Mary and Julie both have a goal of raising $1000 for charity. Mary raises $12 every 4 days. Julie raises $19 every 6 days. Will

Answer:

The artist begins to profit when n > 8.18

That means the quantity of necklaces must exceed 8.18.

Step-by-step explanation:

Given

let n represent the number of necklaces

booth fee= $135

The expense for materials per necklace = $4.5n

the overall selling price for all necklaces = $12n

total costs= booth fee + material costs = $135 + 4.5n

profit = selling price - total costs

12n > 135 + 4.50n

By solving for n, we find

12n=135 + 4.50n

12n + 4.5n = 135

16.5n = 135

n = 135/16.5

n = 8.18

Hence, the artist achieves profits when n > 8.18.

I cannot find the provided table. It must be that one, as the other two options both reflect a slope of 2.

Answer: The option that is correct is

(C) T0,2(x, y)∘ R0, 270°.

Step-by-step explanation: We need to choose the transformation rule that defines how rectangle PQRS is transformed into P''Q''R''S''.

Observing the graph, we can identify that

the points of rectangle PQRS are P(-3, -5), Q(-2, -5), R(-2, -1) and S(-3, -1).

Conversely, the vertices of rectangle P''Q''R''S'' are P''(-5, 5), Q''(-5, 4), R''(-1, 4) and S(-1, 5).

The rectangle PQRS resides in Quadrant III while P''Q''R''S'' is located in Quadrant II,indicating that the rotation could either be 90° clockwise or 270° counterclockwise around the origin.

Among the provided choices, there is no 90° rotation available, hence we will consider the 270° counterclockwise rotation around the origin.

After executing this rotation, the points transform based on the rule

(x, y) ⇒ (y, -x).

Thus, the vertices of the resulting rectangle P'Q'R'S', after a 270° counterclockwise rotation around the origin, become

P(-3, -5) ⇒ P'(-5, 3),

Q(-2, -5) ⇒ Q'(-5, 2),

R(-2, -1) ⇒ R'(-1, 2),

S(-3, -1) ⇒ S'(-1, 3).

To align the vertices of P'Q'R'S' with those of P''Q''R''S'', we must add 2 units to the y-coordinate of all vertices , leading to

P'(-5, 3) ⇒ P''(-5, 3+2) = P''(-5, 5),

Q'(-5, 2) ⇒ Q''(-5, 2+2) = Q''(-5, 4),

R'(-1, 2) ⇒ R''(-1, 2+2) = R''(-1, 4),

S'(-1, 3) ⇒ S''(-1, 3+2) = S''(-1, 5).

Thus, the required transformation rule becomes

a rotation through 270° counterclockwise around the origin coupled with a translation of (x, y) ⇒ (x, y+2).

Since rigid transformations are documented from right to left, option (C) is indeed correct.

44 hours multiplied by $9 per hour equals $396.00.

It's really quite straightforward to calculate. Wishing you a great day!

Answer:

Step-by-step explanation:

1) True. This stems from the fact that the divergence of F is 1, indicating that F is a linear function. The orientation is outward from the surface. Integrating a linear function over a surface with outward orientation leads to the volume enclosed by that surface.

2) True. This is fundamentally what the Divergence theorem states.

3) False. Had F been specified as 3/pi instead of div(F), this claim would have held true.

4) False. The gradient of divergence can vary. The curl of the divergence of a vector function is 0, contradicting the notion of the gradient of divergence being 0.

5) False. While calculating divergence, derivatives are computed for different variables. Since the derivative of constants is 0, both vector functions F and G can contain distinct constant components even when their divergences are equal.