Evaluate the expression. (p + q)​ 2​− (5 − 5); use p = 1, and q = 1

Answer:

\(H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Step-by-step explanation:

Given function:

\(H(x)=\left(\dfrac{2}{3}\right)^x-\dfrac{4}{9}\)

The domain of the given function is unrestricted:  (-∞, ∞).

As aˣ > 0, the range of the given function is restricted:  (-⁴/₉, ∞).

The inverse of a function is its reflection in the line y = x.

To find the inverse of a function, replace x with y:

\(\implies x=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}\)

Rearrange the equation to make y the subject.

Add 4/9 to both sides:

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y-\dfrac{4}{9}+\dfrac{4}{9}\)

\(\implies x+\dfrac{4}{9}=\left(\dfrac{2}{3}\right)^y\)

Take natural logs of both sides:

\(\implies \ln\left(x+\dfrac{4}{9}\right)=\ln \left(\dfrac{2}{3}\right)^y\)

\(\textsf{Apply the power law}: \quad \ln x^n=n \ln x\)

\(\implies \ln\left(x+\dfrac{4}{9}\right)=y\ln \left(\dfrac{2}{3}\right)\)

Divide both sides by ln(2/3):

\(\implies y=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

Replace y with H⁻¹(x):

\(\implies H^{-1}(x)=\dfrac{\ln\left(x+\frac{4}{9}\right)}{\ln \left(\frac{2}{3}\right)}\)

The range of the original function is the domain of the inverse of the function.

Therefore, the domain of the inverse function is  (-⁴/₉, ∞).

The required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

Given that,
A function H(x) = (2/3)ˣ - 4/9, the inverse of the given function is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
H(x) = y
y = (2/3)ˣ - 4/9
y + 4/9 = (2/3)ˣ
log[y + 4/9] = x log[2/3]
Now. invert x and y
log[x + 4/9] = ylog[2/3]
y = log[x + 4/9] / log[2/3]
Now, put y = H⁻¹[x]
H⁻¹(x) = log[x + 4/9] / log[2/3]

Thus, the required inverse function of the given function is given as H⁻¹(x) = log[x + 4/9] / log[2/3].

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Answer:

Step-by-step explanation:

Given,

Length of a tennis court = 78 feet

Therefore,

Width of the tennis court = 78 - 51

= 27 feet (Ans)

Answer:

-3,-2,-1,4,5

I really hope this helps you a lot!

Step-by-step explanation:

Answer:

-3,-2,-1,4,5..

Step-by-step explanation:

janh xD I urself ds

Answer:

\(x=1\)

\(x=-1\)

Step-by-step explanation:

 Let's use the quadratic formula to solve this.

  Quadratic formula is usually defined as the formula for determining the   roots of a quadratic equation from its coefficient. Quadratic equations are  equations containing a single variable of degree 2. Its general form is ax^2   + bx + c = 0, where x is the variable, and a,b, and c are constants (a ≠ 0).

_______

     1 ) move terms to the left side

                                \(x^2=1\)

                            \(x^2-1=0\)

        2) Use the quadratic formula

\(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

       Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

     \(x^2-1=0\)

        \(a =1 \\b = 0\\c=-1\)

      \(x=\frac{-0\pm\sqrt{0^2-4*1(-1)} }{2*1}\)

    3) Simplify

 - evaluate the exponent

\(x=\frac{0\pm\sqrt{0^2-4*1(-1)} }{2*1}\)

\(x=\frac{0\pm\sqrt{0-4*1(-1)} }{2*1}\)

 -   Multiply the numbers

 \(x=\frac{0\pm\sqrt{0-4*1(-1)} }{2*1}\\\)

\(x=\frac{0\pm\sqrt{0+4} }{2*1}\)

- add the numbers

     \(x=\frac{0\pm\sqrt{0+4} }{2*1}\)

    \(x=\frac{0\pm\sqrt{4} }{2*1}\)

-  Evaluate the square root

 \(x=\frac{0\pm\sqrt{4} }{2*1}\)

\(x=\frac{0\pm2}{2*1}\)

- add zero

 \(x=\frac{0\pm2}{2*1}\)

  \(x=\frac{\pm2}{2*1}\)

-  Multiply the numbers

 \(x=\frac{\pm2}{2*1}\)

 \(x=\frac{\pm2}{2}\)

   4) separate the equations

  -  To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

                  \(x=\frac{2}{2}\\x=\frac{-2}{2}\)

          5) solve

 - Rearrange and isolate the variable to find each solution

    \(x=1\\x=-1\)        

___________

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

Answer:

Critica probability (p) = 1 - (Alpha / 2), where Alpha is eqal to 1 - (the confidence level / 100)

Step-by-step explanation:

I think

Answer & step-by-step explanation:

The probability that all three pairwise distances between the points are less than the radius of the circle is 1/12.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Since it doesn't matter where the first point is picked, it can be placed anywhere on the circle.

The following point must be within an arc of 60 degrees on either side, providing a total of 120 degrees and a chance of 1/3. The final point must be situated within 60 degrees of the first two.

If the first two points are apart by 60 degrees, the third point can be placed within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6. If the first two points are the same, the third point can be placed with a maximum degree of freedom of a 120 degree arc and a 1/3 probability.

The chance changes linearly with increasing distance from the first point, up to a maximum of 60 degrees.

As a result, we may find 1/4, the average likelihood we can position the third point based on a fluctuating second point, by averaging the probabilities at either end.

Total probability is 1 × 1/3 × 1/4 = 1/12.

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Whenever possible, research should be designed so that the data can be anlyzed using option (a) statistics

-This includes both parametric tests (which assume that the data is normally distributed and meet certain assumptions) and non-parametric tests (which do not make these assumptions and are useful for non-normal data). SPSS is a software program commonly used for statistical analysis, but it is not necessary for conducting statistical analyses.

a. statistics

Research should be designed so that the data can be analyzed using statistics. Statistics provide a set of methods and tools for analyzing and interpreting data, which can help researchers draw meaningful conclusions from their findings. Statistical analysis can be used to identify patterns, trends, and relationships in data, as well as to test hypothesis and make predictions.

Depending on the research question, data type, and sample size, different types of statistical tests may be appropriate. Both parametric and non-parametric tests can be used to analyze data, depending on the assumptions made about the underlying distribution of the data and the level of measurement of the variables. SPSS is a statistical software program that can be used to perform statistical analysis, but it is not necessary for designing research studies or analyzing data.

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Answer:

11.75

Step-by-step explanation:

5x+3x-4+90 = 180

(the sum of interior angles of a triangle is always 180

8x-4+90 = 180

+4              +4

8x+90=184

-90       -90

8x=90

/8    /8

x = 11.75

The value of x from the given right triangle ABC is 11.75°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given that, triangle ABC is a right triangle with m∠A=5x°, m∠B=(3x−4)° and m∠C=90°.

Here, m∠A+m∠B+m∠C=180°

5x°+(3x−4)°+90°=180°

5x°+(3x−4)°=90°

8x°-4°=90°

8x°=94°

x=94/8

x=11.75°

So, 5x= 5×11.75 =58.75° and (3x−4)°=3×11.75-4

= 35.25-4

= 31.25°

Therefore, the value of x is 11.75°.

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\((\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-9}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-9}-\underset{x_1}{(-2)}}} \implies \cfrac{-15}{-9 +2} \implies \cfrac{ -15 }{ -7 } \implies \cfrac{ 15 }{ 7 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{ \cfrac{ 15 }{ 7 }}(x-\stackrel{x_1}{(-2)}) \implies y -10 = \cfrac{ 15 }{ 7 } ( x +2) \\\\\\ y-10=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }\implies y=\cfrac{ 15 }{ 7 }x+\cfrac{ 30 }{ 7 }+10\implies {\Large \begin{array}{llll} y=\cfrac{ 15 }{ 7 }x+\cfrac{100}{7} \end{array}}\)

a) In standard form, Maximize: 3A + 2B, Subject to: A + B + S₁ = 4, 3A + 4B - S₂ = 24 , A - S₃ = 2, A - B + S₄ = 0. b) The optimal solution is A = 2, B = 2, and the maximum value is 10. c) The values of S₁ = 0, S₂ = 14, S₃ = 0, and S₄ = 0.

a. To write the linear program in standard form, we need to introduce slack and surplus variables to convert all inequalities into equalities.

The given linear program in its original form is:

Maximize: 3A + 2B

Subject to:

A + B ≥ 4

3A + 4B ≤ 24

A ≥ 2

A - B ≤ 0

A, B ≥ 0

To convert the inequalities into equalities, we introduce slack and surplus variables as follows:

Maximize: 3A + 2B

Subject to:

A + B + S₁ = 4 (introducing slack variable S₁)

3A + 4B - S₂ = 24 (introducing slack variable S₂)

A - S₃ = 2 (introducing slack variable S₃)

A - B + S₄ = 0 (introducing surplus variable S₄)

A, B, S₁, S₂, S₃, S₄ ≥ 0

Now the linear program is in standard form.

b. To solve the linear program, we can use the simplex method. However, since this is a small problem, we can also solve it directly by substituting the constraints.

Using the constraint A + B ≥ 4, we have A ≥ 4 - B.

Using the constraint A - B ≤ 0, we have A ≤ B.

Substituting A ≤ B into A ≥ 4 - B, we get B ≥ 4 - B, which simplifies to 2B ≥ 4. This implies B ≥ 2.

Since A ≤ B and A ≥ 4 - B, the possible range for A is 2 ≤ A ≤ B.

Considering the constraint A ≥ 2, we have 2 ≤ A ≤ B. Therefore, A = 2 and B = 2 is a feasible solution.

Plugging the values of A = 2 and B = 2 into the objective function, we get:

3A + 2B = 3(2) + 2(2) = 10.

Thus, the optimal solution is A = 2, B = 2, and the maximum value is 10.

c. To determine the values of the slack and surplus variables at the optimal solution, we substitute the optimal values of A = 2 and B = 2 back into the constraints:

A + B + S₁ = 4:

2 + 2 + S₁ = 4,

S₁ = 0.

3A + 4B - S₂ = 24:

3(2) + 4(2) - S₂ = 24,

S₂ = 14.

A - S₃ = 2:

2 - S₃ = 2,

S₃ = 0.

A - B + S₄ = 0:

2 - 2 + S₄ = 0,

S₄ = 0.

Therefore, the values of the slack variables at the optimal solution are S₁ = 0, S₂ = 14, S₃ = 0, and the value of the surplus variable is S₄ = 0.

Correct Question :

Consider the linear program below and answer the following questions. LO  2, 4 , 6, 7

Max 3A + 2B

s.t.

A+B ≥ 4

3A+4B ≤ 24

A ≥ 2

A-B ≤ 0

A,B ≥ 0

a. Write the problem in standard form.

b. Solve the problem.

c. What are the values of the slack and surplus variables at the optimal solution?

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The relationship between the flying time (t) and the height of the bird (h) can be represented by the following equation:
h = 18 + 2t, In this equation, 18 represents the initial height of the tree, and 2t represents the rate at which the bird rises (2 feet per minute) multiplied by the flying time.

The relationship between flying time and the height of the bird can be represented by the following equation:

Height = Initial Height + Rate × Time

In this case, the initial height is 18 feet, the rate at which the bird rises is 2 feet per minute, and time represents the flying time in minutes. Plugging in these values, the equation becomes:

Height = 18 + 2 × Time

This equation shows how the height of the bird changes as time progresses. The initial height of 18 feet is added to the product of the rate (2 feet per minute) and the flying time in minutes. As time increases, the height of the bird increases at a constant rate of 2 feet per minute.

Therefore, the equation that represents the relationship between flying time and the height of the bird is:

Height = 18 + 2 × Time

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Given statement solution is :- The alternative hypothesis suggests a one-sided (one-tailed) test, focusing on whether the mean number of miles traveled by western residents is greater than that of eastern residents. In this scenario, it is a one-tailed problem.

To determine whether it is a one-tailed or two-tailed problem, we need to examine the hypothesis being tested.

In this case, the transportation company is interested in whether the number of miles traveled by residents of the western and eastern metropolitan areas differ. They argue that the number of miles traveled by western residents is more than that of eastern residents.

If we set up our hypotheses as follows:

Null Hypothesis (H₀): The mean number of miles traveled by western residents is not significantly different from the mean number of miles traveled by eastern residents (μw - μe = 0).

Alternative Hypothesis (H₁): The mean number of miles traveled by western residents is significantly greater than the mean number of miles traveled by eastern residents (μw - μe > 0).

The alternative hypothesis suggests a one-sided (one-tailed) test, focusing on whether the mean number of miles traveled by western residents is greater than that of eastern residents.

Therefore, in this scenario, it is a one-tailed problem.

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Answer:

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

Step-by-step explanation:

The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.

For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.

In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.

A fraction is a way to describe a part of a whole. The number of hours that Mr Mason painted each day is 1.625  hours.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The total number of hours that Mr Mason took to paint the fence is 6 2/4 hours, while the number of days taken by him is 4 hours. Therefore, the number of hours for which Mr Mason painted each day can be written as,

= (6 ²/₄)/4

= (26/4)/4

= 26/16

= 1.625 hours a day

Hence, the number of hours that Mr Mason painted each day is 1.625  hours.

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Based on the information provided, the equation that can be used to find how much money, c, each charm bracelet cost at full price is 5(c – 4) = 45.

An equation is its simplest form in algebra, refers to a mathematical statement that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an equal sign. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:

5(c – 4) = 45

Solving the equation,

5(c – 4) = 45

c – 4 = 9

c = 9 + 4 = $13

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In the given frequency table, the relative frequency of 24 represents the proportion of family members who chose to go on a hike out of the total number of family members.

To calculate the relative frequency, we divide the frequency of the specific category (in this case, hike) by the total frequency. In this case, the frequency of the hike is 24, and the total frequency is 38.

Relative Frequency = Frequency of Hike / Total Frequency

Relative Frequency = 24 / 38

Simplifying the fraction, we get:

Relative Frequency ≈ 0.632

So, the relative frequency of 24 represents approximately 0.632 or 63.2%. This means that around 63.2% of the family members chose to go on a hike at the family reunion.

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In linear equation, 3437.5  feet - lbs is the work done to haul the anchor .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Anchor  weighing = 100 lbs

   given 3  lb/ft

  the combined weight  = 3( 25 -y ) + 100

                                 = 175 - 3y

    the workdone on small solution is = (175 - 3y)Δy

                      w = ∫₀²⁵ (175 - 3y) dy

                        = 175[y]²⁵₀- 3/2[y²]²⁵₀

                       = 175 [ 25 - 0 ] - 3/2 [ 25²- 0²]

                       = 3437.5  feet - lbs

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Answer:I think its last one sorry if I am wrong

Step-by-step explanation:

Answer:the answer is y=3x

Step-by-step explanation:

Multiply x 3 times to get y

Answer:

Step-by-step explanation:

Let the number be x

by given condition,

4x = (x)² - 21

4x = x²- 21

0 = x² - 4x - 21

0 = x² - 7x + 3x - 21

0 =  x ( x-7) + 3 ( x - 7)

0 = (x+3)(x-7)

hence

x + 3 =0.....

x = -3---------1

x - 7 = 0

x = 7 ------------2

we got value of x from 1 and 2.. but the question says positive value of x.

hence, x = 7 is the required value of x.

Linda's walking rate is approximately 4.51 miles per hour.

To calculate Linda's walking rate per hour, we can use the concept of unit conversion.

We know that Linda can walk 6 miles in 80 minutes. To convert this to hours, we need to divide the number of minutes by 60, since there are 60 minutes in an hour.

Walking rate per hour = (Distance walked) / (Time taken in hours)

Time taken in hours = 80 minutes / 60 minutes per hour = 4/3 hours (or 1.33 hours)

Walking rate per hour = 6 miles / 1.33 hours ≈ 4.51 miles per hour

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6

————————-  

it’s not letting just put 6 because its a small sentence-

Answer:

40.5

Step-by-step explanation:

3.75 * 2 = 7.50

48 - 7.50 = 40.5

A diverse workforce can provide a source of competitive advantage by suggesting goods and services that will allow the company to increase its market by catering to a broader customer base.

When an organization embraces diversity and inclusion, it brings together individuals from different backgrounds, cultures, experiences, and perspectives. This diverse pool of employees can offer unique insights and ideas that might otherwise go unnoticed, leading to innovative product development and improved customer experiences.

By having a workforce that represents a wide range of demographics, including race, ethnicity, gender, age, sexual orientation, and more, a company can better understand the needs and preferences of various customer segments. This understanding enables them to develop and market products and services that resonate with a larger audience, ultimately increasing market share and revenue.

A diverse workforce enhances creativity and problem-solving abilities within the organization. Diverse teams bring different ways of thinking and approaching challenges, fostering an environment of innovation and adaptability. This can lead to the development of groundbreaking solutions that meet the evolving demands of an increasingly diverse consumer market.

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Given:

We use the digit places to compute the value of a,b and c.

subtracting unit place.

If we get 1-b=6, b must be greater than 1.

We need to take one from the tenth place that is a in 9a1.

So now we get 11

If we put b=5, this equation will satisfy.

So the value of b is 5.

Subtracting tenth place values.

If we put a=10, we get

a already reduced one value.

so here a should be 11, so we take the unit digit from 11. and it takes 1 from the hundredth place is 9.

Hence the value of a is 1.

subtracting the hundredth place.

a take 1 from 9, so in this stage we have

Hence the value of c is 2.

Adding a,b, and c, we get

The answer is 8.

The size of matrix B is 6x4.

To determine the size of matrix B, we need to consider the dimensions of matrix A and the product AB. You mentioned that matrix A is 5x6, and the product AB is 5x4. The size of B is ____ x ____.

To find the size of B, we follow these steps:

1. Recall the rule for matrix multiplication: If A is an m×n matrix and B is an n×p matrix, then the product AB is an m×p matrix. In our case, A is 5x6, and AB is 5x4.

2. We are given m and n for matrix A, and m and p for the product AB. We need to find the dimensions n and p for matrix B.

3. From the rule, we know that the number of columns in A (6) must be equal to the number of rows in B (n). So, n = 6.

4. Since AB is 5x4, we know that the number of columns in B is p = 4.

Therefore, the size of matrix B is 6x4.

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Answer:

$0.50

Step-by-step explanation:

Suppose that a person  bought  six T-bone steaks that cost $15.99 per pound

The weight that is listed on the package is 5.77 pounds.

The scale that weighed the package is accurate to within 1/32 pound

Let assume x is the range of the  weight listed on the package,

Then:

\(|x-5.77| \leq \dfrac{1}{32} \ --- \ (1)\)

Using the method of absolute value inequality;

\(- \dfrac{1}{32} \leq x -5.77 \leq \dfrac{1}{32}\)

\(5.77- \dfrac{1}{32} \leq x \leq \dfrac{1}{32}+ 5.77\)

\(5.77- 0.03125\leq x \leq 0.03125+ 5.77\)

\(5.73875 \leq x \leq 5.80125\)

The amount per kilogram undercharged or overcharged is :

\(=\dfrac{1}{32} \times 15.99\)

= $0.50