Use the example above and fill in the missing values.
Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using
standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary
interest because the total Interest to be paid is $808.13.
After the fifth month, the borrower decides to prepay the whole loan. Under a stándard amortization plan the borrower
would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of
the total interest based on two series:
((n+35)+(n+34)+(n+33)+(n+32)+(n+31))
If you add 36, 35, 34, 33, and 32, the sum is
If you sum the numbers from 1 to 36, the sum is
{(n)+(n+1)+...+(n+35)}
The fraction (the first sum / the total sum) to the nearest tenth =
total interest.
%. The lender will multiply this fraction by the
The cumulative interest = (the percentage calculated above) x ($808.13) = $
The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78
plan is: $

According to the information, 11 boxes and 2 units are required to complete the order.

To find the number of boxes and units required to complete the order we must perform the following procedure:

If we know that each box can hold 8 units and the order is for 90 units, then we divide the total number of units by the number of units per box.

So we know that we are going to need 11 boxes to complete part of the order. Now, to know how many units we have left without storing we must multiply 8 * 11 and subtract the result from 90:

According to the above, the number of boxes would be 11 and the number of units would be 2.

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Answer:The missing length can be found using the formula for the area of a triangle, which is:

Area = (base * height) / 2.

We know the base is 18.7 inches and the area of the shaded region is 152.405 in^2.

So, the height can be found using the formula:

152.405 = (18.7 * height) / 2

Solving for height:

height = 2 * 152.405 / 18.7

height = approximately 12.67 inches.

Applying the exterior angle theorem, m<JKL = 22 degrees.

According to the exterior angle theorem, the following equation is created to find the value of x:

5x - 3 = x - 1 + 2x + 8

Combine like terms:

5x - 3 = 3x + 7

5x - 3 - 3x = 3x + 7 - 3x

2x - 3 = 7

Add 3 to both sides

2x = 10

x = 5

Find the measure of m<JKL (exterior angle):

m<JKL = 5x - 3

Plug in the value of x:

m<JKL = 5(5) - 3 = 22 degrees.

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The equation that represents the total cost that Debra paid is: C = 5N

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Information about the problem:

The function that models the situation is the following:

C = 5N

Where:

Number of notebooks = N

Cost of each notebook = $5

Total cost = C

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Correctly written question:

Debra purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Debra paid.

Given: f(x)=  4x 2 +1 / x

​When we differentiate both sides in relation to x, we obtain

f ′ (x)=  x(8x)−(4x² +1)/x² = 4x² −1 / x²

​(a) To improve function.

f  (x)≥0

⇒ 4x²-1/ ≥0

⇒ 4x²- 1 ≥ 0

⇒ (2x-1) (2x+1) ≥0

⇒ x ≥ 1/2 or x≤ -1/2

So, f(x) is increasing function on (-∞, -1/2] ∪ [1/2,∞)

(b) for decreasing function,

⇒ 4x²-1/x² ≤0

⇒ 4x²-1 ≤0

⇒(2x - 1) (2x+1)≤0

⇒ x ≤ 1/2 or x≥ -1/2

so, f(x) is decreasing on [-1/2, 1/2]

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​

Between the ages of 14 and 16, g(x) increases by a factor of 64/56 = 1.1429.

A defined range of values inside a piece of data is known as an interval. It measures the spread of the data and is defined as the difference between the maximum and minimum values of the data set. Intervals can be applied in many different contexts, from tracking the evolution of data distribution to spotting trends. Additionally, outliers and unusually high or low values in a data collection can be found using intervals. In statistics, interval data are frequently used to quantify data variability.

Divide the value of g(16) by the value of g to find the factor by which g(x) increases across the range of 14 to 16. (14).

G(14) has a value of 56, and G(16) has a value of 64.

Therefore, 64/56 = 1.1429 is the factor by which g(x) increases between 14 and 16.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

The Organisation for Economic Co-operation and Development (OECD) is an international organization that aims to promote economic growth and prosperity, as well as to improve social well-being through research and policy analysis.

Five research activities related to corporate governance by OECD are:

Corporate Governance Principles and Guidelines

Board Diversity and Gender Equality

Board Evaluation and Succession Planning

Shareholder Engagement and Activism

Anti-Corruption and Integrity in Corporate Governance.

10.44 Percent of increase in the price of a basketball .

A percentage is a number or ratio that is expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to denote it. A percentage is a dimensionless number; there is no specific unit of measurement for it.

By divided the number by the entire value and multiplying the outcome by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

The price of basketball increased = $18.50 -$16.75 = 1.75$

Now the percent of increase in the price= 1.75/16.75×100

= 10.44%

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The solution is Option B.

The scale factor of the translated triangle is S = 16

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the perimeter of the first triangle be P

The value of P = 3 m

Now , the triangle is translated by a scale factor of S

And , the perimeter of the translated triangle = 48 m

So , the scale factor = perimeter of the translated triangle / perimeter of the first triangle

Substituting the values in the equation , we get

The scale factor of the translation S = 48/3

The scale factor of the translation S = 16

Hence , the scale factor is 16

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The scale factor of the triangles will be 16:1. The correct option is B.

A scale factor is a numerical value that is used to represent an object's enlarged or shrunk shape. It is a number that can be used to alter the size of any geometric figure or shape in relation to its original size.

It aids in altering the figure's size but not its shape. The scale factor is defined as the proportion of the new image's size to that of the previous image.

Given that a triangle with a perimeter of 48 meters was created from a triangle with a perimeter of 3 meters using a scale factor.

The scale factor will be calculated as:-

Scale factor = 48 / 3

Scale factor = 16: 1

Therefore, the scale factor of the triangles will be 16:1. The correct option is B.

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The number of number plates assigned is 40,219,200.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a seven-digit license plate with the following pattern: L L N – L N N N.

There are 3 letters with the restriction of no vowels and 4 numbers between 0-9.

With no vowels, we have 21.

= 21!/3!(21-3)! + 10!/(10-4)!

= 7980×5040

= 40,219,200

Therefore, the number of number plates assigned is 40,219,200.

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Answer:

B

Step-by-step explanation:

9x² - y² = 1

use the power rule to differentiate

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = an[tex]x^{n-1}[/tex]

[tex]\frac{d}{dx}[/tex] (y² ) = 2y [tex]\frac{dy}{dx}[/tex]

[tex]\frac{d}{dx}[/tex] ( constant ) = 0

differentiate both sides with respect to x

9 × 2x - 2y [tex]\frac{dy}{dx}[/tex] = 0 , that is

18x - 2y[tex]\frac{dy}{dx}[/tex] = 0

Answer:

4x - 7

Step-by-step explanation:

The x represents Bob's age since, we don't know what it is, I put it as a variable.

2x      This represents Jeff who is 2 times Bob's age.

x - 7    Peter is younger than Bob by 7 years so we need to take away 7                    from Bob's age

2x + x - 7 + x    This would be the expression

4x - 7                Now just combine the like terms. We don't have Bob's age so the expression will stay like this.

The solution set of the given equation is; -10

The equation is expressed as;

(2x + 5)/2 - 3x/(x - 2) = x

Multiply through by 2(x - 2) to get;

(2x + 5)(x - 2) - 6x = 2x(x - 2)

2x² + 5x - 4x - 10 - 6x = 2x² - 4x

2x²  will cancel out to get;

-5x - 10 = -4x

5x - 4x = -10

x = -10

Thus that value of x is the solution

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Answer:

see below

Step-by-step explanation:

2x+5y=50.25

3x+4y=53.50

use 2nd equation minus first equation to get

x-y=3.25

so x = 3.25+y

substitute x with above equation

2*(3.25+y) +5y =50.25

so 6.5+2y+5y = 50.25

7y = 43.75

y=6.25

x=3.25+y =9.5

Gina Wilson is an Australian intersex human rights activist. She was the founding president of Intersex Human Rights Australia

Define parallel lines?

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Following are the different sides of the triangles -

The line segment that divides a triangle in half and connects one vertex to the middle of the other side is known as the median in geometry. There are an equal number of medians at each vertex of a triangle, and they all intersect at the triangle's centroid.

The triangle's three medians are the line segments with endpoints at the triangle's vertices and the midpoint of the opposite side. The point where all medians converge is known as the centroid.

1. The sides are in same ratio,

[tex]\frac{24}{9} = \frac{32}{x}\\[/tex]

⇒ [tex]x = \frac{32 \times 9}{24}[/tex]

⇒ [tex]x = 12[/tex]

2. [tex]\frac{20}{14} = \frac{33}{x}[/tex]

⇒ [tex]x = \frac{33 \times 14}{20}[/tex]

⇒ x = 23.1

3. [tex]\frac{x+ 5}{30} = \frac{16}{20}[/tex]

⇒ [tex]x = \frac{16 \times 30 }{20} - 5\\x = 19[/tex]

4. [tex]\frac{x+8}{2x - 5} = \frac{20}{22.5}[/tex]

⇒ [tex]22.5x + 180 = 40x - 100\\[/tex]

⇒ [tex]17.5 x = 280[/tex]

⇒ [tex]x = 16[/tex]

8. [tex]\frac{33}{41.8} \neq \frac{45}{57}[/tex]

∴ ST is not parallel to PR.

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The best estimation of the equation 7/8 − 6/11 is 1/3

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

the best estimation of the equation 7 8 − 6 11

Express properly

So, we have

7/8 - 6/11

Take the LCM

This gives

7/8 - 6/11 = (77 - 48)/88

Evaluate the difference

7/8 - 6/11 = 29/88

Approximate

7/8 - 6/11 = 30/90

So, we have

7/8 - 6/11 = 1/3

Hence, the estimate is 1/3

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Answer:

below

Step-by-step explanation:

This is isosceles because you have TWO equal sides

Equilateral has THREE equal sides

Therefore , the solution of the given problem of ratio comes out to be

 x = 13/22 cups of dish soap.

A set of equivalent variables "a" and "b" can be defined using the straightforward formula "a / b," where "b" may be bigger than zero. Two ratios are combined to make one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. 3/4 of the group are girls, while 1/4 are boys. Parts can be a division between one or more items, a number, or a portion of the volume of a component.

Here,

Given:

=> 1/2 cup of dish soap

=> 11/2 cups of water

and,

Ratio of dish soap and water is

=> 1/2 : 11/2

=> 1 : 11

After 1 cup addition of water:

=> 11/2 + 1 = 13/2

and

Let x be the new cup of dish soap

So, ratio :

=>  x : 13/2 =  1 : 11

=> 2x : 13 = 1:11

=> 13 = 22x

=> x = 13/22

Therefore , the solution of the given problem of ratio comes out to be

 x = 13/22 cups of dish soap.

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Answer:

  No

Step-by-step explanation:

You want to know if -8 is irrational.

A number is irrational if it has a decimal fraction part that does not terminate and does not repeat.

If you can describe all of the digits of the number explicitly without resort to functions or symbols, the number is not irrational.

  -8 is not irrational

Answer:

On the Venn diagram, these common elements are located inside the intersection of the three circles representing sets A,B and C . From the figure, we see that 7 and 4 belong to this mutual intersection. So, the roster form of set A∩B∩C A ∩ B ∩ C is given as {4,7}

i hope that help, i am not sure if i am correct

The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

Now, According to the question:

The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.

                                                         A = lw

Here, l represents the length of the page and w represents the width of the page.

Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]

and the page has margins on each side, each having a width of 1in.

We will first set up an equation using the details that we know. We know that the printed area is  [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is

[tex]A_p=xy[/tex]

30 = xy

[tex]y = \frac{30}{x}[/tex]

Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2  since we have to consider the margins at the sides. The area of the page is as follows.

A = (x+2)(y + 2)

We can substitute the value of y in terms of x.

A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])

A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4

A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4

A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]

We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.

A'(x) = [tex]2-\frac{60}{x^2}[/tex]

0  = [tex]2-\frac{60}{x^2}[/tex]

[tex]2 =\frac{60}{x^2}[/tex]

[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]

Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.

A"(x) = [tex]\frac{120}{x^3}[/tex]

[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]

[tex]A"(\sqrt{30} )=0.73[/tex]

We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2

x + 2 = √30 + 2

y + 2 = [tex]\frac{30}{x}[/tex] + 2

y +2  = [tex]\frac{30}{\sqrt{30} }[/tex] + 2

y + 2 = [tex]\sqrt{30}+2[/tex]

Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.

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The quadratic regression in this case is y = 126.01x2 - 312.04x + 888.88.

An analysis tool called quadratic regression is implemented to identify the parabola equation that perfectly matches a given collection of data. Finding the equation of the straight line that most closely matches a collection of data is the goal of this sort of regression, which is an expansion of simple linear regression.

Step 1:  Input the data sets into the graphing calculator.

Step 2: Choose "Scatter Plot" from the graphing calculator's interface.

Step 3: Choose "Quadratic Regression" from the graphing calculator's toolbar.

Step 4: The calculator will create the equation y=ax2+bx+c, where a, b, and c are constants.

Step 5: Round the constants to the hundredths place, and the best-suited quadratic model's equation will be: y = 0.06x2 - 3.12x + 4.00.

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Refer to the images attached. Edit: I realized after uploading this answer that the integral in terms of y is MUCH easier, so I attached that as well :) But at least you know it can be done both ways!

Answer: The answer is 6.75

Step-by-step explanation:

I did the math :b

$120.00 increased by 20% is $144.00

The quantity of cells that will be in the culture on the 8 day assuming the number of cells is growing at an exponential rate would be = 128,000 cells.

An exponential rate of growth is defined as the increase in the population of an object under study over a period of time.

The number of cells the scientist started with = 1,000 cells

The number of cells in 4th day = 64,000

Therefore the rate of growth of cells per day;

= 64000/4

= 16,000

Therefore on the 8th day, the number of cells would be = 8×16000 = 128,000 cells.

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The monthly rate percentage is given as follows:

r = 0.65%.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are given as follows:

To obtain the monthly interest, we must consider that:

[tex]\left(1 + \frac{r}{12}\right)^{12 \times \frac{1}{12}} = 1.0777[/tex]

Hence the equation is simplified as follows:

r = 0.0777/12

r = 0.0065.

r = 0.65%.

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The equivalent markup price will be $31.675.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that the cost is $25 and the markup percentage is 26.7%. The markup cost will be calculated as:-

Price = cost x Percentage increase

Price = 25 x 1.267

Price = $31.675

Therefore, the equivalent markup price will be $31.675.

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Using mathematical operations, since 1/3 of the sundaes Lisa is making are mint, and 1/2 of the remaining (or 1/3) are chocolate, the number of vanilla sundaes is 10.

The basic mathematical operations are addition, subtraction, division, and multiplication.

Mathematical operations can be applied to any mathematical problem to find their solutions.

The total number of Sundaes Lisa is making = 30

The proportion of the sundaes that are mint ice cream = 1/3

The proportion of the sundaes that are = 1/3 (1/2 of 2/3)

The vanilla proportion = 1/3 (1 - 1/3 - 1/3)

The number of sundaes that will be vanilla = 10 (30 x 1/3)

Thus, determining the fractional values using mathematical operations, Lisa is making an equal number of mint, chocolate, and vanilla ice cream.

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Answer:

3,636.36

Step-by-step explanation:

Let x be the number

19.8% de x = 720

19.8% =19.8/100 = 0.198

0.198x = 720

x = 720/0.198 =  3,636.36