Problem 3.24 Effective interest rate and APR Aruna invested Rs 150,000 eighteen months ago. Currently, the investment is worth Rs 168,925. Aruna knows the investment has paid interest every three months, but she does not know what the yield on her investment is. Compute both annual percentage rate (APR) and the effective annual rate of interest on her investment. Ans: 8%; 8.24%​

The average rate of change of the function f(x) on the interval [4,9] is equal to 23.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [4, 9]:

a = 4; f(a) = 97

b = 9; f(b) = 212

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (212 - 97)/(9 - 4)

Average rate of change = 115/5

Average rate of change = 23.

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Answer:To convert this to miles per hour, we need to first convert the distance to miles. We know that 1 mi = 5280 ft, so 98 ft = 98 / 5280 mi = 0.0184 mi.

Now we can use the formula speed = distance / time again, but this time using miles and hours as the units. So, speed = 0.0184 mi / (11.5 s / 3600 s/hr) = 0.0184 mi / 0.003194 hr = 5.8 mi/hr.

Step-by-step explanation:

Answer:

5.81 mph

Step-by-step explanation:

We want to first convert the number of feet to miles and then divide by the number of hours. Since we know that 5280 feet is one mile, we essentially want to find how many "groups" of 5280 are in some distance and that's the number of miles. We can do this by dividing.

[tex]\frac{98}{5280}\approx0.018561[/tex]

Now we want to find how many hours 11.5 seconds is. It's basically the same process as we divide this by the number of seconds in an hour 3600.

11.5/3600 = 0.00319

Now divide the distance over the time and this gives us approximately: 5.81 mph

The simplified form of the expression (x² + 7x) / (9 - x²) is x(x + 7) / ( 3 + x )( 3 - x ).

Given the expression in the question;

(x² + 7x) / (9 - x²)

To simplify, first factor out x form x² + 7x

(x × x + 7 × x) / (9 - x²)

Factor out x

x (x + 7) / (9 - x²)

Next, simplify the denominator

x (x + 7) / (9 - x²)

Rewrite 9 as 3²

x (x + 7) / (3² - x²)

Now, since both terms are perfect squares

a² - b² = (a + b)(a - b)

Hence,

x(x + 7) / ( 3 + x )( 3 - x )

Therefore, the simplified form is x(x + 7) / ( 3 + x )( 3 - x ).

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Answer:

The origin is the point (0,0)

(2,-2)  Start at the origin and move 2 unit right along the x axis, from there move down 2 units.  Place a point at that location.

(-2, 1.5) Start at the origin and move 2 units left along the x axis, from there move up 1.5 space and place a point.

(-1, 2/4)  Start at the origin and move left 1 unit along the x axis, from there move up 1/2 a unit and place a point.  2/4 is the same as 1/2

Step-by-step explanation:

The distance between the cities on the map is given by the equations

a) The distance of 50km = ( 1/3 ) cm

b) The distance of 280km = ( 1 13/15 ) cm

c) The distance of 142 1/2 km = ( 19/20 ) cm

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance on the map be represented as A

Now , the equation will be

The scale on the map is given by 1/2 cm = 75 km

So , 1 km = ( 1/2 ) / 75 cm

1 km = ( 1/150 ) cm

a)

when the distance = 50 km

The distance on the map = 50 x ( 1/150 ) cm

The distance on the map = ( 1/3 ) cm

b)

when the distance = 280 km

The distance on the map = 280 x ( 1/150 ) cm

The distance on the map = ( 1 13/15 ) cm

c)

when the distance = 142 1/2 km

The distance on the map = 142 1/2 x ( 1/150 ) cm

The distance on the map = ( 19/20 ) cm

Hence , the equation is solved

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Answer:

2y-3

Step-by-step explanation:

GCF of 32 and 48=16

(32y-48)/16=2y-3

The equation of the linear function represented by the table below in slope intercept form is f(x) = 4x - 1.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

General equation of a linear function in slope intercept form is,

y = f(x) = mx + c

Here c is the y intercept and m is the slope.

y intercept is the point on the line when x coordinate equals zero.

Given four points on the line (-1, -5), (1, 3), (3, 11) and (5, 19).

Consider two points (1, 3) and (3, 11).

Slope, m = (11 - 3) / (3 - 1) = 8 / 2 = 4

So the equation is y = 4x + c.

Substitute (1, 3) in the above equation.

3 = (4 × 1) + c

c = 3 - 4

c = -1

So the equation is y = 4x - 1.

Hence the given function can be represented as f(x) = 4x - 1.

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The solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

A trigonometric equation is one that contains a trigonometric function with a variable.

Given is a trigonometric equation,

6sin²θ-13sinθ+7 = 0

Solving for θ

6sin²θ-6sinθ-7sinθ+7 = 0

6sinθ(sinθ-1)-7(sinθ-1) = 0

(6sinθ-7)(sinθ-1) = 0

sinθ = 1

θ = π/2

or,

6sinθ-7 = 0

sinθ = 7/6 [no solution]

Hence, the solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

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Answer:

The product of (-12 + 4i) and its conjugate is (-12 - 4i).

The conjugate of (-12 + 4i) is (-12 - 4i).

Answer:

B. the area is d x pi its the solution

The first investment is $22500 and second investment is $34000.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Two investments totaling $56,500 produce an annual income of $2480.

let the two investments be x and y.

So, x + y = 56500.........(1)

and, One investment yields 8 % per year, while the other yields 2 % per year then

0.08x+0.02y=2480.......(2)

Solving equation (1) and (2) we get

0.08(56500-y)+0.02y=2480

4520-0.08y+0.02*y=2480

-0.06y=-2040

y= 34000

and, x=56500-y =22500

Hence, the investments were $22500and $34000.

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The quotient is 3x²+5x+5.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given expressions are 3x³-x²-5x-10 and x-2.

Here, (3x³-x²-5x-10)/(x-2)

x-2|3x³-x²-5x-10|3x²+5x+5

  (-)3x³-6x²

____________

          5x²-5x-10

       (-)5x²-10x

   ____________

               5x-10

            (-)5x-10

      ____________

                   0

Therefore, the quotient is 3x²+5x+5.

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Answer:

23.

Step-by-step explanation:

1) if 'G is the midpoint of DF and H is the midpoint of EF', then 0.5*DE=GH, and

2) it is possible to write: 0.5(18+4x)=3x+2, where x=7.

3) if x=7, then GH=3*7+2=23.

To make a tree diagram, start by writing out the given information and drawing a box around it. Then draw two branches off of the box representing the two possible outcomes of selecting a student, male or female. Then draw two more branches off of each of the first two branches, representing the two possible outcomes of receiving aid.

Then draw two more branches off of each of the second two branches, representing the two possible outcomes of receiving federal aid. This will create a tree diagram that looks like this (see the image).

From the tree diagram, we can calculate the probability of selecting a student from the given information as follows:

P(selecting a student) = P(selecting a male) + P(selecting a female) = (of male students/total students) + (of female students/total students) = (of male students + of female students)/total students =

Therefore, the probability of selecting a student from the given information is .

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97.75 - 85 = 12.75

This means the amount of tax was $12.75.

If we divide the amount of tax by the original price of the shirt, it gives us the percent of the tax:

      12.75 ÷ 85 = 0.15 = 15%

Sales tax is 15%.

The key in the calculation is to divide by the original price of the shirt.

The domain of the table below is {-3, 6, 12}

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

The table of values

The domain of a function is the set of the input values

This means that the domain is

Domain =  {-3, 6, 12}

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The stem-and-leaf plot of the given data is attached.

A stem-and-leaf plot refers to a device used to present quantitative data in a graphical format to help in visualizing the shape of a distribution. It is a table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

From the given options, the statements that describe the percentages distributed, distribution skewness and whether there are any gaps are:

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The probabilities for this problem are given as follows:

a) Moderate to high, given that it is an aerospace company: p = 4/9 = 0.4444.

b) Moderate to high, given that it is a food retailer: p = 6/11 = 0.5455.

c) As the probabilities are different, the company type is independent of the level of risk of the firm's stock.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability is given as follows:

p = 8/18

p = 4/9.

For item b, the outcomes are given as follows:

Hence the probability is given as follows:

p = 30/55

p = 6/11.

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The function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

What is the Average Rate of Change?

Here, average rate of change of the function must be calculated over the interval [-2, 2].

(A) The average rate of change of the function m(x):

Here, a = -2, m(a) = -12, and b = 2, m(b) = 4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{4-(-12)}{2-(-2)} \\\implies A(x)=4[/tex]

(B) The average rate of change of the function q(x):

Here, a = -2, q(a) = -4, and b = 2, q(b) = -12

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{q(b)-q(a)}{b-a}\\\implies A(x)=\frac{-12-(-4)}{2-(-2)} \\\implies A(x)=-2[/tex]

(C) The average rate of change of the function n(x):

Here, a = -2, n(a) = -6, and b = 2, n(b) = 6

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{n(b)-n(a)}{b-a}\\\implies A(x)=\frac{6-(-6)}{2-(-2)} \\\implies A(x)=3[/tex]

(D) The average rate of change of the function p(x):

Here, a = -2, p(a) = 12, and b = 2, p(b) = -4

Substituting the values in the formula for average rate of change, we get

[tex]A(x)=\frac{m(b)-m(a)}{b-a}\\\implies A(x)=\frac{-4-12}{2-(-2)} \\\implies A(x)=-4[/tex]

Therefore, the function that has the average rate of change of -4 over the  interval [-2, 2] is (D) p(x).

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Answer:

I think so.

Step-by-step explanation:

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two integers on a number line.

The occurrence of an unfair and/or uneven distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different individuals and in various settings, the word "inequality" may indicate different things.

Inequality is a connection between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The inequalities are :

x + 31 < 1 ⇒ x < - 30 ⇒ x + 3 < -27

|x - 6| ≥ 2  ⇒x- 6 ≥ 2 and 6 - x ≤ 2

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Answer:

269

Step-by-step explanation:

big × square root 05 is Justin Beiber

Answer:

301/8200

Step-by-step explanation:

82 x (X) = 301/100

82x/1 = 301/100

now we cross multiply.

8200x = 301

x = 301/8200

it may be wrong, sorry if it is :(

For the hours is she going to do studying per day is 10 hours.

The Lagrangian method is a mathematical technique used to find the maximum or minimum value of a function subject to constraints. It is used in optimization problems where the objective is to maximize or minimize a function, but there are some constraints that limit the possible values of the inputs.

The Lagrangian method works by combining the objective function and the constraints into a single function, called the Lagrangian, which is then optimized. The Lagrangian is defined as the original objective function minus the product of the constraints and a set of Lagrange multipliers, which represent the trade-off between the objective and the constraints.

To maximize Julie's utility subject to the constraint of 15 hours of waking time, we need to find the optimal level of s (study time) that satisfies the constraint and maximizes the utility function.

We can start by using the Lagrangian method to find the optimal solution. The Lagrangian is given by:

L(s,λ) = S^(1/3)I^(2/3) + λ(15 - s - I)

Where λ is the Lagrange multiplier, representing the marginal rate of substitution between s and I. To find the optimal solution, we need to find the values of s and λ that satisfy the first-order conditions:

∂L/∂s = (1/3)S^(-2/3)I^(2/3) - λ = 0

∂L/∂λ = 15 - s - I = 0

Solving the first-order conditions for s and λ, we get:

s = (15 * (2/3)) / (1 + (2/3)) = 10 hours

I = 15 - s = 5 hours

So, Julie will spend 10 hours per day studying.

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Answer:

The new taxes would be $3300.

Step-by-step explanation:

The assessment value and tax rate determine how much a house will cost in taxes. The amount of taxes would increase if the assessment is raised from $108,000 to $128,000.

To find the new amount of taxes, you need to multiply the increased assessment value by the same tax rate:

$128,000 - $108,000 = $20,000 increase in assessment value

$20,000 * ($2700/$108,000) = $600 increase in taxes

Therefore, the new taxes would be $2700 + $600 = $3300.

Answer:

The table can't be completed as I can't see the table.

However, I can give you the values:

4 Oranges for every 1 Cup of Orange Juice

4, 1

8, 2

12, 3

16, 4

20, 5

Step-by-step explanation:

The amount of money that Yolanda invested in the stock is x = $1600

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

To solve this problem we will only formulate two equations:

(a) The sum of the amount to invest in stocks and bonds will be $6000:

x + y = 6000

(b) The percentage of stocks 6% and bonds 11% for a profit of $580.

0.06x + 0.11y = 580

x + y = 6000 ----⇒ x = 6000 - y

0.06(6000 - y) + 0.11y = 580

360 - 0.06y + 0.11y = 580

0.05y = 220

y = $4400

x = 6000 - 4400

x = $1600

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Answer:

Chair: $2.50

Table: $8.50

Step-by-step explanation:

First, let's create equations with the information given to us:

x= cost of a chair

y= cost of a table

5x + 3y = $38

2x + 12y = $107

The next step is to solve for x in terms of y. To do this, I will be using the equation 5x + 3y = $38.

5x + 3y = $38   [Subtract 3y from both sides]

5x = -3y + 38   [Divide by 5]

x =(-3/5)y + 38/5

Now that we have found the value of x in terms of y, we will plug it into the equation 2x + 12y = $107.

2x + 12y = $107

2 ((-3/5)y + 38/5) + 12y = 107   [Distribute]

(-6/5)y + 76/5 + 12y = 107   [Combine like terms]

(54/5)y + 76/5 = 107   [Subtract 76/5 from both sides]

(54/5)y = 459/5   [Multiply both sides by 5/54]

y = 17/2 or 8.5

So, the cost of a table is $8.50.

Now that we have found the price of the table, let's plug it into the equation  5x + 3y = $38 to find the price of the chair.

5x + 3y = $38

5x + 3 ( 17/2 ) = 38   [Distribute]

5x + 51/2 = 38   [Subtract 51/2 from both sides]

5x = 25/2   [Divide both sides by 5]

x = 5/2 or 2.5

So, the cost of a chair is $2.50.

So, the chair costs $2.50 while the table costs $8.50.

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1. KEA's brand image is centered around affordability, simplicity, and modern design.

2. IKEA has a strong commitment to sustainability, with initiatives that include reducing waste, using sustainable materials in its products, and investing in renewable energy.

3. Sustainability is an increasingly important issue for consumers, and many businesses use it as a marketing tactic to appeal to environmentally-conscious consumers. l IKEA is one such company, and its commitment to sustainability is reflected in its long-term goals and initiatives, as well as its focus on sustainable product design and operations.

The company's "Democratic Design" philosophy reflects this, emphasizing the importance of quality, sustainability, and affordability in its products.

The company has set ambitious goals to become more environmentally friendly, such as producing as much renewable energy as it consumes by 2020 and becoming climate positive (i.e., reducing its net greenhouse gas emissions) by 2030.

In recent years, Gen Z has been a major driving force behind holding retailers accountable for their environmental impact, and IKEA has responded to this by continuing to focus on sustainability and transparency in its operations.

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The smaller of the triangle’s two acute angles is 65 degrees

Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Discover the various sorts of angles and examples of each.

Given:

Angles in a triangle

[tex]sin (4x-5)^\circ= cos (3x+4)^\cir[/tex]

Since, sin [tex]\theta[/tex]= cos(90 - [tex]\theta[/tex]),

cos(90 - (4x - 5 )) = cos(3x +4)

cos(85 - 4x) = cos (3x+4)

Cancel out the cosine functions to have:

85- 4x = 3x+ 4

81 = 7x

x= 11.57

Hence, the smaller of two acute angles is 11.57 degrees

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Answer:

27

Step-by-step explanation:

Answer:

x = ±√13 - 8

Step-by-step explanation:

Move the constant term to the right side of the equation.

x² + 16x + 51 = 0

x² + 16x = -51

We complete the square by taking half of the coefficient, squaring it, and adding it to both sides of the equation. The formula is (b/2)².

x² + 16x = -51

here the formula would be (16/2)² = 64

x² + 16x + 64 = -51 + 64

Now just simplify by factoring the left side and adding up the right side.

(x + 8)² = 13

You have to isolate x to find what it equals. Here start by taking the square root of both sides

x + 8 = √13

Subtract 8 to both sides

x = ±√13 - 8