Evaluate and simplify the following complex fraction.

Answer:

40 times greater

Step-by-step explanation:

Given the following:

Pluto average distance from the sun Ps =  3.6 x 10^8 miles

venus average distance from the sun Vs = 9.0 x 10^6miles

Take the ratio:

Ps/Vs = 3.6 x 10^8/9.0 x 10^6

Ps/Vs = 0.4*10^{8-6}

Ps/Vs = 0.4*10²

Ps/Vs = 40

Ps = 40Vs

Hence the pluto's average distance from the sun is 40 times greater than that of venus

Answer:

d

Step-by-step explanation:

because there is a closed dot at -4 you use the one with a line under it showing it is included and because there is open at 4 you use one without a line to show it is not included

Answer:

N is a negative number, and since you did not provide a clear first option, I will assume the answer is none of the above. However, the accurate answer is n < 0.

Step-by-step explanation:

Hope this helped!

Answer:

The amount by which her monthly payment will be lower if she purchases the points is $57.12.

Step-by-step explanation:

Since Alana will make a 20% down payment, the mortgage loan balance can be calculated as follows:

Mortgage loan balance = Mortgage amount – Down payment = $160,000 – ($160,000 * 20%) = $160,000 - $32,000 = $128,000

The amount by which her monthly payment will be lower if she purchases the points can now be calculated using the following steps:

Step 1: Calculation of monthly payment without purchasing 3 points

The monthly payment can be calculated using the formula for calculating loan amortization as follows:

P = (A * (r * (1 + r)^n)) / (((1+r)^n) - 1) .................................... (1)

Where,

P = monthly payment without purchasing 3 points = ?

A = Mortgage loan balance = $128,000

r = monthly interest rate = 4.9% / 12 = 0.049 / 12 = 0.00408333333333333

n = number of payment months = 30 years * 12 months = 360

Substituting all the figures into equation (1), we have:

P = ($128,000 * (0.00408333333333333 * (1 + 0.00408333333333333)^360)) / (((1 + 0.00408333333333333)^360) - 1)

P = $679.33

Step 2: Calculation of monthly payment if she purchases 3 points

Typically, each points purchased reduces the interest rate by 0.25%. Since Alana is considering a purchase of 3 points, her new interest rate can then be calculated as follows:

New interest rate = 4.9% - (0.25% * 3) = 4.9% - 0.75% = 4.15%

The monthly payment can also be calculated using the formula for calculating loan amortization as follows:

P3 = (A * (r * (1 + r)^n)) / (((1+r)^n) - 1) .................................... (2)

Where,

P3 = monthly payment if 3 points is purchased = ?

A = Mortgage loan balance = $128,000

r = new monthly interest rate = 4.15% / 12 = 0.0415 / 12 = 0.00345833333333333

n = number of payment months = 30 years * 12 months = 360

Substituting all the figures into equation (2), we have:

P3 = ($128,000 * (0.00345833333333333 * (1 + 0.00345833333333333)^360)) / (((1 + 0.00345833333333333)^360) - 1)

P3 = $622.21

Step 3: Calculation of the amount by which her monthly payment will be lower if she purchases the points

This can be calculated as follows:

Amount of reduction = P - P3 = $679.33 - $622.21 = $57.12

Therefore, the amount by which her monthly payment will be lower if she purchases the points is $57.12.

Answer:

28.87

Step-by-step explanation:

i just did the quiz

Answer:

Distance = √17

Step-by-step explanation:

We are looking for the distance between 5 + 4i and 9 + 3i.

This is as equal to saying we have two points in the plane, whose coordinates are; (5, 4) and (9, 3)

Distance between the 2 points will be;

D = √[(5 - 9)² + (4 - 3)²]

D = √(16 + 1)

D = √17

Answer:

y= -4x+7

Step-by-step explanation:

y-y1=m(x-x1)

y+1= -4(x-2)

y+1= -4x+8

y= -4x+7

Answer:

28,000 Ft

Step-by-step explanation:

Answer: 16 is -15700  and 17 28,000

Step-by-step explanation:

Answer: (24 + 60) = (6 × 4 + 6 × 10) = 6 × (4 + 10)

Answer:

$10.2

Step-by-step explanation:

Use this formula:

Price of product after discount = Initial  Price * ( 1 - (discount/100) )

Answer: 19

Step-by-step explanation:

Answer:

I believe the pattern is linear and for each month that goes by she earns $50

For each month that goes by, Michelle will increase her total savings by $50

The given parameters are:

Initial balance = $500

Savings = $50 monthly

This means that at the end of every month, her savings increases by $50.

This kind of pattern is a linear pattern

Read more about linear pattern at;

https://brainly.com/question/2097266

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Answer:

B

Step-by-step explanation:

15+15=30

30/9=3 r3 doesn't work

30+15=45

45/9=5

Answer:

x > 20 and x < 50; Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.

Step-by-step explanation:

Answer:

The range is 40 and the midrange is 20.

For the given number, the range is 40 and the midrange is 20. Option C is correct.

Given that,
42, 20, 36, 51, 60, 28,

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

Here,
In the given series least number = 20
Largest number = 60
Range = 60 - 20 = 40

Midrange = 40 / 2 = 20

Thus, For the given number, the range is 40 and the midrange is 20. Option C is correct.

learn more about the range here:
https://brainly.com/question/12239390

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Answer:

D. the runner can run less than 12 miles

Answer:

no this can't become a number that can be graphed

Answer:

8 years old

Step-by-step explanation:

Pls give brainliest!

Answer:12 cents per pencil

Step-by-step explanation:

1.44/12

Step-by-step explanation:

one second 12345678910

Answer:

The population at the beginning of 2016 is 55,326.

Step-by-step explanation:

Giving the following information:

Population 2010 (PV)= 42,000

Growth rate (g)= 4.7% = 0.047

Number of years (n)= 6 years

To calculate the population at the beginning of 2016, we need to use the following formula:

FV= PV*(1+g)^n

FV= 42,000*(1.047^6)

FV= 55,326

The population at the beginning of 2016 is 55,326.

Answer:

52.2% or A

Step-by-step explanation:

55+50 = 105

105/200 = 0.525

0.525 x 100 (to get the percent) = 52.5%

Answer:

52.5%

Step-by-step explanation:

Add together the number of papers delivered on Saturday and Sunday. Then divide that by the total number of papers delivered.

55+50 = 105

105/200=52.5%

Answer:

(9,12)

Step-by-step explanation:

Answer:

1) 1/3

2) 1/2

3) 4/1

4) 3/4

5) 2/5, 4/10, 4:10, 4 to 10

6) 3:4, 6/12, 6:12, 6 to 12

7) 3 to 1, 9/3, 9:3, 9 to 3

8) 7/9, 14/18, 14:18, 14 to 18

9)

a) 3/2

b) 3/5

c) 27:18

10) 96 birds visited the feeder

11)

a) nuts row: 3, 6, 9, 12

   raisins row: 4, 8, 12, 16

b) 7.5 cups

12)

a) This ratio means that for every 9 boys in the school there are 10 girls

b) 570 students

Answer:

a) <DXC and < CXB are complementary angles

b) Supplementary angles

<AXB and <DXB

<AXC and DXC

Step-by-step explanation:

Complementary angles: Two angles are complementary angles if their sum equals 90°

Supplementary angles: Two angles are Supplementary angles if their sum equals 180°

a) Name a pair of complementary angles

So, <DXC and < CXB are complementary angles

b) Name two Supplementary angles pair

<AXB and <DXB (their sum equals 180°)

<AXC and DXC ((their sum equals 180°))

Answer:

0.0017 years

Step-by-step explanation:

Distance of North Star from Earth = 460 light years

A light year is the distance traveled by light in one year.

As per given statement:

Distance traveled by light in one second = 18600 miles

Distance traveled by light in one year ([tex]60 \times 60 \times 24\times 365[/tex]) = 18600 [tex]\times[/tex] 31536000 miles = 14506560000 = 14.51 [tex]\times[/tex] [tex]10^9[/tex] miles

We know that:

1 billion = [tex]10^9[/tex]

Therefore, 14.51 [tex]\times[/tex] [tex]10^9[/tex] miles = 14.51 billion miles

Also, it is given that speed of rocket = 1 billion miles per hour

Formula to represent relationship between Speed, Distance and Time is given as:

[tex]Distance = Speed \times Time[/tex]

[tex]Time = \dfrac{Distance}{Speed}[/tex]

[tex]Time =\dfrac{14.51\ billion\ miles}{1\ billion\ per\ hour}\\\Rightarrow Time = 14.51\ hours[/tex]

OR

0.0017 years