3. A regular hexagon has six congruent sides. If the
length of each side is represented by the
expression 7x + 4 which expression is equivalent to
the perimeter of the figure?
A. 13x + 24
B. 13x+10
C. 42x + 24
D. 42x + 10

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:

Therefore , the solution of the given problem of integer comes out to be 1/100 = 0.01

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].

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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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:

Sigma notation means the sum of the series.

Given series:

Therefore:

So each term is a₂ₙ

Therefore, the expression in sigma notation is:

[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]

Given series:

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]

The 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]

The 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]

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.

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:

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.

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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The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.

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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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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Width = 8 inch

Length = 10 inch

This can be solved using rectangular area formula.

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.

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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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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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.

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

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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Answer:

80

Step-by-step explanation:

96-16

The z score for the value 66, when the mean is 51 and the standard deviation is 1 is 15.

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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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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Therefore , the solution of the given problem of combination comes out to be  479001.6.

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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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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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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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 domain of the given rational function R(x) = 6x/(x + 1) include the following: A. the domain of R(x) is {x|x ≠ 1}.

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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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.

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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If the final statement when solving a system of linear equations is "5 = 0", it means that: E. none of these statements are true.

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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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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The powers that correspond to each letter are given as follows:

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:

Then the digits are classified as follows:

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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

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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