You need a $12,000 loan to buy a good used car. Your bank offers a 3-year loan with an APR of 5% and a 5-year loan with an APR of 8%. Find the monthly payment and total interest paid for each loan option. Which would you choose? What is the better deal?

Answer:

C.

Step-by-step explanation:

Restrictions that limit the settings of the decision variables. Therefore, option C is the correct answer.

Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.

Constraints are conditions or restrictions imposed on a system in order to ensure that it functions properly. In linear programming, constraints are used to limit the settings of the decision variables in order to ensure that the model's objective is met. For example, a constraint might be that the sum of two decision variables must equal a certain value. The constraints help to ensure that the solution obtained from the model is feasible and meets the objectives of the problem.

Therefore, option C is the correct answer.

Learn more about the linear programming here:

https://brainly.com/question/30763902.

#SPJ2

Answer:

Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.

In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.

This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

SinA cosA = sin2A / 2 is the formula for sinA and cosA. This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

Let LHS =

\(\frac{tan A}{1+ tan^{2} A} + \frac{cot A}{1+ cot^{2} A}\)

= \(\frac{tan A}{(sec^{2}A) ^{2} } +\frac{cot A}{(cosec^{2}A) ^{2} }\)

= \(\frac{\frac{sin A}{cos A} }{\frac{1}{cos^{4}A } } + \frac{\frac{cos A}{sin A} }{\frac{1}{sin^{4}A } }\)

= \(sin A cos^{3} A + cos A sin^{3}A\)

= \(sin A cos A (sin^{2}A + cos^{2}A)\)

= \(sin A cos A\) = R.H.S

Hence proved  as L.H.S= R.H.S

To learn more about SinA cosA refer to:

brainly.com/question/14302298

#SPJ1

The complete question is:

Prove that (tan A)/((1 + tan2 A) 2) + (cot A)/((1 + cot2 A) 2) for cotA  = sinA cosA.

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

For such more question on equation:

https://brainly.com/question/17145398

#SPJ8

Answer:

ddfadf

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

18 divided by 2/3

its wat the guy adove me said

The solution is: transformations have been performed on the graph of f(x)= 3√x to obtain the graph of g(x) = -2 3√x - 1 are:

translate the graph down

reflect the graph over the x-axis

stretch the graph away from the x-axis

We assume your function is intended to be ...

g(x) = -2 3√x - 1

The coefficient -2 does two things. Because it is negative, it causes the graph to be reflected across the x-axis. Because it is greater than 1, it causes the graph to be stretched away from the x-axis.

The added constant of -1 causes each y-value to be lower than it was, so translates the graph down 1 unit.

learn more on function:

brainly.com/question/2412552

#SPJ1

The domain and the range of the function represented by the graph are [-2, 2) and (-4, 4]

In mathematics, the domain and range of a function are used to describe the set of possible input and output values of the function, respectively.

From the graph, we have the set of input values to be

Input = From -2 (closed circle) to 2 (open circle)

This means that the domain is

[-2, 2)

From the graph, we have the set of output values to be

Output = From -4 (open circle) to 4 (closed circle)

This means that the range is

(-4, 4]

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer:

0.56

Step-by-step explanation:

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:

y = -3x -12

Step-by-step explanation:

Just solve for y, and you should get the equation is slope intercept form

Hopefully this helps- let me know if you have any questions

Answer:

-3. is a slope intercept.

Step-by-step explanation:

-3x - y=12

-3x-12=y

y=-3x-12

comparing above equation with y =mx+c

we get

m=-3

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

For similar question on angles.

https://brainly.com/question/25770607  

#SPJ8

Answer:

the second one is 504 that is all I know sorry

Answer:

#1      45√ 5      

#2  504

#3  X1=-15, X2=1

Step-by-step explanation:

9 √5^2 x 5

9 √5^2  √5

9 x 5 √5

45 √5

Answer: 71.57

Step-by-step explanation:

You are going to use SOH CAH TOA to find the angle

because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)

TanΘ=\(\frac{9}{3}\)

now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)

71.57

When AR = AQ, Isosceles triangle is formed, hence the base angels are equal. m< ARQ = m< AQR.

Hence if:

 then m< RAT = m<RAT by SAS theorem

Triangles are said to be congruent when the 3 sides and the 3 angles equal in accordance to the triangle congruency theorem

Some of the rules/theorem include

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two triangles being compared should have their two sides and the included angle being equal

the sides and angle used here include

The angle is said to be included when it is between the two equal sides

Learn more about angles here:

https://brainly.com/question/29393764

https://brainly.com/question/29349045

#SPJ1

Q.12 The polynomials are 2 and 3

What is polynomial ?

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.

Given, p(x) = -x² + x + 2

p has a degree 2

Let, a = 1 + i√2

      b = 1 - i√2

a + b = 1 + i√2 + 1 - i√2

        = 2

a * b = (1 + i√2) * (1 - i√2 )

        = 1 - (i√2)²

        = 1 - i²*2    (where, i² = -1)

        = 1 + 2

        = 3

Therefore, the polynomial are 2 and 3

Q.13 The polynomial is x³ + x

Given, Q(x) = x³ - 2x² - 1

Q has a degree of 3

=>(x - 0) (x - i) (x + i)

=>(x² - ix) (x + i)

=>x³ + x²i - ix² - i²x    (where i² = -1)

=>x³ + x

Therefore, the polynomial is x³ + x

To read more about Polynomial.

https://brainly.com/question/25870256

#SPJ13

Answer:

i) -2.5

ii) 3/4 - 0.250

iii) 0.282

iv) 85% - 0.850

v) \(\sqrt{3\\\) - 1.7320

Answer: Please give me more information, I am sorry :(

Step-by-step explanation: Please give me more information, I am sorry :(

( But I think is the length of the prism is 2cm ......)

Answer:

Step-by-step explanation:

The length of the prism is 2cm

Hope this helps!

Answer: 10

Step-by-step explanation:

2+4+4= 10

Answer:

CE would be half of AD.

Step-by-step explanation:

A, E and D are all points on the circumference of the circle.  

AD is the diameter.  

CE is the radius.  

CE would be half of AD.

Answer:

b

Step-by-step explanation:

did the math?

8 is the best estimate of \(8\frac{1}{8}\).

In simple words, the ratio of the two numbers is called a fraction.

Mixed fraction is a form of a fraction which is defined as the ones having a fraction and a whole number.

For example, 2 (1/3) is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Step 1: Multiply the denominator with the whole number,

i.e. Multiply 8 with 8 in the given example, 8(1/8).

                                            8× 8  =64

Step 2: Add the numerator of the Fraction to the result in step 1. i.e.,             Add                                      1+ 64=65.

Step 3: Keep the Denominator same i.e. 8.

Step 4: The Improper fraction obtained is: 65/8.

Given number can be denoted as 8+\(\frac{1}{8}\) = 8+0.15 = 8.15

So the number is nearest to 8 itself.

i.e. 8 is the best estimate.

To know more about fractions visit:

https://brainly.com/question/10354322

#SPJ1

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

For more such questions on exponent.

https://brainly.com/question/13669161

#SPJ8

Part A: We can complete the model representing Sage's minutes by putting n and 7 in the box.

Part B: We can complete the model representing Tom's minutes by putting n and 7 in the box

Part C: An algebraic expression to represent the number of minutes Sage has left is S = n - 7, where S equals the remaining talk minutes for Sage and n is the initial number of talk minutes.

Part D. An algebraic expression to represent the number of minutes Tom has left is T = n - 7, where T equals the remaining talk minutes for Tom and n is the initial number of talk minutes.

Part E: Sage and Tom have the same number of talk minutes left on their cell phone plans because they started with the same amount and consumed the same amount at the end of the month.

An algebraic expression is a mathematical expression that consists of variables and constants, along with algebraic operations and equality or inequality symbols.

The basic algebraic operations include addition, subtraction, division, and multiplication.

Thus, algebraic expressions can be used to mathematically model or represent the number of minutes that Sage and Tom have left.

Learn more about algebraic expressions at https://brainly.com/question/4344214

#SPJ1

Answer:

N = -7

Step-by-step explanation:

4 = 1 - n -4

Subtract the numbers first

1 - 4 = -3

Then rearrange the terms

4 = -3 - n

-----> 4 = n - -3

The you add 3 to both sides of the equations

4 + 3 = -n - 3 + 3

Answer:

10.2% chance

Step-by-step explanation:

There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.

So we can write it:

\(\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}\) =  \(\frac{11880}{116,280}\) = .102 or 10.2% chance

For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.

12 * 11 * 10 * 9 = 11880

20 * 19 * 18 * 17 = 116,280

We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.

Answer:

10.2% probability

Step-by-step explanation:

12 peaches

8 bananas

Chance of getting a peach the first time is 12/20 the second time is 11/19, third 10/18, and fourth 9/17

11880/116280 = .1022 = 10.2% probability

The probability of the customer wants to take snack B is 144/320 as they have already taken snack A

and the probability of the customer who has not taken snack A before

wants to take snack A =108/252

It is the ratio of favorable outcome to total possible outcome of an event.

based on given data, we calculated the number of customers who has taken snack A before may want to take snack B. The customers have not taken snack A yet may want to snack A.

hence, probability to take snack B = 144/320

probability to take A =108/252

to learn more about probability visit:

https://brainly.com/question/30015100

#SPJ1

a) The probability a person who has eaten snack A before is 59/143.

b) The probability a person who has eaten snack A before is 84/143

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the total number of people that are taken for the event is 572.

The number of people who have eaten snack A before is 236.

The number of people who have not eaten snack A before is 336.

Probability = The number of outcomes of favorable event/ Total number of outcomes

The probability getting a person who has eaten snack A before is

= 236/ 572

= 59/143 [Divide denominator and numerator by 4]

The probability getting a person who has not eaten snack A before is

= 336/ 572

= 84/143 [Divide denominator and numerator by 4]

To learn more about event, click on below link:

https://brainly.com/question/3813651

#SPJ1

Answer:

yes, the laptop would cost  1000 AED

Step-by-step explanation:

2500 dived by 2/5 + 1000