Consider a home mortgage of 200,000 at six APR of 9% for 20 years. Of the total payment over the term of the loan x% is paid toward the principal and x% is paid toward the interest.

Answer:

Step-by-step explanation:

Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.

Or, if you don’t know SAS congruency, you may use SSS congruency;

Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.

AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.

The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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Answer:

18.4

Step-by-step explanation:

ur welcome

There are 252 different ways to assemble the committee.

Permutation:

A simple definition of permutation is the various ways to arrange some or all of the members in a particular order.

It is the process of orderly disorganisation.

A permutation is what is meant by this.

Combination: Combination is the process of choosing one or more objects from a group of objects so that, unlike permutations, the order in which the objects are chosen is irrelevant.

It describes the combination of N items drawn randomly from a collection of K items at a time.

Hence, There are 252 different ways to assemble the committee.

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Answer:

Step-by-step explanation:

i cant see good

Answer:

I think it would be commutative property

Step-by-step explanation:

the commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The commutative property only works with addition and multiplication.

Answer:

approx 20% of the department faculty have 20 or more years of service

Step-by-step explanation:

To find the percentage of the department faculty with 20 or more years of service, we need to add up the number of faculty members in the "20-24.9" and "25 or more" year categories, since anyone with 20 or more years of service would fall into one of these categories.

Looking at the histogram, we see that there are 24 faculty members in the "20-24.9" year category, and an additional 4 in the "25 or more" year category. Therefore, the total number of faculty members with 20 or more years of service is 24 + 4 = 28.

To calculate the percentage of faculty members with 20 or more years of service, we need to divide this number by the total number of faculty members in the department, which we can find by adding up the heights of all the bars in the histogram. Based on the heights of the bars in the histogram, we can estimate that the total number of faculty members is approximately 140.

Therefore, the percentage of faculty members with 20 or more years of service is:

(28/140) x 100% = 20%

So, approximately 20% of the department faculty have 20 or more years of service.

Answer:

ok, what do you want me to answer?

Step-by-step explanation:

So first of all u going to make sure all the base is the same so it 's easier for u to simplify

and then after that in order to make all the base the same so u need to multiple (x²-4) ...

Answer:

[tex]d^{2}[/tex] - 16.

Step-by-step explanation:

To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.

This means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.

So, (d + 4) (d - 4) can be expanded like this:

Adding all of them together, we get: [tex]d^{2}[/tex] - 4d + 4d - 16, which simplifies to [tex]d^{2}[/tex] - 16.

Therefore, (d + 4)(d - 4) = [tex]d^{2}[/tex] - 16.

Answer:

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

Step-by-step explanation:

To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:

tan(15°) = change in altitude / horizontal distance

We can rearrange this equation to solve for the change in altitude:

change in altitude = horizontal distance x tan(15°)

Substituting the given values, we get:

change in altitude = 2 miles x tan(15°)

We can convert the distance to feet by multiplying by 5280:

change in altitude = 2 miles x 5280 feet/mile x tan(15°)

Using a calculator, we get:

change in altitude ≈ 514.77 feet

Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.

To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.

After the first year, the new premium would be:

R450 + (5% of R450) = R472.50 per month

After the second year, the new premium would be:

R472.50 + (5% of R472.50) = R496.13 per month

To calculate the total amount paid over two years, we can use the following formula:

Total amount paid = (monthly premium x 12 months x number of years)

= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)

= R10,800 + R5,670 + R5,953.56

= R22,423.56

Therefore, you would have paid a total of R22,423.56 over two years.

In descending order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

When a pattern of numbers in mathematics has a decreasing value, the numbers are said to be in descending order. It indicates that the numbers are sorted from highest to lowest. Information is considered to be in descending order if it is arranged from highest to lowest. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are ordered in descending order. In other terms, it is considered to be in descending order if the numbers are listed from greatest to smallest.

The given expression is:

x⁴- x³y⁵+ 4xy - 2x²y³

To arrange in descending order, place the highest value first followed by the smaller value.

Therefore, in decreasing order in terms of y, the expression is -x³y⁵ - 2x²y³ + 4xy + x⁴.

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The percentage of bicyclists that finished the race in less than 56 minutes is 96 %

Percentage is a ratio out of hundred

If in a​ race, 24 out of the 25 bicyclists finished in less than 56 minutes. To find what percent of bicyclists finished the race in less than 56 ​minutes, we first write it in a fraction as number/total

Since

We have that

fraction = number/total

= 24/25

Now to write it as a percentage, we multiply by 100.

So, we have that percentage = fraction × 100 %

So, we have that in percentage = 24/25 × 100 %

= 24 × 4 %

= 96 %

So, the percentage is 96 %

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The correct option is 312 cm² as the area of the composite figure calculated to be equal to 312 square centimeters.

The composite figure can be observed to be made up of two identical triangle and a rectangle, so we shall calculate for the area of one triangle, multiply the result by 2, and add the area to the area of the rectangle to get the total area of the composite figure as follows:

area of one of the triangle = 1/2 × 12 cm × 10 cm

area of one of the triangle = 6 cm × 10 cm

area of one of the triangle = 60 cm²

area of one of the two triangle = 2 × 60 cm²

area of one of the two triangle = 120 cm²

area of the rectangle = 16 cm × 12 cm

area of the rectangle = 192 cm²

total area of the composite figure = 120 cm² + 192 cm²

total area of the composite figure = 312 cm²

Therefore, the area of the composite figure is equal to 312 square centimeters.

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Answer:

3 races

Step-by-step explanation:

(Let t = total number of races)

Each race costs $3.50, so the total cost of racing t times is 3.50 × t or 350t. Douglas wants to have at least $7.75 left on his card, so an inequality to represent this would look like this:

Solving this inequality, we get:

Or we can do this.

Therefore, Douglas can race the go-karts 3 times and still have at least $7.75 left on his card to play arcade games.

Therefore , the solution of the given problem of quadratic equation comes out to be x = 2, -3 + √(5)i, -3 - √(5)i.

Regression modelling uses the polynomial answer x = ax2 + b + c=0 for one-variable equations. The First Proposition of Algebra claims that since this proposition has a second order, there can only be one solution. There are simple and complicated solutions available variable . Even as the name suggests, a "non-linear formula" has four factors. According to this, there might be just one squared term. In the formula ax2 + bx + c = 0

Here,

The provided polynomial equation can be rewritten as follows:

=> x³ + 4x² - 7x - 28 = 0

The constant term in this situation is -28, with components of 1, 2, 4, 7, 14, and 28, and a leading coefficient of 1. Therefore, 1, 2, 4, 7, 14, and 28 are among the polynomial's potential rational solutions.

It is possible to factor the polynomial by discovering that x = 2 is one of its roots.

=> (x - 2)(x² + 6x + 14) = 0

The quadratic formula can be used to calculate the quadratic factor:

=> x = (-6 ± √(6² - 4114)) / (2*1)

=> (-6 ± √(-20)) / 2

=>  -3 ± √(5)i

Thus, the following are the answers to the algebraic equation:

=> x = 2, -3 + √(5)i, -3 - √(5)i.

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Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the account balance after a certain amount of time

P is the principal or initial amount invested

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

Given tha data in the question;

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year.

Substituting these values into the formula solve for accrued amount, we get:

A = P(1 + r/n)^(nt)

A = 1,050(1 + 0.035/6)^(6 × 7)

A = 1,050(1 + 0.005833333333333)⁴²

A = 1,050(1.005833333333333333)⁴²

A = $1,340.55

Therefore, the accrued amount is $1,340.55.

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The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.

The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:

(x - h)²/a² - (y - k)²/b² = 1

Where:

Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:

x² = 4ay.

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Answer: a. To find the earnings per share (EPS), we can use the formula:

P/E ratio = Price per share / Earnings per share

Rearranging this formula to solve for EPS, we get:

Earnings per share = Price per share / P/E ratio

Substituting the given values, we have:

Earnings per share = $53.21/13.26 ≈ $4.01

Therefore, the earnings per share were approximately $4.01.

b. To determine if the stock is overpriced, underpriced, or about right given the historical P/E ratio of 12-14, we can compare the current P/E ratio to this range. Since the current P/E ratio is 13.26, which falls within the historical range, the stock seems to be about right in terms of valuation. However, it's important to note that other factors should also be considered before making any investment decisions.

Step-by-step explanation:

The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

Applying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

From the information given, we know the following:

Triangles AED and CED are right-angled triangles

Thus:

AC = AE + CE

Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.

Length of AE:

AE = [tex]\sqrt{5^2 -4^2}[/tex]

AE= [tex]\sqrt{9}[/tex]

AE= 3

Length of CE:

CE = [tex]\sqrt{7^2 -4^2}[/tex]

CE= [tex]\sqrt{33}[/tex]

CE= 5.7

Length of AC:

AC = AE + CE

Put the values together:

AC = 3 + 5.7

= 8.7cm

Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

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The ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

In mathematics, an ordered pair is a collection of two objects, which are arranged in a specific order. The order of the objects in the pair is important, as the ordered pair (a, b) is different from the ordered pair (b, a) if a and b are not equal.

The two objects in an ordered pair can be anything, such as numbers, variables, or other mathematical entities. The ordered pair (x, y), for example, can represent a point on a two-dimensional coordinate plane, where x represents the horizontal coordinate and y represents the vertical coordinate.

The ordered pair notation is commonly used in set theory and other branches of mathematics to represent relationships between two objects. Ordered pairs can also be used to define functions, where the first object in the pair represents an input to the function, and the second object represents the output.

Here's the completed table and ordered pairs:

Cost of plain rings (x) Cost of initial rings (y) (Ordered Pairs (x,y))

              0                                 4                              (0,4)

               1                                 5                              (1,5)

               2                                 6                              (2,6)

               3                                 7                              (3,7)

               4                                 8                              (4,8)

In each ordered pair, the first number represents the number of plain rings purchased (x) and the second number represents the number of initial rings purchased (y). For example, the ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

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The portfolio depicted as a box-and-whisker plot has a random selection of one stock, with probabilities of 0.51, 0.50, and 0.50.

The probability is frequently described as the ratio of favourable results to all favourable results in the sample. The likelihood of an occurrence P(E) = (The number of favorable events) is how it is stated (Sample space).

Probability is just the possibility that something will happen. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Biostatistics seems to be the analysis of occurrences with a probability distribution.

Given the box plot,

(a)

[tex]P(X < 51) = 0.51[/tex]

(b)

[tex]P(22 < X < 51) = 0.50[/tex]

(c)

[tex]P(X \geq 30) = 0.50[/tex]

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The factored version of the provided polynomial is (6x-1) according to the given assertion.(x-3).

An expression that consists of variables, factors, and exponents and is mixed using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial. (No division operation by a variable).

To factor the polynomial x(6x-1)-3(6x-1), we can first simplify the expression by factoring out the common factor of (6x-1):

x(6x-1)-3(6x-1) = (6x-1)(x-3)

Therefore, the factored form of the given polynomial is (6x-1)(x-3).

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The ratio for 2 quantities of flour and milk is given as follows:

d. 6:4.

The ratio 2 quantities of flour and milk is obtained applying the proportions in the context of the problem.

A proportion is applied as to obtain the ratio between two amounts, you simply divide one amount by the other. The ratio is expressed as a fraction, and can also be expressed as a decimal or a percentage.

The amounts for a single recipe are given as follows:

Hence for two quantities, the amounts are multiplied by two as follows:

Meaning that the ratio is given as follows:

6:4.

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Answer:

2500ml

Step-by-step explanation:

1litre=1000millilitres

2.5=?

=2.5×1000

=2500millilitres

Step-by-step explanation:

f(X)=ax+q

domain: X element of real numbers

The five-number summary of the class, determined by the results of the final test, is:

Minimum = 60

Lower quartile = 71.5.

Median = 85.

Upper Quartile = 94.

Maximum = 98

The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.

The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.

The formula: can be used to determine the lower quartile.

= (Second score + Third score) / 2

= (65 + 78) / 2

= 71.5.

The upper quartile is:

= (Third to last score + Second to last score) / 2

= (93 + 95) / 2

= 94

The median is:

= (5th score + 6th score) / 2

= (82 + 88) / 2

= 85

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In the given diagram, using the tangent theorem, the value of x to the nearest tenth is 16.6

From the question we are to determine the value of x.

From one of the tangent theorems, we have that

The tangent to the circle is perpendicular to the radius of the circle at the point of contact.

Thus, the triangle is a right triangle

From the Pythagorean theorem which states that, in a right triangle, the square of the hypotenuse equals sum of squares of the other two sides.

Then, we can write that

x² = 9² + 14²

x² = 81 + 196

x² = 277

x = √277

x = 16.6433

x ≈ 16.6 (to the nearest tenth)

Hence, the value of x is 16.6

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