10 points

answer:

Detailed explanation:

Option A: $1,565 monthly over 72 months

The total comes to $112,680

Option B: $1,012 each month for 10 years,

which is the same as 120 months

Thus, the total amount received is 1012×120

equaling $121,440.

Option C:

Receive $100,000 in a single payment.

All the details presented are accurate.

However,

As the individual has no preference whether to take the money personally or let it go to an heir, we can disregard the lump sum payment option of $100,000.

Furthermore, as they are willing to wait and are indifferent about who benefits from the insurance payout, the 72-month option can also be overlooked.

Therefore, choosing the second option is advisable since it provides the highest total and the most payments over time.

Waiting for ten years will yield $121,440.

A single rose sells for 50 cents, so buying two will cost $1 (50 cents multiplied by 2).

With 2 roses per dollar, spending $20 allows for the purchase of 40 roses.

They make $6 profit on $20 sales, which means they spend $14 on the 40 roses ($20 minus $6).

Dividing $14 by 40 roses gives a cost of $0.35 per rose.

Therefore, the vendor pays 35 cents for each rose.

Answer:

E(t) = [ 4cos(t), 2 sin(t) ]

Step-by-step explanation:

The equation for the ellipse can be represented as:

 (x² ÷ a² ) + (y² ÷ b² ) = 1    Here, a and b symbolize the semi-major and semi-minor axes.

In this specific instance, we have    x²/16 + y²/ 4 = 1

This expression indicates that it follows the form of (x/a)² + (y/b)² =1

Specifically in our case,    x²/16  + y²/4 = 1, which resembles                 sin²α + cos²α = 1.

By setting x = 4 cos(t), we can proceed to calculate y.

Utilizing the equation x²/16  + y²/4 = 1, we find that:

x²/16  + y²/4 = 1   ⇒    (x²  +  4y²) ÷ 16  = 1

Solving for y yields: (x²  +  4y²)  = 16    ⇒  y²  = ( 16 - x²) ÷4

Substituting x = 4 cos(t) gives us y²  =  (16 - 16cos²(t)) ÷ 4, leading to y = √4 (1 - cos²(t)).

Consequently, we have y = 2 sin(t).

Thus, the vector parameterization of the ellipse can be stated as:

E(t) = [ 4cos(t), 2 sin(t) ]