Suppose you have the following three student loans: $12,000 with an APR of 7.5% for 17 years, $18,000 with an APR
of 8% for 22 years, and $13,500 with an APR of 9% for 12 years.
a. Calculate the monthly payment for each loan individually.
b. Calculate the total you'll pay in payments during the life of all three loans.
c. A bank offers to consolidate your three loans into a single loan with an APR of 8% and a loan term of 22 years.
What will your monthly payments be in that case? What will your total payments be over the 22 years?

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer:

0.097

Step-by-step explanation:

Step-by-step explanation:

B. 3 :8 =6:16 is a proportion

3 : 8 = 6: 16

Divide 6 and 16 by 2 we get

3 :8 = 3 : 8

Hope it will help :)❤

Answer:

x=12

Hope this help :)

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer:

7 = -11 + x

you can also do x - 11 = 7 or 7 = x - 11

hope these are the rewrites you are looking for

Step-by-step explanation:

The graph that represents function h is the graph in; Option C

The parent function is; f(x) = tan (x)

The transformed function is; h(x) = -tan(¹/₂x)

Now, from general tangent function we know that; y = tan(Bx)

Thus, period = π/(¹/₂)

From the given transformation that produced the h(x) function and when we look at the given graphs, the one that represents the function h is Option C.

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The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Answer:

To solve the system of linear equations:

x_1 + 3x_2 = 1 ...(1)

2x_1 + 5x_2 = 3 ...(2)

We can use the method of elimination to eliminate one of the variables. To do this, we multiply equation (1) by 2, and subtract it from equation (2), as follows:

2(x_1 + 3x_2 = 1) => 2x_1 + 6x_2 = 2 ...(3)

2x_1 + 5x_2 = 3 ...(2)

(2x_1 + 6x_2 = 2) ...(3)

-x_2 = 1

Thus, we have found that x_2 = -1.

We can substitute this value of x_2 into either equation (1) or (2) to solve for x_1. Let's use equation (1):

x_1 + 3(-1) = 1

x_1 - 3 = 1

x_1 = 4

Therefore, the solution to the system of linear equations is x_1 = 4, x_2 = -1.

So the solution set is {(4, -1)}.

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

are you tempted to calculate the internal angles ?

that is, I guess, the trap set by your teacher here, and it would be the wrong approach.

nevertheless, quickly just as a reminder :

the sum of all internal angles in a polygon is

(n - 2)×180°

n being the number of sides.

in our case that is

(5 - 2)×180 = 3×180 = 540°

so, each internal angle is 540/5 = 108°.

but we are not turning at an edge or vertex. no, we are turning the pentagon around is central point.

we are running each vertex along a circle arc. the center of that circle being P.

after every 1/5 of the circle arc there is a vertex of the pentagon.

and whenever we rotate one vertex on top of the next one, we carry the pentagon visually onto itself.

so, instead of a full circle rotation we need only 1/5 of that :

360 / 5 = 72°

and with every additional 1/5 of the circle arc (or 72°) we get it again.

that means at

72°

144°

216°

288°

360°

the pentagon carries onto itself.

therefore, A, D and E are correct.

It is true that Some people procrastinate because they are perfectionists.

People sometimes procrastinate because of their perfectionism. For case, an analyst might not acknowledge the plausibility of having any imperfections in their paper (indeed if those blemishes are insignificant) and thus keep going over the paper’s draft, indeed after it’s great sufficient to submit.  This is some of the time related to wanting or expecting to seek after a distant better; a much better; a higher; a stronger; an improved"; a higher alternative afterward, for illustration when somebody delays beginning to work out at domestic, since they arrange to in the long run connect an exercise center, indeed even though it would still be way better for them to begin working out presently.

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Answer:

EF, GH

Step-by-step explanation:

both go on forever from one point

Answer:

A and B

Step-by-step explanation:

Because they go infinitly in one direction and end in another.

Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

The point at (-3, 4) is at a distance of 5 units from the point (0, 0).

For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:

distance = √( (x₁ - x₂)² + (y₁ - y₂)²)

In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:

distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5

The distance is 5 units.

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You would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four years.

To calculate the monthly savings required to reach a savings goal of $3,000.00 over four years with a 10% annual interest rate,  we can use the PMT (Payment) function.

The PMT function helps us determine the fixed payment amount needed to achieve a specific future value within a given time frame.

Let's break down the given information:

Present Value (PV): $0.00 (initial account balance)

Future Value (FV): $3,000.00 (savings goal)

Interest Rate (rate): 10% per year (annual interest rate)

Number of Periods (nper): 4 years (48 months)

Using the PMT function, we need to plug in the values and solve for the monthly payment (savings amount).

The formula for the PMT function is:

PMT(rate, nper, pv, [fv], [type])

Where:

rate = Interest rate per period

nper = Total number of periods

pv = Present value (initial account balance)

fv = Future value (savings goal)

type = (Optional) Indicates whether the payment is made at the beginning (1) or end (0) of the period.

We'll assume 0 for monthly savings.

Let's calculate the monthly savings using the PMT function:

PMT(10%/12, 4*12, 0, -3000, 0)

Here, we divide the annual interest rate by 12 to get the monthly interest rate (10%/12), multiply the number of years by 12 to get the total number of months (4*12), set the initial account balance (pv) as $0, set the future value (fv) as -$3,000 (negative because it's an outgoing payment), and assume the savings are made at the end of each month (type = 0).

Using a financial calculator or spreadsheet software, the monthly savings required to reach the goal of $3,000.00 over four years with a 10% annual interest rate is approximately $56.62.

Therefore, you would need to save approximately $56.62 each month to achieve your savings goal of $3,000.00 over four year.

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Question : you want to reach $3,000.00 in savings over four years. Your account will earn 10% interest per yea Initially your account has a zero balance. How much must you save each month to achieve this goal? Use the PMT() function. Look it up in the e-book if you do not know how to use it. TIP: This is monthly so do not forget to adjust the interest rate and number of payment.

Answer:

base = 3.75 inches

Step-by-step explanation:

37.5 = 20b/2

37.5 = 10b

b = 3.75

The apprοximate average rate οf change οf the functiοn f(x)=500(0.5)^x οver the interval x=-2 tο x=2 is apprοximately 105.11.

The average rate οf change οf a functiοn between twο pοints is the same that the slοpe οf the line passes thrοugh these pοints  (secant line).

We need tο calculate the change in the functiοn value and divide it by the change in x.

\(f(x=2) - f(x=-2) \\\\= 500(0.5)^2 - 500(0.5)^(-2) \\\\= 420.42\)

x=2 - x=-2 = 4

Average rate οf change = (f(x=2) - f(x=-2)) / (x=2 - x=-2)

Average rate οf change ≈ 420.42 / 4

Average rate οf change ≈ 105.11

Hence, the apprοximate average rate οf change οf the functiοn \(f(x)=500(0.5)^x\) οver the interval x=-2 tο x=2 is apprοximately 105.11.

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Answer:

j=30

Step-by-step explanation:

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

the answer should be $7,562.00

Answer:

Step-by-step explanation:

2 3/4 + 1 11/16 = ?

   11/4 + 27/16 = ?

44/16 + 27/16 = 71/16 = 64/16 + 7/16

2 3/4 + 1 11/16 = 4 7/16   (D)

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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According to the given data the length of a \(90^{0}\) arc is \(\pi /2\) or approximately \(1.57\) feet.

In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.

According to the given information:

The length of a \(90^{0}\) arc in a circle with radius \(1\) foot can be calculated using the formula:

Length of arc = (angle/\(360\)) x \(2\pi r\)

where angle is the central angle of the arc in degrees, r is the radius of the circle, and \(\pi\) is a mathematical constant approximately equal to \(3.14159\).

Substituting the given values, we have:

Length of arc = (\(90/360\)) x \(2\pi(1 ft)\)

Length of arc = \((1/4)\) x \(2\pi ft\)

Length of arc = \(\pi /2 ft\)

Therefore, the length of the \(90^{0}\) arc is \(\pi /2 feet\) or approximately \(1.57 feet\)

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the length of the 90° arc is π/4 feet or approximately 0.785 feet

What is arc of circle?

In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.

The formula for the length of an arc is:

L = (θ/360) × 2πr

where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.

In this case, θ = 90° and r = 1 ft, so we have:

L = (90/360) × 2π(1) = (1/4) × π = π/4

Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).

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The initial velocity is  0 m/sec

The car speed up to 72km/h which is equivalent to  36m/sec

The acceleration of the car is 2.88 m/sec².

Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken

Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:

Initial Velocity = 0 m/sec

Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec

Time taken = 12.5 second

Now, the car’s acceleration in m/s can be written as,

Acceleration = (Final Velocity - Initial Velocity)/ Time taken

(36 m/sec - 0 m/sec)/12.5 seconds

= 2.88 m/sec²

Hence, the car’s acceleration in m/s is 2.88 m/sec².

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Answer:

180

Step-by-step explanation:

It is always 180 for a angle like this.

\(s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} \)

The shaded region represents 1.5 grids

\(1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} \)

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)