PLEASE HELP Review the equation, then complete the following. f(x)=1/x-4, g(x)=4x+1/x ​Use composition to prove whether or not the functions are inverses of each other. Express the domain of the compositions using interval notation.

Answer:

Step-by-step explanation:

The standard deviation of a data set is represented by the following equation:

Therefore, for the given sample:

For each data point, find the square of its distance to the mean.

Now, solving for the standard deviation:

Answer:

slope is 5/1

Step-by-step explanation:

y=mx+b

m=slope

Answer:

The slope is 5.

Step-by-step explanation:

Y is the y-axis. 5 is the slope. X is the x-axis. -1 is the y-intercept.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Original figure: PQRTS

Dilated figure: P'Q'R'S'T'

Take one of the corresponding sides of the figure and find the scale factor:

The dilation rule as per above is:

Correct option is A

Answer:

infinite number of solutions

Step-by-step explanation:

3(4b - 2) = - 6 + 12b ← distribute parenthesis on left side by 3

12b - 6 = 12b - 6

The expressions on both sides are the same

This indicates the equation has an infinite number of solutions

Answer:

80

Step-by-step explanation:

40 x 2 = 80 :)

The general solution of ax = b can be expressed in parametric vector form as x = tb/a, where t is a parameter.

The equation ax = b can be rewritten as x = b/a. This equation can be solved for any given values of a and b. For example, if a = 3 and b = 9, then x = 9/3 = 3.

The general solution of ax = b can be expressed in parametric vector form as x = tb/a, where t is a parameter. This can be shown by substituting t in place of x. For example, if a = 3 and b = 9, then x = t(9/3) = 3t. This means that all solutions of ax = b can be expressed in the form x = 3t, where t is a parameter.

In other words, the parametric vector form of the general solution of ax = b is x = tb/a, where t is a parameter and a and b are given constants. This equation can be used to find the solutions of the equation for any given values of a and b. The general solution of ax = b can be expressed in parametric vector form as x = tb/a, where t is a parameter.

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Jamie made 8 1/4 cups of fruit punch for a party. Her guests drank 2/3 of the punch. How much fruit punch did her guests drink Jamie made 8 1/4 cups of fruit punch for a party. A mixed number can be converted into an improper fraction by multiplying the denominator by the whole number, and then adding the numerator. Thus, we have 33/4 cups of fruit punch.

Jamie's guests drank 2/3 of the punch. If Jamie made 33/4 cups of fruit punch, then the guests drank2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch The guests drank 1 5/12 cups of fruit punch. More than 100 words: To determine how much fruit punch Jamie's guests drank, we need to calculate the amount of punch made and then multiply it by the fraction of the punch consumed by the guests. Jamie made 8 1/4 cups of fruit punch.

We'll start by converting the mixed number to an improper fraction, which is 33/4. Next, we'll multiply 33/4 by 2/3 to determine how much punch the guests drank. This is calculated as follows:2/3 × 33/4= 22/12 or 1 5/12 cups of fruit punch. Therefore, Jamie's guests drank 1 5/12 cups of fruit punch.

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Answer: \(log (x^3y )\)

Step-by-step explanation:

First we want to make the coefficients of the log the exponents of what is in the log

\(3 log (x) + 2 log (y) - log (y)\\log (x^3) + log (y^2) - log (y)\)

Now adding two log with the same base is the same as multiplying what you are taking the log of

\(log (x^3) + log (y^2) - log (y)\\log (x^3y^2) - log (y)\)

Now subtracting two logs with the same base is the same as dividing what you are taking the log of

\(log (x^3y^2) - log (y)\\log (\frac{x^3y^2}{y} )\)

Now we simplify

The \(y^2\) cancels out the y in the denomiator

\(log (x^3y^2) - log (y)\\log (x^3y )\)

Step-by-step explanation:

xlog3+ylog2-ylog

log3×log2 -ylog

log6-ylog

Answer:

2/3

Step-by-step explanation: parallel lines have the same slope with different y-int

x+10 =5 that is the answer because look at the example

However the exact change in the odds of smoking would depend on various factors such as individuals' preferences, income levels, and the price elasticity of demand for cigarettes.

If the price of cigarettes increases by $1 (all else equal), then the odds of smoking are likely to decrease. This is because an increase in price typically leads to a decrease in demand, and therefore a decrease in the likelihood that someone will choose to smoke cigarettes.

Specifically, the odds of smoking would decrease by a certain percentage that would depend on a variety of factors, such as the current price of cigarettes, the income level of individuals who smoke, and the availability of alternative products or behaviors. However the exact change in the odds of smoking would depend on various factors such as individuals' preferences, income levels, and the price elasticity of demand for cigarettes.

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The exact value of f(3) is f(3) = e^(15) – e^(5) + 3

To find f(3) in the equation f(x) = e^(5x) – e^(x+2) + log(e^3), we simply substitute x = 3 into the equation.

f(3) = e^(5(3)) – e^(3+2) + log(e^3)

Simplifying the exponents:

f(3) = e^(15) – e^(5) + log(e^3)

Since e^x is the base of the natural logarithm, log(e^3) simplifies to 3.

f(3) = e^(15) – e^(5) + 3

This is the exact value of f(3) in the given equation.

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Answer:

C

Step-by-step explanation:

The congruency statement ∠ C ≅ ∠ G  is the only true statement.

So option C is the correct option.

Given,

parallelogram ABCD ≅ parallelogram EFGH

We need to see the properties of parallelograms and make each property congruent to each other and see which of the options given is true.

The given options are:

A. ∠B≅∠E

B. BC≅GH

C. ∠C≅∠G

D. AD≅EF.

It is a quadrilateral that has two pairs of parallel sides and the opposite angles are equal.

Properties of a parallelogram :

- The opposite sides are parallel and congruent.

- The opposite angles are equal.

- The consecutive angles are supplementary.

- If any one of the angles is a right angle, then all the other angles will be at    

 a right angle.

- The two diagonals bisect each other.

So if we compare two parallelograms the above properties are congruent.

Let's draw the two parallelograms ABCD and parallelogram EFGH.

 A____________ B                    E____________F

   \                            \                       \                         \

     \                            \                       \                         \

       \                            \                        \                         \

        D_____________C.                   H____________G

The following are congruent:

AB≅EF

BC≅FG

CD≅GH

AD≅EH

∠ A ≅ ∠ E

∠ B ≅ ∠ F

∠ C ≅ ∠ G

∠ D ≅ ∠ H

Checking the above congruent we see that we have  ∠ C ≅ ∠ G in the given option.

Thus, ∠ C ≅ ∠ G is the only correct option.

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Answer:

$73.25

Step-by-step explanation:

35 + 2.55(15) = 38.25 + 35 = 73.25

The function g(x)=3^x change over the interval from x=8 to x=10 by a factor of 9

The function g(x)=3^x is an exponential function. As x increases, the value of g(x) increases at an increasing rate.

Therefore, over the interval from x=8 to x=10, g(x) will increase at an increasing rate.

To see this, we can calculate g(8) and g(10) and observe the difference between the two values.

g(8) = 3^8 = 6561

g(10) = 3^10 = 59049

So, the rate is

Rate = 59049/6561

Rate = 9

This means that the rate is by a factor of 9

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Upon calculating the sum up to the appropriate term, we find that the sum is approximately 0.0713. So, the correct answer is a. 0.0713

It seems like there is a typo in the series notation. I assume the series you are referring to is ∑(2(-1)^n-1)/(12n^2 + 1) from n=1 to infinity. In this case, we can determine the sum using a well-known function and round the answer to four decimal places. Since the given series is an alternating series, we can use the Alternating Series Estimation Theorem to determine an approximation for the sum. The theorem states that if the absolute difference between consecutive terms is decreasing and the limit of the terms as n approaches infinity is zero, the approximation for the sum is accurate up to the first term that is less than or equal to the desired error bound (in this case, 0.0001). For this series, we can see that the absolute difference between consecutive terms decreases as n increases and the limit as n approaches infinity is zero. So, we can find the smallest value of n for which the term is less than or equal to 0.0001 and calculate the sum up to that term.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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Answer:

a) El error máximo posible es 270 centímetros cúbicos. El error relativo asociado al volumen es 0.01. El error asociado al volumen es 1 por ciento.

b) El máximo error posible del área superficial es 36 centímetros cuadrados. El máximo error posible del área superficial es 36 centímetros cuadrados. El porcentaje de error del área superficial es 0.667 por ciento.

Step-by-step explanation:

Recordemos que el volumen y el área superficial de un cubo quedan representados por las respectivas fórmulas:

\(V = l^{3}\) (Ec. 1)

\(A_{s} = 6\cdot l^{2}\) (Ec. 2)

Donde:

\(l\) - Longitud de la arista, medida en centímetros.

\(A_{s}\) - Área superficial, medida en centrímetros cuadrados.

\(V\) - Volumen, medido en centímetros cúbicos.

a) El error máximo posible del volumen del cubo se estima por el siguiente diferencial:

\(\Delta V = \frac{\partial V}{\partial l}\cdot \Delta l\) (Ec. 3)

Donde:

\(\Delta V\) - Error máximo posible del volumen, medido en centímetros cúbicos.

\(\frac{\partial V}{\partial l}\) - Primera derivada parcial del volumen con respecto a la longitud de la arista, medida en centrímetros cuadrados.

\(\Delta l\) - Error máximo de medición, medido en centímetros.

La derivada parcial de la función de volumen es:

\(\frac{\partial V}{\partial l} = 3\cdot l^{2}\) (Ec. 4)

Ahora expandimos (Ec. 3):

\(\Delta V = 3\cdot l^{2}\cdot \Delta l\)

Si conocemos que \(l = 30\,cm\) y \(\Delta l = 0.1\,cm\), el máximo error posible del volumen es:

\(\Delta V = 3\cdot (30\,cm)^{2}\cdot (0.1\,cm)\)

\(\Delta V = 270\,cm^{3}\)

El error máximo posible del volumen es 270 centímetros cúbicos.

Obtenemos el error relativo al dividir el resultado anterior por el volumen, es decir:

\(\epsilon_{V} = \frac{\Delta V}{V}\) (Ec. 5)

El volumen del cubo es: (\(l = 30\,cm\))

\(V = (30\,cm)^{3}\)

\(V = 27000\,cm^{3}\)

Ahora sustituimos (Ec. 5):

\(\epsilon_{V} = \frac{270\,cm^{3}}{27000\,cm^{3}}\)

\(\epsilon_{V} = 0.01\)

El error relativo asociado al volumen es 0.01.

Por último, encontramos el porcentaje de error asociado al volumen:

\(\%\epsilon_{V} = 0.01\times 100\,\%\)

\(\%\epsilon_{V} = 1\,\%\)

El error asociado al volumen es 1 por ciento.

b) El error máximo posible del área superficial del cubo se estima por el siguiente diferencial:

\(\Delta A_{s} = \frac{\partial A_{s}}{\partial l}\cdot \Delta l\) (Ec. 6)

Donde:

\(\Delta A_{s}\) - Error máximo posible del área superficial, medido en centímetros cuadrados.

\(\frac{\partial A_{s}}{\partial l}\) - Primera derivada parcial del área superficial con respecto a la longitud de la arista, medida en centrímetros.

\(\Delta l\) - Error máximo de medición, medido en centímetros.

La derivada parcial de la función de área superficial es:

\(\frac{\partial A_{s}}{\partial l} = 12\cdot l\) (Ec. 7)

Ahora expandimos (Ec. 6):

\(\Delta A_{s} = 12\cdot l\cdot \Delta l\)

Si conocemos que \(l = 30\,cm\) y \(\Delta l = 0.1\,cm\), el máximo error posible del área superficial es:

\(\Delta A_{S} = 12\cdot (30\,cm)\cdot (0.1\,cm)\)

\(\Delta A_{S} = 36\,cm^{2}\)

El máximo error posible del área superficial es 36 centímetros cuadrados.

Obtenemos el error relativo al dividir el resultado anterior por el volumen, es decir:

\(\epsilon_{A_{S}} = \frac{\Delta A_{S}}{A_{S}}\) (Ec. 8)

El área superficial del cubo es: (\(l = 30\,cm\))

\(A_{S} = 6\cdot (30\,cm)^{2}\)

\(A_{S} = 5400\,cm^{2}\)

Ahora sustituimos (Ec. 8):

\(\epsilon_{A_{S}} = \frac{36\,cm^{2}}{5400\,cm^{2}}\)

\(\epsilon_{A_{S}} = 6.667\times 10^{-3}\)

El error relativo del área superficial es 6.667 × 10⁻³.

Por último, encontramos el porcentaje de error asociado al área superficial:

\(\%\epsilon_{A_{S}} = 6.667\times 10^{-3}\times 100\,\%\)

\(\%\epsilon_{A_{S}} = 0.667\,\%\)

El porcentaje de error del área superficial es 0.667 por ciento.

Answer:

Step-by-step explanation:

2/13=6 reminder 1

2/6= 3 reminder 0

2/3= 1 reminder 1

2/1= 0 reminder 1

13 becomes 1101 base two/ binary form

The conversion of number from decimal to binary:

\((13)_{10}=(1101)_{2}\)

\((121)_{10}=(1111001)_{2}\)

\((252)_{10}=(11111100)_{2}\)

\((1023)_{10}=(1111111111)_{2}\)

\((2049)_{10}=(100000000001)_{2}\)

Recursively multiplying the given decimal number by two is one way to convert a decimal number to a binary number. The remainders are then recorded until we arrive at 0 as the final quotient. The remainders are then entered in reverse order to obtain the binary equivalent of the provided decimal number.

The number is 13.

13 ÷ 2 = 6, Remainder = 1

6 ÷ 2 = 3, Remainder = 0

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, \((13)_{10}=(1101)_{2}\)

The number is 121.

121 ÷ 2 = 60, Remainder = 1

60 ÷ 2 = 30, Remainder = 0

30 ÷ 2 = 15, Remainder = 0

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, \((121)_{10}=(1111001)_{2}\)

The number is 252.

252 ÷ 2 = 126, Remainder = 0

126 ÷ 2 = 63, Remainder = 0

63 ÷ 2 = 31, Remainder = 1

31 ÷ 2 = 15, Remainder = 1

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, \((252)_{10}=(11111100)_{2}\)

The number is 1023.

1023 ÷ 2 = 511, Remainder = 1

511 ÷ 2 = 255, Remainder = 1

255 ÷ 2 = 127, Remainder = 1

127 ÷ 2 = 63, Remainder = 1

63 ÷ 2 = 31, Remainder = 1

31 ÷ 2 = 15, Remainder = 1

15 ÷ 2 = 7, Remainder = 1

7 ÷ 2 = 3, Remainder = 1

3 ÷ 2 = 1, Remainder = 1

1 ÷ 2 = 0, Remainder = 1

So, \((1023)_{10}=(1111111111)_{2}\)

The number is 2049.

2049 ÷ 2 = 1024, Remainder = 1

1024 ÷ 2 = 512, Remainder = 0

512 ÷ 2 = 256, Remainder = 0

256 ÷ 2 = 128, Remainder = 0

128 ÷ 2 = 64, Remainder = 0

64 ÷ 2 = 32, Remainder = 0

32 ÷ 2 = 16, Remainder = 0

16 ÷ 2 = 8, Remainder = 0

8 ÷ 2 = 4, Remainder = 0

4 ÷ 2 = 2, Remainder = 0

2 ÷ 2 = 1, Remainder = 0

1 ÷ 2 = 0, Remainder = 1

So, \((2049)_{10}=(100000000001)_{2}\)

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Answer: 1/4

Step-by-step explanation:

Hope this helps

The 0.25 is equivalent to 1/4, where the numerator is 1 and the denominator is 4.

The fraction that is equal to 0.25 is 1/4. To understand this, examine the decimal representation of 0.25. The decimal point separates the whole number part from the fractional part. In 0.25, the digit 2 is in the tenths place, and the digit 5 is in the hundredths place. As a fraction, the number 2 in the tenths place can be written as 2/10, and the number 5 in the hundredths place written as 5/100. Simplifying these fractions, find that 2/10 reduces to 1/5 and 5/100 reduces to 1/20.

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Answer:

always try to draw a diagram first

Step-by-step explanation:

Jana ran The first 3.5 miles in 1/3 of an hour. remember the problem tells us that we want our answer in miles per hour or mph. so we have to set up our problem so that our units match in the end. The diagram above shows 3.5 mi over 1/3 hour. so we must divide 3.5 miles by 1/3 hour

note:

\(3 \frac{1}{2} mi = \frac{7mi}{2} \)

therefore

\( \frac{7mi}{2} \: \div \: \frac{1hr}{3} = \)

\( \frac{7mi}{2} \times \frac{3}{1hr} = \frac{21mi}{2hr} = 10 \frac{1}{2} \frac{mi}{hr} \)

Answer: A. addition property of equality.

Step-by-step explanation:

Molly added 3d to both sides of the equation.

The solution of the equation will be the value of t, which should yield equal values on either side of the equation, which is 21.

To solve the equation, we need to begin with multiplication or opening of bracket on either side of the equation.

6t - 30 = 4t + 12

Rearranging the equation

6t - 4t = 30 + 12

Performing subtraction on Left Hand Side and addition on Right Hand Side of the equation

2t = 42

Rewriting the equation according to t

t = 42/2

Performing division

t = 21

Hence, the value of t is 21.

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Answer:

-4

Step-by-step explanation:

\((t-4)^{2}\)=\(t^{2} -8t-16\)

Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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When a template is created, dummy data is used to verify the formulas in the template.

A template is a pre-designed format or layout that can be used for various purposes, such as creating reports, invoices, or budgets. One of the most important aspects of creating a template is ensuring that all the formulas and calculations used in it are accurate and produce the desired results.

To verify the formulas in a template, dummy data is often used. Dummy data is a set of fictitious or meaningless data that is used to test and verify the functionality of a system or application. In the context of templates, dummy data is used to ensure that the formulas and calculations used in the template are working correctly.

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