Marsha is considering purchasing 3 points on a $350,000 home mortgage for 20 years. If she
purchases the 3 points, at a cost of 1 percent per point, her monthly mortgage would be
approximately $1,878.63. If she decides not to purchase any points, Mercedes' monthly
payment would be approximately $1,987.13. How much money will Mercedes save over the life
of the loan if she purchases the 3 points?

Answer:

Step-by-step explanation:

To find the highest common factor (HCF) of 12x^12 and 16x^16, we need to factor both expressions.

12x^12 = 2^2 * 3 * (x^2)^6

16x^16 = 2^4 * (x^2)^8

The common factors of 12x^12 and 16x^16 are 2^2 and (x^2)^6. To find the HCF, we take the product of these common factors:

HCF = 2^2 * (x^2)^6 = 4x^12

Therefore, the highest common factor (HCF) of 12x^12 and 16x^16 is 4x^12.

The expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.

So, the expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.

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The estimated radius of the object is about 1.42 mm.

The given information is that the circumference( C) of the object is8.9 mm.

We know that the formula for the circumference of a circle is given by  

C =  2πr  

where r is the compass of the circle.  

To estimate the compass, we can rearrange the formula as

  r =  C/ 2π  

Substituting the given value of C, we get

  r = 8.9/ 2π

we can  estimate this expression to get  

r ≈1.42 mm( rounded to two decimal places)

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The probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.

To calculate the probability of at least one failure, we first need to find the probability of having zero failures in five trials, which is equal to (0.3)^5 or 0.00243. Then, we subtract this value from 1 to obtain the probability of having at least one failure. This is because the sum of the probabilities of all possible outcomes should be equal to 1.

In this case, we can see that the probability of having at least one failure in five trials is quite high, at approximately 83%. This means that it is more likely than not that there will be at least one failure in a series of five trials with a success rate of 30%.

The probability of having at least one failure in five trials of a binomial experiment with a success rate of 30% can be calculated as follows:

1 - (probability of having zero failures in five trials)

= 1 - (0.7)^5

= 1 - 0.16807

= 0.83193

Therefore, the probability of having at least one failure in five trials is approximately 0.83193 or 83.193%.

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The correct equation represents the amount Kennedy makes babysitting is,

⇒ d = 7h

We have to given that,

Kennedy makes $7 per hour babysitting.

Let us assume that,

'h' represent the number of hours

And, d represent amount in dollars.

Hence, By given condition, we get;

⇒ d = 7h

Thus, The correct equation represents the amount Kennedy makes babysitting is,

⇒ d = 7h

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The formula that Kennedy uses to calculate how much money she makes babysitting is:d = 7h

We have,

Kennedy makes $7 per hour babysitting.

let "d" represents the amount of dollars Kennedy makes, and "h" represents the number of hours she babysits.

Since Kennedy earns $7 per hour, the equation can be written as

d = 7h

which relates the dollars earned (d) to the number of hours worked (h).

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Angle S,  Angle T and side ST are common to triangle SUT and triangle SVT.

To identify the angle or side that is common to triangle SUT and triangle SVT, based on given information, we can evaluate them as follows:

A. Angle S is common to both triangles SUT and SVT, as it is the vertex where the two triangles share a point.
B. Side SV is not common to both triangles, as it is only a side of triangle SVT.

C. Side ST is common to both triangles SUT and SVT, as it connects the shared vertex S to points U and V in each respective triangle.
D. Angle T is also common to both triangles SUT and SVT, as it is the other vertex where the two triangles share a point.

Therefore,  Angle S, side ST, and Angle T are all common to triangle SUT and triangle SVT.

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Answer: The dimensions of the rectangular part of the Norman window that would allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.

Explanation:

Let's assume that the height of the rectangular part of the Norman window is "h" and the width is "w". Then the diameter of the semicircle is also "w". The total amount of framing material needed is the sum of the perimeter of the rectangular part and half the circumference of the semicircle:

Perimeter of rectangular part = 2h + 2w

Circumference of semicircle = 1/2πw

Total framing material = 2h + 2w + 1/2πw

We want to maximize the amount of light entering the window, which is proportional to the area of the rectangular part of the window. The area of the rectangular part is given by:

Area of rectangular part = hw

Now we can use the constraint that there is only 12 feet of framing material available:

2h + 2w + 1/2πw = 12

Solving for h in terms of w:

h = (12 - 2w - 1/2πw)/2

Substituting this expression for h into the formula for the area of the rectangular part:

Area of rectangular part = w(12 - 2w - 1/2πw)/2

We can now use calculus to find the value of w that maximizes this area. Taking the derivative of the area with respect to w and setting it equal to zero:

d/dw[w(12 - 2w - 1/2πw)/2] = 0

Simplifying and solving for w:

w = 4π/(4 + π)

Substituting this value of w into the expression for h:

h = (12 - 2w - 1/2πw)/2

h ≈ 8

Therefore, the dimensions of the rectangular part of the Norman window that allow in as much light as possible, given 12 feet of framing material available, are approximately 4 feet by 8 feet.

The perimeter of the track is of 377 m.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

Considering the rectangle with area 5500 m² and base 110 m, the height h, representing the diameter d of the circumference, is obtained as follows:

110d = 5500

d = 550/11

d = 50 m.

The radius is half the diameter, hence it is given as follows:

r = 25 m.

The perimeter is given as follows:

Hence it is given as follows:

P = 2 x 110 + 2 x 3.14 x 25

P = 377 m.

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Answer:

  145.7 cm

Step-by-step explanation:

You want the perimeter of a shape bounded by 4 semicircles of radius 10 cm and two straight lines 10 cm long.

The circumference of a circle with radius 10 cm is ...

  C = 2πr

  C = 2(3.142)(10 cm) = 62.84 cm

The shape is bounded (in part) by 4 semicircles, so 2 full circles. The length of the curved boundary is ...

  curve length = 2 · (62.84 cm) = 125.68 cm

The two straight edges at either end of the figure are equal in length to the radius. That total length gets added to the curve length to form the perimeter.

  P = straight length + curve length

  P = 2·10 cm + 125.68 cm ≈ 145.7 cm

The perimeter is about 145.7 cm.

An exponential function in terms of x is [tex]P(x) = 140,000(1.05)^x[/tex]

The population would be 291049.95 after 15 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

[tex]P(x) = I(1 + r)^x[/tex]

Where:

By substituting given parameters, we have the following:

[tex]P(x) = 140,000(1 + 0.05)^x\\\\P(x) = 140,000(1.05)^x[/tex]

After 15 years, we have:

[tex]P(15) = 140,000(1.05)^{15}[/tex]

P(15) = 291049.95 units.

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Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.

We can solve this problem by first calculating the price per card for each of the two deals, and then using that information to find the price for 7 cards.

Let x be the price of one baseball card, in dollars. From the information given, we know that:

2 cards cost $8.00, so 1 card costs $4.00: 2x = 8.00 => x = 4.00

4 cards cost $14.00, so 1 card costs $3.50: 4x = 14.00 => x = 3.50

So we see that the price per card is different for the two deals. To find the price for 7 cards, we can use a weighted average of the two prices:

Price for 2 cards: $8.00

Price for 4 cards: $14.00

Total price for 6 cards: $22.00

We can now find the price for one more card by subtracting the total price for 6 cards from the price for 7 cards:

Price for 7 cards: $?

Price for 6 cards: $22.00

Price for 1 card: $?

Price for 7 cards = Price for 6 cards + Price for 1 card

Price for 1 card = Price for 7 cards - Price for 6 cards

We know that the total price for 7 cards is the same as the price for 2 cards plus the price for 4 cards plus the price for 1 more card:

Price for 7 cards = Price for 2 cards + Price for 4 cards + Price for 1 card

Price for 7 cards = 2x + 4x + 1x = 7x

Substituting the value we found for x earlier, we get:

Price for 1 card: $3.50

Price for 7 cards: $24.50

Therefore, Barry will charge $24.50 for 7 baseball cards if he keeps selling cards at the same rate.

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1 marble is equal in weight to 84 jujubes.

Let's start by writing down the given information in equations:

5m = 3s (where m represents one marble and s represents one toy soldier)

7s = 5c (where c represents one plush chipmunk)

3c = 14j (where j represents one jujube)

We want to find out how many jujubes equal the weight of one marble, so we need to eliminate all the other variables except for j and m. We can do this by using substitution and algebraic manipulation.

First, we can solve the second equation for s in terms of c:

7s = 5c

s = (5/7)c

Then, we can substitute this expression for s in the first equation:

5m = 3s

5m = 3(5/7)c

m = (3/7)c

Next, we can solve the third equation for c in terms of j:

3c = 14j

c = (14/3)j

Now we can substitute this expression for c in the previous equation:

m = (3/7)c

m = (3/7)(14/3)j

m = 2j

So we have found that one marble is equal in weight to 2 jujubes. But the question asks for the weight of one marble in terms of jujubes, not in terms of jujubes and toy soldiers and plush chipmunks. We can use the other equations to eliminate the other variables:

5m = 3s

5m = 3(5/7)c

5m = (15/7)c

m = (3/7)c

7s = 5c

7s = 5(14/3)j

s = (10/3)j

Putting this all together:

m = (3/7)c

m = (3/7)(7s/5)

m = (3/5)s

m = (3/5)(10/3)j

m = 2j

So we have found that one marble is equal in weight to 2 jujubes. Finally, we can use the third equation to find how many jujubes are equal in weight to 1 marble:

3c = 14j

c = (14/3)j

m = (3/7)c

m = (3/7)(14/3)j

m = 2j

1 marble = 2 jujubes

1 jujube = 1/2 marble

1 marble = 2 jujubes = 2(84) = 168 jujubes

Therefore, one marble is equal in weight to 84 jujubes.

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The closest answer is 9% interest rate and 25 years term of the loan.

Assuming the $70,000 mortgage is a fixed-rate mortgage, we can use the formula for the monthly payment of a mortgage to solve for the interest rate and the term of the loan.

The formula is:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

where:

M = monthly payment

P = principal (amount borrowed)

i = interest rate (per month)

n = number of months

Substituting the given values, we get:

$629.81 = $70,000 [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]

Using a mortgage calculator or by trial and error, we can find that the closest answer is 9% interest rate and 25 years term of the loan.

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The distance from point A to point B is approximately 998 feet (rounded to the nearest foot).

Let's denote the distance from point A to the lighthouse as "x", and the distance from point B to the lighthouse as "y". Also, let's denote the height of the lighthouse as "h". Then we have the following diagram:

Lighthouse

    |\

    | \

    |  \ h

    |   \

    |θ2 \

    |____\

      x   y

      A   B

From the diagram, we can see that:

tan(6°) = h/x (equation 1)

and

tan(4°) = h/y (equation 2)

We need to find the value of "d", the distance from point A to point B. We can use the following equation:

d^2 = x^2 + y^2 (equation 3)

We can solve equation 1 for h:

h = x tan(6°)

Substitute this into equation 2:

x tan(6°) / y = tan(4°)

Solve for y:

y = x tan(6°) / tan(4°)

Substitute this into equation 3:

d^2 = x^2 + (x tan(6°) / tan(4°))^2

Simplify:

d^2 = x^2 (1 + tan^2(6°) / tan^2(4°))

Solve for d:

d = x sqrt(1 + tan^2(6°) / tan^2(4°))

Substitute the given values:

d = 996 sqrt(1 + tan^2(6°) / tan^2(4°))

Using a calculator, we get:

tan(6°) / tan(4°) = 0.1051

So,

d = 996 sqrt(1 + 0.1051^2) ≈ 998.38 feet

Therefore, the distance from point A to point B is approximately 998 feet (rounded to the nearest foot).

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The radius of the line of latitude through X is approximately 5729 km, and the latitude of Y is approximately 43°.

Let X be the starting town with coordinates (28°N, 66°E), and let Y be the destination town which is 3900 km due South of X. We want to find the radius of the line of latitude through X, and the latitude of Y.

First, we can find the distance between X and Y using the Pythagorean theorem. The distance due South is 3900 km, and the distance due East is 28° × R, where R is the radius of the Earth. Using t=2 and R=6406 km, we have:

distance due East = 28° × 6406 km × cos(66°) ≈ 2055.6 km

distance between X and Y = sqrt((3900 km)^2 + (2055.6 km)^2) ≈ 4498.6 km

Next, we can find the latitude of Y using the formula:

latitude of Y = 90° - arctan(distance due South / radius of the Earth)

Using t=2 and R=6406 km, we have:

latitude of Y = 90° - arctan(3900 km / 6406 km) ≈ 43°

Finally, we can find the radius of the line of latitude through X using the formula:

radius of line of latitude = radius of the Earth * cos(latitude of X)

Using the coordinates of X, we have:

latitude of X = 28°N

radius of line of latitude = 6406 km * cos(28°) ≈ 5729 km

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19. The triangle with sides 3, 4, 6 is obtuse triangle.

20. The triangle with sides 9, 11, 16 is acute triangle.

In a triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side for the triangle to be considered "non-degenerate," which means it is a valid triangle with a positive area.

19. We have sides of 3, 4, and 6. We can check whether this triangle is non-degenerate using the above formula:

3² + 4² = 9 + 16 = 25, which is less than 6² = 36.

Therefore, this triangle is non-degenerate and we can classify it based on the size of its angles.

To do so, we can use the Pythagorean Theorem to find that the longest side (6) is opposite the largest angle, which is obtuse. Therefore, triangle #19 is an obtuse triangle.

20. For triangle #20, we have sides of 9, 11, and 16. Checking again with the above formula:

9² + 11² = 81 + 121 = 202, which is less than 16² = 256. So this triangle is also non-degenerate.

Using the same method as before, we can find that the longest side (16) is opposite the largest angle, which is acute. Therefore, triangle #20 is an acute triangle.

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Answer: False

Step-by-step explanation: It is false because the y-coordinate is the range.

The vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point. The parent function of the absolute value function is f(x) = |x|.

To shift this function 3 units down, we need to subtract 3 from the function's output (y) at every point on the graph. This can be expressed as:

f(x) = |x| - 3

The absolute value function is symmetric around the y-axis, which means that any shifts to the left or right do not affect the shape of the graph, only its position on the coordinate plane.

However, a vertical shift up or down will change the location of the vertex, the point where the graph changes direction. In this case, the vertex will be at (0, -3), and the graph will be lower than the parent function by 3 units at every point.

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In the coding section of Lesson 4, Unit 7 on Code.org, you will be working with parameters and return statements to create a Number Crunch function for 2 and 3. To complete this task, follow these steps:

1. Define a function called 'numberCrunch' that takes two parameters: 'num1' and 'num2'.
2. Inside the function, perform the desired calculations using 'num1' and 'num2' (e.g., addition, multiplication, etc.).
3. Use a return statement to return the result of the calculation.
4. Call the 'numberCrunch' function with the values 2 and 3 as arguments, and store the result in a variable (e.g., 'result').
5. Display the result using a console.log or any other preferred method.

Here's an example using addition as the operation:

```javascript
function numberCrunch(num1, num2) {
 return num1 + num2;
}

var result = numberCrunch(2, 3);
console.log(result);
```

Modify the code according to the specific requirements of the lesson and the desired operation.

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Option B is true about the relationship between 1 inch and 1 foot.

What is conversation?

A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.

There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.

Hence, Option B is true about the relationship between 1 inch and 1 foot.

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None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0

What is a statement?

A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.

What is meant by factor?

A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.

According to the given information

If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.

Therefore, the correct statement is: f(4) = 0

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The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.

To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.

tax rate = (tax / cost of bicycle) x 100%

tax rate = (32 / 400) x 100%

tax rate = 8%

Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.

tax on $700 bicycle = (tax rate / 100) x cost of bicycle

tax on $700 bicycle = (8 / 100) x $700

tax on $700 bicycle = $56

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$750 was withheld from my pay after deductions form the gross pay

Gross pay is the money that an employee gets before tax and other deduction are made

Net pay is the amount of money given to am employee after deduction of tax and other mandatory expenses

The gross pay is $2,500

The net pay is $1,750

The money withheld can be calculated as follows

= 2500 - 1750

= 750

The money withheld from the gross pay is $750

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The area of the preimage is 400units²

Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.

A scale factor shows the relationship between the old shape and new shape.

The scale factor is expressed as ;

scale factor = dimension of the new length / dimension of old length

scale factor = 3/2 = 1.5

old length = x

therefore 1.5 = 30/x

1.5x = 30

divide both sides by 1.5

x = 30/1.5 = 20units

therefore the area of the preimage = l²

= 20²

= 400units²

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To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

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To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.

First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25

Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25

So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.

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Answer:

  x = 3  or  x = 12

Step-by-step explanation:

You want the possible values of x that make it true that ...

  (x +1)²/(x -2) = 16 +(x -3)/(x -2)

The given division expression can be written in terms of quotient and remainder as  ...

  p/q = a +r/q   ⇒   p = aq +r

Here, this means ...

  (x +1)² = 16(x -2) +(x -3)

  x² +2x +1 = 16x -32 +x -3

  x² -15x = -36

  x² -15x +56.25 = 20.25 . . . . . complete the square

  (x -7.5)² = 4.5²

  x = 7.5 ± 4.5 . . . . . . . . . . . . . take the square root, add 7.5

  x = 3 or 12

__

Additional comment

The given quotient-remainder equation has a vertical asymptote at x = 2. When we write it as f(x) = 0, the graph of f(x) is symmetrical about the point (2, -11).

The complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

Let's define:

x: length of the package in inches

y: width of the package in inches

Then, the system of inequalities that represents the delivery service requirements is:

x ≤ 22 (length must be 22 inches or less)

y ≤ 22 (width must be 22 inches or less)

x + y ≤ 30 (length plus width must be no more than 30 inches)

We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:

4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)

Therefore, the complete system of inequalities for Yuriy's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

4xy ≤ 840

Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:

14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)

Therefore, the complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

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Answer:

The Answer is 5

Step-by-step explanation:

Pink beads : White beads

30 : 35

( 30 / 5 ) : ( 35 / 5 )

6 : 7

To find the number of beads, You divide the number of pink beads available by the number of pink beads in the ratio:

= 30 / 6

= 5 necklaces

hope this helps :)