3. Bacteria can multiply at an alarming rate when each
bacteria splits into two new cells, doubling. If we start
with only 3 bacteria which can double every hour, how
many bacteria will we have by half the day?

  Answer: [tex]9x^{2} -6x^{2} y+y^{2}[/tex]

  Step-by-step explanation:

Applying the perfect square formula:[tex](a-b)^{2} = a^{2}- 2ab+ b^{2}[/tex]

[tex](3x^2- y)^2= (3x^2)^2- 2*3x^2*y+ y^2[/tex]

Simplifying this further, we get:

[tex]9x^2- 6x^2y+y^2[/tex]

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Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.

=) 2*pi*r = 42cm

=) 2*22/7 * r = 42cm

=) r = 42*7 / 2*22

=) r = 147/22 cm

Since Volume of cylinder = pi* r^2*h

= 22/7 * 147/22 * 147/22 * 16 cm^3

= 2245.09 cm^3.

g

=

p

2

−

m

Step-by-step explanation:

Eye color is an example of a discontinuous variation, as the amount of colors is limited and individuals can only have one of these colors.Blood type is another example of a discontinuous variation, as individuals can only have one of the four blood types.

Discontinuous variation refers to characteristics that have only a limited range of values within a population. Eye color is one example of discontinuous variation, as the range of colors is limited and individuals can only have one of these colors. Similarly, blood type is another example of discontinuous variation, as it is determined by the presence or absence of certain antigens in the blood and individuals can only have one of the four blood types. Discontinuous variation is often inherited, determined by the presence or absence of certain genes or alleles. These variations are usually determined by a single gene with two alleles, one of which may be dominant and one of which may be recessive, leading to the limited range of values. Discontinuous variation, then, is an important part of the human population and helps to create the variety and diversity that exists within it.

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The 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

What are consecutive numbers ?

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

Let the 3 numbers be x ,x+2 , x+4

The sum of numbers is 45

⟹x+x+2+x+4=45

3x+6=45

3x=39

x=13

Hence , the 3 consecutive odd numbers whose sum will be 45 are 13 , 15 and 19 .

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The situation can be expressed in inequality as: 95x + 0.85y ≤ 500

On solving the maximum amount of miles that can be driven to stay under budget is 253

What is inequality?

If two real numbers or the algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.

For example, x > 3 (x should be greater than 3)

According to the given question:

Total amount to spend is restricted to $500

Let the number of days be x and extra miles covered be y

The car rental company charges $95 per day to rent the car and charges $0.85 per mile.

Therefore the situation van be expressed as:

95x + 0.85y ≤ 500

If the car is rent for 3 days then the maximum amount of miles that can be driven to stay under budget are

95(3) + 0.85y ≤ 500

285 + 0.85y ≤ 500

0.85y ≤ 215

y ≤ 253

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The number of rides that it would take for the quickpass to be less expensive would be 28 rides.

The monthly quikpass would cost $ 55 and give a person unlimited rides. The single ride on the other hand, would cost $ 2 per ride.

The number of rides till the monthly quikpass is cheaper, can be found by the formula:

= Cost of monthly quikpass / Cost of single rides

= 55 / 2

= 27.5 rides

= 28 rides

In conclusion, if a person takes 28 rides then the monthly quikpass would be less expensive.

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Preview how to add two-digit numbers to refresh our memory before we look at how to add two numbers with four or more digits.

One result, known as the sum, is produced when two or more integers are added together. It is advisable to arrange two or more integers vertically while adding them, making sure that the digits with the same place value are in the same column. Every one of the ones should be in its own column, followed by every ten in its own column, and so on.

here ,

As you align the place value columns, write the numbers directly above one another.

From the right to the left, add the numbers in each column.

Fill in the space provided beneath each column of digits with the solution to each addition.

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The relationship between a parallelogram's area, base, and height:

Area = Base x height

A parallelogram is just a flat shape having four parallel, straight sides that are congruent with one another.

Accordingly, a parallelogram is a closed shape, a flat figure, and a quadrilateral.

Therefore, each parallelogram is:

In such a parallelogram, the length among one side is referred to as the "base," and the length of the perpendicular segment connecting that side to the opposing side is referred to as the "height."

Area = base x height

Thus, a parallelogram's base can be any of its sides. A given parallelogram always has two base-height pairs.

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Answer:

Step-by-step explanation:

42 is an even number so it is divisible by 2

42 divided by 2=21

42 has digits that add up to give 6

If the sum of a number adds up to give 3, 6 or 9 that number is divisible by 3

42 divided by 3=14

Factors of 42 are 21 and 2 and 14 and 3 and 42 and 1

Answer:

Direct Variation

y = 3x

y = (2/7)x

y = -0.5x

NOT Direct Variation:

x = -1

y = 4

y = 22x + 7

Step-by-step explanation:

Direct Variations are in the form

y = kx

This is very similar to:

y = mx + b except the b MUST be zero.

Also, direct variations always go through (0,0) that's why b must be 0.

So easy to pick out:

y = 3x

y = (2/7)x and

y = -0.5x are all in the form y = kx and have a y-intercept of zero.

y = 22x + 7 has that extra +7 tacked on to the end of the equation. It does not go through (0,0). It has a b that is 7. So it starts at (0,7). It is not a direct variation.

The other two, x = -1 and y=4 are both not direct variations. Neither starts at (0,0).

x=anumber is a vertical line and y=anumber is a horizontal line. These are not direct variations.

The various output values are displayed on the y-axis and make up the range. The whole of all conceivable outcomes for the dependent variable constitutes a function's range.

The statistical range is the range of values between the highest and lowest for a particular data collection. Another way to represent the range is the difference between the highest and lowest observation. The sample interval is determined by subtracting the largest number from the lowest. For continuous variables, the sample range is a critical measure of variability.

here

A function y = f is an example (x).

The function's range is the range between all of the y values, from least to maximum.

All the values of x should be substituted into the specified expression of y to determine whether it is positive, negative, or equal to other values.

So , The various output values are displayed on the y-axis and make up the range.

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Total 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

In the given question, we have to find how many "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

The given word is INQUISITIVE.

The total alphabets in the word INQUISITIVE is 11.

Let us first count the words without U and then insert U wherever applicable.

Now without U we have total 10 alphabets and the alphabet I is repeated by 4 times.

So permutations is 10!/4! = 151,200

Now we need to put U, we can see its 11 alphabets but U should not follow Q so it becomes 10 alphabets.

Hence, Total number of words = 151,200*10

Total number of words = 1,512,000

Hence, 1,512,000 "words" can be formed by rearranging INQUISITIVE so that U does not immediately follow Q.

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The best way to find multiple missing numbers in a given integer array with duplicates in Java is to use a hash set and loop.

First, create a HashSet and add all elements from the array to it. Then, loop from 1 to the maximum element of the array and check if each number is present in the HashSet. If the number is not present, it is a missing number. To explain further, a hash set is an efficient data structure for storing unique elements of a collection, and using a loop to check for missing numbers ensures that all numbers from the array are accounted for.

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SSS means side side side, SAS means side angle side and AAA means angle angle angle.

There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.

If three sides are given then we will use the SSS postulate

If two sides and one angle is given then we will use the SAS postulate

If three angles are given then we will use the AAA postulate.

Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.

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The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

12n > 135 + 4.50n

In order to make a profit and solve inequality,

12n - 4.50n > 135

7.5n > 135

n > 18

Thus, it needed to sell more than 18 to make a profit.

Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".

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The average savings per year in the last five years is 29,814.40 Option D

Generally, Average savings refers to the amount of money that a person or household has saved over a particular period of time, divided by the number of months or years in that period.

It is a measure of the average amount of money that is saved each month or year. The average savings rate can vary widely depending on a person's income, expenses, and financial goals. Some people may have very high average savings rates, while others may have very low average savings rates.

To estimate the average savings per year in the last five years, you need to add up the amounts saved in those years and divide by the number of years.

The amounts saved in the last five years are $70,453, $87,977, $54,718, $40,684, and $28,270, for a total of $291,182.

Dividing this by 5 gives an average of $58,236.40 per year, so the answer is 29,814.40 Option D

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Answer:

this it's no a math problem

These values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

What is the limit?

A limit in mathematics is the value that a function approaches as its input approaches some value. Limits are used to define continuity, derivatives, and integrals in calculus and mathematical analysis.

We have,

f(x) = 4xe³ˣ / 1

f(x) = 4xe³ˣ

[tex]\lim_{x \to \infty} f(x) = ?[/tex]l

[tex]\lim_{x \to -\infty} f(x) = ?[/tex]

[tex]\lim_{x \to -\infty} f(x) = \lim_{x \to -\infty} 4xe^{3x}[/tex]

It is the form -∞ * 0 which is an undetermined form

Write it has a fraction then apply l'Hospital's Rule

[tex]\lim_{x \to -\infty} \frac{4x}{1 / e^{3x} } = \lim_{x \to -\infty} \frac{4}{ -3e^{3x} / e^{6x} }[/tex]

[tex]= \lim_{x \to -\infty} \frac{4}{-3/e^{3x}} } = \lim_{x \to -\infty} \frac{4e^{3x}}{ -3 }[/tex]

[tex]= \frac{4e^{-x}}{ -3 }[/tex]

[tex]= \frac{0}{ -3 } = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \lim_{x \to \infty} 4xe^{3x}[/tex]

Simply evaluate

[tex]\lim_{x \to \infty} 4xe^{3x} = \infty * \infty = \infty[/tex]

 (∞*∞ is not an undetermined form).

f(x) = 4xe³ˣ

[tex]\lim_{x \to -\infty} f(x) = 0[/tex]

[tex]\lim_{x \to \infty} f(x) = \infty[/tex]

Hence, these values were found [tex]\lim_{x \to -\infty} f(x) = 0[/tex]  & [tex]\lim_{x \to \infty} f(x) = \infty[/tex] from the given equation.

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If the sum of two numbers is 36 and the larger number is 10 more than smaller number then the larger number is   .

the Sum of two numbers is given to be = 36 ;

also given that " larger number is 10 more than smaller number " ;

let the larger number be = "x" , and

the smaller number be = "y" .

So , according to the question ⇒ x + y = 36 ;

and x = y + 10 , putting x in above eqn.

we get , y + 10 + y = 36

2y + 10 = 36

2y = 36 - 10

2y = 26

y = 26/2 = 13

and x = 13 + 10 = 23 .

Therefore , the larger number is 23 .

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The Median of 10 and 24 is 17.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The mean and mode are the other two primary trends in addition to the median. The ratio of the total number of observations to the sum of all observations is known as the mean. The value that appears most frequently in the given data collection is called the mode.

Given,

First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median= [tex]\frac{10+24}{2}[/tex]= 34/2= 17

Therefore, The Median of 10 and 24 is 17.

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First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median = 34/2= 17

Therefore, The Median of 10 and 24 is 17.

3/2 is the quotient when 3/4 is divided by 1/2

When two fractions are divided, the first fraction is multiplied by the second fraction's reciprocal. Finding the reciprocal of the second fraction and this can be obtained by reversing its numerator and denominator—is and then dividing the  fractions. Multiply the two numerators after that. Multiply the two denominators after that, After that we need to simplify the fraction to its lowest form.

When we divide one number by another, the result obtained is also known as quotient.

so in order to find the quotient when both fraction is divied

quotient of the division = [tex]\frac{3}{4}[/tex] ÷[tex]\frac{1}{2}[/tex]

=> (3/4) / (1/2)

=> (3/4) * 2

=> 3/2

so quotient of the division = 3/2 or 1.5

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Answer:

  ₹1400

Step-by-step explanation:

You want to know the monthly installment when a refrigerator costing ₹34500 is paid for with ₹6500 down and 24 payments that include 10% simple interest.

The amount remaining after the ₹6500 down payment is ...

  ₹34500 -6500 = ₹28000

The amount to be repaid in installments will be this amount with 2 years' finance charge:

  ₹28000 × (1 +rt) = ₹28000 × (1 +0.10·2) = ₹28000×1.20

  = ₹33600

When that is divided into 24 equal payments, each monthly installment is ...

  ₹33600/24 = ₹1400

Each monthly installment is ₹1400.

As per the system of equation, a. 3y = -12x + 6 l y= -4x+ 2 has infinite number of solutions.

The rule to identify the number of solutions to the system of equation is written as,

In the given equation (a1/a2) ≠ (b1/b2), then there will be a unique solution.

Where as If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions.

Finally If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution.

Here we have given that pair of equations to show if the system has no solution, one solution, or infinitely many solutions.

Here we have to take the first equation

a. 3y = -12x + 6 l y= -4x+ 2

Now, we have to write it in the standard form, then we get,

=> 12x + 3y = 6, 4x + y = 2

Here the values of a1 = 12, b1 = 3, c1 = 6 and the values of a2 = 4, b2 = 1 and c2 = 2.

When we take the rule of system of equation we have identified that

=> 12/4 = 3/1 = 6/2

=> 3/1 = 3/1 = 3/1

Therefore, this one has the infinite number of solution.

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The base is the length of one of the triangle's sides, and the height is the distance from that side to the triangle's opposite corner.

A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. Triangle ABC represents a triangle with three vertices: A, B, and C. Any three non-collinear points constitute a unique triangle and, by extension, a unique plane in Euclidean geometry. Triangles are polygons with three vertices that have three sides. The triangle's angles are constructed by joining the three sides end to end at a point. The triangle's three angles add up to 180 degrees.

Here,

The base of the triangle is the length of one of its sides, and the height is the distance from that side to the triangle's opposite corner.

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The rate of flow for emptying the tank would be 0.15 liter/minute.

The rate at which the water level in the tank is changing is given by the equation:

ΔV/Δt = flow rate in - flow rate out

where ΔV is the change in the volume of water in the tank, Δt is the time interval over which the change occurs, and flow rate in and flow rate out are the rates at which water flows into and out of the tank, respectively.

In this case, the flow rate is 0.15 liter per minute, and the flow rate out is 0.27 liter per minute. The volume of water in the tank is 4.8 liters.

To determine how long it will take to empty the tank, we can set the volume of water in the tank to 0 and solve for the time interval:

0 = flow rate in - flow rate out

flow rate out = flow rate in

0.27 liter/minute = 0.15 liter/minute

Since the equation is not balanced, we cannot determine the time interval. In order to determine the time interval, we need to have information about both the flow rate in and the flow rate out. Without this information, it is not possible to determine how long it will take to empty the tank.

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The domain of the function [tex]f(x)=\frac{1}{x}[/tex]  is all real numbers except 0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.

For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].

For this function, the domain is all the values x can take.

Here x cannot take 0 because 1/0 is not defined.

So, the domain of the function is all real values except 0 which can also be written as:

Domain= R-{0}

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Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the inverse of a number a is [tex]\frac{1}{a}[/tex]

then

the inverse of 2 is [tex]\frac{1}{2}[/tex]

For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.

A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.

Z is the number of standard deviations from the mean given by the formula:

z = ( X - μ ) ÷ ( σ )

where

x is the raw score,

μ is the population mean, and

σ is the population standard deviation

A negative value means that the number of standard deviations of an observation is to the left of the mean.

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