you take a loan out to finance $175,000 on a house. if the rate is 3% and compounds continuously, how much will the loan cost after 30 years?

The area of the rectangle is 1296 square feet.

Let's denote the width of the rectangle as "w" and its length as "4w" since the length is four times the width.

The formula for the perimeter of a rectangle is given by:

P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Given that the perimeter of the rectangle is 180 ft, we can write the equation as:

180 = 2(4w + w)

Simplifying the equation:

180 = 2(5w)

180 = 10w

w = 18

So, the width of the rectangle is 18 ft.

Now, we can find the length of the rectangle:

Length = 4w = 4(18) = 72 ft

The area of a rectangle is given by the formula:

[tex]A = l \times w,[/tex]

where A is the area,

l is the length,

and w is the width.

Substituting the values we found:

Area [tex]= 72 ft \times 18 ft = 1296 ft^2[/tex]

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y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

Let's match each system on the left with the appropriate words that describe the system on the right:

y = 3x - 1: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y - 6x = 4: consistent, independent

Similar to the first system, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

2y = -x + 6: consistent, independent

This system also represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

4y + 2x = 12: consistent, independent

Like the previous systems, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

y = 2x + 3: consistent, independent

This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.

x + y = -9: consistent, dependent

This system represents a linear equation with infinitely many solutions. The equations are multiples of each other, meaning they represent the same line. Therefore, any point on the line satisfies both equations.

y = 3x - 1 and 2y = -x + 6: inconsistent

This system represents inconsistent equations that do not have a common solution. The lines represented by the equations are parallel and do not intersect.

To summarize the matches:

y = 3x - 1: consistent, independent

2y - 6x = 4: consistent, independent

2y = -x + 6: consistent, independent

4y + 2x = 12: consistent, independent

y = 2x + 3: consistent, independent

x + y = -9: consistent, dependent

y = 3x - 1 and 2y = -x + 6: inconsistent

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May Kawasaki's required minimum distribution (RMD) is $3,808. This is calculated by dividing her IRA balance of $98,000 by the distribution period of 26.2, which is found in the Uniform Life Table on page 45 for a 72-year-old.

b) If May Kawasaki fails to take her RMD, she will incur a 50% penalty on the amount she should have withdrawn. In this case, the penalty would be $1,904.

c) If May Kawasaki had made an early withdrawal of $10,000 to take a vacation, she would have paid a 10% penalty on the amount withdrawn. In this case, the penalty would have been $1,000.

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1. May Kawasaki is 72 and has an IRA with a fair market value of $98,000. a) Use the Uniform Life Table on p. 45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a vacation?

Answer:

$1250

Step-by-step explanation:

A = P + Prt

1337.5 = P + P(0.04)(21/12)

1337.5 = 1.07P

P = 1250

Answer: $1250

Answer: Unfactorable

Step-by-step explanation:

5v^2-30v+70

5(v^2-6v+14)

You can't factor v^2-6v+14 with rational numbers

The total tax due for a married couple who have a combined income of $110,000 is $16,079

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

Income = $110,000

Also, we have the table of values

From the tax table, we have the category of tax to be paid by the couple to be

Tax = 8907 + 22% * excess of 77400

So, we have

Tax = 8907 + 22% * (110,000 - 77400)

Evaluate

Tax = 16079

Hence, the tax amount is $16,079

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If the height (h) of the prism is less than or equal to 0.978 cm, then Andrea has enough modeling clay for both prisms. If the height exceeds 0.978 cm, she will be short of modeling clay.

Let's calculate the volumes of both prisms:

Volume of the first prism: V1 = (8.4 cm²) × h

Volume of the second prism: V2 = (16 × 8.4 cm²)×(4h)

= 537.6 cm³ h

We know that Andrea has 533.8 cm³ of modeling clay.

To determine if she has enough clay for both prisms, we need to compare the total volume of the prisms to the amount of clay she has:

Total Volume = V1 + V2 = (8.4 cm²) × h + (537.6 cm³ × h)

Total Volume = (546 cm²) × h

Now we can set up the equation:

Total Volume ≤ Amount of Clay

(546 cm²) × h ≤ 533.8 cm³

Solving for h:

h ≤ 533.8 cm³ / (546 cm²)

h ≤ 0.978 cm

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The cumulative frequency to be used in solving the 28th percentile is 16.

Cumulative frequency is described as  the total of a frequency and all frequencies in a frequency distribution until a certain defined class interval.

we add up the frequencies until we reach or exceed 28% of the total data set in order to find the cumulative frequency for the 28th percentile.

Total frequency = 4 + 9 + 16 + 10 + 9 + 2 = 50

28th percentile = (28/100) * Total frequency

28th percentile = (28/100) * 50 = 14

We start from the beginning of the distribution and add up the frequencies until we reach or exceed 14 so as to find the cumulative frequency.

In conclusion, and with reference to the given data set we notice that the cumulative frequency exceeds 14 at the 91-120 minute interval = 16.

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The length of the arc RT is 11.72 units.

An arc is defined as a portion of the boundary of a circle or a curve.

To calculate the length of the arc RT, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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There are 19 nickels, 15 quarters, and 18 dimes in the collection.

Let's assume that there are n number of nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4.

There are 3 more dimes than quarters, so the number of dimes will be (n - 4) + 3 = n - 1.

The value of each nickel is $0.05, the value of each dime is $0.10, and the value of each quarter is $0.25.Using this information, we can form the following equation to represent the total value of the collection:

0.05n + 0.10(n - 1) + 0.25(n - 4) = 6.5Simplifying this equation, we get:0.05n + 0.10n - 0.10 + 0.25n - 1 = 6.50.40n - 1.10 = 6.50

Adding 1.10 to both sides, we get:0.40n = 7.60Dividing both sides by 0.40, we get:n = 19

Therefore, there are 19 nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4 = 19 - 4 = 15.

There are 3 more dimes than quarters, so the number of dimes will be (n - 4) + 3 = 15 + 3 = 18.

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Answer:

[tex]8 {x}^{2} - 6x - 5 = x[/tex]

[tex]8 {x}^{2} - 7x - 5 = 0[/tex]

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

Mean: 27

Median: 22

Mode: 22

Standard deviation: 17

No outlier (61 might be one just check with people you know and see if they have an outlier or not)

Step-by-step explanation: Give a definition of mean, median, mode…and just add your answers.

A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.

To determine if the points (4,8), (2,10), and (5,7) lie on the line 2x + 2y = 24, we can substitute the x and y values of each point into the equation and check if the equation holds true.

For the point (4,8):

2(4) + 2(8) = 8 + 16 = 24, which satisfies the equation.

For the point (2,10):

2(2) + 2(10) = 4 + 20 = 24, which also satisfies the equation.

For the point (5,7):

2(5) + 2(7) = 10 + 14 = 24, which satisfies the equation as well.

Since all three points satisfy the equation 2x + 2y = 24 when their coordinates are substituted, we can conclude that the points (4,8), (2,10), and (5,7) indeed lie on the line represented by the equation 2x + 2y = 24.

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The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:

area of rectangle+area of triangle= area of figure

6×5 + 1/2×4×6=30+24= 42

or

given figure is a trapezium

so we know are of trapezium= 1/2×sum of parallel sides×height

= 1/2×( 5+9)×6

=42

Using the division operation , Natalie can do 64 loads of laundry with her bottle of detergent.

From the line plot , the detergent with 4 bottles has 8 cups in it.

Fraction of cup used per laundry = 1/8

Total cups of detergent in bottle = 8

Number of laundry Natalie can do :

(Total cups of detergent in bottle / Fraction of cup used per laundry )

Number of loads of laundry that can be done :

= 8 / (1/8)

= 8 × 8/1

= 64

Therefore, Natalie can do 64 loads of laundry with her bottle of detergent.

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Answer:

42 = 23 + j

Step-by-step explanation:

The equation representing the given sentence would be:

42 = 23 + j

Here, the variable "j" represents Janelle's age.

The description of the image is one that has a four-horned star. The description is as follows:

It comprises of four equilateral triangles and One Square.

Next,

The image or shape has twelve (12) symmetrical lines.

Next,

It must be rotated 90° (clockwise or anticlockwise) in order for the image to match itself.

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Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.

f(x) = 2x

g(x) = [tex]2x^2[/tex] + 3x

To find (fg)(x), we substitute g(x) into f(x):

(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)

Now we substitute f(x) = 2x into the expression above:

(fg)(x) = 2([tex]2x^2[/tex] + 3x)

Distribute the 2:

(fg)(x) = [tex]4x^2[/tex] + 6x

So, (fg)(x) = [tex]4x^2[/tex] + 6x.

Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

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Answer: N= 12

Step-by-step explanation: if you follow PEMDAS, you take (4^3)^4 and multiply 3*4 which is 12.

Because the base of 4^12=4^n is the same you leave it alone and N is equal to 12

Answer:

Hi

Please mark brainliest ❣️

Thanks

Answer:

increasing exponential function.

Step-by-step explanation:

We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.

It  must be exponential.

It is increasing at it increases in x, so it is an increasing exponential function.

John's z-score is 0.75.

John's score of 79 on the math test corresponds to a z-score of 0.75 and a percentile of 77.82%.

To get John's z-score, we will use the formula: z = (x - μ) / σ

Data

x = John's score (79)

μ = mean score (73)

σ = standard deviation (8)

z = (79 - 73) / 8

z = 6 / 8

z = 0.75.

To find John's percentile, we can use a standard normal distribution table or calculator.

The percentile represents the percentage of scores that fall below a given value. Using  standard normal distribution table, we find that a z-score of 0.75 equals to percentile of 77.82%.

Full question:

The scores on a math test have a mean of 73 points and a standard deviation of 8 points. John scores a 79 on the test. Convert this score to a z-score and a percentile..

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Answer:

Step-by-step explanation:

Remember PEMDAS

7+(2x4)-8÷(12-6)x(6÷2)​

7 + 8 - 8 : 6 × 3 =

7 + 8 - 8/6 × 3 =

7 + 8 - 4 =

11

The length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.

To determine the length of segment OP on the unit circle, we need to use trigonometry. Let's break down the problem step by step:

Definition: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.

Initial Ray: The initial ray is a line segment that starts from the origin (0, 0) and extends to a point on the unit circle. It forms an angle with the positive x-axis.

Rotation: We are rotating the initial ray counterclockwise by θ degrees. This means we are essentially finding a new point on the unit circle based on the angle θ.

Trigonometric Functions: The trigonometric functions sine (sin) and cosine (cos) are particularly useful for calculating the coordinates of points on the unit circle.

sin(θ) gives the y-coordinate of a point on the unit circle.

cos(θ) gives the x-coordinate of a point on the unit circle.

Coordinates of Point P: Since we are rotating the initial ray counterclockwise by θ degrees, the coordinates of point P on the unit circle can be obtained as follows:

x-coordinate of P: cos(θ)

y-coordinate of P: sin(θ)

Distance from the Origin (Length of Segment OP):

Using the coordinates of point P, we can calculate the distance between the origin (0, 0) and point P using the distance formula.

The distance formula states that for two points (x1, y1) and (x2, y2), the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, point P has coordinates (cos(θ), sin(θ)), and the origin is (0, 0). Thus, the distance (length of segment OP) is:

d = √((cos(θ) - 0)² + (sin(θ) - 0)²)

= √(cos²(θ) + sin²(θ))

= √(1) [Using the trigonometric identity: sin²(θ) + cos²(θ) = 1]

= 1

Therefore, the length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.

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Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

Look Below

Step-by-step explanation:

The statement "definition of finiteness uses the notion of a natural number" means that when defining what it means for a set or collection to be finite, the concept of a natural number is employed.

In mathematics, a set is said to be finite if it can be put into a one-to-one correspondence with a specific subset of the natural numbers. This subset typically starts with the number 1 and includes a finite sequence of consecutive natural numbers, depending on the size of the set.

For example, consider a set A with three elements: A = {a, b, c}. To show that A is finite, we can establish a one-to-one correspondence between the elements of A and the set {1, 2, 3} as follows: a ↔ 1, b ↔ 2, c ↔ 3. This mapping shows that each element of A corresponds to a unique natural number, and vice versa. Since there is a bijection (a one-to-one correspondence) between the elements of A and a subset of the natural numbers, we conclude that A is finite.

Thus, in the definition of finiteness, the notion of a natural number is used to provide a precise and rigorous characterization of what it means for a set to be finite. It allows us to establish a clear distinction between finite sets and infinite sets, which do not have a one-to-one correspondence with any subset of the natural numbers.

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

We have,

To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.

Given the original coordinates of the quadrilateral ABCD:

A = (-3, 3)

B = (-4, -2)

C = (2, -4)

D = (0, 0)

To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:

A' = 2 x (-3, 3) = (-6, 6)

B' = 2 x (-4, -2) = (-8, -4)

C' = 2 x (2, -4) = (4, -8)

D' = 2 x (0, 0) = (0, 0)

Thus,

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

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Rolling two sixes in a row on a number cube (a fair six-sided die) is an independent event. The outcome of one roll does not affect the outcome of the subsequent roll. Each roll of the number cube is an independent trial, and the probability of rolling a six on each trial is always 1/6, regardless of the previous outcome.