What is a formula for the nth term of the given sequence?
-3 , 4 , 11

Answer:

27.41%

Step-by-step explanation:

Data provided in the question

The staffed of Alpha company = 79%

The staffed of Beta company = 62%

Based on the above information, the relative change of staffing from Alpha to beta company is

As we know that

\(\bold {\ Relative \ change = \frac{\alpha- \beta }{\beta }}\)

\(= \frac{(79 -62)}{62} \% \\\\= \frac{17}{62} \times 100\\\\=0.2741 \times 100\\\\=27.41\ \%\)

By applying the above formula we can get the relative change and the same is to be applied so that the correct percentage could come

Answer:0.4

Step-by-step explanation:

4 is bigger than one so it would be like 400>127

Answer:

0.4 would be the greater number

Answer:

1)Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

Step-by-step explanation:

We need to solve the expressions:

1) \(1-2(2x+1)=1-(x-1)\\\)

Solving

\(1-2(2x+1)=1-(x-1)\)

First solving the brackets

\(1-4x-2=1-x+1\)

Simplifying

\(-1-4x=-x\)

Adding 4x on both sides

\(-1-4x+4x=-x+4x\\-1=3x\)

Switching the sides

\(3x=-1\)

Divide both sides by 3

\(\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}\)

So, Solving the expression \(1-2(2x+1)=1-(x-1)\) we get \(\mathbf{x=-\frac{1}{3}}\)

2) \(3.6x-6.1=5.9-2.4x\)

Solving:

\(3.6x-6.1=5.9-2.4x\)

Adding 6.1 on both sides

\(3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x\)

Adding 2.4x on both sides

\(3.6x+2.4x=12-2.4x+2.4x\\6x=12\\\)

Divide both sides by 6

\(\frac{6x}{6}=\frac{12}{6}\\x=2\)

So, solving the equation \(3.6x-6.1=5.9-2.4x\) we get \(\mathbf{x=2}\)

Answer:

Step-by-step explanation:

to find this answer you have to know how to make a percent of something to a normal value so to make 91% to a decimal value you divide by 100. That is 0.91. Then you multipy 0.91 x 80=72.8

He got 72 questions right

Answer:

X=15

Step-by-step explanation:

                    4*x/3+3-(23)=0

Step by step solution :

STEP

1

:

           x

Simplify   —

           3

Equation at the end of step

1

:

       x          

 ((4 • —) +  3) -  23  = 0

       3          

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        3     3 • 3

   3 =  —  =  —————

        1       3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4x + 3 • 3     4x + 9

——————————  =  ——————

    3            3  

Equation at the end of step

2

:

 (4x + 9)    

 ———————— -  23  = 0

    3        

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         23     23 • 3

   23 =  ——  =  ——————

         1        3  

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(4x+9) - (23 • 3)     4x - 60

—————————————————  =  ———————

        3                3  

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  4x - 60  =   4 • (x - 15)

Equation at the end of step

4

:

 4 • (x - 15)

 ————————————  = 0

      3      

                    4*x/3+3-(23)=0

Step by step solution :

STEP

1

:

           x

Simplify   —

           3

Equation at the end of step

1

:

       x          

 ((4 • —) +  3) -  23  = 0

       3          

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        3     3 • 3

   3 =  —  =  —————

        1       3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4x + 3 • 3     4x + 9

——————————  =  ——————

    3            3  

Equation at the end of step

2

:

 (4x + 9)    

 ———————— -  23  = 0

    3        

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         23     23 • 3

   23 =  ——  =  ——————

         1        3  

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(4x+9) - (23 • 3)     4x - 60

—————————————————  =  ———————

        3                3  

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  4x - 60  =   4 • (x - 15)

Equation at the end of step

4

:

 4 • (x - 15)

 ————————————  = 0

      3      

                    4*x/3+3-(23)=0

Step by step solution :

STEP

1

:

           x

Simplify   —

           3

Equation at the end of step

1

:

       x          

 ((4 • —) +  3) -  23  = 0

       3          

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  3  as the denominator :

        3     3 • 3

   3 =  —  =  —————

        1       3  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4x + 3 • 3     4x + 9

——————————  =  ——————

    3            3  

Equation at the end of step

2

:

 (4x + 9)    

 ———————— -  23  = 0

    3        

STEP

3

:

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         23     23 • 3

   23 =  ——  =  ——————

         1        3  

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

(4x+9) - (23 • 3)     4x - 60

—————————————————  =  ———————

        3                3  

STEP

4

:

Pulling out like terms :

4.1     Pull out like factors :

  4x - 60  =   4 • (x - 15)

Equation at the end of step

4

:

 4 • (x - 15)

 ————————————  = 0

      3      

Answer:

3<_x<13/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

125.

The organization’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder is 13%

What is the number of employees who are regarded as remainder?

The number of employees out of the total workforce left after having deducted the number of employees making up the sales team, the customer support team the software development and HR departments is computed as shown below:

remainder of workforce=80,000-16,000-24,000-14,000

remainder of workforce=26,000

finance team=2/5*26000

finance team=10,400

finance team as % of total workforce=10,400/80,000

finance team as % of total workforce=13.00%

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Answer:

l×b perimeter of retangle

Answer:

Final Answer

11+6y

Step-by-step explanation:

Answer:

x=144

Step-by-step explanation:

since they are similar their sides have a common ratio

24/x=42/7

7x=42*24

7x=1008

x=144

The missing sides of the triangle are

10). ∠ ABD = 60 degrees

11). ∠ ADB = 90 degrees

12). ∠ BAD = 30 degrees

13). ∠ CAD = 30 degrees

14. BD is half of the length = BC / 2 = 6/2 = 3

15. AD is the height this is solved using Pythagoras theorem as below

AD^2 = AB^2 - BD^2

AD^2 = 6^2 - 3^2

AD^2 = 36 - 9

AD = sqrt (27)

16. Area of Δ ABC

= 1/2 * base * height

= 1/2 * 6 * sqrt (27)

= 9 sqrt (3)

= 15.59 square units

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Answer:

The answer is 0 if there are 85 inches in the past year then there wouldn't be any in the present year.

Step-by-step explanation:

The solution of given system of equations is (1/5, 6).

What is system of equation?

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one with two equations and two variables. Linear equations are simpler than non-linear equations because they graph as straight lines.

Given equations : 5x+y=7

                             20x+2=y

We can solve it by using substitution method:

Now, we have 5x+y=7

it can be written as,

         y = 7 - 5x .... equation 1

Similarly, we have 20x+2=y

can be written as,

           y = 20x+2 ..... equation 2

Subtracting equation 1 from equation 2

we get,  20x+2 - ( 7 - 5x ) = 0

             20x + 5x + 2 - 7 = 0

             25x = 5

               x = 1/5

Putting x=1/5 in equation 1,

we get, y = 20 × 1/5 + 2

               = 4 +2

               = 6

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Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

8 two-point shots,

4 three-point shots

Step-by-step explanation:

let 'x' = 2-pt shots

let 'y' = 3-pt shots

system of equations can be used as follows:

x + y = 12

2x + 3y = 28

if we solve for 'y' we get 'y = 12-x'

use '12-x' instead of 'y' in the equation 2x + 3y = 28 to solve for 'x':

2x + 3(12-x) = 28

2x + 36 - 3x = 28

-x + 36 = 28

-x = -8

x = 8

if x+y = 12, then y = 4

Answer:

     y = 94

Step-by-step explanation:

Linear Pair:

The two adjacent angles whose non common arms form a straight line is called linear pair. They add up to 180

2x + 36 = 180 {linear pair}

       2x  = 180 - 36

       2x = 144

Sum of all angles of a n-sided polygon = (n-2)*180

                                                                 = ( 6-2)*180

                                                                 = 4 * 180

                                                                  = 720

y + 144 + 111 + 105 + 165 + 101 = 720

                                  y + 626  = 720

                                             y = 720 - 626

                                            \(\sf \boxed{y = 94^ \circ}\)

Answer:

94°

Step-by-step explanation:

2x + 36 = 180 (angles on a straight line)

2x = 180 - 36

2x = 144

2x = 144°

Sum of all angles of a n-sided polygon = (n-2)×180 = ( 6-2)×180

= 4 × 180

= 720

y + 144 + 111 + 105 + 165 + 101 = 720

y + 626 = 720

y = 720 - 626

y=94 °

The cosine function graphed is defined as follows:

y = 2.5cos(4x) + 1.5.

The function is at it's maximum value at the origin, hence it is a cosine function, defined as follows:

y = Acos(Bx) + C.

The parameters are given as follows:

The maximum value of the function is of 4, while the minimum value of the function is of -1, for a difference of 5, hence the amplitude is given as follows:

2A = 5

A = 5/2

A = 2.5.

Without vertical shift, the function would oscillate between -2.5 and 2.5, but it oscillates between -1 and 4, hence the vertical shift is given as follows:

C = 1.5.

The shortest distance between repetitions is of π/2, hence the period is of π/2 and the coefficient B is obtained as follows:

2π/B = π/2

B = 4.

Hence the function is given as follows:

y = 2.5cos(4x) + 1.5.

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Step-by-step explanation:

x4-7x3+14x2-3x-9

This deals with polynomial long division.

Overview

Steps

Topics

Links

1 result(s) found

(x

2

−x−1)⋅(x−3)

2

See steps

Step by Step Solution:

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 2 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

((((x4)-(7•(x3)))+(2•7x2))-3x)-9

STEP

2

:

Equation at the end of step

2

:

((((x4) - 7x3) + (2•7x2)) - 3x) - 9

STEP

3

:

Polynomial Roots Calculator :

3.1 Find roots (zeroes) of : F(x) = x4-7x3+14x2-3x-9

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is -9.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,3 ,9

Let us test ....

The slope of the tangent line to the curve \(f(x)=4x^2$\) at x=3 is 24. We found this by the limit definition of the derivative.

The slope of the tangent line to the curve f(x)=4x² at x=3 is found using the limit definition of the derivative. By taking the limit as h approaches 0, the derivative is found to be 24.

Using the limit definition of the derivative, we have:

\($$f'(3) = \lim_{h \to 0} \frac{f(3+h) - f(3)}{h} \\\\= \lim_{h \to 0} \frac{4(3+h)^2 - 4(3)^2}{h}$$\)

Simplifying, we get:

\($$f'(3) = \lim_{h \to 0} \frac{4(9 + 6h + h^2 - 9)}{h}\\\\ = \lim_{h \to 0} \frac{24h + 4h^2}{h} \\\\= \lim_{h \to 0} (24 + 4h) = 24$$\)

Therefore, the slope of the tangent line to the curve  \(f(x)=4x^2$\) at x=3 is 24.

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The percent increase of the profit is 15%

In this question, the figures are given as

Profit in March = £2750

Profit in April = £3162.50

The percentage of the increase of the profit is then calculated using the following equation

Increase percentage = (Profit in April - Profit in March)/Profit in March * 100%

Substitute the known values in the above equation, so, we have the following representation

Increase percentage = (3162.50 - 2750)/2750 * 100%

Evaluate

Increase percentage = 15%

Hence, the increase in percentage is 15%

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The equation of the line is: y = -3x + 26

What is an equation of the line?

An equation of a line is a mathematical expression that represents a straight line in a two-dimensional Cartesian coordinate system. It can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of a line that passes through two given points, we can use the slope-intercept form of the equation:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Once we have the slope, we can use one of the points and the slope to find the y-intercept, b, using the equation:

b = y - mx

where (x, y) is one of the given points.

For the given information that the line passes through (7,5) and (3,17), we can find the slope as:

m = (17 - 5)/(3 - 7) = -3

Using the point (7,5) and the slope, we can find the y-intercept, b, as:

5 = -3(7) + b

b = 26

Therefore, the equation of the line is: y = -3x + 26

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Answer:

0.2222 of growth in a month

Step-by-step explanation:

2/3feet / 3 months

Answer:

The rate of growth of sprout seed in 3 months is 1.14%

Step-by-step explanation:

Given as:

The length of seed sprout grew =  foot

The time period for sprout grew = 3 month

Let The rate of sprout grew = r%

Let The initial length of seed = l foot

So, The length of seed sprout grew after 3 months =   × l foot

Now, According to question

The length of seed sprout grew after n months =  

Or ,   × l  =  

Or,  =  

Or, 1 +  =  

Or,  = 1.14

∴ r = 1.14 ×100 = 114

So, The rate of growth = r = 1.14 %

Hence The rate of growth of sprout seed in 3 months is 1.14%

The statement "The product of a number and ten decreased by eight" is represented by the correct equation D. 10n - 8.

A number's product is the outcome of multiplying it by another number.

Addition, subtraction, multiplication, division, exponents, and square roots are some other examples of mathematical expressions.

A mathematical action known as an exponent symbolizes the repeated multiplication of the same integer. It is represented by a tiny number above and to the right of a base number.

For instance, 23 signifies that the number 2 has been multiplied three times, for a result of 8.

The sentence "The product of a number and ten decreased by eight" is correctly expressed as D. 10n - 8.

With this formula, a number is multiplied by 10 first, and the result is then reduced by 8.

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Answer:

20%decrease? id.k if its decrease or increase but its 20%

Step-by-step explanation:

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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