someone holds a buy 2 get 1 free sale on water color paint the paint tubes cost $7.25 each. how much money did the store lose by giving away the free tubes of paint?

We want to find the dimensions of the rectangle of maximum area that can be inscribed in the ellipse $3x + 75y = 75$, with sides parallel to the coordinate axes.

Let the length of the rectangle be $x$, and the width be $y$. Then, the area of the rectangle is $A = xy$.

Since the sides of the rectangle are parallel to the coordinate axes, its vertices lie on the ellipse $3x + 75y = 75$. The endpoints of the rectangle's length must lie on the x-axis, so we set $y=0$ and solve for $x$:

 3x + 75*0 = 75  

  x = 25

Similarly, the endpoints of the rectangle's width must lie on the y-axis, so we set $x=0$ and solve for $y$:

3*0 + 75y = 75

y = 1

Therefore, the rectangle with sides parallel to the coordinate axes and maximum area that can be inscribed in the ellipse has length $x=25$ and width $y=1$.

The area of the rectangle is $A=xy=25*1 = {25}$.

To know more about area refer here:

https://brainly.com/question/16151549?#

SPJ11

The given points (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

A point lies on a line if and only if it can be written as the sum of a scalar multiple of a direction vector and a position vector of the line.

To determine if each point lies on the line defined by X = -5 + t, y = 6t, and z = 6+ t, we can substitute each point into this equation to see if it is equivalent.

(a) (0, 30, 11):

-5 + t = 0, so t = 5

y = 6t = 6 × 5 = 30

z = 6 + t = 6 + 5 = 11

So, (0, 30, 11) can be written as -5 + 5i + 6 × 5j + 6k = -5i + 30j + 11k, which lies on the line.

(b) (5, 6, 11):

-5 + t = 5, so t = 10

y = 6t = 6 × 10 = 60

z = 6 + t = 6 + 10 = 16

So, (5, 6, 11) does NOT lie on the line.

(c) (-7, -12, 4):

-5 + t = -7, so t = -2

y = 6t = 6 × -2 = -12

z = 6 + t = 6 + -2 = 4

So, (-7, -12, 4) can be composed as -5 - 2i + -12j + 4k = -7i - 12j + 4k, which lies on the line.

Therefore, (a) lies on the line, (b) does NOT lie on the line, and (c) lies on the line.

To know more about scalar multiple, here

https://brainly.com/question/8349166

#SPJ4

--The given question is incomplete; the complete question is

"Determine whether each point lies on the line.

X = -5 + t, y = 6t, z = 6+ t                                                                                                          (a) (0, 30, 11)                                                                                                                                (b) (5, 6, 11)                                                                                                                                          (c) (-7, -12, 4)"--

The electric field in this region at the coordinate (-7, 1, -3) is 13 V/m in the x-direction, 14 V/m in the y-direction, and -1 V/m in the z-direction.

To determine the electric field in the given region, we need to take the negative gradient of the electric potential function V(x, y, z). The electric field is defined as the negative gradient of the potential:

E = -∇V

The gradient of a scalar function in Cartesian coordinates is given by:

∇V = (∂V/∂x, ∂V/∂y, ∂V/∂z)

To find the electric field at the coordinates (-7, 1, -3), we need to calculate the partial derivatives of V(x, y, z) with respect to x, y, and z.

∂V/∂x = 2x + y^2

∂V/∂y = 2xy

∂V/∂z = y

Now, substitute the coordinates (-7, 1, -3) into these partial derivatives:

∂V/∂x = 2(-7) + (1)^2 = -14 + 1 = -13

∂V/∂y = 2(-7)(1) = -14

∂V/∂z = (1) = 1

the components of the electric field vector at (-7, 1, -3) are (-∂V/∂x, -∂V/∂y, -∂V/∂z):

E = (-(-13), -(-14), -(1)) = (13, 14, -1)

To know more about vector visit:

brainly.com/question/30958460

#SPJ11

Answer:

100x + 150y = 3050

x + y = 23

Step-by-step explanation:

the other answer had the right start and equations, and then did not give the result.

so, here the full picture :

x + y = 23

100x + 150y = 3050

so, the first equation gives us

x = -y + 23

which we can now use in the second equation

100(-y + 23) + 150y = 3050

-100y + 2300 + 150y = 3050

50y = 750

y = 15 (15 adults)

x = -y + 23 = -15 + 23 = 8 (8 minors)

the maximum number of data points that fall below the second quantile is 4.

4 data points.

Quantiles divide a set of data into four equal parts, each with an equal number of data points. In this case, 36 data points are divided into 9 quantiles, meaning each quantile contains 4 data points. Therefore, the maximum number of data points that fall below the second quantile is 4.

Quantiles divide a set of data into equal parts, each with an equal number of data points. The number of quantiles is determined by the total number of data points. For example, if there are 36 data points, then it is divided into 9 quantiles, each with 4 data points. The lower the quantile, the lower the value of the data points it contains. Therefore, the maximum number of data points that fall below the second quantile is 4.

Learn more about maximum here

https://brainly.com/question/29156925

#SPJ4

Answer:

c

Step-by-step explanation:

Answer:

C on edge just took the quiz

Step-by-step explanation:

Answer:

The answer is 66.6346 round it to what ever place you need to.

Step-by-step explanation:

Take the 56,47, multiply it by .18, and add that value to 56.47 Hope it helps

The value of the maximum profit is 680

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the profit function is given as

P(x) = 230 + 30x - 0.5x^2

Differentiate the function

So, we have

P'(x) = 0 + 30 - x

Evaluate the like terms in the function

So, we have

P'(x) = 30 - x

Set the function to 0

So, we have

30 - x = 0

Evaluate

x = 30

Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2

So, we have

P(30) = 230 + 30 x 30 - 0.5 x 30^2

Evaluate

P(30) = 680

Rewrite as

Pmax = 680

Hence, the value of the maximum profit is 680

Read more about quadratic equations at

https://brainly.com/question/1214333

#SPJ1

Answer:

orientation is preserved (stays the same)

Step-by-step explanation:

Using mathematical operations, the amount left in Marilyn's savings account after writing a check for $450 under the overdraft protection scheme is $582.

An overdraft protection is an arrangement with the bank to move funds from linked accounts to a checking account to cover the difference when a check overdraws the account.

The amount in the checking account at the beginning of the month = $432

The balance in the savings account = $600

The amount of the check drawn = $450

The difference between $432 and $450 = $-18

The balance in the savings account at the end = $582 ($600 - $18)

Learn more about overdraft protection at https://brainly.com/question/29586720

#SPJ1

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

Answer:

67% (rounded)

Step-by-step explanation:

Since there is 1-6,

There is 3,4,5,6 which is 4/6 chance being above 2.

2/3 = 66.6%  

Answer:1/36

Step-by-step explanation:

Answer:

y= -1/2x + 1/2

Step-by-step explanation:

First, use the point-slope formula: y-y1 = m(x-x1)

y-2 = -1/2(x-(-3))

y-2= -1/2x + -1.5

(subtract 2 from both sides)

y = -1/2x + 1/2

If 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

Given:

Volume of cube=64cm³

Hence:

Volume of the cube = a³

Volume of the cube, a³= 64 cm³

Using this formula

Cube edge length =∛(side)³

Let plug in the formula

Cube edge length =∛(64cm³)

Cube edge length=4cm

Therefore if 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

Learn more about edge length of a cube here:https://brainly.com/question/16673486

#SPJ1

Answer:

84

Step-by-step explanation:

37 + 47 = 84

Answer:

10

Step-by-step explanation:

47-37=10

Answer: .25

Step-by-step explanation:

Answer:

If you asking how much was shared from if the three friends and the .75 it would be .25 each because .75/3 is .25. But if your asking how much did the three friends eat if the .25 is what they split then the answer would be 1/12 or .08333333

Step-by-step explanation:

B)  p and the q are switched

C) Neither p or q is negated

========================================================

Explanation:

The original conditional "if P, then Q" has P and Q swap places to form the converse. So the converse would be "if Q, then P". We don't negate P, and we don't negate Q either.

Here is the full list

Side notes:

The present balance in Isabella's bank.statement is; -$9.45

From the task content;

Hence, from the problem statements regarding her deposits, withdrawals, auto-payments, direct deposit and service charge; it follows that;

By finding the LCM of common terms;

x = -$9.45

Read more on fractions and Balance;

https://brainly.com/question/7475857

Answer:

x=4/3

Step-by-step explanation:

transpose 3 to the lhs

hope this helps

plzz mark me brainliest

An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

Learn more about outcomes here:

https://brainly.com/question/32511612

#SPJ11

Answer:

x = 2

Step-by-step explanation:

8 + 2(2 - 1) = 10

8 + 2(1) = 10

8 + 2 = 10

10 = 10

Answer:

B. $30.00

Step-by-step explanation:

The value of b = -3/2 and c = -5/4

To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:

(x + b)² = x² + 2bx + b²

Comparing this to the given expression x² - 3x + 1, we see that we need:

2bx = -3x, so b = -3/2

b² + c = 1, so substituting b = -3/2 gives:

(9/4) + c = 1

so c = 1 - 9/4

= 4/4 - 9/4

= -5/4

The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).

Therefore, the value of b = -3/2 and c = -5/4

Learn more about Quadratic Equation here

https://brainly.com/question/30098550

#SPJ4

Given question is incomplete, the complete question is below

the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?

Answer:

First choice, y = 2x + 4

Step-by-step explanation:

y = mx + b

m is the slope, and b is the y-intercept

The slope is 2 because it's going up, represented with y, 2 units while it goes to the right, represents x, each times. So how u write the slope is y/x, plug in the numbers and it's 2/1 which is just 2

b is the y-intercept, as in where the line goes through the y-axis. This y-axis is the vertical line. The line goes through 4 on the y-axis so the slope is 4

Plug in these numbers into the equation and u get y = 2x + 4

Answer:

A line with a slope of – that passes through the point (–14, 4)

Step-by-step explanation:

The equation of a line is typically written as y= mx+b where m is the slope and b is the y- intercept.