Read each question. Then write the letter of the correct answer on your paper.

If x is a real number, for what values of x is the equation 2 x-8 / 4 x⁻¹ = x² -4 x / 2 true?

(F) all values of x

(G) some values of x

(H) no values of x

(I) impossible to determine

The calculation of the 99% confidence interval is 26.57 and 33.43.

We are given that;

Standard deviation = 20

Number of convicted criminals= 225

Now,

1. Calculate the standard error of the mean using the formula:

\($$SE = \frac{SD}{\sqrt{N}}$$\) where SE is the standard error,

SD is the standard deviation and N is the sample size. In this case, SD = 20 and N = 225,

\(so $$SE = \frac{20}{\sqrt{225}} = \frac{20}{15} = 1.33$$\)

2. Calculate the 95% confidence interval using the formula:

\($$\bar{x} \pm z_{\alpha/2} \times SE$$ where $\bar{x}$ is the sample mean, $z_{\alpha/2}$\) is the critical value for a given confidence level and SE is the standard error.

In this case,

\($\bar{x} = 30$, $z_{\alpha/2} = 1.96$ for 95% confidence level and SE = 1.33, so $$30 \pm 1.96 \times 1.33 = 30 \pm 2.61 = (27.39, 32.61)$$\)

This means that we are 95% confident that the true population mean of years worked by white collar criminals is between 27.39 and 32.61.

3. Calculate the 99% confidence interval using the same formula but with a different critical value:

\($$\bar{x} \pm z_{\alpha/2} \times SE$$ In this case, $z_{\alpha/2} = 2.58$\)

for 99% confidence level and everything else remains the same,

\(so $$30 \pm 2.58 \times 1.33 = 30 \pm 3.43 = (26.57, 33.43)$$\)

Therefore, by percentage the answer will be 26.57 and 33.43.

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The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer:

14, 42

Step-by-step explanation:

-7 is only a multiple of 7

-4 is only even

2 is only even

21 is only a multiple of 7

34 is only even

Answer:

\(2\frac{6}{7}\)

Step-by-step explanation:

-5(-4/7)

First:

A negative multiplied by a negative is positive, so we can remove the negative symbols.

5(4/7)

Multiply:

\(\frac{5(4)}{7}\)

20/7

Convert into a mixed number:

2 6/7

Answer:

Answer in explanation.

Step-by-step explanation:

Lets take

\(y = \frac{3}{4} x - 5\)

as L1.

Take L2 the line perpendicular to L1.

Standard form of equation of line:

y=mx+c, where m = slope and c = y-intercept.

Since L1 and L2 are perpendicular,

mL1 x mL2 = -1

Substitute mL1 into the equation,

3/4 x mL2 = -1

mL2 = -1 ÷ 3/4

mL2 = -4/3

L2 : y = mx+ c

Substitute y = 6, x = 8 and m = -4/3 into the equation,

\(6 = - \frac{4}{3} (8) + c \\ 6 = - \frac{32}{3} + c \\ c = 6 + \frac{32}{3} \\ = 16 \frac{2}{3} \)

therefore L2:

\(y = - \frac{4}{3}x + 16 \frac{2}{3} \)

Lets take L3 as the line parallel to L1.

Since L3 and L1 are parallel,

mL3 = mL1 = 3/4

equation of line: y = mx+c

substitute y = 6, x = 8 and m = 3/4 into equation.

\(6 = ( \frac{3}{4} )(8) + c \\ 6 = 6 + c \\ c = 6 - 6 \\ = 0\)

therefore L3:

\(y = \frac{3}{4} x\)

Okay, then the expression for the total amount of money he received is

total money= 8.10(hours he worked) + origional starting pay

Step-by-step explanation:

(1 + 3.75%)^2.5 = 1.0964

FV = 1580 (1.0964)

= 1732.31

Answer:

Don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Step-by-step explanation:

Geométricamente hablando, el área y el perímetro del rectángulo rodeado por el cerco son representadas por las siguientes fórmulas:

\(A = w\cdot l\) (1)

\(p = 2\cdot (w+l)\) (2)

Donde:

\(A\) - Área, en metros cuadrados.

\(p\) - Perímetro, en metros.

\(w\) - Ancho, en metros.

\(l\) - Longitud, en metros.

Puesto que el área a cercar debe ser la máxima posible y la longitud disponible de malla es de 100 metros, cabe despejar el ancho en (2):

\(w = \frac{p}{2}-l\)

Ahora, aplicamos esta expresión en (1) y expandimos la expresión resultante:

\(A = \left(\frac{p}{2}-l\right) \cdot l\)

\(A = \frac{p\cdot l}{2} -l^{2}\) (3)

A continuación, obtenemos la primera y segunda derivada de (3):

\(A' = \frac{p}{2}-2\cdot l\) (4)

\(A'' = -2\) (5)

Igualando (4) a cero, tenemos que el valor crítico de la longitud del rectángulo es:

\(\frac{p}{2}-2\cdot l = 0\)

\(2\cdot l = \frac{p}{2}\)

\(l = \frac{p}{4}\)

Por (5), sabemos que ese valor crítico está asociado al área máxima.

Si sabemos que \(p = 100\,m\), entonces la longitud del rectángulo es:

\(l = 25\,m\)

Ahora, tenemos el ancho de la figura por (2):

\(w = \frac{p}{2}-l\)

\(w = 25\,m\)

En consecuencia, don Abel debe construir un cuadrado con lados de 25 metros de longitud.

Step-by-step explanation:

\( \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \)

\( \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \)

\( \frac{1}{v} = \frac{u - f}{uf} \)

\(v = \frac{uf}{u - f} \)

The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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Answer:

Step-by-step explanation:

-1 = 7 - x

On this case, what you want to achieve is for all the constants to go to one side of the equation and all the variables would be on the other side of the equation. Let us transpose 7 to the left side of the equation.

subtract 7 on both sides

-1 = 7 - x

-1 - 7 = 7 - 7 - x

Simplify

-8 = -x

Divide both sides by -1

-8/-1 = -x/-1

8 = x

The answer to the question is x=8. It is an example of a linear equation.

A linear equation is an algebraic equation that represents a straight line when graphed on a coordinate plane. It consists of variables, constants, and coefficients, with the variables raised to the power of 1 (i.e., they are not squared or cubed).

A general form of a linear equation with one variable, let's say x, is:

ax + b = 0

Here, 'a' and 'b' are constants, and 'x' is the variable. The coefficient 'a' represents the slope or gradient of the line, while the constant term 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

In this question,

-1 = 7-x (Given)

so, x = 7+1

        =8

Therefore, the solution to the equation is x=8.

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The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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Answer:

32X^9

Step-by-step explanation:

Answer:

450 grams of plums per container

Step-by-step explanation:

Since you have to convert the 36 kilograms to grams, it will make it 36,000 grams.  You have to divide it into 80 boxes, so 36,000/80 is 450, so 450 it is.

1. The equations for Sand, Clay, and Humus, we get: x = (12 - 3y)/4, x = (12 - 6y)/5, x = (10 - 12y)/5 2. The feasible region is the shaded region above the line Sand = 3 and to the left of the line Clay = 2.

What is linear programming?

Linear programming is a mathematical method used to optimize a linear objective function subject to linear constraints.

1. Formulating the problem as a linear programming:

Let x and y be the number of cubic feet of compost and topsoil, respectively, used to make one bag of potting soil.

We want to minimize the cost of the potting soil, which is given by:

Cost = 0.12x + 0.2y

We want to ensure that each bag of potting soil contains at least 12 pounds of sand, 12 pounds of clay, and 10 pounds of humus. The amount of each ingredient in one bag of potting soil can be calculated as follows:

Sand = 4x + 3y

Clay = 5x + 6y

Humus = 5x + 12y

We can now formulate the constraints as follows:

Sand ≥ 12

Clay ≥ 12

Humus ≥ 10

Solving for x and y in the equations for Sand, Clay, and Humus, we get:

x = (12 - 3y)/4

x = (12 - 6y)/5

x = (10 - 12y)/5

We also have the non-negativity constraints:

x ≥ 0

y ≥ 0

2. Plotting the constraints and showing the feasible region:

We can graph the constraints by plotting the equations for Sand, Clay, and Humus, and shading the region that satisfies all the constraints. The resulting feasible region is shown below:

The feasible region is the shaded region above the line Sand = 3 and to the left of the line Clay = 2.

3. Identifying the optimal solution:

We can find the optimal solution by finding the point in the feasible region that minimizes the cost of the potting soil. This point occurs where the cost function is minimized.

Cost = 0.12x + 0.2y

Substituting x = (12 - 3y)/4 and x = (12 - 6y)/5, we get:

Cost = 0.12[(12 - 3y)/4] + 0.2y

Cost = 0.12[(12 - 6y)/5] + 0.2y

Simplifying, we get:

Cost = 0.6 - 0.09y

Cost = 0.72 - 0.044y

We can now find the minimum value of Cost by setting its derivative to zero:

dCost/dy = -0.09 + 0.044 = 0

Solving for y, we get:

y = 2

Substituting y = 2 into x = (12 - 3y)/4 and x = (12 - 6y)/5, we get:

x = 3/4

x = 6/5

Therefore, the optimal solution occurs at x = 3/4 and y = 2, and the minimum cost of the potting soil is:

Cost = 0.12x + 0.2y = 0.12(3/4) + 0.2(2) = 0.39 dollars.

4. Interpreting the optimal solution:

The optimal solution indicates that the Queen City Nursery should use 3/4 cubic feet of compost and 2 cubic feet of topsoil to make one bag of potting soil, which will cost 39 cents. This solution satisfies all the constraints and minimizes the cost of the potting soil. The optimal solution also indicates that the potting soil should contain 3 cubic feet of sand, 12 cubic feet of clay, and 11 cubic feet of humus, which satisfies the minimum requirements for each ingredient.

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(a) Strings in L: "abb", "aabbb". (b) Strings not in L: "aabb", "bb".

(c) State diagram for a deterministic Turing Machine with 10 states is given below.

(a) Two strings that are in L are:

1. `abb` (Here, i = 0, and w is an empty string).

2. `aabbb` (Here, i = 2, and w = "aa").

(b) Two strings over the same alphabet that are not in L are:

1. `aabb` (Here, the length of w is 2, but there are more than two 'a's before the 'bb').

2. `bb` (Here, the length of w is 0, but there are 'b's before the 'bb', violating the condition).

(c) Here is the state diagram for a deterministic Turing Machine with 10 states that decides L:

```START --> A --> B --> C --> D --> E --> F --> G --> H --> ACCEPT

  a      b      b      a      a      b      b      a      b

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  A      E      F      REJECT REJECT REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT  G      H      REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT REJECT REJECT REJECT```

In this state diagram, the machine starts at the START state and reads input symbols 'a' or 'b'. It transitions through states A, B, C, D, E, F, G, and H depending on the input symbols.

If the machine reaches the ACCEPT state, it accepts the input, and if it reaches any of the REJECT states, it rejects the input. The machine accepts inputs of the form `a^i b^bw` where the length of w is i.

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The complete question is:

Let L = {a(^i)bbw|w ∈ {a, b} ∗ and the length of w is i}.

(a) Give two strings that are in L.

(b)Give two strings over the same alphabet that are not in L.

(c)Give the state diagram for a deterministic Turing Machine that decides L. To receive full credit, your Turing Machine shall have no more than 10 states.

Answer:

11 2/3

Step-by-step explanation:

2 1/3 * 5

Change the mixed number to an improper fraction

2 /13 = ( 3*2+1)/3  = 7/3

7/3 * 5/1

35/3

Now change it back to a mixed number

3 goes back into 35 11 times with 2 left over

11 2/3

Answer:

11 2/3

Step-by-step explanation:

First:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

7/3 * 5/1  

Applying the fractions formula for multiplication,

7*5 = 35, 3*1= 3  overall= 35/3

Simplifying 35/3, the answer is

= 11 2/3

Answer:

n = 7.2

Step-by-step explanation:

I just divided both sides by 5.

5n (÷ 5) = 36 (÷ 5)

n = 7.2 or 7 \(\frac{1}{5}\)

You can choose between using the decimal or the fraction.

Answer:

n=7.2

Step-by-step explanation:

=> 5n=36

=> 5n/5 =36/5 [Divide by 5 on both the sides]

=> n=7.2

Hope this helps you.

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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Answer: 13.8

Step-by-step explanation:

Answer:

13.8

Step-by-step explanation:

The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

I think the first one is 30.

I think the second one is 6

Step-by-step explanation:

Let x be the number

40% of x = 8

Multiply both-side of the equation by 100

Divide both-side of the equation by 40

Therefore, 8 is 40% of 20

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

Answer:

x > -3

Step-by-step explanation:

-2x + 4 > 10

-2x (+ 4 - 4) > 10 - 4

-2x > 6

-2x/-2 > 6/-2

x > -3

Answer:

× < -3

Step-by-step explanation:

Move constant to the right hand side and change its sign

-2x > 10 - 4

Subtract the numbers

-2x > 6

Divide both sides by -2 and flip the sign

x < -3

Answer:

Step-by-step explanation:

Since there are 985 square feet to cover, and it costs 12.50 per square foot, you multiply 12.50 by 985 to get 12,312.50, the total cost and answer.

Answer:

I think it is 24 but I don't know the rest sorry 乁( •_• )ㄏ

Answer:

Step-by-step explanation:

Girls Basketball = x

Girls Soccer = x + 3

Total = 51

x + x + 3 = 51        Combine like terms

2x + 3 = 51            Subtract 3 from both sides

     - 3   - 3

2x = 48                 Divide by 2

2x/2 = 48/2

x = 24

The basketball team has 24 players

The soccer team has       27