it has. The product of the rectangle's length and width is essentially the area formula.
By multiplying the rectangle's length by its breadth, we may get its area.
Length of the picture = l inch
Width of the picture = w inch
Given that, the length of a picture is 2 more than the width.
So, l = w + 2
There is a frame of uniform width around the picture that is 3 inches wide, now length becomes: l = w + 2 + 3
l = w + 5
The width becomes: w = w + 3
The area of everything is 224 inch².
l × w = 224 inch²
(w + 5) × (w + 3) = 224 inch²
w² + 8w + 15 = 224
(w + 19) (w - 8) = 0
w = 8, -19
Width never be negative so w = 8 inch
Now, length = w + 2
l = 8 + 2
l = 10 inch
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Pls Answer ASAP!
The following problem shows an expression in exponential notation. The missing powers of 10 are represented by letters.
Type the powers into the boxes that correspond to each letter. Use a slash (/) to show a fraction. Use a caret (^) before an exponent.
61.32 = 6 x A + 1 x B + 3 x C + 2 x D
The powers that correspond to each letter are given as follows:
A = 1.B = 0.C = -1.D = -2.How to obtain the powers that correspond to each letter?The number for this problem is defined as follows:
61.32.
Before obtaining the powers that correspond to each letter, we need to obtain the integer and decimal parts, as follows:
Integer: 61.Decimal: 32.Then the digits are classified as follows:
Digit 1 is the unit digit, hence the power of 10 is 0, which is the value of B.Digit 6 is the tens digit, hence the power of 10 is 1, which is the value of A.Digit 3 is the tenths digit, hence the power of 10 is -1, which is the value of C.Digit 2 is the hundredths digit, hence the power of 10 is -2, which is the value of D.More can be learned about integer and decimal parts at https://brainly.com/question/1827193
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Aubrey is older than Chase. Their ages are consecutive integers. Find Aubrey's age if the product of their ages is 56.
For how many positive integers $n$ does $\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit
Therefore , the solution of the given problem of integer comes out to be 1/100 = 0.01
What is integer?Zero, a positive integer, or a negative integer denoted by a minus sign are all examples of integers. A negative number is the additive reciprocal of a positive number that it corresponds to. A bold Z or a bold "mathbb Z" is frequently used in mathematical notation to denote a group of integers. A positive, negative, or zero integer—not a fraction—is referred to as an integer (pronounced IN-tuh-jer). The numbers -5, 1, 5, 8, 97, and 3,043 are examples of integers. 1.43, 1 3/4, 3.14, and other numbers are non-integer examples. Integers are a collection of integers and their antipodes. Decimals and fractions are not part of the set of integers.
Here,
=> 1/4 =0.25
=> 1/20 = 0.05
=> 1/25 = 0.04
=> 1/50 = 0.02
=> 1/100 = 0.01
Therefore , the solution of the given problem of integer comes out to be 1/100 = 0.01
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In order for the number to form a terminating decimal, 2 and 5 must be its only prime factors. Obviously any number less than [tex]0.01[/tex] or any value of [tex]n > 100[/tex] will not have a nonzero hundredths digit.
We now count the possibilities for [tex]n[/tex]:
[tex]5^0 : 2^0, 2^1,..., 2^6 \rightarrow 7 \text{ values}\\5^1 : 2^0, 2^1,..., 2^4 \rightarrow 5 \text{ values}\\5^2 : 2^0, 2^1, 2^2 \rightarrow 3 \text{ values}[/tex]
for a subtotal of [tex]15[/tex] values.
However, some of these have a nonzero tenths digit and a zero hundredths digit. In other words, we need to remove all of the single-digit terminating decimals from this list. These are [tex]\dfrac{1}{1} = 1.00,\dfrac{1}{2} = 0.50,\dfrac{1}{5}=0.20, \text{ and }\dfrac{1}{10} = 0.10 \implies 4 \text{ values}[/tex]
which means the final answer is [tex]15-4=11[/tex].
On a particular day, the amount of untreated water coming into the plant can be modeled by f(t) = 100 + 30cos(t/6) where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(/2)a) Define a new function, a(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critical values of this function over the interval [0, 24).d) Determine whether the critical values represent local maximums or minimums.e) Determine the maximum and minimum amount of untreated water in the plant for the day.
Answer:
where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(/2)a) Define a new function, a(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critica
Solve for x over the complex numbers. x2+8x+20=0 Enter your answers in the boxes in standard form. x = or x =
The two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.
The given equation is a quadratic equation in x, of the form ax2 + bx + c = 0, where a = 1, b = 8 and c = 20.
To solve this equation, we use the quadratic formula, which states that the two roots of the equation are:
x = [-b ± √(b2 - 4ac)] / 2a
Since a = 1, the formula simplifies to:
x = [-8 ± √(82 - 4(1)(20))] / 2
Substituting the values for a, b and c, we get:
x = [-8 ± √(-64)] / 2
Taking the positive and negative square roots of -64, we get:
x = [-8 ± 8i] / 2
Simplifying, we get:
x = -4 ± 4i
Therefore, the two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.
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Y=2/3x doe thi repreent a proportional relationhip? what i the contant of proportionality?
Yes, the equation Y = 2/3x represents a proportional relationship.
If one variable is always equal to a constant multiplied by the other variable(quantity), then we can say that those variables are in a proportional relationship.
In the direct relationship between two quantities, if one quantity increases, the other quantity also increases and vice-versa.
For example, if each square foot of carpet costs $1.50, then the cost of the carpet is proportional to the number of square feet. The direct proportion relationship is written as y ∝ x.
y = kx where k is the constant of proportionality.
The constant of proportionality is 2/3. It tells us that for every 1 unit increase in x, Y increases by 2/3 units.
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does. Anyone get a and b please help I’ll mean a lot
Answer:
5x + 190 = 300
[tex]\frac{300-190}{5}[/tex]
Step-by-step explanation:
The equation
5x + 190 = 300 helps us to figure out how many minutes it will take for the tank to be empty.
5x + 190 = 300 Subtract 190 from both sides
5x + 190 - 190 = 300 - 190
5x = 110 Divide both sides by 5
[tex]\frac{5x}{5}[/tex] = [tex]\frac{110}{5}[/tex]
x = 22
It will take 22 minutes for the tank to be empty.
What is the answer of 2 Power 4?
2 to the power of 4 is 16.
2^4 = (2 x 2 x 2 x 2) = 16
2 to the power of 4 is 16.
The answer to 2 to the power of 4 is 16. This means that 2 is multiplied by itself 4 times. To calculate this, it is easiest to start with the base number, 2. Then, multiply 2 by itself 3 more times. The result is 2 multiplied by 2 multiplied by 2 multiplied by 2, or 2 x 2 x 2 x 2, which equals 16. Therefore, 2 to the power of 4 is equal to 16.
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the congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm. in centimeters, what is the length of the base?
The congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm. the length of the base is 7 cm.To calculate the length of the base of an isosceles triangle, we can use the formula of the perimeter.
The perimeter is the sum of all sides of a triangle, so the formula is Perimeter = Side1 + Side2 + Base. In this case, the two congruent sides are each 5 cm long, and the perimeter is 17 cm. So, if we set up an equation, we have 17 = 5 + 5 + Base. We can then solve the equation for Base by subtracting 10 from both sides.
This gives us 17 - 10 = 5 + Base, and then subtracting 5 from both sides gives us 12 = Base. Then, we can divide both sides by 12 to get 1 = Base / 12. Lastly, we can multiply both sides by 12 to get 12 = Base. Therefore, the length of the base is 7 cm.
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Large numbers require a large number of zeros when writing in ________________ notation.
To express such quantities in a simpler and more efficient manner, mathematicians and scientists use ______________ notation.
Answer:
Large numbers require a large number of zeros when writing in scientific notation.
To express such quantities in a simpler and more efficient manner, mathematicians and scientists use scientific notation.
Step-by-step explanation:
Answer the screenshot
The domain of the given rational function R(x) = 6x/(x + 1) include the following: A. the domain of R(x) is {x|x ≠ 1}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.
In order to determine the domain of this rational function, we would use an online graphing calculator to plot it and then write its domain in interval notation based on the graph as follows:
Domain = (-∞, 1) U (1, ∞)
By using set builder notation, the domain of this rational function R(x) = 6x/(x + 1) can be re-written as follows;
Domain = {x|x ≠ 1}.
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2.If the sum of three integers is a negative integer, we can say WITH CERTAINTY that A all the three integers are equal. B two of the three integers are positive and one is negative. C one of the three integers is positive and two are negative. D at least one of the three integers is negative.
Answer:
D)
That is the only one we can be certain with.
1st option is obviously incorrect
2nd option is wrong as it can also be two are negative one is positive
3rd option is wrong as it can also be one is negative two are positive
4th option is correct as u can't get negative values without a negative numberl.
a ferris wheel with a radius of 10m is rotating at a rate of one revolution every 2 minutes. how fast is a rider rising when his seat is 16m above ground level?
With a speed of 0.419 m/s, the rider fast is a rider rising when his seat is 16m above ground level
The formula for tangential velocity is 2*pi*r/T --> 2*pi*10/120 --> pi/6.
It is 6 meters above the center of the wheel while the rider is 16 meters above the ground.
The horizontal portion of this distance must be 8 meters as its separation from the wheel's center is 10 meters (depending on the radius).
This indicates that the velocity and seat both make angles of 36.87 degrees off vertical and arctan(6/8) over the origin, respectively.
We will take into account the vertical component of the tangential velocity since the rate at which the seat is rising is what we're interested in.
Pi/6 * cos(arctan(6/8)) yields a value of 0.419 m/s.
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In certain areas the water is so scarce that every attempt is made to conserve it. For instance, on one oasis in the Sahara Desert, the amount of water necessary for each date palm is carefully determined. How much water is each tree given?
The water is given on alternate days.
According to the explanation given in the question, the Saharan islands make strong efforts to conserve their water resources. Part of these efforts includes not wasting water on plants that don't require it. Sometimes, we overwater plants, and the extra water simply evaporates into the atmosphere.
Palm trees, on the other hand, only require watering every other day, which is why they are only watered on alternate days. The precise amount of water provided to each tree in a real-world oasis would depend on a number of variables, including the age and health of the tree, the climate, and the availability of water. However, this is a hypothetical situation.
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A cloud is drifting across the sky at 552metersperminute. it is at an altitude of 9,200 meters. if its speed remains steady, how far will the cloud move in 17.5minutes?
The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.
How is altitude measured and what does it mean?Utilizing the measurement of air pressure, altitude may be calculated. The pressure decreases with increasing altitude. An instrument is referred to as a pressure analyzer or pneumatic altimeter when a barometer is given a nonlinear calibration to display altitude.
This may be calculated by dividing the cloud's speed (552 metres per minutes) by the distance it must travel (17.5 minutes). We now know the distance to be 9,616 meters.
The speed of said cloud and the length of time it is going are four pieces of information that must be known in order to determine the minimum distance the cloud might cover in 17.5 minutes. We must increase the cloud's stated speed of 552 meters a minute by the distance it is going across, which in itself is 17.5 minutes. As a result, we now have 9,616 meters overall.
Another way to see this is to picture the cloud beginning at place A (9,200 meters) or terminating at point B. (9,616 meters). The distance between points A and B will be covered in 17.5 minutes if the cloud is moving at a pace of 552 meters per minute.
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Find the z-score for the value 66, when the mean is 51 and the standard deviation is 1.
The z score for the value 66, when the mean is 51 and the standard deviation is 1 is 15.
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
Given that:
mean = 51, standard deviation = 1. For a value of 66:
z = (66 - 51) / 1 = 15
The z score is 15.
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Which of the following is equivalent to
4x^2 6x/ 2x+2?
a. 2X - 10/2X+2
b. 2X - 5 + 10/2X+2
c. 2x-3
d. 2X + 5 - 10/2X +2
An equation Dividing 4x^2+6x by 4x+2 gives : Therefore , the expression ... 4x + 2, as follows: 4x^2 + 2x + 4x + 2 − 2, or x(4x + 2) + (4x + 2) − 2.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here,
the given equation is
this above equation is equivalent to
2X - 10/2X+2,
as root of both equation are same
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You have $11.50 and you need to make copies of a flyer at a store that charges $0.15
per copy. Find the inequality that represents the number of copies you can make. Use
x as the variable.
What is the maximum number of copies you can afford to make?
Answer:
76
This is because, when you exceed 76 copies, the cost will be greater than 11.50 and you will not be able to afford it.
Step-by-step explanation:
To solve this inequality, you can divide both sides by 0.15: x <= 76.67
I added a picture below
If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.
What is the Solution to a System of Linear Equations?A solution to a system of linear equations is a set of values for the variables that satisfy all the equations in the system simultaneously. In other words, it is a collection of values for the variables that make all the equations in the system true at the same time.
The solution can be represented graphically as the intersection of the lines or planes defined by the equations in the system, or it can be represented algebraically as a set of values for the variables.
The equation "5 = 0" is false. It means that 5 cannot be equal to 0. This could indicate that the system of linear equations has no solution or that there is an error in the method being used to solve it.
Therefore, the answer is: "none of these statements are true".
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let $s$ be the set of all real numbers $\alpha$ such that the function\[\frac{x^2 5x \alpha}{x^2 7x - 44}\]can be expressed as a quotient of two linear functions. what is the sum of the elements of $s$?
The sum of all the elements of set S is -(220/7).
To express the function (x^2+5x +y)/(x^2+7x - 44) as a quotient of two linear functions, the denominator must be a factor of the numerator. In other words, (x^2+7x - 44) must divide (x^2+5x +y) without leaving any remainder. To find the sum of the elements of S, we can set the numerator equal to the denominator multiplied by a constant and solve for y.
x^2+5x +y = c(x^2+7x - 44)
The constant c is a scalar value.
x^2+5x +y = cx^2 +7cx - 44c
we can now equate the coefficients of x^2 and x.
1 = c
and, 5 = 7c
now we can solve for c:
c = 5/7
Now we can substitute the value of c back into the equation:
x^2+5x +y = (5/7)(x^2+7x - 44)
=> x^2+5x +y = (5/7)x^2 + (35/7)x - (220/7)
we can now equate the constant terms:
y = -(220/7)
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One day eleven babies are born at a hospital. assuming each baby has an equal chance of being boy or girl, what is the probability that exactly eight of the eleven babies are girls?
The probability of getting exactly 8 girls out of 11 births is 21.9%.
The binomial probability formula is used to calculate the probability of getting a certain number of successes (in this case, girls) out of a fixed number of trials (in this case, 11 births).
The first part of the formula (11 choose 8) is the number of ways to choose 8 girls out of 11 births, which is 330.
i.e; (11 choose 8) * (0.5)^8 * (0.5)^3 = 330
The second part of the formula (0.5)^8 represents the probability of getting 8 girls out of 11 births assuming each birth has a probability of 0.5 of being a girl.
The third part of the formula (0.5)^3 represents the probability of getting 3 boys out of 11 births assuming each birth has a probability of 0.5 of being a boy.
i.e; (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875
When we multiply all of these values together we get the final probability of getting exactly 8 girls out of 11 births, which is approximately 0.21875 or about 21.9%.
Therefore, the probability of getting exactly 8 girls out of 11 births is given by the binomial probability formula: (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875 or about 21.9%.
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Select the correct answer.
James wants to estimate the absolute age of an animal fossil. However, test results show that the fossil doesn't contain any atoms of carbon-14.
What can James conclude about the lack of carbon-147
James can conclude about lack of carbon-14 is ; ( E ) Without carbon-14, James can use relative dating to estimate the age of the fossil.
What is relative dating?Relative dating, while it will not give an exact age, can estimate the age of the fossil. James could take a look at the relative order of past events and estimate the age of the fossil that way.
It is important to know that all animals have carbon-14. Carbon 14 is in the air in carbon dioxide molecules, which animals produce through cellular respiration.
James can utilize relative dating, which can be used as a substitute to determine the age of fossils in the absence of Carbon-14, which is essential for Carbon dating, as Carbon-14 is not present in the animal fossils he is studying.
A scientific method of identifying an object's age in relation to another is called relative dating ( i.e. determining the relative order of events ).
We may thus draw the conclusion that James can determine the age of the fossil using relative dating in the absence of carbon-14.
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Complete question:
(complete solution)
can someone help me here please thank you everyone! lovelots
Answer:
The expression a2+a4+a6+a8+......a20 can be written in sigma notation as:
∑ a(2n) where n = 1 to 10
To expand this summation, we can substitute in the values of n and evaluate the series:
a(21) + a(22) + a(23) + ... + a(210) = a2 + a4 + a6 + ... + a20
The expression (-1) + 2 +(-3) + 4 + (-5) ....+(-25) can be written in sigma notation as:
∑ (-1)^n*n where n = 1 to 25
To expand this summation, we can substitute in the values of n and evaluate the series:
(-1)^11 + (-1)^22 + (-1)^33 + ... + (-1)^2525 = -1 + 2 - 3 + 4 - 5 +... - 25
Note that the series (-1)^n*n is an alternating series, where the signs of the terms alternate between positive and negative. This series has no closed form solution, but we can evaluate them by adding and subtracting each term.
Answer:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Step-by-step explanation:
Part ISigma notation means the sum of the series.
Given series:
a₂ + a₄ + a₆ + a₈ + ... + a₂₀Therefore:
First term is a₂Second term is a₄Third term is a₆So each term is a₂ₙ
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]
Given series:
(-1) + 2 + (-3) + 4 + (-5) + ... + (-25)The absolute value of each term of the series is n.
The signs of each term alternate between negative and positive.
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Part IIThe expansion of each summation has been given in Part I.
However, the full expansions are:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12+\\\phantom{wwwwwwww}(-13)+14+(-15)+16+(-17)+18+(-19)+20+(-21)+22+\\\\\phantom{wwwwwwww}(-23)+24+(-25)[/tex]
Part IIIThe evaluation of each series is:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=-13[/tex]
four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12. each ambassador must sit in an even-numbered chair. each advisor must sit in a chair adjacent to his or her ambassador. there are $n$ ways for the 8 people to be seated at the table under these conditions. find the remainder when $n$ is divided by $1000$.
Therefore , the solution of the given problem of combination comes out to be 479001.6.
Combination : What is it?Combinations are mathematical procedures that count the number of possible configurations from a set of items, where the selection direction is immaterial. You can select any arrangement of the parts in any combination. It's possible to mix together combinations and permutations.
Here,
Given : four ambassadors and one advisor for each of them are to be seated at a round table with 12 chairs numbered in order 1 to 12..
and n ways for seating 8 people.
Thus , to find this permutation- combination arrangement .
So,
nPr => 6 P 6 and * 12P6
nPr => 665280 * 720
nPr = > 47,90,01,600
and divide it by 1000 .
So ,
=> 479001600/1000
=> 479001.6
Therefore , the solution of the given problem of combination comes out to be 479001.6.
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How many real solutions does the quadratic equation 4x² 4x 1 0 have?
The given quadratic equation 4x^2 - 4x + 1 = 0 has one real solution
by its discriminant.
The discriminant of a quadratic equation ax^2 + bx +c = 0 is given by
D = b^2- 4ac
Now from the equation that we have 4x^2 - 4x +1 = 0
a = 4
b = -4 and
c = 1
Hence the discriminant (D) is given by :
D = b^2- 4ac
= (-4)^2- 4(4)(1)
= 0
Now check for discriminant D, (D=0)
Therefore the discriminant of a given equation is 0.
So the roots of given equation are real and equivalent.
Hence the equation given 4x^2 - 4x + 1 =0 has only one real solution.
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