Using f(x) = 2x + 7 and g(x) = x - 3, find f(g(-2)).

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.

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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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?

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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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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When calculating the population standard deviation, the sum of the squared deviation is divided by N and then the square root of the result is taken.

When calculating the sample standard deviation, the sum of the squared deviations is divided by n - 1 and then the square root of the result is taken.

The sum of the squared deviation is often divided by N, the population's data entry count, for calculating any population standard deviation. After that, the result's square root would be calculated.

The total of the squared deviations is typically divided by n – 1, where n is the number of entries in the sample data set, when calculating the sample standard deviation, on the other hand. After that, the result's square root would be calculated.

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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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if f(x) = (x-2)² and g(x) = (x-2)² -7, to get g, we shift f to the down

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

The general formula of transformations is given as f(x) = a(bx − h)n + k.

Where h is the horizontal change and k is the vertical change

therefore if f(x) = (x-2)² and g(x) = (x-2)² -7,

k = -7

therefore to get f(x) we shift g(x) down

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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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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 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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Answer:

Step-by-step explanation:

The registration fee for a used car is 0.59% of the car's cost. To find the registration fee for a specific car, you would multiply the cost of the car by 0.0059 (0.59% as a decimal). For example, if the cost of the used car is $10,000, the registration fee would be:

$10,000 * 0.0059 = $59

So the registration fee for a used car costing $10,000 would be $59.

Answer:

A

Step-by-step explanation:

The correct input-output table for the function f(z) = 4 is option A:

Input (x) | Output f(x)

-3 | 4

-2 | 4

1 | 4

2 | 4

3 | 4

Answer: A

Step-by-step explanation:

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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Suppose that you observe that when the price of cigarettes rises by 10%, the quantity of cigarettes purchased falls by 8.7%. this implies that cigarettes are price inelastic in demand and that the price elasticity of demand is equal to 0.87.

The degree to which use of a product changes in response to changes in its price is known as price elasticity of demand. If a product's price elasticity of demand were extremely low, or even zero, then demand would only barely increase or decrease in reaction to price changes.

If price elasticity of demand for a good were about 1.0, then demand for that good would fall by 1% for every 1% increase in price. For every 10% price increase, demand would decrease by 10%, by 20% for a 20% price increase, by 100% for a 100% price increase, and so on.

Hence, it implies that cigarettes are price inelastic in demand and that the price elasticity of demand is equal to 0.87.

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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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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 area of the trapezoid is 188.5 inches²

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs.

Given here: A trapezoidal window with top side 12  inches and height 13 inches

And The base of the triangle formed from the height on the right is labeled 2 inches.

Thus the length of the longer side is equal to 13+2+2=17

Hence, The area of the trapezoid is = 1/2 × (12+17)×13

                                                        A= 188.5 inches²

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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 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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There are 284 adults who ate pizza.

The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

Given  A survey of 518 adults,

let  T denote TV, H for out with friends, and P for pizza

and given, n(T ∪ H ∪ P) = 518

n(T) = 175, n(H) = 181

n(P) = to find

TP = 39, TH = 26

FP = 39, n(TPH) = 42

n(TP) = 39 + 42 = 81

n(TH) = 26 + 42 = 68

n(HP) = 39 + 42 = 81

using the formula of triple intersection,

 n(T U H U P) = n(T) + n(H) + n(P) - n(TH)   - n(TP)   - n(HP)   + n(TPH).

518 - 66 = 175 + 181 + n(P) - 81 - 68 - 81 + 42

n(P) = 452 - 168

n(P) = 284

Hence 284 people ate only pizza.

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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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1. If A, then B: True. 2. If B, then A: False. 3. A if and only if B: True.  A and B must both be true for the third statement to be true.

In this scenario, we are presented with a pair of statements A and B. For each pair, we must determine if the following three sentences are true or false: 1. If A, then B. 2. If B, then A. 3. A if and only if B. The first statement is true if statement A is true and statement B is true. The second statement is false if statement A is true and statement B is false. The third statement is true if both statements A and B are true. To determine this, we must consider both statements A and B to see if they are both true or false. If both are true, then statement 3 is also true. If either statement A or B is false, then statement 3 is false. Therefore, if both statements A and B are true, then the third statement is true, otherwise, it is false.

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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 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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Answer:

21,866,655ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer: 21866655

Step-by-step explanation:

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

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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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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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