What is the effective interest rate of a simple discount note for $3,500 at a bank discount rate of 11%, for 24 months?

Answer:

26° 180 -81 - 73 = 26

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

triangle= 180

81 + 73 = 154

180 - 154= 26

Answer:

  -15

Step-by-step explanation:

You want the average rate of change of g(x) = 3x² +3 on the interval [-9, 4].

The average rate of change is defined as ...

  AROC(g) = (g(b) -g(a))/(b -a)

We can evaluate this directly, or we can simplify it a bit first.

 AROC = ((3b² +3) -(3a² +3))/(b -a)

  = (3b² -3a²)/(b -a)

  = 3(b -a)(b +a)/(b -a)

  = 3(b +a)

The AROC on the interval [a, b] = [-9, 4] is then ...

  AROC = 3(4 +(-9)) = 3(-5)

  AROC = -15

__

Additional comment

In the attachment, a graphing calculator is used to evaluate the rate of change directly from the definition. It gives the same value, as expected.

Answer:

B.  There is no maximum value.

C.  There is no maximum value of z.

Step-by-step explanation:

To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:

We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.

Rearrange the first three inequalities to isolate y:

[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]

Graph the inequalities.

The feasible region is the region that is shaded by all of the inequalities.

Please see the attached graph.

A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.

If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.

Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.

Answer: what shape?

Step-by-step explanation:

More info please

The angles and lines that match the angles and lines in the diagram consisting of two lines and their common transversal to the correct description  are;

Alternate Interior Angles; 2. ∠4 and ∠8

Consecutive Exterior  Angles; 5. ∠1 and ∠6

Alternate Exterior Angles; 3. ∠1 and ∠5

Transversal; line l

Consecutive Interior Angles; 4. ∠3 and ∠4

Corresponding Angles; 1. ∠1 and ∠7

A transversal is a line that intersects two or more other lines.

The description of the relationship between the angles in the question are;

Alternate Interior Angles

Alternate interior angles are a pair of angles formed when a transversal intersects two lines. They are located between the two lines on opposite side of the transversal.

Consecutive Exterior Angles

Consecutive Exterior Angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the same side of the transversal

Alternate Exterior Angles

Alternate exterior angles are a pair of angles formed when a transversal intersects two lines. They are located outside the two lines on the opposite sides of the transversal.

Consecutive Interior Angles

Consecutive Interior Angles, also known as Same-Side Interior Angles are a pair of angles formed when a transversal intersects two parallel lines. They are located between the two parallel lines on the same side of the transversal.

Corresponding Angles

Corresponding angles are a pair of angles formed when a transversal intersects two lines. They are located on the same relative positions with respect to the transversal and the two lines.

Learn more on transversal lines here: https://brainly.com/question/24607467

#SPJ1

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

To know more about Dilation visit:

brainly.com/question/10855880

#SPJ1

Regine's father is currently receiving a salary of 29037.50.

A percentage increase in mathematics is the proportion by which a quantity or value has grown in comparison to its initial value. It is computed by subtracting the original value from the new value, multiplying the result by 100, and then subtracting the difference between the two values. The percentage increase formula is:

(new value - original value) / 100% of the original value is the percentage increase.

The yearly increase is 15%, thus:

salary increase = 25250 x 0.15 = 3787.50

The current salary is:

current salary = salary from two years ago + salary increase

current salary = 25250 + 3787.50

current salary = 29037.50

Hence, Regine's father is currently receiving a salary of 29037.50.

Learn more about percentage increase here:

https://brainly.com/question/20818421

#SPJ1

Answer:The leading term in a polynomial is the term with the highest degree.

Step-by-step explanation:

Step-by-step explanation:

y = 3 x^2 - 4 x - 1

leading coefficient is 3  and its sign is ' + '   or positive

Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.

(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:

relative rate of growth = (dn/dt) / n(t)

= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])

= 0.15

Therefore, the relative rate of growth is 15%.

(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):

n(0) = 90[tex]e^0.15[/tex]*0

= 90

Therefore, the initial population of the culture is 90.

(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):

n(5) = 90[tex]e^0.15[/tex]*5

= 385.97 (rounded to two decimal places)

Therefore, the culture will contain approximately 385.97 bacteria at time t=5.

To learn more about derivative please click on below link        

https://brainly.com/question/29090070

#SPJ1

Answer:

5683200

Step-by-step explanation:

Move the decimal 4 places to the right because [tex]10^4[/tex] has 4 zeros.

Step-by-step explanation:

y = x^2 / z      now triple x and z

y = (3x)^2 / 3z = 9x^2 / 3z = 3 * x^2 / z  <==== this is 3 times the original

    y is tripled

The length of the rectangle is 10.5 units.

What is perimeter?

Perimeter is the distance of a two-dimensional shape. It is equal to the sum of the lengths of all the sides of the shape. The perimeter is measured in units, such as centimeters, meters, feet, or inches, depending on the unit of measurement used for the dimensions of the shape.

The perimeter of a rectangle is given by the formula:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

In this case, we know that the perimeter is 34 units, and the width is 6.5 units. So we can substitute these values into the formula and solve for the length:

34 = 2l + 2(6.5)

Simplifying, we get:

34 = 2l + 13

Subtracting 13 from both sides, we get:

21 = 2l

Dividing both sides by 2, we get:

l = 10.5

So the equation to determine the length of the rectangle is:

2l + 2w = P

Substituting the known values, we get:

2l + 2(6.5) = 34

Simplifying and solving for l, we get:

2l + 13 = 34

2l = 21

l = 10.5

Therefore, the length of the rectangle is 10.5 units.

To learn more about perimeter visit the link:

https://brainly.com/question/397857

#SPJ9

Complete question: The perimeter of a rectangle is 34 units, its width is 6.5 units. Write an equation to determine the length (l) of the rectangle.

Answer:

Step-by-step explation: Revised 8/15. F001. Surface area of a pond, acres = Length, ft x Width, ft. 43560. F002. Volume

b equal for the top of the bookcase to have the correct area= 5 cm2

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.

Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

L × b = 300

b = 300 / L

b = 300 / 60 = 5

Hence, b equal for the top of the bookcase to have the correct area= 5 cm2.

learn more about surface area click here:

brainly.com/question/16519513

#SPJ1

Answer:

There is 5% of the juice left.

Step-by-step explanation:

We know that originally, the container had 80 oz of orange juice, this is 100% in our case.

Then we can write a relation:

80 oz = 100%

Now there are 4 ounces left, in the same way as before, we can write this as:

4 oz = X%

We want to find X%

First, let's write our equations:

4 oz = X%

80 oz = 100%

We can take the quotient between these two equations to get:

(4oz/80oz) = (X%/100%)

We need to solve this for X%, then we get:

(4oz/80oz)*100% = X% = 5%

This means that 4 oz is 5% of the initial volume of the juice container.

Then we can conclude that there is 5% of the juice left.

Answer:

x = 9

Step-by-step explanation:

     √x + 7 - 1  = x

          √x + 6 = x

Isolate √x,

             √x = x - 6

Square both sides,

           (√x)² = (x - 6)²

Use identity (a -b)² = a² - 2ab  + b²

             x   = x² - 2*x*6 + 6²

             x = x² - 12x + 36

x² - 12x + 36 - x = 0

x² - 13x + 36  = 0

We look for two integers which when added give (-13) and when multiplied gives 36.

So, the factors are (-9) and (-4).  

-9 + (-4) = -13  & (-9)*(-4) = 36.

Rewrite the middle term using the factors.

x² - 13x + 36 = x² - 9x - 4x + 36

Take out the common factor 'x' from first and second term & take out the common factor (-4) from third and fourth term.

                   =x(x -9) -4(x - 9)

                   = (x -9)(x- 4)

x - 9 = 0    ; x - 4 = 0

    x = 9    ; x = 4

    But 4 doest not satisfy the equation. So, only 9 is the solution.

Answer:2.04

Step-by-step explanation:

Answer:

Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

The correct statement is: Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x.

Answer:

Step-by-step explanation:

To find the LCM of the given expressions, we need to factor each expression completely and then find the product of the highest powers of all the factors.

ax² - (a² + ab)x + a²b can be factored as:

ax² - (a² + ab)x + a²b = a(x - b)(x - a)

bx² - (b² + bc)x + b²c can be factored as:

bx² - (b² + bc)x + b²c = b(x - c)(x - b)

cx² - (c² + ac)x + c²a can be factored as:

cx² - (c² + ac)x + c²a = c(x - a)(x - c)

Now, the LCM is the product of the highest powers of all the factors.

The highest power of a is a², the highest power of b is b², and the highest power of c is c². So, the LCM is:

LCM = a²b²c²(x - a)(x - b)(x - c)

Therefore, the LCM of ax² - (a² + ab)x + a²b, bx² - (b² + bc)x + b²c and cx² - (c² + ac)x + c²a is a²b²c²(x - a)(x - b)(x - c).

The constant of proportionality of this table  is: k = 1/7.

The ratio between two quantities that are directly proportional is the constant of proportionality.

When y and x are two values that are direct proportion to one another, the proportionality constant k is defined as k=y/x.

Thus, using the x and its respective y values.

As the values are in direct proportion.

The constant of proportionality is:

k = 1/7

know more about the constant of proportionality

https://brainly.com/question/28413384

#SPJ1

Answer:

To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.

We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:

4/a | 2   -5   -11   -4

   |     8a  12a  4a-16

   +------------------

   2   8a-5  a-11  4a-20

The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.

Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:

f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4

Simplifying this expression, we get:

f(a x - 4) = 0

This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.

Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

Answer:

The question you provided is a math problem involving fractions, specifically solving for an unknown quantity using a proportion. Here is how you can solve it:

1/15 = 5/8

To solve for the unknown quantity, you can use cross-multiplication, which means multiplying the numerator of the first fraction by the denominator of the second fraction and vice versa:

1 * 8 = 15 * 5

Simplifying this equation, we get:

8 = 75

This is a contradiction, so the given equation has no solution. Therefore, none of the answer choices (A, B, C, D) are correct.

I hope this helps! If you have any further questions, feel free to ask.

The demand equation for commodity A is Xa = (4/10)Xb.

A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.

In the given question,

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

To know more about demand equation, visit:

https://brainly.com/question/13245362

#SPJ1

The demand equation for commodity A is Xa = (4/10)Xb.

What is demand equation?

A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

To know more about demand equation, visit:

brainly.com/question/13245362

#SPJ1

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

Length, which is typically expressed in units like meters, feet, or inches, is a measurement of an object's size or the separation between two locations. It alludes to the measurement of an object's longest dimension or the separation between two ends. The term "length" can also be used to describe the extent of a line or the linear separation between two locations, such as the length of a triangle's side, a road, or a length of rope. In geometry, length is a crucial mathematical notion that is used to gauge an object's size, shape, and location.

given

The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. Here are the facts:

60° sine + (BC/AB)

Using sin 60°, whose value is 3/2, as an example:

√3/2 = (BC/AB)

Multiplying AB by both sides:

BC = AB * √3/2

The hypotenuse's length is determined by adding the squares of the lengths of the other two edges. Here are the facts:

We have the following by substituting the earlier-obtained formulas for AC and BC:

Adding 3 to both sides:

4AB2 + 9AB2 = 12AB2

AB = 3x

As a result, the length of the hypotenuse AB is three times that of the side that is perpendicular to angle B, denoted by the symbol x.

To know more about length visit :-

https://brainly.com/question/30100801

#SPJ1

Answer:

The cone takes up one-third of the volume of the cylinder. (the cylinder is 3x bigger than the cone)

Step-by-step explanation:

Answer:

B. is right.

Step-by-step explanation:

Volume of cone = volume of cylinder/3

Therefore the volume of the cylinder is 3 x that of cone

The constant of proportionality for vanilla to chocolate ice cream is 2/3.

The constant of proportionality represents the fixed relationship between two quantities in a proportional relationship.

In this case, we are given that there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream.

To find the constant of proportionality in terms of vanilla to chocolate, we need to express this relationship as a fraction with the same units.

We can start by setting up the ratio of vanilla to chocolate ice cream, which would be 2:3.

This can then be expressed as

2/3

Therefore, the constant of proportionality for vanilla to chocolate ice cream is 2/3.

Read more about proportional relationship at

https://brainly.com/question/14425347

#SPJ1