A neighborhood is trying to set up school carpools, but they need to determine the number of students that need to travel to the

The parametric equations defining the tangent line are:x = Cos(10) - t×Sin(10)

y = Sin(10) + t×Cos(10)

z = 20 + 2t

When Z=20:Z=2t=20 ⇒ t=10

The point where tangency occurs is:

r(10)= Cos(10)

+ Sin(10)

+ 20 kTo derive the tangent line, we need the derivative of r(t):r'(t)= -Sin(t)

+ Cos(t)

+ 2 kThe directional vector at t=10 yields:r'(10)= -Sin(10) i

j

kThus, the equation for the tangent line can be formatted as:x = cos (10) - t×Sin(10)

Answer:

4. A)

3. A)

2. D)

1. C)

Step-by-step explanation:

4. Two families combined must have at least 3 pets.

3. $1500 represents your total, making everything else straightforward, as the keywords at least indicate that the a sum of $1500 must be greater or equal to $1500.2. Find the correspondents, then identify the inequality to apply. Here, use less than or equal because overpaying is unnecessary.1. Eight dollars

pizza and twelve dollars for each pizza yields 12x and 8x. The remainder follows logically, as we have our initial costs of $45 and $5, so Company A’s total would be less than Company B's total, leading directly to our conclusion.I’m happy to assist with any further queries.

Answer:

a.  P(x = 3) = 0.061313

b. The anticipated number of radio blackouts = 4

c.  It's unclear when the next radio blackout will occur.

d. P(x = 4) = 0.19537

Step-by-step explanation:

Based on the provided details:

A Poisson process is utilized to model the occurrence of this event:

Minor radio blackouts occur, on average, two times annually.

Therefore:

For question (a)

time t = 1/2 (i.e., six months)

Let x represent the likelihood of 3 incidents during the remaining months of the year.

Then:

P(x = 3) = 0.061313

b).

The expected number of radio blackouts over two years is calculated as follows:

We start with:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

Thus, the predicted number of radio blackouts = 4

c).

The time we must wait until the probability of witnessing the next radio blackout reaches at least 0.5 is as follows:

In this case, time (t) =???

Thus:

P(x =1) = 0.5

Consequently, we are unable to ascertain the probability (50%) of the next radio blackout.

d)

We can compute the probability that the time until the fourth blackout is at most 2 years as follows:

Here;

x =4, t = 2

Thus:

P(x = 4) = 0.19537

Response:

Volume of the trapezoidal prism = 15x^2 cubic units

Detailed explanation:

First, let’s calculate the area of the trapezoidal bases.

The lengths of the parallel sides are x and 2x, averaging to 1.5x.

The height stands at x

Consequently, area of the trapezoidal base comes out to be 1.5x * x = 1.5x^2

The volume of this prism is computed as area of the base multiplied by height

(the length is not a factor, but height certainly is)

Thus, 1.5x^2 * 10 yields 15x^2