At a particular gas station gas costs $3.15 per gallon, but if you buy a
$5.50 car wash gas only costs $2.85 per gallon.
At how many gallons will you break even?
when is it cheaper to buy the car wash?

please help!!

Answer:

7

Step-by-step explanation:

The number of triangles in the figure is given as 15 triangles.

Given that,
To determine the number of triangles inside the triangles.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

here,
here in the figure inside the parent figure, there are 6 segments that contribute two triangles in the figure,
Number of triangle  = 6C2
Number of triangle = 15

Thus, the number of triangles in the figure is given as 15 triangles.

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Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

Answer:

\(9 + n\)

Step-by-step explanation:

Well it's an arythmetic sequence, so it will look like:

\(a + d\cdot n\)

Note that the first element is:

\(a + d\cdot 1\)

and the second element is:

\(a + d \cdot 2\)

So the difference between the two gives us d!

\(d = 11 - 10 = 1\)

Now let's find the \(a\):

\(a + d\cdot 1 = 10\\a + 1 \cdot 1 = 10\\a + 1 = 10\\a = 9\)

Answer:

700,000 is 1000 times as much as 700

Step-by-step explanation:

700,000 divided by 700 is 1000

Answer:

The answer wouldn't be 100 but it would be 1000

Hoped I helped

Answer:

80-3x = 5x+8

Step-by-step explanation:

Answer:

the answer is 3 b. multiplied by 6

Answer: The product xy is not constant, so the relationship is not an inverse variation.

Step-by-step explanation:

For it to be an inverse variation, the product of x and y must be constant.

This means the product xy is not constant, so the relationship is not an inverse variation.

(a) To find the partial derivatives, we differentiate the function f(x, y) with respect to x and y while treating the other variable as a constant.

fx(x, y) = d/dx [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]

          = [(8x(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2x)) / (x^2 + y^2)^2]

          = [(8x^3 + 8xy^2 - 8x^3 - 4x^2y - 8xy^2) / (x^2 + y^2)^2]

          = [-4x^2y / (x^2 + y^2)^2]

fy(x, y) = d/dy [ (4x^2 + 2xy + 4y^2) / (x^2 + y^2) ]

          = [(8y(x^2 + y^2) - (4x^2 + 2xy + 4y^2)(2y)) / (x^2 + y^2)^2]

          = [(8xy^2 + 8y^3 - 8xy^2 - 4x^2y - 8y^3) / (x^2 + y^2)^2]

          = [-4x^2y / (x^2 + y^2)^2]

(b) To find fx(0, 0) and fy(0, 0), we substitute x = 0 and y = 0 into the partial derivative expressions:

fx(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0

fy(0, 0) = -4(0)^2(0) / ((0)^2 + (0)^2)^2 = 0

(c) Both partial derivatives, fx(x, y) and fy(x, y), are continuous at every point in the set {(x, y): (x, y) ≠ (0, 0)}.

However, at the point (0, 0), the partial derivatives fx(0, 0) and fy(0, 0) are both 0, indicating that the partial derivatives are continuous at that point as well.

Therefore, the correct answer is (a) Yes, both the partial derivatives are continuous at every point in that set.

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The correct sum of the polynomial is \(\rm 6x^3 + 3x - 6\).

We have to determine

The correct sum of the polynomials.

Sum of the polynomials is just a matter of combining like terms, with some order of operations.

Then,

The correct sum of the polynomial is;

\(\rm (4x^3 - 2x - 9) + (2x^3 + 5x + 3) \\\\ 4x^3 - 2x - 9 + 2x^3 + 5x + 3\\\\ 6x^3 + 3x - 6\)

Hence, the correct sum of the polynomial is \(\rm 6x^3 + 3x - 6\).

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The probability that at least one of them is not interested in investment banking is 13/14.

It is a branch of mathematics. The possibility of the outcome of any random event is termed as probability. The range of the probability must be between o to 1. Here o indicates impossibility of an event and 1 indicates certainty. Probability can be expressed in proportions. Probability deals in finding the occurrence of an event.

Probability of the first person who is not interested in investment banking is 6/21

Probability of the second person who is not interested in investment banking and also first person was not interested then it is taken as 5/20.

probability that at least one is not interested in investment banking

=1- The probability that neither one of them is not interested in investment banking

=1-((6/21)×(5/20)

=13/14

Therefore, the probability that at least one of them is not interested in investment banking is 13/14.

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The intended population in this study is all members who received physical therapy in the past 12 months. The sample is the 212 members who returned the questionnaire.

The health care provider wants information about the satisfaction of its members who received physical therapy in the past 12 months. Therefore, the intended population in this study is all members who received physical therapy in that time period. This includes both the members who returned the questionnaire and those who did not.

On the other hand, the sample refers to the group from which the health care provider actually obtains information. In this case, the sample consists of the 212 members who returned the questionnaire. These are the individuals who voluntarily participated in the survey and provided their feedback on the satisfaction with physical therapy services. The sample represents a subset of the intended population.

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Answer: x = -3

Step-by-step explanation: You isolate the variable by dividing each side by factors that don't contain the variable.

The value of x after solving the given equation gives x = -3.

Given equation is,

7.5x + 0.5 = 2/3 (6x - 15)

We have to find the value of x after solving the given equation.

For that, we have to operate together the like terms.

Using distributive property, the right hand side of the equation becomes,

2/3 (6x - 15) = (2/3 × 6x) - (2/3 × 15)

                    = 4x - 10

Substituting this to the right hand side,

7.5x + 0.5 = 4x - 10

Taking the like terms on one side,

7.5x - 4x = -10 - 0.5

3.5x = -10.5

Dividing both sides by 3.5, we get,

x = -3

Hence the value of x is -3.

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From the given picture, we can note that

Similarly,

In the same way, we have

and finally,

Answer:

B

Step-by-step explanation:

The number of bushels of apples he picks (B) would be times by 5 as he would earn that much per bushel to get his pay (P)

Answer:

hey mate here is ur answer.

Step-by-step explanation:

Right angle : Whose one side is exactly 90°

Obtuse angle : Whose one side is more than 90° but less than 180°.

Equiangular triangle : Whose three sides is perfect or equal angles.

Acute Triangle: Whose all sides are below 90° angles. but since the sum of any triangle should be 180° (refer to google)

hope it helps you,

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Answer:

Triangles ABC and DEF have the following characteristics :B and E are right angles A=D, BC=EF which congruence theorem can be used to prove ABC =DEF

Answer:

D

Step-by-step explanation:

c=5/2-d/2

The / is the show fraction.

I am not 100% sure but it is what I am 99% sure about.

If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.

Probability

Total marbles:

Total marbles=15+14

Total marbles = 29

Chance that a red will be pulled=2/29

Chance that the second marble will be red =1/28

Hence,

Probability :

Probability = 2/29*1/28

Probability = 0.00246

Therefore  If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812

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Answer:

Step-by-step explanation:

a. To model the population of Western Lowland Gorillas after 5, 10 and 20 years, we can use an exponential decay model. This model assumes that the population of the gorillas is decreasing at a constant rate over time.

Let y equal the population of the gorillas and x represent the number of years since 2022.

The exponential decay model is represented by the equation:

y = a*e^(-rt)

Where a is the initial population, r is the decay rate and t is the number of years.

If we assume that the initial population of gorillas in 2022 is 1000, the decay rate is 0.1, and we can calculate the population of gorillas after 5, 10, and 20 years.

For 5 years after 2022:

y = 1000e^(-0.15) = 810 gorillas

For 10 years after 2022:

y = 1000e^(-0.110) = 648 gorillas

For 20 years after 2022:

y = 1000e^(-0.120) = 404 gorillas

b. Table:

Years Gorilla Population

5            810

10            648

20            404

c. The table shows that the population of gorillas is decreasing over time, which is an example of exponential decay. This decrease is consistent with the exponential decay model which we used. Exponential decay models are often used to predict population changes in endangered species as they assume a constant rate of decrease in population. Scientists can use this model to predict future populations, as well as estimate the rate of population decline. Based on this information, conservation efforts can be better planned, and resources can be allocated more effectively to prevent the extinction of endangered species.

Answer:

C = 10π ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius )

to find r use the area formula, that is

A = πr² = 25π ( divide both sides by π )

r² = 25 ( take square root of both sides )

r = \(\sqrt{25}\) = 5

then

C = 2π × 5 = 10π ft

Answer:

3 and 2 is the right answer and others are rongh

Answer:

2.3=v+0.47v=

We move all terms to the left:

2.3-(v+0.47v)=0

We add all the numbers together, and all the variables

-(+1.47v)+2.3=0

We get rid of parentheses

-1.47v+2.3=0

We move all terms containing v to the left, all other terms to the right

-1.47v=-2.3

v=-2.3/-1.47

v=1+0.83/1.47

Answer:

\(v = 1.564\)

Step-by-step explanation:

\(1v + 0.47v = 2.3\)

\( = > 1.47v = 2.3\)

\( = > v = \frac{2.3}{1.47} = 1.564\)

Answer:

Step-by-step explanation:

Lines l and m are the parallel lines and 't' is a transversal line,

Therefore, ∠1 ≅ ∠5 [Corresponding angle postulate]

∠5 ≅ ∠7 [Vertical angles theorem]

∠1 ≅ ∠7 [Transitive property]

Therefore, ∠1 ≅ ∠7 [Alternate exterior angles theorem]

Blue boxed text is ur answer

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Answer:

9

a

3

b

2

(

3

b

−

5

a

)

Step-by-step explanation:

The area of the third side of the triangle is either 20 square unit or 12 square units.

Triangle:

in math, triangle refers a simple closed curve made of three line segments and it has three vertices, three sides and three angles.

Given,

Two sides of a right triangle measure 2 units and 4  units.

And we need to find the area of the square that shares a side with the third side of the triangle  ​

Let us consider is  Two sides of a right triangle measure 2 units and 4  units.

Here if sides are perpendicular sides, then by using Pythagorean theorem

=> third side² = 2² + 4²

When we simplify this one, then we get,

=> third side² = 4 + 16

So, the  third side² = 20

Then the area of the square that shares a side with the third side of the triangle =  third side² = 20 sq units

Similarly, if 4  units is hypotenuse side, then by using Pythagorean theorem, the third side is calculated as,

=> third side² = 4² - 2²

And when we simplify this one, then we get,

=> third side² = 16 - 4

Therefore, the third side² = 12

And the area of the square that shares a side with the third side of the triangle =  third side² = 12 sq units

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Answer:

jhj

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

In 2 hours they wash 8 cars total so...

8

16

24

The extra time is 15 mins for 2 cars

Answer:

D.

Step-by-step explanation:

Your answer is D which is 10 because when you calculate 110/11 you would get 10 therefor When you calculate 110/11 you would get 10. Hope it helps you!

                             -Hope you have a great day ahead

The first-order necessary conditions for the given NLP problem involve the KKT conditions, and a specific solution satisfying these conditions needs further analysis.

(a) The first-order necessary conditions for constrained optimization problems are defined by the KKT conditions. These conditions require that the gradient of the objective function be orthogonal to the feasible region, the constraints be satisfied, and the Lagrange multipliers be non-negative.

(b) Assuming the first Lagrangian multiplier constraint is active means that it holds with equality, while the second one is inactive implies that it does not affect the solution. By incorporating these assumptions into the KKT conditions and solving the resulting equations along with the given constraints, a solution can be obtained.

(c) To determine if the solution satisfies the first-order necessary conditions, one needs to verify if the obtained values satisfy the KKT conditions. This involves checking if the gradient of the objective function is orthogonal to the feasible region, if the constraints are satisfied, and if the Lagrange multipliers are non-negative. Only by performing this analysis can it be determined if the solution satisfies the first-order necessary conditions.

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The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

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