5. How much interest will you pay for a $198.000 mortgage if you finance the home

for 30 years at 4% interest (Use a mortgage calculator)

$1, 141

The probability that a randomly selected label produced by the company will contain a defective compact disk is 0.034.

In this, it should be noted that there are 3 possible cases in the chosen disc can be from any of the manufacturing companies, so the total probability will be the sum of probabilities of getting a faulty disc from companies 1-3.

The probability from company 1 will be;

= 0.03*0.36

The probability from company 2 will be:

= 0.04*0.52

The probability from company 3 will be:

= 0.02*0.12

The total probability will now be:= (0.36*0.03)+(0.04*0.52)+(0.02*0.12)

= 0.0108 + 0.0208 + 0.0024

= 0.034

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Answer:    (0.5, 1)

Step-by-step explanation:

Hope this helped

Answer:

\( \huge{ \boxed{ \sf{ ( \: \frac{1}{2} \: , \: 1})}}\)

Step-by-step explanation:

\( \star { \sf{ \: Let \: the \: points \: be \: A \: and \: B}}\)

\( \star{ \sf{Let \: A \: (-4,-1) \: be \: (x1 \:, y1) \: and \: B \: ( \: 5 \:, 3 \: ) \: be \: (x2 \:, y2) }}\)

\( \boxed{ \underline{ \sf{ \: Midpoint = \: ( \: \frac{x1 + x2}{2} \:, \frac{y1 + y2}{2})} }}\)

\( \mapsto{ \sf{Midpoint = ( \frac{ - 4 + 5}{2}} \: ,\frac{ - 1 + 3}{2} }) \)

\( \underline{ \sf{Rmember}}\)!

\( \sf{Midpoint = ( \frac{ 1}{2} \:, \frac{2}{2}} )\)

\( \sf{Midpoint = ( \: \frac{1}{2 }, \: 1)}\)

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

After answering the provided question, we can conclude that the average (arithmetic mean) of 2x and 2y is 48.

The mean of a dataset is the sum of all values divided by the total number of values; this is also known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the total number of values in the dataset by the sum of those values yields this result. Calculations can be performed using both raw data and data that has been combined into frequency tables. The average of a number is referred to as its average. It is simple to calculate: Divide the total number of digits by the number of digits. the total divided by the count.

The average (arithmetic mean) of 2x and 2y is 48.

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Answer:

5/6

Step-by-step explanation:

The slope of a perpendicular line is the negative reciprocal of the other.

Given: m = -6/5

Negative: m = 6/5

Reciprocal: m = 5/6

Answer:

a. The correct option is f(x) = 3x + 65.

b. Sasha earns 146 that day.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.

The explanation to the answer is now given as follows:

a. Choose the linear function f to determine Sasha's pay.

Note: See the attached excel file to see the determination of the correct linear function f to determine Sasha's pay.

From the list of linear functions f given in the question, x represents the number of T-shirts Sasha sold in one day.

Therefore, the correct linear function f to determine Sasha's pay can be determined by simply substituting number of T-shirts for x in each of the linear function f to see which one is the same as the table provided in the question.

From the attached excel file, the correct option is f(x) = 3x + 65. This is indicated in bold red color in the attached excel file.

b. If Sasha sells 27 T-shirts in one day how much money does she earn that day?

This can be calculated using f(x) = 3x + 65 which is the correct linear function f determined in part a above and substituting 27 for x as follows:

Sasha’s earning = 3(27) + 65

Sasha’s earning = (3 * 27) + 65

Sasha’s earning = 81 + 65

Sasha’s earning = 146

Therefore, Sasha earns 146 that day.

Answer:

f(x) = 3x + 65

Step-by-step explanation:

The vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

To find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7, we first need to find the direction vector of the line of intersection.

We can find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the plane 2x - 3y + 5z = 2 is <2, -3, 5>, and the normal vector of the plane 4x + y - 3z = 7 is <4, 1, -3>. Taking the cross product of these two vectors, we get:

<2, -3, 5> × <4, 1, -3> = <-16, 22, 11>

This vector <-16, 22, 11> is the direction vector of the line of intersection of the two planes.

To find a vector parallel to this line, we can simply multiply the direction vector by a scalar. For example, we can choose a scalar of 2 to get:

2<-16, 22, 11> = <-32, 44, 22>

Therefore, the vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

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The model could be improved by using a step function.

The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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No, 4, 8, and 12 are not valid side lengths for a triangle. So 4, 8 and 12 does not make a triangle.

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

If a triangle has sides of length 4, 8, and 12, then the triangle inequality theorem would be:

8 + 12 > 4 (true, as 8+12 =20)

12 + 4 > 8 (true, as 4+12=16)

4 + 8 > 12 (false, as 4+8 =12)

Since 4 + 8 = 12, and 12 is not greater than 4 or 8, a triangle cannot be formed with sides of length 4, 8, and 12.

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Value if p is $16 which maximizes the total revenue.

We need to first find the total revenue equation and then maximize it. Here are the steps:

Step 1: Write the demand equation.
x = 960 - 30p

Step 2: Write the total revenue equation.
Total Revenue (R) = price (p) × quantity (x)
R = px

Step 3: Substitute the demand equation into the total revenue equation.
R = p(960 - 30p)

Step 4: Simplify the total revenue equation.
R = 960p - 30p²

Step 5: Differentiate the total revenue equation with respect to p.
dR/dp = 960 - 60p

Step 6: Set the derivative equal to zero to find the critical points.
0 = 960 - 60p

Step 7: Solve for p.
60p = 960
p = 960/60
p = 16

So, the value of p that maximizes the total revenue is $16.

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Answer:

416

Step-by-step explanation:

Answer:

£500

Step-by-step explanation:

The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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Answer:

D) 9:00 am

Step-by-step explanation:

Because 9:00 is the midpoint of 7 and 12

Step-by-step explanation:

you earned $43.88 for 6.5 hours of work.

an hourly rate means how much money you get for 1 hour of work.

to get that we need to divide now both by 6.5, as 6.5/6.5 = 1 hour.

and

43.88/6.5 = $6.750769231... per hour ≈ $6.75/ hour

The ordered pairs for the equation is ( 0 , 0.5 ) and ( 1 , 0 )

Given data ,

Let the equation be represented as A

Now , the value of A is

-3x - 6y = -3

To generate two ordered pairs by substituting zero for x and y, we can substitute x = 0 and y = 0 into the given equation -3x - 6y = -3 and solve for y.

For x = 0:

-3(0) - 6y = -3

0 - 6y = -3

-6y = -3

y = -3 / -6

y = 0.5

So the first ordered pair is (0, 0.5)

For y = 0:

-3x - 6(0) = -3

-3x - 0 = -3

-3x = -3

x = -3 / -3

x = 1

So the second ordered pair is (1, 0)

The rate of change is the change in y-coordinate divided by the change in x-coordinate.

In this case, as we move from the first ordered pair (0, 0.5) to the second ordered pair (1, 0), the change in y-coordinate is -0.5 and the change in x-coordinate is 1.

Therefore, the rate of change is -0.5 / 1 = -0.5.

Hence , the ordered pairs are ( 0 , 0.5 ) and ( 1 , 0 )

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Point estimate from the sample is 0.985, margin error is 0.003.

Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.

(a) To calculate point estimate or sample mean :

Point estimate is the mid point of the confidence interval.

Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.

Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985

(b) Margin error is the one half of the total width of the interval.

Margin error = (0.988 - 0.982) / 2 = 0.003

(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.

Hence the point estimate and margin error are 0.985 and 0.003 respectively.

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Answer:

a. $1669

Step-by-step explanation:

Price in 1994 = [ (CPI in 1994) / (CPI 1973) ] * (Price in 1973) =

[ 148.2 / 44.4 ] * 500 =  1668.91891892 = $1669 rounded to the nearest dollar.

The largest area is found to be 8702.5 \(ft^{2}\).

We know that area of rectangle

A = xy ........ (1)

Perimeter of rectangle (given) = 590 ft

Using x and y as two variables ;

5x + 2y = 590

solve yb in term of x

y = -5/2 x + 295......(2)

Now we will get area only in one variable from (1) and (2)

A = x ((-5/2)x + 295)

A = -5/2 \(x^{2}\) + 295x

differentiate it with respect gto x

A' = -5x + 295........ (3)

find the critical point to get your minima and maxima value.

Put A' = 0,  x = 295/5 = 59

x = 59

then , from (2)

y= (-5/2 × 59) + 295 = 147.5

y = 147.5

again differentiate (3)

A'' = -5 < 0. i.e critical point x = 59 is point of maxima.

So, maximum area = 59 × 147.5

Largest area = 8702.5 \(ft^{2}\)

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The problem asks for number of biscuits, packages of pemmican, and packages of butter and cocoa that a person needs each day, based on percentage of total daily calories. We need to calculate the quantities.

To determine the number of biscuits, packages of pemmican, and packages of butter and cocoa needed, we require additional information, such as the calorie content of each item and the total daily calorie requirement for an individual.Once we have the calorie content of each item and the total daily calorie requirement, we can calculate the percentage of calories provided by each item. From there, we can divide the total daily calorie requirement by the percentage of calories provided by each item to find the quantity needed.

Without the specific calorie content and total daily calorie requirement, it is not possible to provide a precise answer. It is important to know the specific values to accurately determine the quantities of biscuits, packages of pemmican, and packages of butter and cocoa needed for an individual's daily intake.

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When we say that the tails of the normal curve are asymptotic to the x axis, it mean the tails get closer and closer to the x axis but never touch it

The tails of normal curve are actually asymptotic. To say they are asymptotic, then it means that they approach the x axis but never quite meet its horizons.

These tails will extends indefinitely in both directions without crossing and touching the x axis or the horizontal axis.

Tails of normal curve or normal curve itself is asymptotic to the x-axis. That is the curve touches the x-axis only at -∞ and +∞. So the curve only approaches nearer and nearer to x-axis but never touches or crosses it.

For this reason, the correct choice is get closer and closer to the x-axis but never touches it.

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Answer:

It’s true

Step-by-step explanation:

Proof by induction

Let the four chosen numbers be x_1, … x_4 and, without loss of generality, let x_1 < x_2, … < x_4.

For x_1 = 1, the smallest possible choice, let x_2 = x_1 + 20 = 21 be the smallest possible choice that has a difference larger than 19. Likewise, x_3 = x_2 + 20 = x_1 + 40 = 41. Then x_4 has to be at least x_3 + 20 = x_1 + 60 = 61 which is out of range.

For the induction, suppose that x_4(n) = x_1(n) + 60 > 60 and therefore x_4(n) can’t be chosen for a given x_1(n). Then incrementing x_1(n+1) = x_1(n) + 1 would require x_4(n+1) to be at least x_1(n) + 1 + 60 = x_4(n) + 1 > 61, so this is out of range as well.

For another induction, suppose that x_4(n) = x_2(n) + 40 > 60 and therefore x_4(n) can’t be chosen for a given x_2(n). Then incrementing x_2(n+1) = x_2(n) + 1 would require x_4(n+1) to be at least x_2(n+1) + 40 = x_4(n) + 1 > 61, so this is out of range as well.

Likewise, for the induction, suppose that x_4(n) = x_3(n) + 20 > 60 and therefore x_4(n) can’t be chosen for a given x_3(n). Then incrementing x_3(n+1) = x_3(n) + 1 would require x_4(n+1) to be at least x_3(n+1) + 20 = x_4(n) + 1 > 61, so this is out of range as well.

Therefore all choices of x_1, x_2, x_3 with differences greater than 19 leaves no choice of x_4 within range with x_4 > x_3 + 19.

Given:

Consider the completer question is "Find the derivative \(\dfrac{dy}{dx}\) for \(y=\dfrac{x^2-4x}{x^3-5}\)."

To find:

The derivative \(\dfrac{dy}{dx}\).

Solution:

Chain rule: \(\dfrac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)\)

Quotient rule: \(\dfrac{d}{dx}\dfrac{f(x)}{g(x)}=\dfrac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}\)

We have,

\(y=\dfrac{x^2-4x}{x^3-5}\)

Differentiate with respect to x.

\(\dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{x^2-4x}{x^3-5}\right)\)

Using chain rule and quotient rule, we get

\(\dfrac{dy}{dx}=\dfrac{(x^3-5)\dfrac{d}{dx}(x^2-4x)-(x^2-4x)\dfrac{d}{dx}(x^3-5)}{(x^3-5)^2}\)

\(\dfrac{dy}{dx}=\dfrac{(x^3-5)(2x-4)-(x^2-4x)(3x^2)}{(x^3-5)^2}\)

\(\dfrac{dy}{dx}=\dfrac{2x^4-4x^3-10x+20-3x^4+12x^3}{(x^3-5)^2}\)

\(\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}\)

Therefore, the required answer is \(\dfrac{dy}{dx}=\dfrac{-x^4+8x^3-10x+20}{(x^3-5)^2}\).

Answer: 148.5

Step-by-step explanation:

To find the area of this shape, comprised of a rectangle and a triangle, we can find the area of each shape and add them together.

The area of a triangle is 12⋅b⋅h. We are given the triangle's height, 13. The base of the triangle will be the same as the width of the rectangle, which we also know: 11. Now we can calculate the area of the triangle:

A = 1/2⋅b⋅h

A = 12⋅11⋅13

A = 71.5

Now we can find the area of the rectangle, which is l⋅w. The width of the rectangle is 11, which is the same as the base of the triangle; the length is 7:

A =l⋅w

A = 7⋅11

A = 77

Finally, we can add together the area of the triangle and the rectangle to find the total area:

A = 71.5 + 77 = 148.5

The total area of the front of a house will be 148.5.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A rectangle has a width = 11

The triangle's height = 13

The rectangle's height = 7

Now,

Since, The base of the triangle will be the same as the width of the rectangle.

Hence, The area of rectangle = 7 x 11

                                              = 77

And, The area of triangle = 1/2 x 11 x 13

                                      = 71.5

Thus, The total area of the front of a house = 77 + 71.5

                                                                  = 148.5

Therefore, The total area of the front of a house will be 148.5.

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the function y = f(x) that satisfies the given conditions is y = 2x^3 - x^2 - 5x + C2, where C2 is a constant that can take any real value.

First, integrate y' with respect to x to find the first derivative y:

∫(y') dx = ∫(12x - 2) dx

y = 6x^2 - 2x + C1

Next, integrate y with respect to x to find the function f(x):

∫y dx = ∫(6x^2 - 2x + C1) dx

f(x) = 2x^3 - x^2 + C1x + C2

To determine the specific values of C1 and C2, we use the given condition that the line y = -x + 5 is tangent to the graph at x = 1.

Since the tangent line has the same slope as the function f(x) at x = 1, we can equate their derivatives:

f'(1) = -1

Taking the derivative of f(x), we have:

f'(x) = 6x^2 - 2x + C1

Substituting x = 1 and equating f'(1) to -1, we can solve for C1:

6(1)^2 - 2(1) + C1 = -1

6 - 2 + C1 = -1

C1 = -5

Now we have the values of C1 and C2. Plugging them back into the equation for f(x), we obtain the final function:

f(x) = 2x^3 - x^2 - 5x + C2

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Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

Given that;

First, we determine the mark price.

Since the Furniture Store marks up all furniture by 45%.

Mark up price = mark up × purchase price

Mark up price = 45% × $113.00

Mark up price = 0.45 × $113.00

Mark up price = $50.85

Now, the selling price will be;

Selling price = Purchase price + mark up price

Selling price = $113.00 + $50.85

Selling price = $163.85

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

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Answer:

SSS

Step-by-step explanation:

I think it would be SSS (side, side, side)... let me know if I'm wrong and I'll try again:)

Check out the diagram below. I've marked the angles and sides that are congruent. Notice how the marked sides are not between the marked angles for either triangle. So we're dealing with AAS instead of ASA. The order is important. If we wanted to use ASA, then we would have to know DE = TU, both of those sides are between the marked angles.

In this problem, we are given a variable resistor R and an 8-Ω resistor in parallel. We are asked to find the rate at which the resistance R is changing when it is equal to 6.0 Ω.

Given that RT = 8R / (8 + R), we can differentiate this equation with respect to time t using the quotient rule. Let's denote dR/dt as the rate of change of R with respect to time. Applying the quotient rule, we have:

dRT/dt = \([ (8)(dR/dt)(8 + R) - (8R)(dR/dt) ] / (8 + R)^2\)

To find the rate at which R is changing when R = 6.0 Ω, we substitute R = 6.0 into the above equation:

dRT/dt = \([ (8)(dR/dt)(8 + 6.0) - (8)(6.0)(dR/dt) ] / (8 + 6.0)^2\)

Simplifying further, we have:

dRT/dt = \([ (8)(dR/dt)(14) - (48)(dR/dt) ] / (14)^2\)

dRT/dt = (112(dR/dt) - 48(dR/dt)) / 196

dRT/dt = 64(dR/dt) / 196

dRT/dt = 16(dR/dt) / 49

Therefore, the rate at which R is changing when R = 6.0 Ω is equal to 16/49 times the rate of change of RT.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation: