a car uses 9 gallons of gasoline to go 162 miles. how many gallons of gasoline will the same car use to travel 216 miles?

The break - even point is 5.

C=15x + 150

R=45x

Here, C = R

15x + 150 = 45x

30x = 150

x = 5

The break - even point is 5

                                                 = 225

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The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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The validity of the given argument by utilizing the rules of implication and replacement rules.

To perform a proof of validity for the given argument, we'll use the rules of implication and replacement rules.

Here is the step-by-step proof:

1. P v (D v G) (Premise)

2. G -> O (Premise)

3. ~P & ~O (Premise)

4. /D (Assumption for conditional proof)

5. D v G (Disjunction Elimination from premise 1, using disjunction elimination rule)

6. G (Disjunctive Syllogism from step 4 and 5)

7. O (Modus Ponens using premise 2 and step 6)

8. ~P (Conjunction Elimination from premise 3)

9. P (Disjunctive Syllogism from premise 1 and step 8)

10. P & ~P (Conjunction Introduction from step 9 and step 8)

11. ~(Q v T) (Modus Tollens using premise 3 and step 10)

12. ~B (Premise)

13. (~B v A) (Disjunction Introduction from step 12)

14. (Q v T) v ~(~B & A) (Disjunction Introduction from step 13)

15. (~B & A) -> (R & S) (Premise)

16. (Q v T) v (R & S) (Hypothetical Syllogism using step 14 and step 15)

17. ~(~B & ~A) & B (Premise)

18. ~(~B & ~A) (Conjunction Elimination from step 17)

19. B (Conjunction Elimination from step 17)

20. (~B & A) (Conjunction Introduction from step 18 and step 19)

21. R & S (Modus Ponens using step 16 and step 20)

22. Valid (Conclusion)

The above proof shows the validity of the given argument by utilizing the rules of implication and replacement rules.

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Answer:

35.6%

Step-by-step explanation:

31/87(100)

3100/87

35.6%

Answer:

35,6%

Step-by-step explanation:

31/87 = 0,35632184

As a percentage: 35,632184%

Rounded to one deciman place: 35,6%

Answer:

There is nothing positive or negative about zero. Zero is just zero. It is NEITHER positive NOR negative. To the right of zero on number line are positive numbers and on the left of zero, lie the negative numbers on the number line.

Answer:

Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and located to the left of 0 on a number line. The number zero is neither positive nor negative.

Answer:

A

Step-by-step explanation:

Answer:

0.5 X 4 X 4 = 8 8 X 2 = 16

5.7 X 3 =17.1

3 X 4 X 2 = 24

16+17.1+24= 57.1 mm squared

Answer:Find the surface area of the prism.

The surface area is square millimeters.​

Step-by-step explanation: :>

Answer:

B) (-2, -4)

Step-by-step explanation:

the x-axis is the horizontal axis so (-2,4) reflected over it keeps the point two units away from the x-axis and 4 units away from the y-axis

The molar solubility of Ba₃(PO₄)₂ is its concentration of pure substance

The correct equation for the ksp is Ksp = 6x⁵

Start by writing the reaction for the solution of Barium phosphate

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Next, we make an ICE chart

Let "x" be the molar solubility of Barium phosphate

          Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp)

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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The molar solubility of Ba₃(PO₄)₂ is its concentration of a pure substance.

The correct equation for the ksp is Ksp = 6x⁵.

The solubility product constant is the equilibrium constant for the dissolution of a solid substance into an aqueous solution. It is denoted by the symbol Ksp.

Start by writing the reaction for the solution of Barium phosphate.

Ba₃(PO₄)₂  ⇌3Ba²⁺ +2PO₄³⁻

Let "x" be the molar solubility of Barium phosphate

         Ba₃(PO₄)₂(s)  ⇌3Ba²⁺ +2PO₄³⁻

I                                 0                  0

C                              +3x               +2x

E                                3x³                 2x²

Lastly, we write the expression for the solubility product constant (Ksp),

This is represented as:

Ksp = [3Ba²⁺] × [2PO₄³⁻]²

Ksp = 3x³ × 2x²

Evaluate the product

Ksp = 6x⁵

Hence, the correct equation for the ksp is Ksp = 6x⁵

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Answer:

A rectangle doesn't have equal sides

Both sides are not equal

Answer:

A: 6:30 = 3:15

B: 4:24 = 2:12 = 1:6

Step-by-step explanation:

The allowable increase or decrease represents the maximum amount by which the right-hand side of a constraint can change without affecting the shadow price of that constraint.

The amount by which the right-hand side of a constraint can change before the shadow price of that constraint changes is often referred to as the allowable increase or decrease.

In linear programming, the shadow price represents the rate of change of the objective function value with respect to a unit change in the right-hand side of a constraint. It provides valuable information about the sensitivity of the solution to changes in the constraint coefficients.

The allowable increase refers to the maximum amount by which the right-hand side can be increased while maintaining the same shadow price. If the right-hand side is increased beyond this limit, the shadow price will change, indicating a change in the optimal solution. On the other hand, the allowable decrease refers to the maximum amount by which the right-hand side can be decreased while still maintaining the same shadow price.

Determining these allowable changes is important for understanding the flexibility and stability of the optimal solution in response to changes in the problem's constraints.

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If you have more than $250,000 to deposit, you should consider spreading your money across multiple accounts or banks to ensure that your funds are fully insured by the FDIC (Federal Deposit Insurance Corporation).

If you have more than $250,000 to deposit, you can safely store your deposits by spreading them across multiple accounts and/or banks. This strategy is commonly referred to as "deposit insurance coverage" and is provided by the Federal Deposit Insurance Corporation (FDIC). In this way, if any one bank fails, you will still have access to your insured funds through the other banks.

A second option is to use the CDARS program. The Certificate of Deposit Account Registry Service is a program that can be utilized by investors to deposit their funds in CDARS member banks. The service allocates these deposits across multiple banks to guarantee that the funds are fully insured.

The third option is to seek the services of an FDIC-insured bank that offers deposit insurance coverage beyond the $250,000 limit. These banks may provide higher deposit insurance coverage, and you can inquire with your bank to determine if they offer this service.

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Initial size of the culture = 400 , Doubling period = (35 minutes - 10 minutes) / (1900 - 400) = 0.1437 minutes , Population after 60 minutes = 400 * (2^(60/0.1437)) = 10201 and Population will reach 11000 after approx. 74.51 minutes.

The initial size of the culture can be found by substituting t = 0 into the exponential growth formula:

P(t) = P0 * (2^(t/T))

where P(t) is the population at time t, P0 is the initial population, and T is the doubling period. Substituting t = 0, we get:

400 = P0 * (2^(0/T))

Therefore, P0 = 400.

The doubling period can be found by rearranging the exponential growth formula:

T = (t2 - t1) / (ln(P2) - ln(P1))

where t1 and t2 are the time points, and P1 and P2 are the populations at those time points. Substituting t1 = 10, t2 = 35, P1 = 400, and P2 = 1900, we get:

T = (35 - 10) / (ln(1900) - ln(400)) = 0.1437 minutes

The population after 60 minutes can be found by substituting t = 60 into the exponential growth formula:

P(60) = P0 * (2^(60/T))

Substituting P0 = 400 and T = 0.1437, we get:

P(60) = 400 * (2^(60/0.1437)) = 10201

Finally, the population will reach 11000 after approx. 74.51 minutes can be found by setting P(t) = 11000 in the exponential growth formula and solving for t:

11000 = 400 * (2^(t/0.1437))

t/0.1437 = ln(11000/400)

Therefore, t = 0.1437 * ln(11000/400) ≈ 74.51 minutes

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Answer: I would say about $2.06 when rounded

Step-by-step explanation:

18.79/9.1=~$2.06

Answer: This is what I got??  It doesn't feel right.

X = -5.7

Step-by-step explanation:

Let B = 12/C

Solve the other two equations for A.

Then set both equations, solved for A, equal to each other.

Substitute 12/C for B.

Cross Multiply.

Answer:

x=4

Step-by-step explanation:

The product of these two numbers -

What is a factors in math?

Marie is thinking of a multiple of = 63

Jay is thinking of a factor of = 63

The multiples of 63.

63,126,189,252,315

The factors of 63 = 1,3,7,9,21,63

As we can see, 63 is common, so is -63 if we go to the negative side.

So we multiply 63 and -63 and we get -3969

63 multiplied by -63 is equal to -3969

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Answer:

I think #2

Step-by-step explanation:

Answer:

288.4

Step-by-step explanation:

V=πr^2h=π·3^2·10.2≈288.39821

The means to study and analyze economic phenomena, formulate economic models, make predictions, and derive policy recommendations.

1. Importance of studying mathematics in economics:

a. Modeling and Analysis: Mathematics provides the tools and techniques for constructing models that represent economic phenomena.

These models help economists analyze and understand complex economic systems, predict outcomes, and make informed decisions.

b. Quantitative Analysis: Economics involves analyzing numerical data and making quantitative assessments. Mathematics equips economists with the necessary skills to handle and manipulate data, perform statistical analysis, and draw meaningful conclusions from empirical evidence.

c. Logical Reasoning and Problem Solving: Mathematics trains students to think critically, logically, and abstractly. These skills are essential in economics, where students need to formulate and solve economic problems, derive solutions, and interpret results.

2. Mathematical tools used in economics:

a. Calculus: Calculus plays a crucial role in economics by providing techniques for analyzing and optimizing economic functions and models. Concepts such as derivatives and integrals are used to study economic relationships, marginal analysis, and optimization problems.

b. Linear Algebra: Linear algebra is employed in various economic applications, such as solving systems of linear equations, representing and manipulating matrices, and analyzing input-output models.

c. Statistics and Probability: Statistics is used to analyze economic data, estimate parameters, test hypotheses, and make inferences. Probability theory is essential in modeling uncertainty and risk in economic decision-making.

d. Optimization Theory: Optimization theory, including linear programming and nonlinear optimization, is used to find optimal solutions in various economic problems, such as resource allocation, production planning, and utility maximization.

e. Game Theory: Game theory is a mathematical framework used to analyze strategic interactions and decision-making among multiple agents. It is widely applied in fields such as industrial organization, microeconomics, and international trade.

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The key thing to look for to determine whether a sequence is geometric is to see whether the ratio between consecutive terms - the number I would multiply one term by to get the next - is constant.

By inspection, we see that the fourth answer choice satisfies that, as \(\frac{81}{27}=\frac{27}{9}=\frac{9}{3}=\frac{3}{1}=3.\) Why not the first? We have \(2=\frac{12}{6}\ne\frac{6}{2}=3.\)

The third choice is not a geometric sequence, but rather an arithmetic sequence, where the difference between consecutive terms is constant. Just to make sure that it isn't geometric, we compute \(\frac{14}{9}\ne\frac{9}{4}.\)

The second sequence is not geometric (although it does eventually converge to 1, but not its corresponding series), as \(\frac{4}{3}=\frac{2/3}{1/2}\ne\frac{3/4}{2/3}=\frac{9}{8}.\)

Answer:

its D

Step-by-step explanation:

Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

Hope this helps!

Answer:

64 is the answer glad to help

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

The sum of the two vectors A and B is given by: R = A + B

Here, vector A = i + 4j And, vector B = 2i - j

Now, to find R, we will add the respective components of the two vectors, i.e,

R = (i + 4j) + (2i - j)

= 3i + 3j

The magnitude of vector R is given by the formula:

|R| = \(\sqrt{(R_x^2 + R_y^2)}\)

Substituting the values,

|R| = √(3² + 3²) = √18 = 3√2

The direction of vector R is given by the formula:

θ = tan⁻¹(\(R_y/R_x\))

θ = tan⁻¹(3/3)

θ = 45°

Therefore, the magnitude of vector R is 3√2 and its direction is 45°.

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

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The simplification of the given polynomial 0.4x⁵ - 0.7x in terms of algebraic factor will be x(0.4x⁴ - 0.7).

An algebraic factor is the multiplication of two algebraic terms.

That term could be in form of summation multiplication or in subtraction.

The root of the quadratic equation formed by the algebraic factor is always real.

As per the given expression,

0.4x⁵ - 0.7x

Take x as common

x(0.4x⁴ - 0.7)

The above form is factor form.

Hence "The simplification of the given polynomial 0.4x⁵ - 0.7x in terms of algebraic factor will be x(0.4x⁴ - 0.7)".

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Answer:

$8

Step-by-step explanation:

If it's 75% of that mean 2=25%

multiply it by 4 to get 8

If the sand falls at a rate of 16 cubic millimeters per second, a player would have approximately 6.25 seconds for their turn.

The rate of sand falling from the hourglass is given as 16 cubic millimeters per second. We need to find out the time available for a turn. Let's assume that the hourglass is filled with 'x' cubic millimeters of sand.

We can use the formula:

Volume = Rate x Time

Here, the volume of sand is 'x' cubic millimeters, the rate is 16 cubic millimeters per second, and we need to find the time available for a turn, which we can represent as 't' seconds.

So,

x = 16t

We can rearrange this equation to find 't':

t = x/16

This means that the time available for a turn is equal to the volume of sand in the hourglass divided by the rate at which the sand falls.

We don't know the exact volume of sand in the hourglass, but let's assume it's 100 cubic millimeters.

Then,

t = 100/16

t = 6.25 seconds

So, in this case, a player would have approximately 6.25 seconds for their turn before all of the sand falls to the bottom of the hourglass.

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