\(\bold{Heya...}\)

\(\sf{6 \: - \: (1 \: x \: 4) \: - \: 2}\)

Explain into your own words.

Thanks~

Answer:

Here we have four individual events.

First selection, second selection, third selection and fourth selection.

Where initially, the options are 16 Americans and 13 Canadians.

Now, to see if the events are dependent or independent.

Suppose that in the first selection, an American is selected.

Then the second selection has 15 Americans and 13 Canadians as options.

Now, if in the first selection, a Canadian is selected.

Then in the second selection, the options will be 16 Americans and 12 Canadians.

Then the events are not independent.

Now we want to find the probability of randomly selecting a four-person committee consisting entirely of Canadians from a pool of 16 Americans and 13 Canadians

The probability of randomly selecting a Canadian is equal to the quotient between the number of Canadians, and the total number of postulants.

For the first selection, we have 13 Canadians, and 29 people in total, then the probability is:

P1 = 13/29.

Suppose that a Canadian is selected, now there are 12 Canadians and 28 people in total, then the probability for the second selection is:

P2 = 12/28

with the same reasoning as above, the probabilities for the third and fourth selections will be:

P3 = 11/27

P4 = 10/26.

The joint probability will be equal to the product of the individual probabilities, this is:

P = P1*P2*P3*P4 = (13/29)*(12/28)*(11/27)*(10/26) = 0.03

Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.

A linear function is modeled by:

y = mx + b

In which:

One example of function is:

y = 4x + 3.

When x = 1:

y = 4 + 3 = 7.

When x = 2:

y = 8 + 3 = 11.

The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.

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Answer:

∠ DTR = 109°

Step-by-step explanation:

∠ DQT and ∠ TRS are alternate angles and are congruent, then

∠ TRS = 68°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ DTR is an exterior angle of Δ TRS , then

∠ DTR = 41° + 68° = 109°

Answer:

12.86

Step-by-step explanation:

this is rounded to the nearest hundredth

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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The set builder notation of the solution inequality represented on the number line is; {x: 3< x <=5}.

It follows from the task content that at point positive 3, there's an open circle which signifies that the number 3 is less than the solution.

And since the number line is shaded from positive 3 to 5, it follows that the maximum value in the solution set is 5.

The representation is therefore; {x: 3< x <=5}.

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On the number line, the solution inequality is represented by the notation x: 3=5, which is the set builder notation of the inequality.

This is further explained below.

Given the information provided in the job, it is logical to conclude that at point positive 3, there will be an open circle. This will indicate that the number 3 will be lower than the answer.

And since the shading on the number line goes from positive 3 to 5, it follows that the highest value that can be found in the set of solutions is 5.

As a result, the representation is written as:

"x: 3 x = 5."

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

Step-by-step explanation:

You haven't provided functions to choose from!

The geometrical series is a series of numbers. The nth term of the series is [8× 0.5⁽ⁿ⁻¹⁾].

The geometrical series is a series of numbers where the ratio of any two consecutive numbers is constant.

In a geometric series, r is the ratio between any two consecutive terms, therefore, the ratio of these terms can be written as,

r = (4/8) = (1/2)

Also, a₁ is the first term of the series, therefore, the first term of the series will be 8.

Thus, the nth term of this series will be equal to,

\(n^{th} = a_1 \times r^{(n-1)}\\\\n^{th} = 8 \times (\dfrac{1}{2})^{(n-1)}\)

Hence, the nth term of the series is [8× 0.5⁽ⁿ⁻¹⁾].

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Answer:

112 in2

Step-by-step explanation:

6 x 4 / 2 + 10 x 10 = 24 / 2 + 100

12 + 100 = 112 in2

Hope that helps!

Answer:

Your answers are right.

Step-by-step explanation:

Angle2 and Angle5 are same-side interior, so they are supplementary.

Showing work definitely includes writing and solving an equation and can also include using theorems and definitions as justifications.

mAngle2 + mAngle5 = 180

136° + 4x = 180°

-136° -136°

4x = 44

/4 /4 Divide by 4

x = 11

Angle5 = 4x = 4(11)

= 44°

Angle7 = Angle5 by Vertical angles.

Angle7 = 44°

Angle3 = Angle5 by Alternate Interior angles.

Angle3 = Angle1 by Vertical angles

Angle3 = 44°

Angle1 = 44°

Angle4 = Angle2 by

Vertical angles.

Angle4 = 136°

Angle8 = Angle4 by corresponding angles.

Angle8 = 136°

Angle6 = Angle8 by Vertical angles

Angle6 = 136°

Solution:

Note that:

Solve for x to find the weight of each patty.

The weight of a patty is 4/15 of a pound.

Answer:

4/15

Step-by-step explanation:

Hope this helps! Sorry if I am wrong.

The revenue function derived from the given marginal revenue function is \(R(x) = 1/11)x^{11} - (18/6)x^6 + (12/4)x^4 + 2x + C.\)

A formula means an equation representing the way in which particular items of income behave when plotted on a graph

To get revenue function, we will integrate the marginal revenue function with respect to x.

The integration is the reverse operation of differentiation, so we will integrate each term individually.

Given:

\(MR = x^10 - 18x^5 + 12x^3 + 2\)

Integrating, we have:

\(= \int\limits^a_b {x^10 - 18x^5 + 12x^3 + 2} \, dx \\= (1/11)x^{11} - (18/6)x^6 + (12/4)x^4 + 2x + C.\)

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Answer:

4x^2+12x+9

Step-by-step explanation:

(2x+3)(2x+3)

Multiply 2x by 2x first.

then 2x by 3

and then repeat that step and you add like terms

then recieve your answer.

Answer:

4x^2 + 12x + 9

Step-by-step explanation:

Actually, you are to find (2x + 3)^2, which is "the square of 2x + 3."

2x + 3 is a binomial.  There is a formula for the square of a binomial:

(a + b)^2 = a^2 + 2ab + b^2

Following this pattern,

(2x + 3)^2 becomes:

[2x]^2 + 2[2x][3] + [3^2], or

4x^2 + 12x + 9

Answer:

The percentage  of nights does it take employees less than 3 hours to clean the largest  building  

 P( x < 3) = 2.28 hours

Step-by-step explanation:

Step(i):-

Given mean of the Population = 3.8 hours

Given Standard deviation of the Population = 0.4 hours

Let 'X' be the random variable in Normal distribution

Let 'X' = 3 hours

\(Z = \frac{x-mean}{S.D}\)

\(Z = \frac{3-3.8}{0.4} = - 2\)

Step(ii):-

The probability that  nights does it take employees less than 3 hours to clean the largest  building

P( x < 3) = P(Z < -2)

            = 0.5 -A(-2)

           = 0.5 - A(2)

          =  0.5 - 0.4772

          = 0.0228

The probability that  nights does it take employees less than 3 hours to clean the largest  building

P( x < 3) = 0.0228

Conclusion:-

The percentage  of nights does it take employees less than 3 hours to clean the largest  building  

 P( x < 3) = 2.28   hours  

Respuesta: Es más probable sacar un mango.

Explicación:

La probabilidad se refiere a la posibilidad de que un evento occura y no otro. En el caso que se describe, la probabilidad de sacar cada fruta puede ser calculada dividiendo el total de cada fruta en el número de frutas totales:

Probabilidad de sacar un mango:

\(\frac{cantidad de mangos}{cantidad de frutas en la canasta}\) =  \(\frac{30}{50}\)  =\(0.6\)

Probabilidad de sacar una piña:

\(\frac{cantidad de pinas}{cantidad de frutas en la canasta} = \frac{20}{50}\) \(= 0.4\)

De acuerdo a lo anterior la probabilidad de sacar un mango es de 0.6 o de 60% (multiplica la probabilidad por 100 para saber su equivalente en porcentaje), mientras que la probabilidad de sacar un mango es de 0.4 o 40% lo cual es mucho más bajo. Es decir que es más probable sacar un mango.

Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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Answer: -5 < x < 3

Step-by-step explanation:

Subtract 6 from both sides of the equation (-4 and 12, with a result of -10 < x < 6) and then divide by two on both sides (with the result being the answer.

Answer:c

Step-by-step explanation:Because there giving you a signal

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

17.81, but I would estimate 17.80 so it doesnt look exact.

Step-by-step explanation:

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

Answer:

31/66

Step-by-step explanation:

15+5+20+11+15=66

13+1+9+5+7=31

31/66

Answer:

i think it 20 if im wrong im sorry

The height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

Please refer to the attached picture for the figure:

We have:

The area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

As we know the area of the rectangular face = lengthxwidth

From the figure:

The area of the rectangular face = hx5

h is the height of the rectangular prism.

45 = hx5

h = 45/5

h = 9 inches

Thus, the height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.

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Answer:

To find the value of "a" when you know the perimeter of a shape, you need to know the specific shape you're referring to. Please provide more information about the shape in question, such as whether it's a rectangle, triangle, or another geometric figure. Additionally, if you have any specific measurements or relationships between the sides of the shape, please provide them as well.

a. 65 is the median

b. 61.16 or 66.42

c. 2 modes and its 6

explanation step by step

A.) you need to arrange it first lowest to highest : 52, 56, 57, 65, 65, 72, 98

B. add all the numbers and divided by how many are them. as you see there is 2 answers in it, the lowest one is I didn't add the outliner and the high one is outliner is added 98

C. look at the same number.(twice, triple etc)