A small company makes two types of music boxes, jeweled and enameled. The company originally made a total of 25 music boxes a week. Then the number of jeweled boxes produced was tripled and the number of enameled boxes was doubled, so that 65 boxes are now produced cach wee.. How many of each type of music box are now being produced each week?

The graph is proportional as it represents a linear function and is depicted using a straight line.  

The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

The graph is proportional as it represents a linear function and is depicted using a straight line. The function can also be said as a direct variation function.

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subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

e^2 - 4x = 8

4x = e^2 - 8

x = (e^2 - 8)/4

To solve for x in this equation, the first step is to subtract 8 from both sides of the equation. The next step is to divide both sides of the equation by 3.This results in the equation:  x = 4.Once 8 is subtracted from both sides, the equation becomes e^2 - 4x = 0. Then, divide both sides of the equation by 4, which gives 4x = e^2/4. Finally, subtract e^2/4 from both sides of the equation to get x = (e^2 - 8)/4. This is the final answer of the equation.

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By using what we know about right triangles, we will see that the hobbits are at 744.39 meters from the Dark Tower.

This position can be visualized as a right triangle, with the catheti being the tower's height and the distance between the hobbits and the Dark Tower.

Then we can use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

Where θ = 28°

The adjacent cathetus to this angle exists the height of the tower, then:

Adjacent cathetus = 1,400 m

The opposite cathetus exists the distance,

Tan(28°) = D/1,400m

Solving for D we get:

Tan(28°)*1,400m = D = 744.39m

The hobbits are at 744.39 meters from the Dark Tower.

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Answer: y = x + 19

Step-by-step explanation:

y=4x+15-4x+4=12

y=4x-4x=15+12+4

y=x+19

Deductive reasoning is used.

Deductive reasoning is the logic process of drawing a conclusion applying a general rule to a specific case.

To solve the equation 5x + 7 = 12 you apply this:

Rule                                                        application      

Subtraction property of equality          5x = 12 - 7

Simplification                                         5x = 5

Division property of equality                 x = 5/5

Simplification                                          x = 1.

Thus, by using the general rules to the specific equation, you get the result x = 1, which shows that this is a case of deductive reasoning.

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The combination of factors will increase the chances of rejecting the null hypothesis is:

A small standard error and a large alpha level will increase the chances of rejecting the null hypothesis.

The standard error represents the variability of the sample mean from the true population mean. A small standard error indicates that the sample mean is a good estimate of the true population mean, making it easier to detect differences and thus increasing the chances of rejecting the null hypothesis.

Alpha (α) is the level of significance, or the threshold for rejecting the null hypothesis. A large alpha level means that a smaller difference between the sample mean and the null hypothesis is required to reject the null hypothesis. This makes it more likely that the null hypothesis will be rejected if the sample mean is significantly different from the true population mean.

So, when both the standard error is small and the alpha level is large, it increases the chances of rejecting the null hypothesis.

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Answer:

The function table for g(x) = -x + 4 is as follows:

X Y -5 9 -1 5 0 4 1 3 2 2

Answer:

Nick earns a commission of 12/100 * $668 = $80.16 for the software he sold this week.

Step-by-step explanation:

The correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

To determine the conclusion about the behavior of the function f, we can use the tangent line approximation and whether it overestimates or underestimates the actual value of f(0.987).

Given that the tangent line approximation at x = 1 is 2.37, and if this approximation is an overestimate of the actual value of f(0.987), it means that the function lies below the tangent line in the interval 0.987 < x < 1.

Since the tangent line has a positive slope (given that f'(1) = 4), if the function f lies below the tangent line, it must be decreasing in the interval 0.987 < x < 1.

Therefore, the correct conclusion is:

a. f opens down on the interval 0.987 < x < 1

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Complete question =

For f differentiable such that f(1) = 3 and f'(1) = 4, the tangent line approximation of (0.987) = 2.37.

If this is an overestimate, what conclusion can be made about f ??

a. f opens down on the interval 0.987 x < x < 1

b. f opens up on the interval 0.987 x < x < 1

c. f opens down at x =  0.987

d. f opens up at x = 1

The general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.

The given differential equation is 9yy′ = x. This is a separable equation, meaning it can be solved by separating the variables and integrating both sides. To solve the equation, we start by dividing both sides by 9y to get y′ = x/9y. Now, we can solve for y by integrating both sides with respect to x. This gives us y = (1/9)∫xdy + c, where c is a constant of integration.

To determine c, we can use the initial condition given, y(9) = 5. We substitute 9 for x, and 5 for y to get 5 = (1/9)∫9dy + c. We can solve for c by subtracting (1/9)∫9dy from both sides, giving us c = 5 - (1/9)∫9dy.

Finally, we can substitute c into our equation to get the solution, y = (1/9)∫xdy + (5 - (1/9)∫9dy). This is the general solution to the separable differential equation 9yy′ = x, with the initial condition y(9) = 5.

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The graph of the equation is attached, and the coordinates are (0, 2), (2, -3), (1, -0.5), and (-2, 7).

When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.

Given equation, 2y = 4 - 5x

let's find the coordinates for the graph,

when x = 0

2y = 4

y = 2

(0, 2)

when x = 2

2y = 4 - 5*2

2y = -6

y = -6/3

y = -3

(2, -3)

when x = 1

2y = 4 - 5

2y = -1

y = -0.5

(1, -0.5)

when x = -2

2y = 4 - 5(-2)

2y = 14

y = 7

(-2, 7)

coordinates for the graph are (0, 2), (2, -3), (1, -0.5), (-2, 7).

Hence graph lies in coordinates (0, 2), (2, -3), (1, -0.5), (-2, 7).

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The bank routing number on a check is a 9-digit code used to identify a financial institution in a transaction. It is also known as an ABA routing number, an RTN, and a routing transit number.

In order to determine the routing number on a check:

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The columns of a are linearly dependent, we can conclude that y = (4, 9) is not in the range of t(x).

What is vector ?

A vector is a mathematical object that has both magnitude (or length) and direction. Vectors can be used to represent physical quantities such as velocity, force, or displacement, where the magnitude represents the size of the quantity and the direction represents its orientation in space.

The range of t(x) = ax, where a = 1 −3 0 5 3 1, is the set of all possible values of t(x), which is the set of all linear combinations of the columns of the matrix a. To check if y = (4, 9) is in the range of t(x), we need to see if there exists a vector x such that t(x) = y. If a vector x exists, then y = (4, 9) is in the range of t(x). If no such vector exists, then y is not in the range of t(x).

Since the columns of a are linearly dependent, we can conclude that y = (4, 9) is not in the range of t(x).

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Answer:

Below

Step-by-step explanation:

Standard form of a circle =     (x-h)^2  + (y-k)^2 = r^2

   where h,k is the center  

for this circle h,k = 2,-1     and radius, r= 4

so the equation would be

(x-2)^2 + (y+1)^2 = 4^2

Answer:

My answer to your question is a "No".

We can know that a and b are the same numbers. If we multiply the same number on each side, the answer will be the same. However, x and y have different values. So, it will show differently.

Let's have an example:

It we say a = 5, x = 6, y = 7.

We know a and b are the same number so, both a and b will be 5. If we multiply a by x, it will be 5 x 6 which is 30. It will show the same answer on multiplying b because as you said a and b are the same. The equation will be 5(a) x 6(x) = 5(b) x 6(x) Let's look at multiplying y. If we multiply a by y, it will be 5 x 7 which is 35. As you said it will show the same answer on multiplying b because a and b are the same. The equation for this will be 5(a) x 7(y) = 5(b) = 7(y). Finally, let's compare the two equations.

5(a) x 6(x) = 5(b) x 6(x) -> 30 = 30

5(a) x 7(y) = 5(b) = 7(y) -> 35 = 35

You can see it more clearly when we compare those to the equations that I made.

Thank you

Yes, if a = b, then ax = bx and ay = by for any value of x.

This is because the equation a = b implies that a and b are equal in value, so any expression involving a can be replaced with an equivalent expression involving b. In other words, any operation performed on a can be performed on b and produce the same result.

For example, if a = b, then multiplying both sides of the equation by x yields ax = bx, and multiplying both sides of the equation by y yields ay = by. This means that any power, root, logarithm, or other mathematical operation performed on a can also be performed on b and produce the same result.

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The function h(x) can be expressed as a composition of two other functions: f(x) and g(x).

In mathematics, functions are a way to describe relationships between variables.

The function f(x) is defined as 2 raised to the power of x. This means that for any value of x, the output of the function f(x) will be 2 raised to that power.

If x is 3, then f(3) = 2³ = 8.

The function g(x) is defined as x. This means that the output of the function g(x) will be the same as its input.

If x is 4, then g(4) = 4.

Combining these two functions, we can express h(x) as f(g(x) + 6). This means that for any value of x, the output of h(x) will be 2 raised to the power of g(x) plus 6.

If x is 2, then g(2) = 2, and

=> h(2) = f(g(2) + 6) = f(8) = 2⁸ = 256.

In summary, the function f(x) raises 2 to the power of x, and the function g(x) returns its input.

By combining these two functions, we can express h(x) as the result of 2 raised to the power of g(x) plus 6.

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Answer:

Step-by-step explanation:

These are the simplified expressions with A = -3 , |-3 - B|.

What is algebraic expression ?

An algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations. For example, 3x² − 2xy + c is an algebraic expression.

Given that A = -3, we can substitute this value into the expressions:

A + B = -3 + B

4a + 5b = 4(-3) + 5b = -12 + 5b

|A| = |-3| = 3

|A - B| = |-3 - B| = |-3 - B|

These are the simplified expressions with A = -3 , |-3 - B|.

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By using the Root Test on the series "∑n" , we found that the series is Divergent and diverges to infinity .

The Root Test states that, if the limit of nth root of the absolute value of the nth term of a series is less than 1, then the series converges. and

If the limit is greater than or equal to 1, the test is inconclusive.

In the series ∑n , the nth term of the series is "n" ,

So, the nth root of the absolute value of nth term is the nth root of |n|, which is = n^(1/n).

we see that as n approaches infinity, the nth root : n^(1/n) approaches 1, So,  the limit of the nth root of the absolute value of the nth term is equal to 1. Which means that the Root Test is inconclusive for this series.

Therefore , the series ∑n diverges, it is a known series called as Harmonic series, which diverges to infinity.

The given question is incomplete , the complete question is

Use the Root Test to determine whether the series convergent or divergent.  ∑n , where n is from 1 to infinity .

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(a) No solutions when r ≠ 6 and s ≠ 5. (b) Exactly one solution when r = 6 and s = 5. (c) Infinitely many solutions when r = 6 and s is arbitrary.

For the system of equations to have (a) no solutions, both r and s must have values that do not satisfy the equations. For example, if r ≠ 6 and s ≠ 5, then the equations cannot both be true. For the system to have (b) exactly one solution, both r and s must have values that satisfy the equations. For example, if r = 6 and s = 5, then the equations are both true and have one unique solution. For the system to have (c) infinitely many solutions, one of the variables must have a value that satisfies the equations, while the other variable may take on any value. For example, if r = 6 and s is arbitrary, then the equations are both true and have infinitely many solutions.

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The dimension of side a in the right triangle is 3.516.

From the diagram, the figure is a right triangle.

From  trigonometric ratio;

Tangent = Opposite / Adjacent

Hence;

tan( θ ) = a / b

Plug in the given values and solve for a

tan( 38 ) = a / 4.5

a = tan( 38 ) × 4.5

a = 3.516

Therefore, the value of a is 3.516.

Option B) 3.516 is the correct answer.

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Answer:

-----------------------------------

The vertical change is the difference of the y-coordinates.

The y- coordinates are 0 and 2, their difference is:

The exponential function is an exponential decay.

A general exponential function can be written as:

y = A*(b)^x

Where A is the initial value and b is the base.

Here the exponential equation is:

y = 10*(2/3)^x

Notice that the base is:

b = 2/3 = 0.66

This is smaller than 1 and larger than zero, so we have an exponential decay.

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Answer:

answer choice C.

Step-by-step explanation:

complementary angles are 2 angles that add up to 90 degrees

90=58+x

90-58=x

x=32

The equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is

y = (123/15)x + (98 - (123/15) * (-7))

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. To find the equation of the secant line, we need to find the slope (m) and the point of intersection (x,y) of the line with the y-axis.

To find the slope (m) of the secant line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1,y1) = (-7, g(-7)) and (x2,y2) = (8, g(8)).

So, m = (g(8) - g(-7)) / (8 - (-7)) = (g(8) - g(-7)) / 15

Now, we can substitute the value of g(x) in the above equation and get the value of m

g(x) = 2x^2-7

m = (2(8^2)-7 - 2(-7^2)-7) / 15 = (2(64)-7 - 2(49)-7) / 15 = (128-7-98-7) / 15 = 123/15

To find the point of intersection (x,y) of the line with the y-axis, we can use one of the given points and the slope. Let's use the point (-7,g(-7))

y = mx + b

g(-7) = m * (-7) + b

b = g(-7) - m * (-7)

We can substitute the value of g(x), m and x = -7 in the above equation and get the value of b.

g(x) = 2x^2-7

b = 2(-7)^2-7 - m * (-7) = 2(49)-7 - 123/15 * (-7) = 98 - 123/15 * (-7)

So, the equation of the secant line containing the points (-7,g(-7)) and (8,g(8)) is

y = (123/15)x + (98 - (123/15) * (-7))

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The possible set of inequalities that represent the situation is -

r + c ≥ 80

1.45r + 0.65c ≤ 200

Given is that Victor went to buy some flowers from the flower shop.

We can write the possible set of inequalities as -

r + c ≥ 80

1.45r + 0.65c ≤ 200

Therefore, the possible set of inequalities that represent the situation is -

r + c ≥ 80

1.45r + 0.65c ≤ 200

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Parallel lines have the same slope.

The slope of y = 9x + 9 is 9, because of the 9 in 9x.

The slope of a parallel line would also be 9.

Answer:

Length = 7.83, Width = 3.83

Step-by-step explanation:

Assign variables. Let x represent the width

Area (L x W) = 30 m²

(4 + x)(x) = 30

4x + x² = 30

x² + 4x - 30 = 0

Apply Quadratic Formula

[tex]\frac{-4 + \sqrt{4^2 - 4(1)(-30)}}{(2)(1)}[/tex]

Solve

x = -2 ± √34

x = 3. 83... or x = -7.83 (reject this one)

Width = 3.83

Length = x + 4 = 7.83