A culture of bacteria has an initial population of 920 bacteria and doubles every 7
hours. Using the formula P = Po 22, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 8 hours, to the nearest whole number?

The convergence interval, I, is the set of all x values for which the series converges. Because the series converges for all |x + 5| > 1, the convergence interval is I =  (-∞, -6) ∪ (-4, ∞).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The radius of convergence, R, of a power series is the maximum value of x for which the series converges for all values of x within that range.

To find the radius of convergence for the given series, we can use the ratio test:

[infinity] n = 1 n 7n (x + 5)n

lim |(a_{n+1})/(a_n)| = lim |(7(n+1) (x + 5)^(n+1)) / (n 7n (x + 5)^n)|

= lim |(7(x + 5)) / n|

The series converges when the limit is less than 1 and diverges when the limit is greater than 1. If the limit is equal to 1, the test is inconclusive.

For |x + 5| < 1, the limit is equal to |7 * (x + 5)|, which is greater than 1, so the series diverges in this region.

For |x + 5| > 1, the limit is equal to |7| / n, which goes to zero as n approaches infinity, so the series converges in this region.

So, the radius of convergence, R, is R = 1.

The interval of convergence, I, is the set of all values of x for which the series converges. Since the series converges for all |x + 5| > 1, the interval of convergence is I = (-∞, -6) ∪ (-4, ∞).

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Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.

The overall uninspired velocity of an object will be its distance. Distance is the amount of space an object has traveled, regardless of where it began or ended. Distance would be the measurement of said size or extent of the separation between two places. It is important to keep in mind that the distance between two spots and the traveled between them aren't the same thing. Distance traveled is the sum of a line's length joining various places. Distance refers to the actual travel path of a body. Path length is another term for it. For instance, if an object is traveling from board to point P, the path's length will be similar to OP = 360 m.

given

We are aware of: t = 1 1/5   d = 7/8

Write down and replace 7/8 = v * (1* 1/5)

Remove the connecting element: 7/4 * 1/3

As a single fraction, write:

7 / 4*3

Determine the quotient or product: 7/12

Response: 7/12

Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.

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The time in minutes until there are 280 grams of the element remaining is given as follows:

16 minutes.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 660, r = 0.051.

Hence the function is modeled as follows:

y = 660(0.949)^t.

The time until there are 280 grams remaining is given as follows:

280 = 660(0.949)^t.

(0.949)^t = 280/660

tlog(0.949) = log(280/660)

t = log(280/660)/log(0.949)

t = 16 minutes.

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The formula for the area of the parallelogram-like figure is A = πr

parallelogram can be defined as  a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

bh, where h is the height of the parallelogram-like figure.

Therefore, The formula for the area of the parallelogram-like figure is A = πr.

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Part A: The perimeter of the tree house floor is 32 m.

Part B: The area of the tree house floor is 40 m².

Part A: The perimeter of the rectangular floor can be found by adding up the lengths of all four sides.

Part B: The area of the rectangular floor can be found by multiplying the length by the width.

This is about a tree house design using a coordinate plane in which the coordinates are measured in meters (m). The task is to calculate the perimeter and the area of the rectangular floor of the tree house, given the vertices of the floor. The perimeter is found by adding up the lengths of all four sides of the rectangular floor, and the area is found by multiplying the length by the width.

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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{9, 10, 11, 12, 14} U {x | x > 18} represents the values of x in Mai's dot plot.

Let's say x represents Mai's score in each basketball game. Based on Mai's description, the following can be inferred about the values of x:

8<=x<=14  for most of the 10 games.

x > 18 for one game

(because it was more than double Mai's typical score of 9 points).

Here is a representation of the dot plot

8___9___10___11___12___

14___16___18___20___22

The dots placed at 9, 10, 11, 12, and 14 represent the values of x where Mai scored between 8 and 14 points in most of the 10 games. The dot placed at a value greater than 18 represents the exceptional game where Mai scored more than double her typical score of 9 points.

Therefore, the set of values for x can be represented as:

{9, 10, 11, 12, 14} U {x | x > 18}

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The number of 2 letter codes that can be formed is 6 with no letter repeated using Permutation.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already sorted, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. As a result, we multiply the alternatives at our disposal to get the total number of configurations for seating 3 people in 5 seats. 5 4 3 are the methods we carry it out. It can be done in 60 different ways. You may write 5 4 3 as (5!) / (2!) (or) (5!) / (5 - 3), as you can see. .

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The first 3 letters of alphabet are a, b and c

The number of 2 letter codes that can be formed is 3*2 = 6 with no letter repeated.

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A linear expression is an algebraic expression that contains a variable to the power of one. 2y is an example. A coefficient is a rational number that is multiplied by a variable. A rational number is a number that can be written as the ratio, or fraction, of two integers. 4 in the expression 4z is an example of a coefficient. Like terms are terms whose variables and their exponents are the same. One example is 4z and -7z.

In the linear expression 2y, the coefficient is the numerical factor 2. The coefficient is the rational number that is multiplied by the variable, which in this expression is y.

The coefficient of a linear expression is usually the first factor, and it is used to determine the rate of change for a variable.

For example, if the coefficient of 2y is 2, then for every increase in y by one, the result of the linear expression will increase by 2.

The coefficient of a linear expression is the numerical (or rational) factor that is multiplied by the variable. In the linear expression 2y, the coefficient is 2, since the expression is equivalent to 2*y. The coefficient is usually the first factor in a linear expression, followed by the variable and, if present, its exponent.

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9 i think

i’m pretty sure it’s 9 i just done it

The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C where  q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).

1. First calculate the electric field, E, using the equation E = k * q/r^2, where k is Coulomb's constant (8.99e9 N * m^2/C^2), q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).

2. Plugging in the values, we get E = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.

The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.

The complete question is :

Consider a point at a location 2.79 cm away from a 4.89-nc charge. What is the electric field at this point?

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The statement which is true is D. 65% of the seventh-grade students prefer the water park.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

A : Total number of students = 120

Number of students who prefer amusement park = 14 + 16 = 30

Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%

B : Total number of eighth grade students = 80

Number of eighth grade students who prefer amusement park = 16

Percentage = 16 / 80 = 0.2 = 20%

C : Total number of students = 120

Number of students who prefer water park = 26 + 64 = 90

Percentage = 90 / 120 = 0.75 = 75%

D : Total number of seventh grade students = 40

Number of seventh grade students who prefer water park = 26

Percentage = 26 / 40 = 0.65 = 65%

Hence the option D is the correct percentage.

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Answer:

9.5

Step-by-step explanation:

72 + 10t = 34 + 14t

72 - 34 = 14t - 10t

38/4 = 4t/4

9.5 = t

Answer:

49 cards would be left from the deck of card.good luck with future questions I hope I am right

To multiply a polynomial by a monomial, you must first identify the terms in the polynomial, as well as the factors in the monomial. Once you have identified the components, use the distributive property to multiply each term of the polynomial by the monomial. Then, combine like terms and simplify the resulting polynomial.

For example:

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Yes, the three lines have a common point of intersection. This point is located where all three equations equal the same value, which in this case is (4,-4).

Yes, the three lines 3x1−12x2=4, 6x1 39x2=−76, and −3x1−51x2=80 have a common point of intersection. This point is located where all three equations equal the same value. To find this point, one must solve the three equations simultaneously. First, one can subtract the first equation from the third equation, which will result in a new equation equal to −3x1 + 48x2 = 76. From there, one can subtract the second equation from the new equation, resulting in a new equation equal to −45x2 = 132. From this equation, one can solve for x2 and the result is x2 = -4. Then, one can substitute the value of x2 into any of the original equations to solve for x1 and the result is x1 = 4. Therefore, the common point of intersection for these three equations is (4, -4).

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Suppose a deck of 52 cards is shuffled and the top two cards are dealt..

[tex]\left \P {{52} \atop {2}} \right.[/tex] =52!50! = 52 ×51 = 2652.

Now assuming each of the pairs has the same chance, calculate the probabilities for the following events

the chance that the first card is an ace;

There are 4aces in a deck, so the probability is

P (A)=

[tex]\frac{4}{52}\\ =\frac{1}{13}[/tex]

the chance that the second card is an ace

Again, there are 4aces in a deck, so the probability is

P(B)=

[tex]\\ \\ \frac{4}{52}\\ =\frac{1}{13}[/tex]

the chance that both cards are aces

There are 4aces in the deck. We already have the number ofpossible ordered pairs from P(A), each of which is equally likely. How many different ordered pairs give both aces? The answer is the number of permutations of two cards among four.

= [tex]\left \ P{4} \atop {2}} \right. \\\frac{4!}{2!}[/tex]

= 4*3

= 12

The probability that both cards are aces is therefore

[tex]\frac{\left \P {{4} \atop {2}} \right. }{\left \P{{52} \atop {2}} \right. }[/tex]

=12 /2652

=1/221

the chance of at least one ace among the two cards.

How many different permutations of the first two cards give at least one ace? The number that give two aces is P42, from above. The number that give an ace as the first card but not the second card is 4×48, since there are4aces, and after choosing one ace, there are 48 that possible non-aces for the second card. Likewise there are 48 ×4ways to choose an ace as the second card, but not the first. Thus the total number of ways that the two cards can have at least one ace is

P42+ 4 ×48 + 4 ×48 = 396.

The probability of of selecting at least one ace among the first two cards

= 396/3652

P (D)= 33 /221

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Answer:

12.82

Step-by-step explanation:

6.4/49.92

multiply both the numerator and denominator with 100 since the denominator is to hundredth place

6.4×100/49.92×100

640/49.92=

compute in the calculator to get answer as;

12.82

Answer:

This is an approximate answer so I not sure if it is accurate.

0.1282051282

Hoped it helped and was the right answer

The No Of ways are there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribution the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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The No Of ways there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribute the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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The statement that identifies the scale used in this map would be = 1 inch equals 19 miles. That is option C.

A map is a diagram that can be used to represent the location and distance of various areas of a country or state.

In the map, there are 4 towns which are separated by 3 inches apart.

The actual distance apart = 57 miles

Therefore the actual scale that was used is calculated as follows;

3 inches = 57 miles

1 inch = X miles

make X mile the subject of formula;

X miles = 57/3 = 19 miles.

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The first value of the given exponential expression would be 3.

What is an exponential function?

An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant and x is a real number. The function represents an exponential growth or decay, depending on the value of "a". If "a" is greater than 1, the function increases rapidly as x increases. If "a" is between 0 and 1, the function decreases as x increases.

In the exponential expression y = 3 * q⁵, the first value is 3.

Hence, the first value of the given exponential expression would be 3.

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The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference

Given the first term as 37, we have that;

a₁ = a + (1 - 1) d = 37

a₁ = a = 37

for the second term 42, substituting 37 for a;

a₂ = 37 +(2 - 1)d = 42

37 + d = 42

d = 42 - 37 {subtract 37 from both sides}

d = 5

Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

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Based on the IUCN Red Data list of species, by solving the data we get the number of species in each category as

The answer which has been provided above gives the number of species that are present in each of the 7 categories of the IUCN Red Data List.

The IUCN Red Data List is a list of species that are globally threatened.

The categories that are present in the IUCN Red Data List are

Extinct in the Wild, Extinct, Critically Endangered, Endangered, Threatened, Vulnerable, Near Threatened, and Least Concern.

The number of species in each category is calculated based on the given information:

There are 78 species that are extinct in the wild.

Hence,

11 times that many have gone extinct since 1500 AD.

Hence,

6 and 9 times as many species have gone extinct are on the critically endangered and endangered lists respectively.

Hence,

24,570 species are listed as threatened In the IUCN Red Data list.

Hence,

According to the list, the number of near-threatened species is 468 more than a third of the number which is vulnerable.

Hence,

According to the data, there are 7,098 more species on the least

The total number of species on the IUCN Red Data List is calculated by adding up the number of species in each category:

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The function written in vertex form is:

f(x) = 4(x + 6)² - 26

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 4(x² + 12x) + 10

Now,

f(x) = 4(x² + 12x) + 10

f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10

f(x) = 4(x + 6)² - 26

Thus,

f(x) = 4(x + 6)² - 26 is the function in vertex form.

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Answer:

B is correct

Step-by-step explanation:

The width of the box of books which Mr. Lin recieved which is in the shape of Rectangular Prism is (486/l*h) units.

A three-dimensional solid form having six sides, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

According to the face form or the angle the faces make with the base, there are two different varieties of rectangular prisms.

Below are several characteristics of a rectangular prism that make it simple to recognize one.

The length of the rectangular Prism is l.

Width is w , height is h

Therefore,

Volume (V) = lbh

We know Volume is 486

so we casn find the width of the rectangular prism as 486/lh

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Answer: 529/8

Step-by-step explanation:

The speed distance of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

The speed of the faster runner is 8 mph.

The speed of the slower runner is 6 mph.

The distance from the starting point is 5.5 miles.We can use the formula d = rt, where d is the total distance, r is the rate (speed) and t is the time taken to cover the distance.

Let us assume that the speed of the faster runner is x mph. Then, the speed of the slower runner is (x-2) mph.

Since the two runners meet 1 hour 6 minutes after starting, the total time taken is 1 hour 6 minutes = 66 minutes.

Thus, the total distance covered = (x * 66) + (x - 2) * 66 = 132x - 132

But, the total distance covered is 11 miles, so

132x - 132 = 11

Solving for x, we get

x = 8 mph

Therefore, the speed of the faster runner is 8 mph, and the speed of the slower runner is (8 - 2) = 6 mph.

Since they meet 1 hour 6 minutes after starting, they have travelled a total distance of (8 * 66) + (6 * 66) = 5.5 miles. Therefore, the distance from the starting point at which they meet is 5.5 miles.

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Mary's monthly pension benefit is $3,649.80.

First, we have to find the average salary.

The average is the sum of the salaries divided by the number of salaries.

($78,000 + $80,000)/2 = $79,000

Next, we can find the annual retirement rate.

The annual retirement pension is the product of the average, the rate and the number of years employed.

$79,000 x 1.98% x 28 = $43,797.60

Finally, we can find the monthly retirement pension.

The monthly retirement pension is then the annual retirement pension divided by the number of months in a year.

There are 12 months in a year.

$43,797.60 / 12 = $3,649.80

Therefore, Mary's monthly pension benefit is $3,649.80.

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The proof of divisibility is correct in this question.

The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.

According to the question

It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.

The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes 75^30 = 31 * 52^30 = 3^30 * 5^60. Similar to how 45 may be expressed as 3^2 * 5^1, 3^90 * 5^45 is equal to 45^45 = (3^2 * 5^1)^45. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.

75 = 3^1 * 5^2,

∴ 75^30 = (3^1 * 5^2)^30 = 3^30 * 5^60.

It follows that 75^30, or 3^30 * 5^60, divides 45^45 * 15^15, or 3^90 * 5^45 * 3^15 * 5^15, as 3^30 divides 3^90 and 5^60 divides 5^45.

45 = 3^2 * 5^1,

∴ 45^45 = (3^2 * 5^1)^45 = 3^90 * 5^45.

15 = 3^1 * 5^1,

∴ 15^15 = (3^1 * 5^1)^15 = 3^15 * 5^15.

In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.

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The proof of divisibility is correct in this question.

Divisibility

The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.

According to the question,

It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.

The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes [tex]75^{30}=(31*52^{30})=(3^{30}*5^{60})[/tex]. Similar to how 45 may be expressed as [tex](3^2*5^1)[/tex]. [tex](3^{90}*5^{45})[/tex] is equal to [tex]45^{45}=(3^2*5^1)^{45}[/tex]. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.

[tex]75=3^1*5^2[/tex],

∴ [tex]75^{30}=(3^1*5^2)^{30}=3^{30}*5^{60}[/tex].

It follows that [tex]75^{30}[/tex], or [tex](3^{30}*5^{60})[/tex], divides [tex](45^{45}*15^{15})[/tex] or [tex](3^{90}*5^{45}*3^{15}*5^{15})[/tex], as [tex]3^{30}[/tex] divides [tex]3^{90}[/tex] and [tex]5^{60}[/tex] divides [tex]5^{45}[/tex].

[tex]45=3^2*5^1[/tex]

∴ [tex]45^{45}=(3^*5^1)^{45}=3^{90}*5^{45}[/tex]

[tex]15=3^1*5^1[/tex]

∴ [tex]15^{15}=(3^1*5^1)^{15}=3^{15}*5^{15}[/tex]

In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.

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Answer: 3.99

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