The cost for each soda is $2.25. If your friend Calvin buys a certain number of Coca-Colas (c) and Mountain Dews (m), which answer choice shows an expression that represents the total cost of the Coca-Colas and Mountain Dews that Calvin bought?

Bill and his friends were thirsty and decided to buy Gatorade at the store. The cost of each bottle of Gatorade was $4. Bill and his friends spent $20 in total. Therefore, we can find out how many bottles of Gatorade they purchased by dividing the total amount spent by the cost per bottle. We can express this relationship as:

$$Total\ cost\ =\ Price\ per\ unit \times Quantity$$This relationship is also known as the cost-volume relationship. The cost-volume relationship indicates how changes in the quantity of goods or services purchased affect the total cost. Using the cost-volume relationship, we can find out how many bottles of Gatorade Bill and his friends purchased.

If they spent $20 in total, and each bottle of Gatorade cost $4, we can express this relationship as: $$20 = 4 \times Quantity$$where Quantity represents the number of bottles of Gatorade purchased. Solving for Quantity, we can divide both sides of the equation by 4: $$Quantity = 20/4 = 5$$Therefore, Bill and his friends bought 5 bottles of Gatorade.

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The given LP formulation is Minimize 6x1 + 3x2 + 4x3subject to2x1 + 2x3 − 2x3 ≤ 100x1 + 2x2 + 4x3 ≤ 180x1 − x2 + x3 ≥ 60To solve this LP formulation using Excel Solver, we follow the steps below:

Step 1: Enter the given LP formulation into an Excel sheet. We can do this by entering the coefficients of the variables and constraints in the sheet. The sheet should have a column for the variables and a column for the coefficients. We can also enter the right-hand side (RHS) values in the sheet.

Step 2: Click on the "Data" tab in the Excel ribbon and then click on "Solver" in the "Analysis" group. If the Solver Add-in is not installed, we can install it by clicking on "Solver" in the "Analysis" group and then following the instructions on the screen.

Step 3: In the Solver Parameters dialog box, set the objective function to be minimized. To do this, we select the cell containing the objective function, which is cell F2 in this case. We then click on the "Min" radio button in the "Set Objective" section.

Step 4: Set the variable cells in the "By Changing Variable Cells" box. We select the cells containing the variables, which are cells B2, C2, and D2 in this case.

Step 5: Set the constraints. To do this, we click on the "Add" button in the "Constraints" section. In the "Add Constraint" dialog box, we set the cells for each constraint and the relationship between the cell and the constraint. We also set the RHS value for each constraint.

Step 6: Click on the "OK" button to close the "Add Constraint" dialog box. We can add more constraints if necessary by repeating steps 5 and 6.

Step 7: Click on the "Solve" button to solve the LP formulation using Excel Solver. The optimal solution and optimal value are displayed in the sheet.

To solve the given LP formulation using Excel Solver, we first enter the coefficients of the variables and constraints in an Excel sheet. The sheet should have a column for the variables and a column for the coefficients. We also enter the right-hand side (RHS) values in the sheet. We then click on the "Data" tab in the Excel ribbon and then click on "Solver" in the "Analysis" group to open the Solver Parameters dialog box.In the Solver Parameters dialog box, we set the objective function to be minimized by selecting the cell containing the objective function and then clicking on the "Min" radio button in the "Set Objective" section.

We then set the variable cells in the "By Changing Variable Cells" box by selecting the cells containing the variables. We set the constraints by clicking on the "Add" button in the "Constraints" section. In the "Add Constraint" dialog box, we set the cells for each constraint and the relationship between the cell and the constraint. We also set the RHS value for each constraint. We can add more constraints if necessary by repeating this step.

We then click on the "OK" button to close the "Add Constraint" dialog box and click on the "Solve" button to solve the LP formulation using Excel Solver.

In this LP formulation, the optimal value is 64, which means that the minimum value of the objective function is 64. The optimal solution is x1 = 12, x2 = 24, and x3 = 8. These values satisfy all the constraints and minimize the objective function. Therefore, the conclusion is that the optimal solution is x1 = 12, x2 = 24, and x3 = 8, and the minimum value of the objective function is 64.

In this problem, we solved the given LP formulation using Excel Solver. We followed the steps of entering the coefficients of the variables and constraints in an Excel sheet, setting the objective function to be minimized, setting the variable cells in the "By Changing Variable Cells" box, setting the constraints, and clicking on the "Solve" button to solve the LP formulation using Excel Solver.

The optimal solution and optimal value were displayed in the sheet. We then interpreted the results so that the optimal solution is x1 = 12, x2 = 24, and x3 = 8, and the minimum value of the objective function is 64.

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The interaction degrees of freedom for an ANOVA with six levels of Factor A and six levels of Factor B would be 25.

In an ANOVA with interaction, the interaction degrees of freedom are calculated as the product of the degrees of freedom for Factor A and Factor B.

In this case, since both Factor A and Factor B have six levels, the degrees of freedom for Factor A would be 6 - 1 = 5, and the degrees of freedom for Factor B would also be 6 - 1 = 5. Therefore, the interaction degrees of freedom would be 5 * 5 = 25.

The interaction degrees of freedom represent the variability in the data that is attributed to the interaction between Factor A and Factor B. It reflects the unique information gained from considering the joint effects of both factors and allows us to assess whether the interaction is statistically significant.

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In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Answer:

28 cm²

Step-by-step explanation:

Given:

Parallelogram with 2 given sides, 4cm and 7cm respectively, and angle between them = 100°

Required:

Area of the parallelogram to 2 significant figure.

Solution:

Area of the parallelogram = a*b*sin(θ)

a = 4cm

b = 7 cm

θ = 100°

Area of parallelogram = 4*7*sin(100)

Area = 28*0.9848

Area = 27.57

Area of parallelogram to 2 significant figure = 28 cm²

Answer:

it is about 0.008353

Step-by-step explanation:

I will give the explanation later but i hope the answer helps  

The rate of change of the area when the radius is 2 centimeters is 32π square centimeters per minute.

To find the rate of change of the area of a circle with respect to its radius, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius.

We are given that the radius is increasing at a rate of 8 centimeters per minute, so we can express this as dr/dt = 8 cm/min.

To find the rate of change of the area when the radius is 2 centimeters, we need to differentiate the area formula with respect to the radius:

dA/dt = d/dt (πr²)

Using the chain rule, we have:

dA/dt = dA/dr * dr/dt

Since we want to find the rate of change of the area when the radius is 2 centimeters, we substitute r = 2 into the derivative:

dA/dt = dA/dr * dr/dt = (π(2)²) * 8 = 4π * 8 = 32π

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Answer:

i think is 81

Step-by-step explanation:

multiply 3.3.3.3 you would get 81

\(3^{4}\) will be equivalent to 81 .

Given,

\(3^{4}\)

Now,

A quantity representing a power upto which a number of expression is raised often written in superscript of number or an expression.

Simplify the given form,

\(3^{4}\)

= 3*3*3*3

= 9* 9

= 81

Hence,

3 to the fourth power is equal to 81 ( \(3^{4} = 81\) ) .

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Answer:

flooring crew > plumbers > paint crew > electricians

Step-by-step explanation:

when you turn all of the numbers into percentages, you get:

paint crew: 1/7 = 14%

plumbers: 0.15 = 15%

flooring crew: 1/6 = 16%

electricians = 12% (given)

Answer:

if you multiply the denominator by the AB^3 by 7 you wll get your common factor

Step-by-step explanation:

Step-by-step explanation:

Question 15:

5(x - 9) - 2(x + 3)

= (5)(x) + (5)(-9) - (2)(x) - (2)(3)

= 5x - 45 - 2x - 6

= 3x - 51

= 3(x - 17).

Question 16:

The terms 36x, 18y and 9 have GCF of 9.

Hence 36x - 18y + 9 = 9(4x - 2y + 1).

Answer:

That the object is moving

as time goes by the distant goes lower

Step-by-step explanation:

I think

Answer:

the object is moving forward with decreasing speed.

Step-by-step explanation:

Answer:

25/28

Step-by-step explanation:

5/4 x 5/7 = 25/28

Answer:

25/28

Step-by-step explanation:

Based on the number of names of winners that can be drawn, and the number of names in the basket, the number of different ways they can be drawn is 190 different ways

There are 20 names that you can draw from, in the raffle. There are however, only 2 names that can be picked for the same prize. This means that this is a combination problem.

The number of ways to pick the two winners can be modelled as:

= ₂₀C₂

= 20! / ( 2 ! ( 20 - 2) ! )

= 190 different ways

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Answer:

I think is 1 and 4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

he has 2 shirts for 1  pair(s) pants so if you multiply 9 times 2 you get 18 and if you multiply 9 time 1 you get  your answer which  is 9

A square is any 2-dimensional shape that has all 4 sides equal and opposite sides parallel.

A square is typically identified when we see any shape which has 4 sides. These sides are equal to one another. The opposite sides are parallel. Another very important feature to be noted is that a square makes an angle of 90° with its adjacent sides.

If the angles are not 90°, then the shape is a rhombus and not a square.

A perfect example of a square is the game board of ludo. That is a perfect square. Another example is a handkerchief.

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Answer:

60 inches

Step-by-step explanation:

Radius is 1/2 of a diameter, so diameter is twice a radius. 30 x 2 = 60 inches

Hope that helps! :)

-Aphrodite

Answer: 0.0849

Step-by-step explanation:

Use Scientific Notation

The average rate of change over the interval x = 3 and x = 7 is 30

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The equation is given as

g(x) = 2ˣ - 1

The interval is given as:

x = 3 and x = 7

Start by calculating g(3) and g(7)

So, we have

g(3) = 2³ - 1 = 7

g(7) = 2⁷ - 1 = 127

So, the average rate over these intervals is calculated as:

Average rate = [g(b) - g(a)]/[b - a]

This gives

Average rate = [g(7) - g(3)]/[7 - 3]

Substitute known values

Average rate = [127 - 7]/[7 - 3]

Simplify

Average rate = 120/4

Average rate = 30

Hence, the average rate of change is 30

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Explanation

The equation of a circle with center (h,k) and radius r units is given by:

then

Step 1

find the diameter of the cirlce:

to do this, we can use the distance between two points formula:

if

the distance from A to B is

so,let

distance CD=

hence, the diameter of the circle is

Step 2

find the center of the circle:

the center of the circle is the midpoint of CD

so

replace

so, the center of the circle is (-3,-1)

Step 3

finally, replace in the formula to get the equation of the circle

let

replace

therefore, the answer is

I hope this helps you

Answer: i hope this will help you

a^x=y this is a simple equation

where as loga(in the base) y=x this is a logarithmic equation

Answer:

The domain of the given graph is

\(( - 2,0,3,4)\)

Step-by-step explanation:

Hope it helps!!!

Answer:

a) any amount that isn't 1.5

b) 1.5

c) y = x/4 - 0.5

Answer:

$350,000

Step-by-step explanation:

lets say the original price is x, then 378000=1.08x, divide by 1.08 to get 350000

Answer:

D

Step-by-step explanation:

Radius is the length from center of circle to circumference