a) Find the monthly payment needed to repay a $40,000 loan over 20 years, given that, as usual, the first repayment is made at the end of the first month, and the last at the end of the 240th. The interest rate is 0.5% per month.
b) Another $40,000 loan is repaid monthly, also over 20 years in a similar fashion. The monthly payment is $544.53. Find the monthly interest rate.

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.

In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.

Here we have

The mean price for liquid crystal display (LCD) computer monitors is $ 170  and the standard deviation is $ 53.  

Find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ

where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.

z = (180 - 170) / 53

z = 0.189

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.  

To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.

The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.

Now we need to find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ/√n

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

z = (180 - 170) / (53 / √9)

z = 1.13

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.  

To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:

z = (x - μ) / σ/√n

z = (180 - 170) / (53 / √36)

z = 3.02

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.

Therefore,

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

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Answer: A. Segment CD only

Step-by-step explanation:

Perpendicular lines form 90 degree angles. The only segment that creates a 90 degree angle is CD. And we know this due to the little box that represents 90 degrees.

The direction the plane flew is 14.6 degrees North of East.

So, the final answer is:

Distance = 342 miles

Direction = 14.6 degrees North of East

The distance the plane flew can be found using the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c^2 = a^2 + b^2. In this case, the distance east (331 miles) is one side of the triangle and the distance north (86 miles) is the other side.

So, we can plug in the values and solve for c:

c^2 = 331^2 + 86^2

c^2 = 109561 + 7396

c^2 = 116957

c = √116957

c = 342 miles

Therefore, the distance the plane flew is 342 miles.

To find the direction, we can use trigonometry. The direction is the angle between the east-west line and the line connecting the starting point and the landing point. We can use the tangent function to find this angle:

tan θ = opposite/adjacent

tan θ = 86/331

θ = tan^-1(86/331)

θ = 14.6 degrees

Therefore, the direction the plane flew is 14.6 degrees North of East.

So, the final answer is:

Distance = 342 miles

Direction = 14.6 degrees North of East

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The total yards gained by Jordan's team is 4.

What is Expression ?

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

On first day, Jordan's football team gained 12 yards.

On second day, Jordan's football team lost 8 yards.

So, The total yards(net) would be :

= total yards gained by team - total yards lost by team

=  12 - 8

= 4 yards.

Here, total yards gained by team is the first expression while total yards lost by team is the second expression.

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Plot the coordinates on the graph to obtain the graph of the system of inequalities.

As Math World correctly notes, to solve a system of linear equations by graphing, we simply graph both equations in the same coordinate plane and locate the intersection of the two lines.

The visual technique actually just requires three easy actions to complete: Slope-Intercept Form should be applied to both equations.

Each linear equation's graph should be shown in the same coordinate plane. Identify the system's solution.

If the lines cross, the system's solution may be found by using the coordinates of the crossing point. The problem cannot be solved if the lines are parallel.

Let us suppose number of members =x.

Let us suppose the number of non members = y.

The system of equation for the following situation is:

5x + 10y ≤ 300

x ≥ 2y

Substitute different values of x to obtain different values of y.

Plot the coordinates on the graph to obtain the graph of the system of equations.

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Answer: A) -4.2, B) -3.8 C) -9/2 (-4.5)

Step-by-step explanation: Think of a number line, you have 0-10, and -10-0, as you keep going down the number like, the numbers become less and less, just like how -4.2 is less than -3.5, because it is further to the left of the number line, meaning it is less than. Hope this helps!

Hence, the amount of glass needed in square feet is 2 × 14.4 = 28.8 sq feet.

A square in geometry is a two-dimensional plane figure with four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, but only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.

Only the window of a new house was advertised.

a kite with a height of 3.2 and 4 feet, a width of 2 feet, and a width of 2 feet.

Two panes make up the window.

To determine: How so many sq ft of glass is needed for the window,

Triangle area equals (1/2) base x height.

= (1/2) × 2 × 3.2 + (1/2) ×2 × 3.2 + (1/2) × 2 × 4 + (1/2) × 2 × 4

=2 × 3.2 + 2 × 4

= 2 × (3.2 + 4)

= 2 × 7.2

= 14.4 sq feet

Double-paned glass is a given.

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To find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).

Volume is a measure of the amount of space occupied by an object or substance. It is expressed as a numerical value, usually in cubic units, such as milliliters (mL) or cubic centimeters (cc). It is also used to measure the capacity of a container, such as a bottle, or a tank.

Dilation is a transformation that changes the size of a shape. When a solid is dilated by a scale factor of k, the new solid will be k times larger than the original solid. For example, if a solid has a volume of 100 cubic units and is dilated by a scale factor of 2, the image solid will have a volume of 200 cubic units (2 x 100).

To find the image for each given value of k, we need to multiply the original volume of the solid (100 cubic units) by the scale factor (k). We can use the equation V = kV0, where V0 is the original volume and V is the new volume, to calculate the new volume of the solid.

For example, if k = 3, the new volume will be 3 x 100 = 300 cubic units. If k = 4, the new volume will be 4 x 100 = 400 cubic units. In general, for any given value of k, the new volume will be k times the original volume.

To summarize, when a solid with a volume of 100 cubic units is dilated by a scale factor of k, the image solid will have a volume of k times the original volume (V = kV0). Therefore, to find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).

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Answer:

A. 5 cm

Step-by-step explanation:

AB = BC

x + 3 = 3x - 1

x - 3x = -1 - 3

-2x = -4

x = -4/-2

x = 2

BC = 3x - 1 = 3(2) - 1 = 6 - 1 = 5

heres the answer:

8x10=80

2x1=2/100= 0.02

9x1=9/1000= 0.002

0.002+0.02+80=

80.002!!

Answer:

Step-by-step explanation: First lets multiply the numerators, so 3*3 is 9, then we multiply the denominators, so 4*5 is 20. 9/20 or 0.45 will be your answer.

Answer: stop being a brat

Step-by-step explanation:

Answer:

8k - (5 + 2k) can be simplified by distributing the negative sign to the terms inside the parentheses:

8k - 5 - 2k

Then, we can combine like terms by adding the constants -5 and 8k:

6k - 5

Therefore, an equivalent expression to 8k - (5 + 2k) without parentheses is 6k - 5.

The quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

To find the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1), we will use synthetic division.

Write down the coefficients of the dividend polynomial in descending order of the exponent of x. In this case, the coefficients are 1, -1, 9, -9, 9, -12.

Write down the constant term of the divisor polynomial. In this case, the constant term is -1.

Bring down the first coefficient of the dividend polynomial.

Multiply the constant term of the divisor polynomial by the first coefficient of the dividend polynomial and write the result under the second coefficient of the dividend polynomial.

Add the second coefficient of the dividend polynomial and the result from step 4.

Repeat steps 4 and 5 until all the coefficients of the dividend polynomial have been used.

The last result from step 5 is the remainder. The other results are the coefficients of the quotient polynomial.

The synthetic division is shown below:

-1 | 1 -1 9 -9 9 -12
 | -1 2 -11 20 -29
 ---------------------
   1 -2 11 -20 29 -41
 
The quotient is 1x^(4)-2x^(3)+11x^(2)-20x+29 and the remainder is -41.

Therefore, the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

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Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

To calculate Renee's monthly payment, we need to first determine the total cost of the new car after taxes and fees and subtract the trade-in value of her old car. Then, we can use the loan information to calculate the monthly payment.

Total cost of the new car:

List price: $19,675

Vehicle registration fees: $1,420

Documentation fees: $85

Sales tax: 8.92% of ($19,675 + $1,420 + $85) = $1,894.51

Total cost = $19,675 + $1,420 + $85 + $1,894.51 = $22,074.51

Trade-in value of the old car:

2002 Buick LeSabre in good condition: $3,374 (from the table)

85% of trade-in value: 0.85 x $3,374 = $2,867.90

Net cost of the new car:

$22,074.51 - $2,867.90 = $19,206.61

To calculate the monthly payment, we can use the formula for the present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (11.34%/12), and n is the number of payments (4 years x 12 months/year = 48).

Solving for PMT:

PMT = PV x r / (1 - (1 + r)^(-n))

PMT = $19,206.61 x 0.1134/12 / (1 - (1 + 0.1134/12)^(-48))

PMT = $504.46

Therefore, Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

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The total number of hours Eric worked is 7 3/4 hours.

What is addition in mathematics?

Addition is one of the four basic arithmetic operations in mathematics, along with subtraction, multiplication, and division. Addition is the process of combining two or more quantities or numbers to find their sum, or total. The symbol used to represent addition is the plus sign (+).

For example, if we want to find the sum of 3 and 4, we would write:

3 + 4 = 7

The number 3 and the number 4 are called addends, and the result of the addition operation is called the sum. Addition can involve whole numbers, fractions, decimals, and even negative numbers.

Addition has many applications in mathematics, science, and everyday life. It is used to calculate simple arithmetic problems, such as adding up the cost of items in a shopping cart, as well as more complex calculations, such as adding up the values in a data set or solving equations in algebra.

To find the total number of hours Eric worked in the neighborhood garden, we need to add the number of hours he worked on Monday and Wednesday.

Eric worked 3 1/2 hours on Monday, which can also be written as 7/2 hours.

Eric worked 4 1/4 hours on Wednesday, which can also be written as 17/4 hours.

To add these two amounts, we need to find a common denominator. The smallest number that both 2 and 4 divide into is 4. So we can convert 7/2 to 14/4 by multiplying the numerator and denominator by 2:

7/2 = 14/4

Now we can add the two fractions:

14/4 + 17/4 = 31/4

This is the total number of hours Eric worked in the neighborhood garden, in fraction form. To write it as a mixed number, we can divide the numerator by the denominator:

31 ÷ 4 = 7 with a remainder of 3

So the total number of hours Eric worked is 7 3/4 hours.

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The graph of y = [1/2(x -10)] - 3, compared to the graph of 1/x, represents these following transformations:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The translations for this problem are given as follows:

Additionally, there was a multiplication by 2 in the domain, meaning that the parent function was horizontally compressed by a factor of 2.

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To make equivalent rational expressions, we need to multiply the numerator and denominator of the left-hand side of the equation by the same value.

In this case, we can multiply both the numerator and denominator by (5x^(3))/(5x^(3)) to get the equivalent expression on the right-hand side. (3)/(x^(6)) * (5x^(3))/(5x^(3)) = (15x^(3))/(5x^(9))

Therefore, the value that we need to fill in the blank is (15x^(3)). So the equivalent rational expression is:

(3)/(x^(6))=(15x^(3))/(5x^(9))

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Area of circle A is 113.04 in²

Area of circle B is 200.96  in²

Area of circle C is 452.16  in²

Area of circle B is 254.34  in²

The number of times that the area of Circle D greater than Circle A is 2.25

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

here, we have,

Area of circle A = 3.14 x 6² = 113.04 in²

Area of circle B = 3.14 x (6 + 2)² = 200.96  in²

Area of circle C = 3.14 x (8 + 4)² = 452.16  in²

Area of circle B = 3.14 x (12 - 3)² = 254.34  in²

Number of time that is the area of Circle D greater than Circle A = 254.34  in² / 113.04 in² = 2.25

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Complete question:

The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each​ circle? How many times greater than the area of Circle A is the area of Circle D​?

The answer of function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

A 6th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function[tex]y=(x-3)^4(x+1)^2[/tex].

This is because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times, and the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

Therefore, the values of a, b, and c in the function y=(x-3)^(a)(x-b)^(c) are:

a = 4, because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times.

b = -1, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

c = 2, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

So, the function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

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Answer:

x3

Step-by-step explanation:

Answer: 12 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume = length x width x height

Volume = 4 m x 1.5 m x 2 m

Volume = 12 cubic meters

Given - two tangent lines are drawn from the point B

To find - the value of BC

Explanation - when tangent lines are drawn for outside of the circle then the length of line formed is equal

We get

AB=BC

[tex]x+3 =3x-1\\x-3x=-1-3\\-2x=-4\\x=2[/tex]

BC= [tex]3x-1 =3(2)-1=6-1=5[/tex]

The length of BC = 5

Final answer - The option A is correct, the length is 5

The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is​ R9,338.80.

The future payment to be made at the end of the seventh year is determined by computing the future values in two stages. The first stage computes the future value before the payment at the end of the first year.  The second stage computes the future value for six years.  

here, we know,

The future value is computed by compounding the present value at an interest rate.

Current debt = R6,421,00

Compound interest rate = 11% per year

Compounding period = Quarterly

Future Value in 1 Year:

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R6,421.00

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R7,156.98

Total Interest = R735.98

Future Value (FV) = R7,156.98

Payment in one year's time = R2,287.00

Balance = R4,869.98

Future Value at the end of the 7th Year:

N (# of periods) = 24 quarters (6 years x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R4,869.98

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R9,338.80

Total Interest = R4,468.82

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Answer:

x = -8, 8

Step-by-step explanation:

The student did make an error. When factoring [tex]x^2-64[/tex], they used incorrect factors. Using FOIL method, the students factored equation would become [tex]x^2 +32x-32x-1024 = x^2-1024[/tex], which is not [tex]x^2-64[/tex].

Instead, the factors 8 and -8 should be used.

[tex]x^{2} +5x-60=5x+4\\x^2 +5x - 64=5x\\x^2-64=0\\(x+8)(x-8)=0\\x=-8, 8[/tex]

Answer: x = ±8

Step-by-step explanation:

The given equation is:

x² + 5x - 60 = 5x + 4

The student's work shows that they simplified the equation correctly to:

x² - 64 = 0

However, their factorization of the resulting equation is incorrect. Factoring x² - 64 using difference of squares we get:

(x + 8)(x - 8) = 0

So, the solutions for x are x = -8 and x = 8. The student's solutions of x = ±32 are incorrect.

Therefore, the student made an error in factoring the equation, and the correct solutions for x are x = -8 and x = 8.

The probability of A and B, using conditional probability, is given as follows:

0.24 = 24%.

The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which the probabilities are listed and explained as follows:

To obtain the probability of A and B, the needed parameters are already given in the problem, and are as follows:

Hence the probability of A and B is calculated as follows:

P(A and B) = P(A) x P(B|A)

P(A and B) = 0.6 x 0.4

P(A and B) = 0.24.

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Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

It functions by dividing distance by speed. The time can also be calculated by dividing the distance traveled by the speed. You can determine the third input if you know the first two. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.

The equation of the line of best fit is:

y = -1.4x + 117.8

where x is the age in years and y is the typing speed in words per minute. To find the expected typing speed of a 17-year-old student, we can substitute x = 17 into the equation:

y = -1.4(17) + 117.8

y = -23.8 + 117.8

y = 94

Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

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we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.

To prove the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A), we can use the following steps:

Step 1: Use the identity sin^2(A) + cos^2(A) = 1 to express sin^4(A) in terms of cos^4(A).

sin^4(A) = (1 - cos^2(A))^2

Step 2: Expand the expression on the right hand side.

sin^4(A) = 1 - 2cos^2(A) + cos^4(A)

Step 3: Rearrange the terms to get the expression on the left hand side.

sin^4(A) - cos^4(A) = 1 - 2cos^2(A)

Step 4: Verify that the expression on the left hand side is equal to the expression on the right hand side.

1 - 2cos^2(A) = 1 - 2cos^2(A)

Therefore, the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) is proven to be true.

In conclusion, we have proven the statement sin^4(A) - cos^4(A) = 1 - 2cos^2(A) using the identity sin^2(A) + cos^2(A) = 1 and basic algebraic manipulation. Our work is legible, and our logic is clear and justified.

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The missing side lengths are computed below

Triangle 22

The side length x can be calculated using

sin(30) = 9/x

So, we have

x = 9/sin(30)

Evaluate

x = 18

For length y, we have

y = √(18² - 9²)

Evaluate

y = 9√3

Triangle 23

The side length y can be calculated using

sin(30) = y/√3

So, we have

y = √3 * sin(30)

Evaluate

y = 1/2√3

For length x, we have

x = √(√3² + (1/2√3)²)

Evaluate

x = √(15/4)

x = 1/2√15

Triangle 24

The side length y can be calculated using

cos(60) = y/2√3

So, we have

y = 2√3 * cos(60)

y = √3

For x, we have

x = √((2√3)² - (√3)²)

x = √9

x = 3

Triangle 25

The side length x can be calculated using

cos(60) = 5/x

So, we have

x = 5/cos(60)

x = 10

For y, we have

y = √(10² - 5²)

y = 5√3

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