A-

An account grows at an annual interest rate of r⁡ ⁣, so it grows by a factor of x=1+r⁡ ⁣⁣ ⁡ each year. The function A(x)=800x

Paladinen [302]

Given:

Annual interest rate = r⁡%

Growth factor : x = 1 + r⁡

The below function gives the amount in the account after 4 years when the growth factor is x⁡ ⁣⁣.

$A(x)=800x^4+350x^3+500x^2+600x$

To find:

The total amount in the account if the interest rate for the account is 3% each year and initial amount.

Solution:

Rate of interest = 3% = 0.03

Growth factor : x = 1 + ⁡0.03 = 1.03

We have,

$A(x)=800x^4+350x^3+500x^2+600x$

Substitute x=1.03 in the given function, to find the total amount in the account if the interest rate for the account is 3% each year.

$A(1.03)=800(1.03)^4+350(1.03)^3+500(1.03)^2+600(1.03)$

$A(1.03)=800(1.12550881)+350(1.092727)+500(1.0609
)+618$

$A(1.03)=900.407048+382.45445+530.45+618$

$A(1.03)=2431.311498
$

$A(1.03)\approx 2431.31
$

Therefore, the total amount in the account is 2431.31 if the interest rate for the account is 3% each year.

For initial amount the rate of interest is 0.

Growth factor : x = 1 + ⁡0 = 1

Substitute x=0 in the given function to find the initial amount.

$A(1)=800(1)^4+350(1)^3+500(1)^2+600(1)$

$A(1)=800+350+500+600$

$A(1)=2250$

Therefore, 2250 was put into the account at the beginning.

3 0

3 years ago

Which shows the number 27 factored into prime numbers? A. 2 · 3 · 3 B. 1 · 3 · 3 · 3 C. 3 · 3 · 3 D. 3 · 9

Vilka [71]

Hi!

<h3>To find the prime factorization of a number, keep dividing by the smallest factor that goes into it. </h3>

27/3 = 9

9/3 = 3

3/3 = 1

<h2>The answer is C. 3 · 3 · 3</h2>

Hope this helps! :)

-Peredhel

8 0

3 years ago

The Board of Directors of a small company consists of five people. Two of those directors are considered "strong leaders". If th

Pavel [41]

1: 40%
2: 30%
3: 20%

If we know one of the succeeded, then
1: 44.44%
2: 33.33%
3: 22.22%

If under the circumstance that they all fail to meet a strong leader, the board picks one of them at random,
1: 43.33%
2: 33.33%
3: 23.33%

The first person has a 2 in 5 chance of randomly getting a strong leader. If the first person doesn't find a strong leader, the second person has a 2/4 chance of getting a strong leader. If neither the first nor second person gets a strong leader, the third sales person has a 2/3 chance of getting a strong leader.

1: 2/5=40% Chance
2: (3/5)*(2/4)=30% Chance You have to take the probability the first rep failed to get a strong leader, then multiply by the probability the second rep gets a strong leader.
3: (3/5)*(2/4)*(2/3)=20% You have to take the probability both the other people failed, then multiply by the probability they succeeded.

7 0

3 years ago

When the family arrived in New Delhi from Rome, the youngest son asked the pilot how fast he was flying the plane. The pilot tol

Elden [556K]

Answer:

7 hours

Step-by-step explanation:

It is given that the plane was flying at 847 km/hour. So the speed of the plane was 847 kilometers per hour.

It is also given that the distance between Rome and New Delhi is 5,929 kilometers.

We know that the distance is equal to the product of speed and time, so we have,

$d= s\times t$ , where 'd' represents the distance, 's' represents the speed, and 't' represents the time.