Use this pattern when a binomial
can be written as the square of
one number minus the square of
another number.
4x² - 49 = (2x-7)(2x + 7)
a² + 2ab + b² = (a + b)²

In  2000, the population of bacteria reached 5 million, and it is projected to have 7.5 million in 2025. the value of a is 1.49.

A particular class of mathematical model used to explore population dynamics is called a population model.

P(x)  = C a ^ ( X - 2000)

C = 5m = 5(10⁶)

p( X ) = 5(10⁶) a ^ ( X - 2000)

7. 5 * 5(10^6) = 10 ^6 a^ 25

7. 5 = a ^ 5

 log 7.5 = 5 log a

  a =10 ^( log 7.5 / 5 )= 1.49

 P ( x ) =  ( 1.49m ) ^  ( X- 2000)

Models enable a better comprehension of the operation of intricate relationships and processes. Understanding how numbers change over time or in connection to one another may be made more manageable through the modelling of dynamic interactions in nature. Using population modelling as a technique allows for the detection of several trends.

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In  2000, the population of bacteria reached 5 million, and it is projected to have 7.5 million in 2025. the value of a is 1.49.

A particular class of mathematical model used to explore population dynamics is called a population model.

P(x)  = C a ^ ( X - 2000)

C = 5m = 5(10⁶)

p( X ) = 5(10⁶) a ^ ( X - 2000)

7. 5 * 5(10^6) = 10 ^6 a^ 25

7. 5 = a ^ 5

log 7.5 = 5 log a

 a =10 ^( log 7.5 / 5 )= 1.49

P ( x ) =  ( 1.49m ) ^  ( X- 2000)

Models enable a better comprehension of the operation of intricate relationships and processes. Understanding how numbers change over time or in connection to one another may be made more manageable through the modelling of dynamic interactions in nature. Using population modelling as a technique allows for the detection of several trends.

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The next three terms are -2.56, -1.024 and -0.4096

The definition of the function is given as

Sequence -100, -40, -16, -6.4

The above definitions imply that we simply multiply 0.4 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

Next term = -6.4 * 0.4 = -2.56

Next term = -2.56 * 0.4 = -1.024

Next term = -1.024 * 0.4 = -0.4096

This means tat the next three terms are -2.56, -1.024 and -0.4096

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Kyle needs 0 mL of the 24% solution and 42 mL of the 18% solution to make 20% acid solution.

percentage, a relative value indicating hundredth parts of any quantity.

Let's call the amount of 24% solution used x, and the amount of 18% solution used y.

We can set up two equations to represent the concentration of the mixture and the total volume of the mixture:

Concentration equation: (0.24 x + 0.18 y) / (x + y) = 0.20

Volume equation: x + y = 42 mL

we can substitute 42 mL for y in the volume equation and solve for x:

y = 42 mL

x = 42 - y = 42 - 42 = 0 mL

So, Kyle needs 0 mL of the 24% solution and 42 mL of the 18% solution to make 20% acid solution.

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Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

The maximum value of the function f (x) = -1.8x² + 7x - 11 to the nearest hundredth is,  - 4.19.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ f (x) = -1.8x² + 7x - 11

Now, We can differentiate with respect to x as;

⇒ f ' (x) = - 1.8 × 2x + 7 × 1 - 0

⇒ f ' (x) = - 3.6x + 7

Put f ' (x) = 0

⇒ - 3.6x + 7 = 0

⇒ 3.6x = 7

⇒ x = 1.94

Now, Again differentiate with respect to x as;

⇒ f ' (x) = - 3.6x + 7

⇒ f '' (x) = - 3.6 × 1 + 0

⇒ f '' (x) = - 3.6 < 0

Hence, Substitute x = 1.94 in function to get maximum value,

⇒ f (x) = -1.8x² + 7x - 11

⇒ f (x) = -1.8 (1.94)² + 7 × 1.94 - 11

⇒f (x) = - 6.77 + 13.58 - 11

⇒ f (x) = - 4.19

Thus, The maximum value = - 4.19

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The length of the unknown leg is given as follows:

x = 2.

The possible mistake is given as follows:

C. He did not square the length of the given leg.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For this problem, we have that:

Hence the unknown leg is obtained as follows:

2.1² + x² = 2.9².

4.41 + x² = 8.41²

x² = 4

x = 2.

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Answer:

21,866,655ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer: 21866655

Step-by-step explanation:

The result after the point is translated is (-5, -5)

From the question, we have the following parameters that can be used in our computation:

Point = (-9, -2)

The transformation rule is given as

translation left 4 units and down 3 units

Mathematically, this is represented as

(x, y) = (x + 4, y - 3)

So, we have

Image = (-9 + 4, -2 -3)

Evaluate

Image = (-5, -5)

Hence, the image is (-5, -5)

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Least common denominator is 100.

Fractions in Math, represent a numerical value that expresses a part of a whole. The whole can be any number, a specific value, or a thing.

Given fractions are,

20 7/10 = 207/10

20 3/4 = 83/4

18 9/10 = 189/10

20 18/25 = 518/25

Common Denominator is 10 × 4 × 10 × 25

                                       = (5 × 2) × (2 × 2) × (5 × 2) × (5 × 5)

Common factor among three numbers are 5 , 2.

Uncommon factors are 5 , 2                                        

Least common denominator = 5 × 2 × 5 × 2 = 100

Hence, 100 is least common denominator of the given fractions.

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The linear equation Maya solves, 5·x + 7 = -5·x + 7, indicates that we get x = 0. The correct option is therefore;

A linear equation is an equation of the form; y = m·x + c, where, m is the slope and c is the y-value of the intercept of the graph of the equation with y-axis, known as the y-intercept.

The specified equation can be presented as follows;

5·x + 7 = -5·x + 7

Adding 5·x to both sides of the equation, we get;

5·x + 5·x + 7 = -5·x + 5·x + 7

Collecting and adding like terms, is obtained as follows;

10·x + 7 = 0 + 7

Adding 7 to both sides of the equation, we get;

10·x + 7 - 7 = 0 + 7 - 7

10·x + 0 = 0 + 0 = 0

10·x = 0

x = 0/10 = 0

x = 0

Therefore; the equation has only one solution, x = 0

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Answer:

11

Step-by-step explanation:

6^2+9^2=c^2

36+81=c^2

117=c^2

[tex]\sqrt{117\\[/tex]

11

A deposit is a term used to describe the process of depositing money into a bank account for protection. The depositor acquires ownership of the funds and is eligible for interest on the remaining balance whether the deposit is made with cash, cheques, or other financial instruments.

For Bank A, the initial deposit, money multiplier, reserve rate, and total amount deposited that would make sense are:

Initial Deposit: $6000

Money Multiplier: 50

Reserve Rate: 5%

Total Amount Deposited: $100,000

Justification:

The initial deposit of $6000 is consistent with the information given in the problem statement.

The money multiplier of 50 is within the range of typical money multipliers for banks, which are typically in the range of 10-60, depending on the reserve rate.

The reserve rate of 5% is consistent with industry standards, which typically range from 0-10%.

The total amount deposited of $100,000 is consistent with the initial deposit of $6000 and the money multiplier of 50.

Given these values, we can calculate the amount loaned out by Bank A as follows:

Loan Amount = Initial Deposit * (1 - Reserve Rate) * Money Multiplier

Loan Amount = $6000 * (1 - 0.05) * 50 = $285,000

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Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

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The candle burns at the rate of 0.5 inches per hour.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

The proportional relationship between the number of inches a candle has burned away, b, at any time in hours, t.

The expression can be represented by the equation

b = 0.5t.

The equation shows a proportional relationship.

That means,

b/t = 0.5.

Therefore, the rate is 0.5 inches per hour.

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The third-degree polynomial function that has an output of 1,025 when x=5, and has zeros −20 and −4i is:

f(x) = 4.55(x + 20)(x² - 16)

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

A third-degree polynomial function with real coefficients that have zeros at -20 and -4i can be written in the form:

f(x) = a(x + 20)(x + 4i)(x - 4i)

where a is a constant.

Expanding the expression and using the fact that i² = -1:

f(x) = a(x + 20)((x² + 4² × i²)

f(x) = a(x + 20)(x² - 16)   ....(i)

To find the value of a, we can use the fact that f(5) = 1,025:

So f(5) = a(5 + 20)(5² - 16) = 1,025

a(25)(25-16) = 1,025

a(25)(9) = 1,025

a(225) = 1,025

a = 1,025 / 225

a = 4.55

Substitute the value of a = 4.55 in equation (i), and we get

f(x) = 4.55(x + 20)(x² - 16)

Therefore, the third-degree polynomial function is f(x) = 4.55(x + 20)(x² - 16).

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The value of Y when X = 4 in the regression line that has the slope of 2,5 is a) 26

The equation of a straight line with slope m and y-intercept b is given by  :

y = mx + b.

Where

1. y is the dependent variable (i.e., the value of y depends on x)

2. x is the independent variable

3. m is the slope of the line, representing the rate of change of y with respect to x

4. b is the y-intercept, the point where the line intersects the y-axis when x = 0.

This equation can be used to describe the relationship between two variables, and it can be used to make predictions about the value of y for a given value of x, or to find the value of x for a given value of y.

From the question we have the following information :

1. Slope ( or m ) is 2.5

2. The intercept ( y-intercept or b ) is 16

So, using the values given (slope = 2.5, y-intercept = 16), we have:

y = mx + b

y = 2.5x + 16

When X is 4, substituting X with 4 in the equation gives us:

y = 2.5 * 4 + 16 = 26

So the value of Y when X is 4 is 26. Answer: a) 26.

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Answer:

Step-by-step explanation:

35 + 0.18 *x miles ≤ 71

x ≤ 200

0.18 *x miles ≤ 71 - 35

35≤ 71 - 0.18 *x miles

Maria pay $3,040 in income tax for last year.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Maria made $35,000 in taxable income last year.

Here, The Income tax rate is 15% for the first $9500 plus 17% for the amount over $9500.

Hence, The income tax is,

⇒ 15% of 9500 + 17% of 9500

⇒ 15/100 × $9500 + 17/100 × $9500

⇒ $1425 + $1625

⇒ $3,040

Thus, Maria pay $3,040 in income tax for last year.

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The acceleration of the rocket is 11.1 m/s^2.

We know that the acceleration can be obtained from the net force that is  acting on the rocket. Given that force is a vector quantity the direction of the forces that are acting is very important in the problem.

We know that;

Net force = Thrust force - Frictional force

If the net force is given by ma then;

2100a = 2.4×10^4 - 650

a = 2.4×10^4 - 650 /2100

a = 11.1 m/s^2

Thus, we can see that the magnitude of the acceleration is 11.1 m/s^2.

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The project start date for the project is 2/12/23.

In order to calculate the start date for the project, in excel, the WORKDAY Function is used. The WORKDAY Function is found under Excel Date and Time functions. The function provides a date that is N working days in the future or in the past. Working days exclude weekends and any dates identified as holidays.

The formula is: ‘=WORKDAY(start_date,days,[holidays]). The start_date (which represents the start date) and days (which represents the number of workdays to be added) are required fields. The [holiday] (which represents the array of dates that are included as workdays) is an optional field. In the given case, the formula used will be WORKDAY(G2, 0, C3:C13) and the project start date will be 2/12/23. Note that the start date of the first phase will be the same as start of the project.

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The polynomial function for the number of ships in thousands that visited the port in a given year is

The polynomial is found by substituting the values of x and the function that has same value as in the table is the correct function

The function P(x) = 2.3x² + 0.2x + 1.8 gave the correction option, this can be ascertained using

x = 1

P(1) = 2.3 * 1² + 0.2 * 1 + 1.8 = 4.2

x = 2

P(2) = 2.3 * 2² + 0.2 * 2 + 1.8 = 8.2

x = 3

P(3) = 2.3 * 3² + 0.2 * 3 + 1.8 =  14.1

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It is not possible to determine whether the range of data set ii is smaller than the range of data set i.

The statement "Data set ii has a smaller range than data set i" cannot be justified based on the boxplots. This is because the range of a data set is the difference between the largest and smallest values in the set, and this information is not represented on a boxplot. To calculate the range of a data set, we use the formula Range = Max - Min, where Max is the largest value in the set and Min is the smallest value in the set. Since the boxplot does not show the actual values in the data set, it is impossible to calculate the range of the data set. Therefore, it is not possible to determine whether the range of data set ii is smaller than the range of data set i.

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Complete question: Which of the following statements about these two data sets cannot be justified based on the boxplots?

The minimum value of c such that the system has exactly two distinct solutions is 4. When c=4, the two parabolic equations intersect at exactly two points (1, 4) and (x, y), which are the two distinct solutions.

Answer:

Step-by-step explanation:

The square root of a negative real number can be represented as the imaginary unit, "i", multiplied by the square root of the absolute value of the negative number. In this case, the square root of -180 is:

√(-180) = i * √(180)

The standard form of a complex number is "a + bi", where "a" and "b" are real numbers and "i" is the imaginary unit. In this case, a = 0 and b = √(180), so the complex number can be written as:

0 + i * √(180) = i * √(180)

Therefore, the complex number √-180 in standard form is: i * √(180).

Let's say that F(y) = P(Y <= y), then F(F^-1(x)) = P(F^-1(X) <= F^-1(x)) = P(X <= x), which means F(F^-1(x)) = x, since X is uniformly distributed on [0,1].

In mathematics, a uniformly distributed function is a function whose values are randomly distributed over a defined interval or set, such that any value within the interval or set has equal probability of being selected. A uniform distribution is a type of probability distribution where all values in the range have equal probability of occurring

Therefore, the c.d.f. of Y = F^-1(X) is F.

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The quadrilateral ABCD is a parallelogram as the opposite sides are equal but not a rectangle because all the interior angles are not right angles.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

To make any conclusion about the quadrilateral we have to look at the lengths of each side by the distance formula [tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

AB = [tex]\sqrt{(4 - 0)^2 + (2 - 8)^2[/tex].

AB = [tex]\sqrt{16 + 36[/tex].

|AB| = √52.

Similarly, |DC| = √52.

So, AB = DC.

Now, |AD| = √85 and |BC| = √85.

So, AD = BC.

Therefore, The lengths of the opposite sides are equal so it is a parallelogram.

Now, To be a rectangle DC ⊥ CB.

Slope(DC) = 6/- 4 = - 3/2.

Slope(CB) = - 6/ - 7 = 6/7.

So The quadrilateral ABCD is a parallelogram.

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The arithmetic sequence is A = 14 , 11 , 8 , 5 , ...

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the arithmetic sequence be represented as A

Now , the equation will be

The first term of the AP is a₁ = 14

The common difference of the AP is d = -3

So , the second term of the AP is a₂ = a + d

a₂ = 14 - 3 = 11

The third term of the AP is a₃ = a + 2d

a₃ = 14 - ( 6 ) = 8

The fourth term of the AP is a₄ = a + 3d

a₄ = 14 - ( 9 ) = 5

Therefore , the value of A is A = 14 , 11 , 8 , 5 ...

Hence , the AP is solved

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Answer:

14, 11, 8, 5, . .

Step by-step explanation:

got it right on test

The solution to the system of equations is  x= -12/7  and y= 9/7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

5x + 2y = -6.............(1)

2x - 2y = -6............(2)

Solving equation (1) and (2) we get

5x+ 2x = -12

7x = -12

x= -12/7

and, 2(-12/7) -2y= -6

-2y = -6 + 24/7

y= 9/7.

Hence, the values are x= -12/7  and y= 9/7.

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The exact length of the sides of the quadrilateral are as follows:

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, A quadrilateral ABCD with vertices A(4, 5), B(-3,3), C(-6,-13) and D(6,-2).

From the general formula of the distance between two coordinates in 2D plane.

Distance = √((x - x')² + (y-y')²)

For AB,

Distance = √((4  + 3)² + (5-3)²)

Distance = √49 + 4

Distance = √53

For BC,

Distance = √((-6 +3 )² + (-13-3)²)

Distance = √9 + 256

Distance = √264

Distance = 2√66

And the same process is to be continued For the CD and DA

While

CD = √265

DA = √53

Therefore, The exact length of the sides of the quadrilateral are as follows:

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False. If more than 10% of his high-risk homes exceed this limit, the Water Framework will need to take action.

EPA's lead and copper rule specifies a maximum cutoff of 15 for each billion (ppb) of lead in drinking water. If 10% or more of high-risk household tap water tests exceed this activity level, the water framework is considered in violation of the standard and will do everything possible to reduce lead levels. is needed. This does not guarantee that your water supply will be considered "hazardous," but it does mean that it exceeds the most extreme limits for lead proposed by the EPA.

The EPA requires lead levels in waterframes to be kept below 15 ppb to limit potential health risks.

This 10% of leads is called "Activity Level". EPA suggests that water frames respond to lead levels below 15 ppb to limit potential health opportunities, but assumes levels above 15 ppb are not considered hazardous. increase

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The complete question is:

According to EPA regulations, if more than 10%of homes in a city have high lead content in their water(>15 parts per billion), the city’s water supply is unsafe?