. . Roulette: In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2, 3, 4, .., 36. The odd-numbered slots are Red, and even-numbered slots are black. The numbers are green. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. What is the probability that the metal ball does not land on green? (leave the answer as a simplified fraction like 4/5)

The solution to the equation log[15(x − 8)] = log[6(2x)] is x = 40. To solve this equation, we can use the property of logarithms that states if log(base a) x = log(base a) y, then x = y.

Applying this property to the given equation, we have 15(x − 8) = 6(2x).

Expanding the equation, we get 15x - 120 = 12x.

Next, we can simplify the equation by subtracting 12x from both sides: 15x - 12x - 120 = 0.

Combining like terms, we have 3x - 120 = 0.

To isolate x, we add 120 to both sides: 3x = 120.

Finally, we divide both sides by 3: x = 40.

Therefore, the solution to the equation log[15(x − 8)] = log[6(2x)] is x = 40.

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Answer:

a)2975

b)3450

Step-by-step explanation:

Let's draw a picture of our triangle:

We know that the larger acute angle is always in front of the large leg (denoted by x). So, we can relate the unknown angle with the shorter leg and the hypotenuse by means of the cosine function, that is,

which gives

Then, we have

Now, by applying the respective inverse function, we have

which gives

Therefore, by rounding the nearest tenth, the answer is 50.8 degrees

Answer:

111°

Step-by-step explanation:

look at it. It is the same angle. as m∠VUR

Answer:

You bought 4 items.

Step-by-step explanation:

3.16 divided by 0.79 = 4

Answer:

You bought 4 items because 0.79 x 4 = 3.16

Step-by-step explanation:

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer:

The factors are (x+9),(x−9).

Step-by-step explanation:

Answer: x = 12

Step-by-step explanation:

Divide both sides by 10 to isolate x:

10x/10 = 120/10

x = 12

Answer:

x=12

Step-by-step explanation:

Divide each term in 10x=120 by 10 and simplify.

x=12 Is what you would get.

Term: Any expression written as a product or quotient.

Quotient: The answer to a division problem.

Hope this helps!

Answer:

Take  the expression  x^2/3  which has an exponent  of 2/3.  The top of the fraction refers to the power  - that is  x^2 ( x squared). and the 3 indicates  a cubic root.

So in radical form  it is  ∛(x^2)

Converting radical to exponent  an example would be

∛(x^5)   =  x^(5/3)    

Step-by-step explanation:

hope this helps.

Answer:

500- (m*20)=?

Step-by-step explanation:

The expression shows the total amount in Diego's savings account after m months is 500 - 20m.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Diego has $500 in his savings account. Each month, he takes out $20 to pay for karate class.

Let m be the number of months. Write an expression to show the total amount in Diego's savings account after m months.

The expression:

= 500 - 20m

Here m is the number of months

Thus, the expression shows the total amount in Diego's savings account after m months is 500 - 20m.

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9514 1404 393

Answer:

  (a) isosceles

  (b), (c) scalene

Step-by-step explanation:

The lengths of the sides can be found from the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

Here, there are 9 lengths to be computed, so it is useful to let a spreadsheet or graphing calculator do it.

We find triangle (a) has two sides the same length, so it is isosceles.

The other two triangles have three different side lengths, so they are scalene.

_____

Additional comment

It is impossible to specify an equilateral triangle using rational coordinates.

Answer: 50 sets

Step-by-step explanation:

Scrubs=9x fee=13 total=463

463-13 dollar fee =450 450/9 equals 50 sets of scrubs to check it do 9x+13=463 x=50 so 9(50)+13=463 then 450+13=463 463=463 :) you're welcome hope it's the right type of math you need!

In many cases, when we evaluate functions, we just have to replace x with a given value and simplify the expression.

\(g(x)=\dfrac{1}{4}x+1\)

⇒ To solve for g(-16), plug in -16 as x:

\(g(x)=\dfrac{1}{4}(-16)+1\\\\g(x)=-4+1\\\\g(x)=-3\)

g(-16) = -3

The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5

To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.

Item A:

Period 1: Gross requirement of 20 units.

Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.

Item B:

Item B is a component of A, and each A requires 2 units of B.

We need to calculate the net requirements for B based on the planned order release for A.

Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.

B has a scheduled receipt of 30 units in period 1.

Net requirement for B in period 1: 40 units - 30 units = 10 units.

Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.

Item C:

Item C is a component of A, and each A requires 3 units of C.

We need to calculate the net requirements for C based on the planned order release for A.

Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.

C has a lead time of two periods, so we need to account for that.

Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.

Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.

Item D:

Item D is a component of C, and each C requires 1 unit of D.

We need to calculate the net requirements for D based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.

D has a lead time of one period, so we need to account for that.

Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).

Since the net requirement is negative, we do not release any planned order for D.

Item E:

Item E is a component of C, and each C requires 1 unit of E.

We need to calculate the net requirements for E based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.

E has a lead time of two periods, so we need to account for that.

Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.

Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.

Item F:

Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.

We need to calculate the net requirements for F based on the planned order releases for B and C.

Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.

Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.

F has a lead time of two periods, so we need to account for that.

Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.

Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.

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the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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The 1000th term in Cai's list is 1505.

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols. It represents the arithmetic and algebraic structure of the numbers and offers a distinctive representation for each number.

Now, For the 1000th term in Cai's list of positive integers excluding squares and cubes, we need to continue the sequence until we reach the 1000th term.

Starting with 2, we skip 1 and 4 (which is 2 squared),

so 3 is the third positive integer.

Next, we skip 8 (which is 2 cubed) and include 5, 6, and 7.

Skipping 9 (which is 3 squared), we add 10 and 11.

Skipping 16 (which is 2 to the fourth power), we include 12, 13, 14, and 15.

Skipping 25 (which is 5 squared), we add 17, 18, 19, 20, 21, 22, 23, and 24.

Skipping 27 (which is 3 cubed), we add 26 and 28.

Skipping 36 (which is 6 squared), we include 29, 30, 31, 32, 33, 34, 35, and 37.

Skipping 49 (which is 7 squared), we add 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, and 48.

Skipping 64 (which is 2 to the sixth power), we include 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, and 63.

Skipping 81 (which is 3 to the fourth power), we add 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, and 89.

Skipping 100 (which is 10 squared), we include 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, and so on.

By the time we reach the 1000th term, we will have found the first 999 positive integers excluding squares and cubes.

Therefore, the 1000th term in Cai's list is 1505.

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The first term is, 4.

The second term is, 12.

That is,

The third term is 36. That is,

Similarly forth term 108 can be written as,

Therefore, the sequence is,

Therefore, the next term will be, 108 x 3. That is,

OPtion a is correct.

The solution to the system containing Equation 1 and Equation 3 is (x,y) = (13/11, 5/11).

There are different methods to solve a system of equations, but one common way is to use elimination. The idea is to manipulate the equations so that one of the variables is eliminated when we add or subtract the equations.
To eliminate y, we can multiply Equation 1 by 5 and Equation 3 by 3, so that the coefficients of y have opposite signs:
5(2x - 3y = 1) becomes 10x - 15y = 5
3(4x + 5y = 7) becomes 12x + 15y = 21

10x - 15y + 12x + 15y = 5 + 21
22x = 26
Dividing both sides by 22, we get:
x = 26/22 = 13/11
To find y, we can substitute this value of x into one of the equations and solve for y. Let's use Equation 1:
2x - 3y = 1
2(13/11) - 3y = 1
26/11 - 3y = 1
-3y = 1 - 26/11
-3y = -15/11
y = 5/11

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Answer:im so sorry but i cant see the page you should take a more clear picture and send it again

Step-by-step explanation:

The best sample frame when studying the nature of product defects generated by two types of stamping machines is a D) list of all stamping machines in the factory, divided into two groups by type of machine.

When studying the nature of product defects generated by two types of stamping machines, the best sample frame is the list of all stamping machines in the factory divided into two groups by the type of machine. A sample frame refers to a list of items or individuals from which a sample is drawn.

The sample frame is an important element of a research study as it forms the basis for choosing the sample. It should be inclusive, accurate, and up-to-date. It is also critical to define the sampling unit and the population so that the correct sample frame can be selected.

The list of all machines in your factory would not be an appropriate sample frame because not all machines would be involved in the production of the stamped products.

A list of all serial numbers of stamping machine output during one month would not be suitable as the sample frame as it would be biased towards a specific time period and may not represent the entire population of the stamping machines in the factory.

None of the options listed above provide the best sample frame.

Therefore, the best sample frame when studying the nature of product defects generated by two types of stamping machines is a list of all stamping machines in the factory divided into two groups by the type of machine.

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(a) The derivative of the implicit function are y' = - (x + 1) / [2 · (y³ + 1)].

(b) The equation of the tangent line is y = (1 / 4) · x + 3 / 2.

(c) The two points on the curve with vertical line tangents are (x, y) = (- 4, - 1) and (x, y) = (2, - 1).

In this problem we find the definition of an implicit function of the form f(x, y) = C, where C is a real number. (a) First, we determine the first derivative of the implicit function:

2 · x + 2 + 4 · y³ · y' + 4 · y' = 0

2 · (x + 1) + 4 · (y³ + 1) · y' = 0

y' = - 2 · (x + 1) / [4 · (y³ + 1)]

y' = - (x + 1) / [2 · (y³ + 1)]

(b) The equation of the tangent line is described by:

y = m · x + b

Where:

First, we determine the slope of the tangent line:

m = - (- 2 + 1) / [2 · (1³ + 1)]

m = - (- 1) / 4

m = 1 / 4

Second, the intercept is finally found:

b = y - m · x

b = 1 - (1 / 4) · (- 2)

b = 1 + 1 / 2

b = 3 / 2

Third, write the equation of the tangent line:

y = (1 / 4) · x + 3 / 2

(c) A point on the curve has a vertical line tangent if and only if y³ + 1 = 0. Then,

y³ = - 1

y = - 1

Now we determine all possible x-values:

x² + 2 · x + (- 1)⁴ + 4 · (- 1) = 5

x² + 2 · x - 8 = 0

(x + 4) · (x - 2) = 0

x = - 4 or x = 2

The two points are (x, y) = (- 4, - 1) and (x, y) = (2, - 1).

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If the area to the right of z, given that it is a standard normal random variable, is 0.1112, then the value of z is 1.22. The answer is C.

A standard normal random variable has a mean of 0 and a standard deviation of 1. The area to the right of a value for a standard normal random variable can be found using a standard normal table or a calculator with a normal cumulative distribution function (CDF).

Given that the area to the right of z is 0.1112, we can use a standard normal table or normal CDF calculator to find the value of z such that the area to its right is 0.1112. This value will be approximately equal to 1.22.

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If $1800 is pledged in individual donations, the bank will fund the charity $216, which is obtained using the proportion $1400 / $168 = $1800 / x.

How much would the bank fund the charity if $1800 was pledged in individual donations?

We can use a proportion to solve this problem. Let x be the amount the bank will fund the charity if $1800 is pledged in individual donations. Then we can set up the following proportion:

$1400 / $168 = $1800 / x

We can cross-multiply to get:

$1400x = $1800 * $168

Simplifying the right-hand side, we get:

$1400x = $302400

Dividing both sides by 1400, we get:

x = $216

Therefore, if $1800 is pledged in individual donations, the bank will fund the charity $216.

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The value of the voltage of the electricity is 6 + j + 2j²

From the question, we have the following parameters that can be used in our computation:

C = 2 - j

I = 3 + 2j

The formula of voltage is given as

V = CI

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

V = (2 - j) * (3 + 2j)

Open the brackets

So, we have

V = 6 + 4j - 3j + 2j²

Evaluate the like terms

V = 6 + j + 2j²

Hence, the voltage is 6 + j + 2j²

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Answer:

7

Step-by-step explanation:

5+0.5x4=4+0.75x4

5+2=4+0.75x4

7=4+3

7=7

At steady state conditions, the temperature distribution in a large thin plate with uniform surface temperature will be parabolic. This is due to the fact that heat flows from hotter regions towards colder regions until the temperature across the entire plate reaches equilibrium.

In other words, the temperature distribution throughout the plate will be such that the rate of heat transfer at any point within the plate is equal to the rate of heat transfer at any other point within the plate.

The parabolic temperature distribution can be mathematically represented by an equation of the form T(x,y) = T0 - (Q/4k)(x^2 + y^2), where T0 is the uniform surface temperature of the plate, Q is the rate of heat input per unit area, k is the thermal conductivity of the material, and x and y are the distances from the center of the plate in the two orthogonal directions.

This equation shows that the temperature distribution is parabolic, with the highest temperature at the center of the plate and decreasing temperatures towards the edges. This type of temperature distribution is commonly observed in many engineering applications involving heat transfer in thin plates, such as in electronics cooling or in the design of heat exchangers.

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None of the polynomials has four terms in it.

It is the sum of terms in which the variable is in decreasing power of n.

Polynomial is in factor form

\(\rm 1.\ (x^{2} )(6x-27)(x^{2} )(3x)(-9x -27)\\ 2.\ (x^{3} )(x-9)(x^{2} )(6x)(-3x-27)\\ 3.\ (x^{6} )(x-3)(x^{2} )(9x)(-3x-27)\\ 4.\ (x^{9} )(x-3)(x^{2} )(3x)(-6x-27)\\ 5.\ (x^{3} )(x-6)\)

\(\begin{aligned} \rm 1.\ &(x^{2} )(6x-27)(x^{2} )(3x)(-9x -27)\\ &-162x^{7}- 243x^{6} +2187x^{5} \\ 2.\ &(x^{3} )(x-9)(x^{2} )(6x)(-3x-27)\\ &-18x^{8} +1458x^{6} \\ 3.\ &(x^{6} )(x-3)(x^{2} )(9x)(-3x-27)\\ &-27x^{11}-162 x^{10} 729x^{9} \\ 4.\ &(x^{9} )(x-3)(x^{2} )(3x)(-6x-27)\\ -&18x^{13} -27x^{12} +243x^{11} \\ 5.\ &(x^{3} )(x-6)\\ &x^{4} -6x^{3} \\ \end{aligned}\)

Thus, none of the polynomials has four terms in it.

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Answer:

All real values of x such that x ≥-3

Step-by-step explanation:

g(x) = sqrt(x+3)

A sqrt must be greater than or equal to zero

sqrt (x+3) ≥ 0

Square each side

x+3≥ 0

Subtract 3 from each side

x ≥-3

The restrictions on x are x ≥-3

That means the domain is x ≥-3

All real values of x such that x ≥-3

Answer:

\(\boxed{\mathrm{B}}\)

Step-by-step explanation:

\(g(x)=\sqrt{x+3}\)

A square root must have a value of greater than or equal to 0.

\(\sqrt{x+3}\geq 0\)

Square both sides.

\(x+3\geq 0\)

Subtract 3 from both sides.

\(x\geq -3\)