# Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). Heavier cars tend to have lower fuel efficiencies (lower mpg ratings). Which variable (weight or fuel efficiency) is most naturally considered the explanatory (predictor) variable in this context? A. Weight B. Fuel efficiency

Correct option: A. Weight.

Step-by-step explanation:

In regression analysis there are two kinds of variables: Explanatory and Response variable.

The explanatory variable are used to predict the changes in the response variable. They are also known as independent or predictor variable.

The response variable are observed for any changes caused by the explanatory variable. They are also known as the dependent or experimental variable.

In this case it is provided that heavier cars have lower fuel efficiencies.

It implies that there is linear inverse relationship between the variables weight of the car and fuel efficiency.

The response variable is the fuel efficiency and the explanatory variable is the weight of the car. Since the weight of the car is used to determine the fuel efficiency.

Thus, the explanatory variable is the weight of the car.

The explanatory variable in this context is the weight of the car, as it is used to predict or explain the car's fuel efficiency.

### Explanation:

In this context, the most naturally considered explanatory or predictor variable would be the weight of the car. This term is used to denote the variable that is used to predict or explain changes or variations in another variable. In this case, the weight of the car is used to predict or explain the fuel efficiency (measured in miles per gallon). For instance, if the weight of a car increases, we would expect the fuel efficiency to decrease (lower mpg) because heavier cars often require more energy to move, which in turn results in higher fuel consumption.

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F(x)=-2(x-5)^2+7 what is the parent graph

Let C be the unit circle in the xy-plane, oriented counterclockwise as seen from above. The divergence of the vector field F~ = (z, x, y) is zero, and as a result the flux through every surface with boundary C should be the same. Confirm that this is the case with the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane

Upper half of the unit sphere (call it ): parameterize by

with and . Take the normal vector to be

Then the flux of over this surface is

Lower half of the sphere (call it ): all the details remain the same as above, but with . The flux is again .

Unit disk (call it ): parameterize the disk by

with and . Take the normal vector to be

Then the flux across is

The flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same and it is zero.

### Explanation:

The divergence of the vector field F~ = (z, x, y) is zero. Therefore, the flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same.

This can be confirmed by considering that the electric flux through a closed surface is zero if there are no sources of electric field inside the enclosed volume. Since there are no charges inside the surfaces mentioned, the flux through each surface is zero.

Therefore, the flux through the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane is the same, and it is zero.

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The owner of a grocery store wants to mix two kinds of candy together to make 15 lb that he can sell for $5.00 per lb. He wants to use chocolate candies that he sells for$7.00 per lb and sugar candies that he sells for $2.00 per lb. How many pounds of each should the owner use?_ pounds of chocolate candies _ pounds of sugar candies =OWO= ### Answers Answer: 9 pounds of chocolate and 6 pounds of sugar candies Let's define the variables: C = pounds of chocolate candies used. S = pounds of sugar candies used. We know that he wants to make a total of 15lb, then: C + S = 15 We also want that the price per pound to be equal to 5$.

This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.

C*$7.00 +$2.00*S = $5.00*15 Then we have a system of equations: C + S = 15 C*$7.00 + $2.00*S =$5.00*15

To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:

C = 15 - S

now we can replace that in the other equation:

(15 - S)*$7.00 +$2.00*S = $5.00*15 Now we can solve this for S.$105 - $5.00*S =$75

$105 -$75 = $5.00*S$30 = $5.00*S$30/$5 = S = 6 Then there are 6 pounds of sugar candy, and we can use the equation: C + S = 15 C + 6 = 15 C = 15 - 6 = 9 There are 9 pounds of chocolate candy in the mix. Step-by-step explanation: ### Final answer: To find the pounds of chocolate and sugar candies the owner should use, set up and solve equations based on the given information. ### Explanation: Let's assume that the owner uses x pounds of chocolate candies and y pounds of sugar candies. According to the problem, the total weight of the candies should be 15 pounds. So, we can set up the equation: 1. x + y = 15 The owner wants to sell the candies for$5.00 per pound. We can set up another equation to represent the total value of the candies:

1. 7x + 2y = 5 * 15

Now we can solve these equations to find the values of x and y.
By solving the equations, we find that x = 9 and y = 6.

Therefore, the owner should use 9 pounds of chocolate candies and 6 pounds of sugar candies.