A movie theater manager of a small theater sells two sizes of popcorn at the concession stand. A jumbo popcorn has a profit of $4 and a mini popcorn has a profit of $3. The manager knows the maximum number of popcorn boxes that will fit in the concession stand, the cost of making the popcorn, and the minimum number of boxes he wants to sell each day. Let j represent the number of jumbo popcorns sold and let m represent the number of mini popcorns sold. What is the objective function, and how can it be used to maximize the profit based on the the given conditions?

Answer:

the answer is y = 1/2 x + 4

Step-by-step explanation:

I really don't know if it was -4 but if it was negative four you put -4 so hopefully this help

rational nummbers are supposed to be less than one so idk what your talking about

a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

Learn more about natural numbers here

https://brainly.com/question/2228445

#SPJ11

Thus, the df between subjects is 5. This represents the variation between the individual subjects in the study, which helps in determining if the treatment effects are statistically significant or if the differences are due to random chance.

In a two-factor analysis of variance, the dfbetween subjects refer to the degrees of freedom associated with the differences between the group means. In this particular scenario where there are six subjects who each underwent three treatments, we can calculate the dfbetween subjects for each factor separately.

For the first factor (treatment), we have three levels. Therefore, the dfbetween subjects would be equal to the number of treatments minus one, which is 2.
For the second factor (subjects), we have six subjects. Therefore, the dfbetween subjects would be equal to the number of subjects minus one, which is 5.

To calculate df between subjects, you will use the following formula:

df between subjects = (number of subjects - 1)

In this case, there are six subjects, so the formula becomes:

df between subjects = (6 - 1)

Hence, the df between subjects is 5. This represents the variation between the individual subjects in the study, which helps in determining if the treatment effects are statistically significant or if the differences are due to random chance.

Know more about the statistically significant

https://brainly.com/question/15848236

#SPJ11

the limits of integration become u = 576(-1.079 + 3)²/4² to u = 576(3 + 3)²/0²:

L =

(2/3)∫(u = 207.36 to u = ∞) sqrt[1 + u] (-y³ / 1152(x + 3)²) du

We can use the formula for arc length of a curve given by:

L = ∫(a to b) sqrt[1 + (dy/dx)²] dx

First, we need to solve for x in terms of y:

y² = 16(x + 3)³

(x + 3)³ = y²/16

x + 3 = (y/2)^(2/3)

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

Next, we find the derivative dy/dx:

y² = 16(x + 3)³

2y dy/dx = 16(3(x + 3)²)

dy/dx = 24(x + 3) / y

Now, we substitute x = (y/2)^(2/3) - 3 and dy/dx = 24(x + 3) / y into the formula for arc length:

L = ∫(0 to 1) sqrt[1 + (dy/dx)²] dx

L = ∫(0 to 1) sqrt[1 + (24(x + 3) / y)²] dx

L = ∫(0 to 4) sqrt[1 + (24(x + 3) / y)²] (2/3)y^(1/3) dy

L = (2/3)∫(0 to 4) sqrt[1 + 576(x + 3)²/y²] y^(1/3) dy

Now, we make the substitution u = 576(x + 3)²/y²:

du/dy = -1152(x + 3)²/y³

dy/du = -y³ / 1152(x + 3)²

When y = 4, x = (4/2)^(2/3) - 3 = -1.079

When y = 0, x = (0/2)^(2/3) - 3 = -3

To learn more about

Length of the curve

brainly.com/question/31376454

#SPJ11

Answer:

32.48 square inches

Step-by-step explanation:

The area of a polygon is \(A=\frac{nsa}{2}\) where \(n\) is the number of sides of the polygon, \(s\) is the side length of the polygon, and \(a\) is the length of the apothem.

We are given the polygon is a heptagon, so it has 7 sides, making \(n=7\)

We are given the heptagon's side length is 3.2 inches, making \(s=3.2\)

We are also given an apothem of 2.9 inches, making \(a=2.9\)

Therefore, by using the formula for the area of a polygon, we get\(A=\frac{nsa}{2}=\frac{7*3.2*2.9}{2}=\frac{64.96}{2}=32.48\)

In conclusion, the area of the heptagon is 32.48 square inches

Professional tennis players may constitute a(n) symbolic group for an amateur tennis player

A symbolic group is one in which a person is unlikely to be accepted even if they act like a member by emulating their beliefs, attitudes, and behaviors. For young people, cricket players like Sachin Tendulkar, Sourav Ganguly, etc., may serve as a representative group. By concentrating on the small scale, symbolic interactionism examines the individual within a community and their relationships with others.

Similar to this, professional tennis players may serve as a symbolic group for an amateur tennis player who identifies with certain players by mimicking their behavior whenever possible, even though the amateur tennis player does not meet the criteria for membership in the category of professional tennis players because he or she does not have the necessary skills or access to the professional circuit.

Read more about the symbolic group on:

https://brainly.com/question/29038156

#SPJ4

The antiderivative F(x) that satisfies the condition f(4) = 54 is F(x) = 15(x - √x)² - 6 The value of F(1) is -6.

To find the antiderivative f(x) of the function f(x) = 15√(x - √x) that satisfies the condition f(4) = 54, we need to integrate the given function.

Let's denote the antiderivative of f(x) as F(x). To find F(x), we can apply the power rule of integration, which states that the integral of xⁿ with respect to x is (xⁿ⁺¹)/(n+1), where n is not equal to -1.

Integrating f(x), we have:

F(x) = ∫[15√(x - √x)] dx

To evaluate this integral, let's make a substitution to simplify the expression. Let u = x - √x. Taking the derivative of both sides with respect to x, we get:

du/dx = 1 - (1/2√x)

Rearranging the equation, we have:

dx = (2√x) du

Substituting this back into the integral, we have:

F(x) = ∫[15√(x - √x)] (2√x) du

= 30 ∫[u] du

= 30 * (u²/2) + C

= 15u² + C

Now, we can substitute back u = x - √x:

F(x) = 15(x - √x)² + C

To determine the constant of integration C, we use the given condition f(4) = 54:

F(4) = 15(4 - √4)² + C

= 15(4 - 2)² + C

= 15(2)² + C

= 60 + C

Since F(4) = 54, we can solve for C:

60 + C = 54

C = 54 - 60

C = -6

Therefore, the antiderivative F(x) that satisfies the condition f(4) = 54 is:

F(x) = 15(x - √x)² - 6

To find F(1), we substitute x = 1 into the equation:

F(1) = 15(1 - √1)² - 6

= 15(1 - 1)² - 6

= 15(0)² - 6

= 0 - 6

= -6

Hence, the value of F(1) is -6.

To know more about antiderivative:

https://brainly.com/question/31396969

#SPJ4

Answer:

10 9/64

Step-by-step explanation:

To answer this, multiply '1 3/8 miles' by '7 3/8.'  

The improper fraction form of '1 3/8' is 11/8, and that of 7 3/8 is 59/8.

Multiplying 11/8 by 59/8, we get 649/64, or (as a mixed number) 10 9/64

Answer:

The x intercepts would be (-6; 0) and (2; 0).

Step-by-step explanation:

Take a look at the picture.

Calculate it replacing f(x) with 0. The result will be: x1 = -6, x2 = 2 (consequently, both y's equal 0).

Answer:

(-6,0),(2,0)

Step-by-step explanation:

x-intercept

at x-intercept y=0

f(x)=x^2+4x-12

x^2+4x-12=0

by using factorisation method

product=-12

sum=4

factors=6,-2

(x^2 -2x)+(6x-12)=0

x(x-2)+6(x-2)=0

(x+6)(x-2)=0

x+6=0, x-2=0

x= -6,x=2

Using the slope formula, we can conclude that the slope of the line is m = 2.

So, the slope of the line is:

Now, put the values and solve for the slope as follows:

Therefore, using the slope formula, we can conclude that the slope of the line is m = 2.

Know more about slope here:

brainly.com/question/3493733

#SPJ13

Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

To know more about derivative,

https://brainly.com/question/29752525

#SPJ11

Answer:

its D. 480 cubic meters for Ape.x

Step-by-step explanation:

Answer:

f(3) = 37

Step-by-step explanation:

If the formula for this arithmetic sequence is f(n)  = 19 + 6n, then the value of f(3) is 19 + 6(3), or f(3) = 37

Answer: C

you are right.

The property that describes the relationship where "x" depends on "z" when "x" depends on "y" and "y" depends on "z" is known as the transitive property.

The transitive property states that if "a" is related to "b" and "b" is related to "c," then "a" is also related to "c." In this case, "x" is related to "y" and "y" is related to "z," so it follows that "x" is related to "z" through the transitive property.

The transitive property is a fundamental principle in mathematics and logic that describes the relationship between three elements. It states that if there is a relationship between two elements and a second relationship between the second element and a third element, then there is also a relationship between the first element and the third element.

The three variables: "x," "y," and "z." The statement "x depends on y" implies that the value or behavior of "x" is influenced by the value or behavior of "y." Similarly, the statement "y depends on z" indicates that the value or behavior of "y" is influenced by the value or behavior of "z."

By applying the transitive property, we can conclude that "x" is dependent on "z." In other words, the value or behavior of "x" is indirectly influenced by the value or behavior of "z" through the intermediate variable "y."

This property is widely used in various fields of mathematics, including algebra, set theory, and graph theory, to establish connections and draw conclusions based on related dependencies. It helps to simplify complex relationships and enables reasoning about indirect influences between elements.

For more such questions on transitive property , Visit:

https://brainly.com/question/2437149

#SPJ11

Answer:

cosB = cos (π/2-A)

= sinA

=8/9

Step-by-step explanation:

Answer:

5 in

Step-by-step explanation:

If you look at the graph when the time was 0 is when the storm started so we read that there where 5in of snow initialy.

let the consecutive multiples be 7(n-1) , 7n and 7(n+1)

so 7(n-1)+7n+7(n+1)=777

or 3n=111,

n=37

252,259,266

\(7n+7n+7+7n+14=777\\21n=756\\n=36\\\\7n=252\\7n+7=259\\7n+14=266\)

252,259,266

First number 30 and second number is 30 to write one of the factors as a sum of two numbers.

What do math factors mean?

Let first number 30 and second number is 30

then  the sum of two factors

30+30=60

50+10=60

20×3=60

Learn more about factor

brainly.com/question/24182713

#SPJ1

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

To learn more about density visit;

https://brainly.com/question/29775886

#SPJ11

Answer:

42

Step-by-step explanation:

You can make a maximum of two tomato-cheese sandwiches. because you can only make as many tomato-cheese sandwiches as the number of cheese slices you have

To make a tomato-cheese sandwich, you need one tomato slice and one cheese slice. Since you have three tomato slices and two cheese slices, you are limited by the availability of cheese slices.

Therefore, you can only make as many tomato-cheese sandwiches as the number of cheese slices you have, which in this case is two.

The ingredient that limits the number of sandwiches you can make is the cheese slice. You have more tomato slices than cheese slices, so you cannot make more than two tomato-cheese sandwiches.

Even if you have extra tomato slices, you cannot make additional sandwiches because you do not have enough cheese slices to pair with them.

In summary, the number of tomato-cheese sandwiches you can make is determined by the ingredient with the lowest quantity,

which in this case is the cheese slice. Therefore, you can make a maximum of two tomato-cheese sandwiches.

To know more about number click here

brainly.com/question/28210925

#SPJ11

The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4

is B. 86.9%

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.

Therefore, The percentage of actual yield to theoretical yield is,

= (500/575)×100%.

= 0.8695×100%.

= 86.95%.

learn more about percentages here :

https://brainly.com/question/24159063

#SPJ1

Answer: below

Step-by-step explanation:

5x2x2x6 = 120

5x2x3x2x2 = 120

3x2x2x2x5 = 120

Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

To know more about subset, click here

https://brainly.com/question/31739353

#SPJ11

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x + 3), x >= -3

-2y = sqrt(x + 3)

4y² = x + 3

x = 4y² - 3

and now we need to rename x to y and y to x to make it a "normal" function :

y = 4x² - 3

since in the original function x >= -3, this gave us y <=0.

and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.

so, again, the full answer is

f^-1(x) = 4x² - 3, x <= 0

Answer:

The circumference of the firepit is 6π or approximately 18.84 feet.

Step-by-step explanation:

The circumference of a circle is 2πr.

Substitute the variable r with 3 and then solve the rest; 2π(3) = 6π or ≅18.84