Combine and simplify these radicals.<br> √3-√16<br><br> A 3√4<br> B 3√16<br> C 16√3<br> D 4√3

A restaurant manager has the option of a 30-year loan of $417,000 at an annual interest rate of 3.85% or the same interest rate

victus00 [196]

a) The monthly payment for each loan is as follows:

30-year $1,954.93

15-year $3,053.25

b) The savings in interest by using the 15-year loan is <u>$154,189,20</u> ($286,774.20 - $132,585).

c) No. the monthly payment for the 15-year loan is <u>not twice</u> that of the 30-year loan as the loan term.

d) The interest savings for the 15-year loan are <u>more</u> than one-half of the interest paid on the 30-year loan.

<h3>How are the calculations for periodic payments done?</h3>

The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:

N (# of periods) = 360 months (12 x 30 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $1,954.93

Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)

Total Interest = $286,774.20 ($703,774.80 - $417,000)

N (# of periods) = 180 months (12 x 15 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

<u>Results</u>:

PMT = $3,053.25

Sum of all periodic payments = $549,585 ($3,053.25 x 180)

Total Interest = $132,585 ($549,585 - $417,000)

Learn more about periodic payments at brainly.com/question/13098072

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7 0

1 year ago

Which of the following explains why the given radical is not in simpliest form ^3√162

nasty-shy [4]

This is a cube root, so we look for factors of 162 which are perfect cubes.

Find the prime factors of 162:-

162 = 2 * 3 * 3 * 3* 3

27 = 3^3 is a perfect cube

162 = 6 * 27

so ^3√ 162 = ^3√6 * ^3√27 = ^3√6 * 3

so the simplest form is 3 ^3√6

6 0

2 years ago

Read 2 more answers

g Suppose that a die is rolled twice. What are the possible values that thefollowing random variables can take on:(a) the maximu

KengaRu [80]

Answer:

(a) A = {1, 2, 3, 4, 5, 6}

(b) B = {1, 2, 3, 4, 5, 6}

(c) C = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(d) D = {-5, -4, -3, -2, -1, -0, 1, 2, 3, 4, 5}

Step-by-step explanation:

Assume each roll can result in the numbers 1, 2, 3, 4, 5, or 6.

(a) If both rolls result in a 1, the maximum value is 1. If either roll results in a 6, the maximum value is 6; all integers between 1 and 6 are also possible. Therefore, the possible values are:

A = {1, 2, 3, 4, 5, 6}

(b) If either roll results in a 1, the minimum value is 1. If both rolls result in a 6, the minimum value is 6; all integers between 1 and 6 are also possible. Therefore, the possible values are:

B = {1, 2, 3, 4, 5, 6}

(c) If both rolls result in a 1, the sum is 2. If both rolls results in a 6, the sum is 12; all integers between 2 and 12 are also possible. Therefore, the possible values are:

C = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(d) If the first roll results in a 1 and the second results in a 6, the result is -5. On the other hand, if the first roll results in a 6 and the second results in a 1, the result is 5; all integers between -5 and 5 are also possible. Therefore, the possible values are:

D = {-5, -4, -3, -2, -1, -0, 1, 2, 3, 4, 5}

7 0

2 years ago

Please help me now plz <br> I will mark you brainliest

jek_recluse [69]

Answer:

The vertex angle is 180-(60+75)=45.

k/sin75=900/sin45 so k=900sin75/sin45=1229km approx.

Step-by-step explanation:

6 0

3 years ago

An object is heated to 100°. It is left to cool in a room that

stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one. It involves natural logs and being able to solve equations that require natural logs. The formula is as follows:

$T(t)=T_{1}+(T_{0}-T_{1})e^{kt}$ where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value. That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

$80=30+(100-30)e^{5k}$ which simplifies to

$50=70e^{5k}$ Divide both sides by 70 to get

$\frac{50}{70}=e^{5k}$ and take the natural log of both sides:

$ln(\frac{5}{7})=ln(e^{5k})$

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared). That gives us:

$-.3364722366=5k$