a woman decides to purchase a $23,800 car and makes a down payment of $3,500. she arranges to borrow the remainder from a bank that will charge her 4.5% interest. she will make monthly payments for 4 years. a. find her monthly payment amount.

The mean mark of the group would be 8.

Used the concept of mean that states,

Mathematicians find the mean by adding up all the numbers in a data collection, then dividing that total by the number of numbers.

Given that,

There is a group of students who were given a spelling test.

The table shows their marks.

By dividing the total number of students by the sum of each mark's frequency and each mark, you can determine the group's mean grade:

[tex]\text { Mean Mark } = [ (6 \times 5) + (7 \times 4) + (8 \times 7) + (9 \times 10) + (10 \times 4) ] \div30[/tex]

                    [tex]= [ 30 + 28 + 56 + 90 + 40 ] \div 30[/tex]

                    [tex]= 244 \div 30[/tex]

                    [tex]= 8.1333333333...[/tex]

                    [tex]= 8 (\text{ nearest whole number}})[/tex]

Therefore, the value of the mean is 8.

To learn more about the mean visit:

https://brainly.com/question/1136789

#SPJ12

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

sin²x = (sec x - cos x) / sec x is,

sin²x + cos²x = 1

(proved)

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

sin²x = (sec x - cos x) / sec x

We will prove that,

sin²x + cos²x = 1

sec x = 1/cos x

Now,

sec x - cos x

= 1/cos x - cos x

= (1 - cos²x) / cos x

Now,

sin²x = (1 - cos²x) / [(cos x) x 1/cos x]

sin²x = 1 - cos²x

sin²x + cos²x = 1

Proved

Thus,

sin²x = (sec x - cos x) / sec x is,

sin²x + cos²x = 1

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

The value of the expression will be;

⇒ 56.5

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 8.1p + 7.9

And, The values are,

p = 6 and r = 7

Now,

Since, The expression is,

⇒ 8.1p + 7.9

Substitute p = 6, we get;

⇒ 8.1 × 6 + 7.9

⇒ 48.6 + 7.9

⇒ 56.5

Thus, The value of the expression will be;

⇒ 56.5

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

T is the linear transformation described by T(w,z) in L(C2). This indicates that the linear transformation T changes two-dimensional vectors of the type (w,z) to (-z,w).

To get T's eigenvalues, solve the equation T(v) = v, where is the eigenvalue and v is the eigenvector. By solving this equation, we discover that T's eigenvalues are λ1 = -1 and λ2 = 1.

For each eigenvalue, the associated eigenspaces are the subspaces of C2 that are spanned by the eigenvectors of T. The eigenspace is the subspace covered by the eigenvector λ1= -1 is (1,0). The eigenspace is the subspace spanned by the eigenvector λ2= 1 is (0,1).

As a result, the subspaces covered by (1,0) and (1,1) are the generalized eigenspaces corresponding to the different eigenvalues of T. (0,1).

Learn more about eigenvalues here:

https://brainly.com/question/15423383

#SPJ4

Answer:

12x+3

Step-by-step explanation:

distribute the 5 to both the 2x and -1

10x-5

do the same with the the 2. Distribute the 2 to the x and to the 4.

2x+8

10x-5+2x+8

add like terms: the 10x and the 2x are like terms and the -5 and 8 are like terms

12x+3 : the answer

The coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

Point A(6,-6) is reflected over the origin and it’s image is point B

The rule for transformation:

(x, y) --> (-x, -y)

(6, -6)  --> (-6, 6)

Thus, the coordinates of point B is (-6, 6) if the point A(6,-6) is rejected over the origin and it’s image is point B

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

Answer:

3 ,0

Step-by-step explanation:

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field \nabla f whose value at a point p is the "direction and rate of fastest increase". Wikipedia

Answer:

1/3

Step-by-step explanation:

We need two easy-to-read points on grid intersections.

Look at the point on the y-axis. It is (0, 3).

Now go up to the right until you find the next easy-to-read point.

It is (3, 4) which is on a grid intersection.

gradient = run/rise

rise = distance in y (vertical distance)

run = distance in x (horizontal distance)

We start at (0, 3) and go to (4, 4) by going only vertically and horizontally.

From (0, 3), go 1 unit up. That is a rise of 1.

Then go 3 units right. That is a run of 3.

gradient = rise/run = 1/3

Answer: 1/3

The equation of the line that passes through the points (-5,1) and (1,3) is x - 3y = -8

From  the question, we are to determine the equation of the line that passes through the given points.

The given points are (-5, 1) and (1, 3)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Then,

(y - 1) / (x - (-5)) = (3 - 1) / (1 - (-5))

Simplify

(y - 1) / (x + 5) = 2 / (1 + 5)

(y - 1) / (x + 5) = 2 / 6

(y - 1) / (x + 5) = 1/3
Cross multiply

3(y - 1) = 1(x + 5)

3y - 3 = x + 5

x + 5 = 3y -3

x - 3y = -3 - 5

x - 3y = -8

Hence, the equation is x - 3y = -8

Learn more on Equation of a line here: https://brainly.com/question/21967006

#SPJ1

The measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car is 0 or origin.

Terminal ray:

In geometry, terminal ray refers the ray in the terminal position, after the rotation, is called the terminal side of the angle.

Given,

Here we need to find if θ measures 0 radians, then the measure of the angle with an initial ray in the 3 o'clock position and a terminal ray passing through the car.

While we looking into the given question,

the value of θ = 0 radians

And the Slope of terminal ray is calculated by using the formula,

=> tan θ

Then Slope = tan 0

Now, by using radians calculator,

=> tan 0 = 0

Therefore, the slope of the terminal ray is  0 which means the origin of the line.

To know more about Terminal ray here.

https://brainly.com/question/14058033

#SPJ4

A comparison of hot coffee and cold lake is, the heat from the coffee will be absorbed by the cold lake through convection method of heat transfer.

Heat is transferred through the convection, which is basically large-scale movement of molecules inside gases and the liquids. Conduction is basically used to move heat from one of the object to the fluid initially, but fluid motion is all responsible for the bulk of the heat transfer.

Conservation of energy

The principle of conservation of the energy states that the total energy of an isolated system is always in conserved state.

Heat lost by all the hot coffee = Heat absorbed by all the cold lake

Heat transfer process

Heat from the coffee will all be absorbed by the cold lake through convection method of the heat transfer.

Thus, the comparison of hot coffee and the cold lake is, the heat from the coffee will all be absorbed by the cold lake through convection method of the heat transfer.

Learn more about heat transfer, visit :

brainly.com/question/12072129

#SPJ4

The equation for given Parallel & Perpendicular Lines points and slope and given below.

what is parallel and perpendicular lines?

In a plane, parallel lines are those whose distances between them are constant. Parallel lines do not cross. Lines that cross at a right angle of 90 degrees are said to be perpendicular.  

The equation of a line in slope-intercept form y = mx + c

1. substitute x = 0, y = 3 and m = -2 in equation

3 = -2*0 + c

c = 3, substitute in equation

Then y = -2x + 3

2. substitute x = -3 , y = - 5 and m = -( 3/5 ) in equation

-5 =  -( 3/5 )*(-3 ) + c

c = - 34/5 , substitute in equation

Then  5y = -3x - 34

3. substitute x = -8 , y = 6 and m = -(1/4) in equation

6 =  -(1/4)*(-8 )+ c

c = 8, substitute in equation

Then y = -2x + 8

The equation of line passing through two points is m = ( y2 - y1) / ( x2 - x1)

4. The given points is ( 1, 3) and  ( -3, -5) and substitute in above equation.

Then m = 2

substitute m = 2 and ( 1, 3) in equation y = mx + c

Then  c = 1

substitute m = 2 and c = 1 in equation of y = mx + c

Then the equation is y = 2x + 1

5. The given points is ( 1, 4) and  ( 6, -1 ) and substitute in above equation.

Then m = - (5/4)

substitute m = - (5/4) and ( 1, 4) in equation y = mx + c

Then  c = 21/4

substitute  m = - (5/4) and c = 21/4 in equation of y = mx + c

Then the equation is  4y = -5x + 21

6. The given points is ( -12,14)  and  ( 6, -1 ) and substitute in above equation.

Then m = - (5/6)

substitute m = - (5/6) and( -12,14) in equation y = mx + c

Then  c = 4

substitute  m = - (5/6) and  c = 4 in equation of y = mx + c

Then the equation is y = - ( 5/6 ) + 4

To learn more about parallel and perpendicular lines from the given link

https://brainly.com/question/29632338

#SPJ1

The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.

The German economy would be better off if it produced beer and traded motorcycles with the US.

Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).

A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.

To Learn more about similar opportunity cost questions:

https://brainly.com/question/15959659

#SPJ4

The exponential equation of the logarithmic equation ㏑ (x² - 5 · x + 17) = 3 · x + 2 is x² - 5 · x + 17 = e³ˣ ⁺ ².

In this question we find that a logarithmic equation, in which we must eliminate the log operator must be eliminated by relationship between logarithmic and exponential equations, whose relationship is shown below:

Logarithm of an exponential equation

㏒ aˣ = x

Exponential up to an logarithmic equation

[tex]a^{\log x}[/tex] = x

Now, we proceed to eliminate the log operator by algebra properties and relationship between logarithmic and exponential equations:

㏑ (x² - 5 · x + 17) = 3 · x + 2

By using an "exp" operators, we get the following expression:

x² - 5 · x + 17 = e³ˣ ⁺ ²

To learn more on exponential equations: https://brainly.com/question/29506679

#SPJ1

The date that Chris will have both training sessions again is May 9.

In mathematics, a multiple simply means the product of any quantity. It should be noted that a multiple illustrate to the product of a number given.

In this situation, since Christ has bowling training every 8 days and hockey training every 2 days. The lowest common multiple for 2 and 8 is 8.

Therefore, the next date will be the addition of the day of the training and the number of days that are needed when the lowest common multiple was calculated. This will be illustrated thus:

= May 1 + 8 days

= May 9

The next training is May 9.

Learn more about multiples on:

brainly.com/question/26856218

#SPJ1

Answer:  18 cookies

Step-by-step explanation:

27 divided by 1.50 = 18

Answer:

Step-by-step explanation:

6 cookies

Answer: x = 126

Step-by-step explanation:

We know that 50% of 120 is 60. So, to increase 120 by 50%, we add 60. This gets us 180. Next, we find 30% of 180. This is 54. So, we subtract 54 from 180. So, x = 126

Answer:

yes I will get suspicious and then

Step-by-step explanation:

he was in a meeting

The probability that mean blood pressure less than 118 is 0.9938.

We have given that,

blood pressure are normally distributed mean of 116

i.e. μ = 116

standard deviation σ = 4.8

n = 36

and we have to find probability that their mean blood pressure will be less than 118.

The formula to find the above probability is,

P(Z=X) = (x - μ) / (σ/[tex]\sqrt{n}[/tex] )

⇒ P(Z < 118) = (118 - 116) / 4.8/[tex]\sqrt{36}[/tex]

                   = 2 / (4.8/6)

                   = 2/0.8

  P(Z < 118) = 2.5

From the z-table the value of z at 2.5 is 0.9938,

⇒ P(Z < 118) = 0.9938.

Therefore the probability that their mean blood pressure will be less than 118 is 0.09938.

To know more about probability here

https://brainly.com/question/13143657

#SPJ4

The function will have a value of 0 at x = 1. In that case, the variable "k" will have a value of 2.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Given f(x) = 3x³ + kx – 5, and the factor of the given function is (x – 1).

If the factor (x – 1) is zero. Then the value of the function will be zero.

x – 1 = 0

x = 1

At x = 1, the value of the function will be zero. Then the value of the variable 'k' will be calculated as,

f(1) = 3(1)³ + k(1) – 5

0 = 3 + k – 5

k = 5 – 3

k = 2

The function's value will be 0 at x = 1. The variable "k" will then have a value of 2.

To know more about function,

https://brainly.com/question/25808525

#SPJ4

Answer:

µT = 2 (The mean of T is 2)

σT = 1 (The standard deviation of T is 1)

Step-by-step explanation:

This involves the transformation and combination of random variables. We know that the coin flips are independent as the knowledge of one coin flip will not affect the next or another coin flip.

The question has a transformation of H by essentially multiplying it by 4 that, then turns it into T. Knowing that we can multiply the mean of 0.5 by 4 with rules of a linear transformation when multiplying each observation by a positive constant. With that, we get the mean of T to equal 2.

Since we know it is independent, we can solve for standard deviation. To do so, we have to add 0.5 squared 4 times and square root it. That will look like this: Squareroot(0.5^2+0.5^2+0.5^2+0.5^2). That will give you 1 as the standard deviation for T.

The closest distance the family will come to the landmark while on the road is 12.03 miles.

Here, the situation represented in the question can be depicted as shown in the image below.

The family moves from F1 to F2 as the angle changes from 62 to 38.

Now, using trigonometric ratios in the smaller triangle we have-

Cot 62 = X/Y

X = Y Cot 62

Similarly, Cot 38 = (X + 9)/ Y

Substituting the value of X in the above equation we get-

Y Cot 38 = (Y Cot 62 + 9)

Y Cot 38 - Y Cot 62  = 9

Y(Cot 38 - Cot 62) = 9

Y = 9/ (Cot 38 - Cot 62)

Y = 9/ (1.2799 - 0.5317)

Y = 9/ 0.7482

Y = 12.028

Thus, the closest distance the family will come to the landmark while on the road is 12.03 miles.

Learn more about trigonometry here-

https://brainly.com/question/7331447

#SPJ4

The number of customers Alejandro will need in order to break even is 38 customers.

Given data:

Cost of business = 48 x + 500

Income = R = 65 x - 145

Let x is the number of customers.

Income equation  

R= 65x- 145

Substitute 48x + 500  for y

48x + 500 = 65x -145

Substract 48x from both side

500 = 17x - 145

Add 145 to each side

645 = 17x

Divide both side by 17x

x =645 /17

x = 37.9

x = 38 customers (Approximately)

Therefore the number of customers is 38 customers.

Learn more about break even here

brainly.com/question/21137380

#SPJ1

The value x in the equation h(x) = 4x-4 is, x =1

Polynomial functions are functions of a single independent variable.

To solve for x

Since h(x) =0

substitute h(x) into equation  

h(x) = 4x - 4

0=4x - 4

Add 4 to both sides

4x = 4

Divide both side by 4

4x/4 = 4/4

x = 1

therefore, the value of X= 1

Learn more about polynomial here; https://brainly.com/question/2833285

#SPJ1

The sampling distribution is t= 88 degrees of freedom.

To find the sampling distribution of the sample mean difference we need to do a two-sample t-test: equal variances.

When we do a two-sample t-test, we have to take into account the following assumptions:

1) the sample variances are normal.

2) the sample variances of both populations are equal.

Now, let the sample size be [tex]n_x[/tex] and [tex]n_y[/tex] respectively and the means be [tex]x^-[/tex] and [tex]y^-[/tex] respectively.

Now, we are assuming that the distribution of x and y are

[tex]x\sim N([/tex]mewx, [tex]\sigma x = \sigma[/tex])

[tex]y\sim N[/tex] (mewy, [tex]\sigma y = \sigma[/tex])

Accordingly, the system of hypothesis is defined by:

Null hypothesis: mewx=mewy

alternatively, it can also be mewx≠ mewy

Then, the random  sample t is distributed as [tex]t\sim t_n_x+ny-2[/tex] with the degrees of freedom given as df= [tex]n_x+n_y-2[/tex] =40+50-2= 88

So, in this case answer will be 88 degrees of freedom.

To know more about sampling distribution: https://brainly.com/question/14090787

#SPJ4

Plants C and D have the same ratios of green bottles to total bottles recycled.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The table is given in the question,

As per the given question, the required solution would be as:

For plant A,

The ratio of green bottles to total bottles

⇒ 16/172 = 4/43

For plant B,

The ratio of green bottles to total bottles

⇒ 12/135 = 4/45

For plant C,

The ratio of green bottles to total bottles

⇒ 14/154 = 1/11

For plant D,

The ratio of green bottles to total bottles

⇒ 18/198 = 1/11

Thus, plants C and D have the same ratios of green bottles to total bottles recycled.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ1

I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.

What is subset regression model?

Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.

There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.

To know more about subset regression model,

brainly.com/question/19920754

#SPJ4

[tex]\frac{2x+3}{3}[/tex]

-3 + x - [tex]\frac{1}{3}[/tex]x + 4

-3 + x + [tex]\frac{-x}{3}[/tex] + 4

-3 + x + [tex]\frac{-x}{3}[/tex] + 4

1 + x + [tex]\frac{-x}{3}[/tex]

1 + x + [tex]\frac{-x}{3}[/tex]

[tex]\frac{3}{3}[/tex] + [tex]\frac{3x}{3}[/tex] + [tex]\frac{-x}{3}[/tex]

[tex]\frac{3}{3}[/tex] + [tex]\frac{3x}{3}[/tex] +[tex]\frac{-x}{3}[/tex]

[tex]\frac{3 + 3x - x}{3}[/tex]

[tex]\frac{3 + 3x - x}{3}[/tex]

[tex]\frac{3 + 2x}{3}[/tex]

[tex]\frac{3 + 2x}{3}[/tex]

[tex]\frac{2x+3}{3}[/tex]

[tex]\frac{2x+3}{3}[/tex]

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The simplified version of the expression (x¹/² y¹/⁹)³ is (x³/² y¹/³)

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

(x^1/2 y^1/9 )^3

Rewrite the expression properly

So, we have

(x¹/² y¹/⁹)³

Open the brackets

This gives

(x¹/² y¹/⁹)³ = (x¹/²)³ * (y¹/⁹)³

Evaluate the expression in brackets

(x¹/² y¹/⁹)³ =(x³/² y¹/³)

Hence, the solution is (x³/² y¹/³)

Read more about expressions at

https://brainly.com/question/4344214

#SPJ1