Consider the function f(x)=−3/4 x+1.

What is f(12)?

Enter your answer, as a simplified fraction, in the box.

Answer:

f-1(x)=x-4

f-1(4)=0

Step-by-step explanation:

to get an inverse function, replace x with y, and y with x.

y=x+4  ---> x=y+4

solve for y: x=y+4 --> y=x-4 --> f-1(x)=x-4

f-1(4)=(4)-4=0

Answer:

a(11) = 4^10 = 1048576

Step-by-step explanation:

The first term of this geometric sequence, a(1), is 1, and the common ratio, r, is 4.  Each new term is 4 times the previous term.  Thus,

a(n) = 1*4^(n - 1), and

a(11) = 4^10 = 1048576

Answer:

The 11th term is  1048576

Step-by-step explanation:

Answer:

-15/4 or -3 3/4

Step-by-step explanation:

14n = 2/3n - 50

13 1/3n = -50

40/3n = -50

cross-multiply to get:

40n = -150

n = -15/4 or -3 3/4

Answer:

21

Step-by-step explanation:

63 divided by 3 is 21

210 divided by 10 is 21

The function that models the population t years after 2000 is22300 × e^(0.06t), The estimated fox population in the year 2008 is 36081. This can be answered by the concept of exponential function.

The question asks to find a function that models the population of foxes in a certain region with a continuous growth rate of 6 percent per year starting from the year 2000. It also asks to estimate the fox population in the year 2008 using this function.

a. Let P(t) be the population of foxes t years after 2000. Since the growth rate is continuous, we can use an exponential function with base e to model the population. We know that P(0) = 22300 (the population in the year 2000), and the annual growth rate is 6%. Therefore, we can write:

P(t) = 22300 × e^(0.06t)

b. To estimate the fox population in the year 2008, we need to find P(8) since t = 8 represents 8 years after 2000. Substituting t = 8 into the equation above, we get:

P(8) = 22300 × e^(0.06×8) = 22300 × e^0.48 ≈ 36081

Therefore, the estimated fox population in the year 2008 is 36081.

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Answer:

$69.40

Step-by-step explanation:

$9.50 × 6 = $57

$57 + $12.40 = $69.40

The number of total different values of the binomial experiment variable X is given by = 6.

Hence the correct option is (d).

Here the experiment is an example of Binomial experiment.

And the number of trials in this experiment is given by = 5.

So, the value of parameter, n = 5.

So the different values of the binomial distribution variable X can be given by = {0, 1, 2, 3, 4, 5}

So the number of total different values of the binomial distribution variable X is given by = 6.

Hence the correct option will be given by (d).

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Answer:

(0, - 7 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

(0, 7 ) → (0, - 7 )

The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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The distance between given points (-3, 7) and (4, 7) is approximately equal to 7 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them.

In this case, the two points are (-3, 7) and (4, 7), so we can plug in the values into the distance formula:

d = √[(4 - (-3))² + (7 - 7)²]

= √[7² + 0²]

= √49

= 7

To visualize this, imagine a number line extending from -3 to 4, with the two points located at 7 on the y-axis. The distance between the two points is the length of the line segment connecting them, which is a horizontal line of length 7 units.

This is because the two points have the same y-coordinate, so the only difference between them is their x-coordinates.

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Using for loop we can get the syntax in order to calculate this arithmetic series n is A = 0.9999.

An arithmetic collection is the sum of the phrases in an mathematics collection with a specific range of phrases. Following is a easy system for locating the sum: Formula 1: If S n represents the sum of an mathematics collection with phrases.

This system calls for the values of the primary and ultimate phrases and the range of phrases. Finite Sequence- Finite sequences have countable phrases and do now no longer cross as much as infinity. An instance of a finite mathematics collection is 2, 4, 6, 8. Infinite Sequence- Infinite arithmetic collection is the collection wherein phrases cross as much as infinity.

using while

A=0; n=1; while n<=10000     A=A+(1/(n*(n+1)));     n=n+1; end A

output

A =      0.9999

using  for loop

A=0; for n=1:10000     A=A+(1/(n*(n+1))); end A

output

A = 0.9999.

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Correct Question:

The following series can be written with a shorthand form of sigma notation (A). Use while syntax to calculate this arithmetic series:

1/(1x2) + 1/(2x3) + 1/(3x4) + ... + 1/(n x (n+1)) ......1

A = ∈ 1/(n x (n+1)); n=[1:10000]

Answer:

The input variable is 5 i.e 15/3

Answer:

Use the keep change flip method!

Keep the first fraction, the same:

4/5

Change the division to multiplication:

4/5 *

Flip the numerator and denominator of the second fraction:

4/5 * 2/3 =

Multiply straight across:

4 * 2 = 8

5 * 3 = 15

Answer:

8/15

Step-by-step explanation:

Hope it helps! =D

Answer:

$3

Step-by-step explanation:

 \(\bold{Hello!}\\\bold{Your~Answer~Is~Below!}\)

______________________________

 \(\bold{Solution~Steps:}\)

\(1.)~54+3(1-1):\)

\(2.)~54+3(2-1):\)

\(3.)~54+3(3-1):\)

\(4.)~54+3(4-1):\)

______________________________

 \(\bold{Answers:}\)

______________________________

 \(\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~~~-TotallyNotTrillex}\)

Step-by-step explanation:

log(5x) - log(2) = log(5x/2)

therefore,

log(4x - 1) = log(5x/2)

4x - 1 = 5x/2

8x - 2 = 5x

3x - 2 = 0

3x = 2

x = 2

since this is basically a linear equation in x, there is only one solution, and that is x = 2.

for x = 2 all arguments of the log functions are positive.

4x - 1 = 4×2 - 1 = 8 - 1 = 7

5x = 5×2 = 10

these are all valid arguments for the log function.

so, x = 2 is a valid and not extraneous solution.

Answer:

1.79m^2

Step-by-step explanation:

(0.1×1)+2(0.5×0.8×0.1)+(1×0.8)+(1×0.81)

=1.79

Answer:

17.5m

Step-by-step explanation:

You gotta do this:

0.81 x 1 = Top area

((0.8 x 0.1) ÷ 2) x 2 = left side and right side area

1 x 0.1 + Back Area

0.8 x 1 = Bottom

Add them all together and remember that the final answer has to be in metres, you get - 17.5m

Answer: 4y - (2/3)x + 20

Step-by-step explanation:

Write out problem: 4(y+5) - (2/3)x

Expand: 4y + 20 - (2/3)x

Reorder: 4y - (2/3)x + 20

The number of distinct initial possible pairings is determined by the formula (n/2) * ((n-2)/2) * ((n-4)/2) * ... * 1, where the number of terms in the product is (n-1)/2.

In a single-elimination ping-pong tournament, each player gets to play against every other player once. It is a type of tournament in which players are eliminated after losing once until there is only one winner.

The total number of games that need to be played in such a tournament is (n-1), since each game eliminates one player from the tournament.

As a result, we know that the number of games played in a single-elimination ping-pong tournament with n players is (n-1).

The possible pairings for the first game in the tournament are n/2, since the first player may be paired with any of the remaining n-1 players, the second player may be paired with any of the remaining n-2 players, and so on.

Then we may have (n-2)/2 possible pairings for the second game, (n-4)/2 possible pairings for the third game, and so on.

In general, we can see that there are (n-2k)/2 possible pairings for the k-th game.

Because a distinct tournament bracket is generated by each of these distinct initial pairings, the number of distinct initial pairings resulting in a distinct tournament bracket is given by:

(n/2) * ((n-2)/2) * ((n-4)/2) * ... * 1,

where the number of terms in the product is (n-1)/2

Since a distinct tournament bracket is generated by each of these distinct initial pairings, this formula calculates the number of distinct initial possible pairings resulting in a distinct tournament bracket.

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Answer:

  2.6

Step-by-step explanation:

A is after the 6th of 10 spaces between 2 and 3. It has the value 2 +6/10 = 2.6.

According to the information provided, the state is at point C, Michigan.

Based on the information provided, the state located at point C is Michigan.

Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.

Logical thinking follows he is divided into two types.

Oral reasoning:

It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:

It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.

Much of the logic curriculum can be classified into his two types above. 

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The x-coordinate of the vertex is 0.  the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

To find the dimensions that will create the maximum area of the prop section, we need to analyze the given equation A = -x^2 + 40. The equation represents a quadratic function in the form of A = -x^2 + 40., where A represents the area of the prop section and x represents the dimension.

The quadratic function is in the form of a downward-opening parabola since the coefficient of is negative (-1 in this case). The vertex of the parabola represents the maximum point on the graph, which corresponds to the maximum area of the prop section.

To determine the x-coordinate of the vertex, we can use the formula x = -b / (2a), where the quadratic equation is in the form Ax^2 + Bx + C and a, b, and c are the coefficients. In this case, the equation is -x^2 + 40, so a = -1 and b = 0. Plugging these values into the formula, we get x = 0 / (-2 * -1) = 0.

Therefore, the x-coordinate of the vertex is 0. To find the corresponding y-coordinate (the maximum area), we can substitute x = 0 into the equation  A(x) = -x^2 + 40: A(0) = -(0)^2 + 40 = 40.

Hence, the equation that reveals the dimensions that will create the maximum area of the prop section is A = 40. This means that regardless of the dimension x, the area of the prop section will be maximized at 40 units.

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Explanation:

See the diagram below. I've extended one of the rays to form a full line. This is shown in red. The alternate interior angles 60 and x are congruent due to the parallel lines, so x = 60.

We can then find angle y

x+y+20 = 180 ... angles of a triangle add to 180

60+y+20 = 180

y+80 = 180

y = 180-80

y = 100

Use this to find z

y+z = 180

100+z = 180

z = 180-100

z = 80

Or you could use the remote interior angle theorem

x+20 = z

60+20 = z

80 = z

z = 80

The  summary of the description of the Commutative, Associative, and Distributive properties is given below

The commutative property is one whose  law is known to states that with the use of addition and multiplication of numbers, a person can be able to alter the order of the numbers in a given problem and it will not have an affect on  the answer.

The associative property is known to be one that that if in the process of adding or multiplying, the grouping symbols is one that a person can  rearranged and it will not alter the result. This therefore is  stated as (a+b)+c=a+(b+c).

The distributive property is known to be one that is seen as a multiplication method that entails the multiplication of a number by the use of all the separate add ends of another given number.

Hence, The distributive Property implies that when a factor is said to be multiplied by the sum/addition of two terms, it is said to multiply each of the two numbers by its factor, and finally carry out the addition operation.

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Answer:

a^4 with a^2

Step-by-step explanation:

The volume of inhaled air at a maximum at t = 2, 4, 6, ...

The volume of inhaled air is at a maximum when the function V(t) is at a maximum. This occurs when the derivative of V(t) is equal to zero.

The derivative of V(t) is:

V'(t) = (3/5) pi * (pi/2) * sin(pi t/2)

Setting this equal to zero gives:

(pi/2) * sin(pi t/2) = 0

This occurs when pi t/2 is equal to a multiple of pi. This means that t/2 is equal to a multiple of 1, or t is equal to a multiple of 2. Therefore, the volume of inhaled air is at a maximum when t = 2, 4, 6, ...

The correct answer is: t = 2, 4, 6, ...

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To solve inequalities with fractions and variables in the denominator, multiply both sides of the inequality by the least common multiple (LCM) of the denominators and solve the resulting equation.

To solve inequalities with fractions and variables in the denominator, follow these steps:

1. Clear the denominator: Multiply both sides of the inequality by the least common multiple (LCM) of the denominators to eliminate the fractions. This step helps in simplifying the inequality.

2. Simplify and combine terms: Distribute and simplify any terms resulting from multiplying through by the LCM. Combine like terms if necessary.

3. Solve as a regular inequality: Treat the resulting inequality as a regular inequality without fractions. Use algebraic techniques to isolate the variable on one side of the inequality sign.

4. Determine the direction of the inequality: Determine the direction of the inequality by considering the signs of any coefficients or variables in the simplified inequality. If the coefficient of the variable is positive, the direction of the inequality remains the same. If the coefficient is negative, the direction of the inequality is reversed.

5. Express the solution: Write the solution as an inequality or as an interval, depending on the context of the problem.

It's important to note that when multiplying both sides of an inequality by a negative number, the direction of the inequality needs to be reversed.

Example: Solve the inequality (3/x) - (2/5) ≥ 1

1. Clear the denominator: Multiply both sides by 5x, which is the LCM of the denominators:

5x * [(3/x) - (2/5)] ≥ 5x * 1

Simplifying, we get:

15 - (2x) ≥ 5x

2. Simplify and combine terms:

15 - 2x ≥ 5x

3. Solve as a regular inequality:

Add 2x to both sides to isolate the variable:

15 ≥ 7x

4. Determine the direction of the inequality:

Since the coefficient of x is positive (7), the direction remains the same.

5. Express the solution:

Divide both sides by 7 to solve for x:

15/7 ≥ x

The solution is x ≤ 15/7.

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