A car is travelling at 40 mph

How long will it take this car to travel 130 miles?

Give your answer in hours and minutes.

-3 > n is the same as n < -3 after you flip both sides and flip the inequality.

To graph this, we place an open hole at -3 on the number line. Then we shade to the left to indicate all values smaller than -3. The open hole says "the endpoint is not included". This is because -3 is not smaller than itself.

We would have a filled in circle if we had "or equal to" as part of the inequality, but we don't.

The graph is shown below.

Answer

Option A is correct.

B' (15, 6) is the answer.

Explanation

To dilate a given coordinate (x, y) about the origin by a scale factor of n, we will obtain (nx, ny).

So, for the given coordinate (5, 2), dilating by the scale factor of 3, we will obtain

B (5, 2) = B' (5×3, 2×3) = B' (15, 6)

Hope this Helps!!!

the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).

To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.

Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.

Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.

Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).

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The width of a standard television set is equal tp 16.8 inches.

We will solve this by using the  Pythagorean theorem which is below:

Or we can say

w = width

h = height

d = diagonal measure

We know the height is 0.75 times the width so 0.75w. We also know d = 26 , is our diagonal measure.

w = need to find

h = 0.75w

d = 26

\(w^2 + h^2 = d^2\\w^2 + 0.75w^2 = 26 ^2\\1.5625 w^2 = 441\\w^2 = 441/1.5625\\w ^2 = 282.24\)

w =16.8

Therefore width of a standard television set is 16.8 inches.

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A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a feasible solution that optimizes the objective function.

In optimization problems, decision variables are the quantities that we can control or adjust to achieve a desired outcome. Constraints are the limitations or conditions that these decision variables must satisfy. The objective function represents the goal or objective we want to optimize.

A feasible solution refers to a set of values for the decision variables that satisfy all the given constraints. This means that the solution meets all the specified requirements and does not violate any constraints. However, there can be multiple feasible solutions that meet the constraints.

Among these feasible solutions, the one that yields the best objective function value is the optimal solution. The objective function value is a measure of how well the solution aligns with the desired objective. The goal is typically to maximize or minimize this objective function value, depending on the problem.

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The solution to the system of equations 4 x-7 y=8 and -2 x+5 y=-1

 is x = 5.5 and y = 2.

Let's solve the first equation for x:

\(4x - 7y = 8\\4x = 7y + 8\)

x  = \(\dfrac{7y+8}{4}\)

Substitute the expression for x into the other equation.

Substitute\(\dfrac{7y+8}{4}\)for x in the second equation:

\(-2(\dfrac{7y+8}{4}) +5y = -1\)

\(-14y - 16 + 20y = -4\)

\(6y - 16 = -4\\6y = 12\\y = 2\)

Substitute the value of y back into either of the original equations to find the value of x.

Using the first equation:

\(4x - 7(2) = 8\\4x - 14 = 8\\4x = 22\\x = 22/4\\x = 5.5\)

Therefore, the solution to the system of equations is x = 5.5 and y = 2.

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The probability of rolling a 1 three out of the four rolls is 5/1296 or approximately 0.00384, which is a very small probability.

The probability of rolling a 1 on a single roll of a fair 6-sided die is 1/6. To find the probability of rolling a 1 three out of the four rolls, we can calculate the probability of rolling a 1 three times in a row, and then multiply that by the probability of rolling a non-1 on the fourth roll.

The probability of rolling a 1 three times in a row is (1/6) * (1/6) * (1/6) = 1/216.

The probability of rolling a non-1 on the fourth roll is 5/6.

So, the probability of rolling a 1 three out of the four rolls is (1/216) * (5/6) = 5/1296.

Therefore, the probability of rolling a 1 three out of the four rolls is 5/1296 or approximately 0.00384, which is a very small probability.

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However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.

Here,

If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?

The answer is: sin⁻¹(0.5) = 30°.

Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.

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Complete question:

Using the equality above, copy and complete the following:

The value of sin⁻¹ (0.5)​ when sin 30° = 0.5.

Answer:

325 or 325/1

Step-by-step explanation:

The formula for slope is:

y1 - y2/x1 - x2

Plugging the numbers in gives you:

40 - 690/0-2

Do subtraction first:

-650/-2

Two negatives make a positive and simplifying the fraction gives you:

325 or 325/1

Whichever makes you happier

(Also, remember that slope is rise/run, which is why it is y/x not the other way around(When graphing you go left/right then up/down))

Hope this helps you :)

The markup percentage for the clarinet is 33.33%

The store buys a guitar at the price of $45

The price tag on the trumpet in the store is $104.

30% in decimal value is approximately 1.3 and so the price should either be multiplied or divided by it to know the store markup and margin.

The store's selling price for the guitar would be $45 x 1.3 = $58.50.

The store paid $104 / 1.3 = $80 for the trumpet.

The store marked up the clarinet by $100 - $75 = $25.

The markup percentage for the clarinet is ($25 / $75) x 100 = 33.33%.

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The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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Answer:

1/3

Step-by-step explanation:

because if is tripled the size of original

The pharmaceutical company uses the quantitative variable to conducts an experiment.

Variables:

A variable is a characteristic of an object. Their values may occur more than once for a set of data. We consider just two main types of variables in this course.

Quantitative Variables - Variables whose values result from counting or measuring something.

Qualitative Variables - Variables that are not measurement variables. Their values do not result from measuring or counting.

Given,

A pharmaceutical company conducts an experiment in which a subject takes 75 mg of a substance orally.

And  the researchers measure how many seconds it takes for one quarter of the substance to exit the bloodstream.

Here we need to find the kind of variable is the company​ studying.

Here the company uses the Qualitative Variable because here they measure the effects of the medicine not the measurement.

So, the experiment uses the Qualitative Variable.

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Answer:

Step-by-step explanation:

Answer:

a) 12 feet per minute

b) 84 feet

c) 10 minutes

d)

Step-by-step explanation:

a) find the slope using furmula: y1 - y2/x1 - x2

24 - 12/2 - 1

12/1

12

12 feet per minute

b) 12 feet per minute so multiply the slope, 12 by 7

12 * 7 = 84

c) 12 * time, t, = feet deep

12 * t = 120

12t = 120

/12 /12

t = 10

10 minutes

Probit coefficients are typically estimated using:

A. the method of maximum likelihood.

The method of maximum likelihood is used to estimate the probit coefficients. This method aims to find the coefficients that maximize the likelihood of observing the given sample data. It involves an iterative process to identify the most likely parameter values for the model, making it suitable for nonlinear models like the probit model. Maximum likelihood estimation is a widely used method in econometric analysis due to its desirable properties, such as consistency and asymptotic efficiency.

In summary, probit coefficients are estimated using the method of maximum likelihood, which provides the most accurate and efficient estimates for this type of model.

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Answer:

Step-by-step explanation:

the number is y

you are told

y+0.5y=27

Therefore,

1.5y = 27.

If you divide by 1.5 on both sides, you'll get 18 which is your answer.

18+9=27

Step-by-step explanation:

Simplifying

5x + 12 = 58

Reorder the terms:

12 + 5x = 58

Solving

12 + 5x = 58

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.

12 + -12 + 5x = 58 + -12

Combine like terms: 12 + -12 = 0

0 + 5x = 58 + -12

5x = 58 + -12

Combine like terms: 58 + -12 = 46

5x = 46

Divide each side by '5'.

x = 9.2

Simplifying

x = 9.2

The compensating variation is $13.52.

The compensating variation is the amount of money that Greg would need to be compensated for a price increase in order to maintain his original level of utility. In this case, Greg's utility function is u = x^0.38x^0.962. His income is $83.00, and he faces these prices: (P1, P2) = (4.00, 1.00). If the price of x increases by $1.00, then the new prices are (P1, P2) = (5.00, 1.00).

To calculate the compensating variation, we can use the following formula:

CV = u(x1, x2) - u(x1', x2')

where u(x1, x2) is Greg's original level of utility, u(x1', x2') is Greg's new level of utility after the price increase, and CV is the compensating variation.

We can find u(x1, x2) using the following steps:

Set x1 = 83 / 4 = 20.75.

Set x2 = 83 - 20.75 = 62.25.

Substitute x1 and x2 into the utility function to get u(x1, x2) = 22.13.

We can find u(x1', x2') using the following steps:

Set x1' = 83 / 5 = 16.60.

Set x2' = 83 - 16.60 = 66.40.

Substitute x1' and x2' into the utility function to get u(x1', x2') = 21.62.

Therefore, the compensating variation is CV = 22.13 - 21.62 = $1.51.

To two decimal places, the compensating variation is $13.52.

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Let's call x to the number of hours

She writes 3 pages per hour, then after x hours she writes 3x pages

She already wrote 1 page and wants to write a total of 49, so she has to write 49 - 1 = 48 pages.

Then, the equation is:

3x = 48

x = 48/3

x = 16 hours

Answer:

3.75

Step-by-step explanation:

That is the decimal

Answer:

it's D

Step-by-step explanation:

if you were to divide the numerator by the denominator you would get 0.26 and the 6 is repeating

You can find the coefficient of variation for your data set using a TI-84 calculator by following the below steps.

To find the coefficient of variation (CV) using a TI-84 calculator, follow these steps:

1. Enter the data set values into a list on your calculator. For example, if your data is stored in the list L1, enter the values into L1.

2. Calculate the mean of the data set using the calculator's statistical functions. Press the [STAT] button and navigate to the "Calc" menu. Choose the appropriate mean function (e.g., "1-Var Stats" or "mean") and select the list that contains your data (e.g., L1).

3. Calculate the standard deviation of the data set using the calculator's statistical functions. Press the [STAT] button, navigate to the "Calc" menu, and choose the appropriate standard deviation function (e.g., "1-Var Stats" or "stdDev"). Select the list containing your data (e.g., L1).

4. Divide the standard deviation by the mean and multiply by 100 to calculate the coefficient of variation. Store the standard deviation and mean values in variables if necessary. Use the formula CV = (stdDev / mean) * 100 to calculate the coefficient of variation.

By following these steps, you can find the coefficient of variation for your data set using a TI-84 calculator.

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To find the coefficient of variation on a TI-84 Plus calculator, enter the dataset into a list, calculate the mean and standard deviation, and then divide the standard deviation by the mean and multiply by 100.

To find the coefficient of variation on a TI-84 Plus calculator, follow these steps:

By following these steps, you can find the coefficient of variation for a dataset using a TI-84 Plus calculator.

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   "

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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Answer:The first table would be a proportional relationship.

Step-by-step explanation:

It's the only table with a constant, which is required in a proportional relationship. The constant would be 1300 which you can find by divided the two numbers in each row.

Answer:

Width = 25

Length = 58

Step-by-step explanation:

Let the width = w

Length = 2w + 8

2(w + 2w + 8) = 166               Combine terms in the brackets

2(3w + 8) = 166                      Divide both sides by 2

(3w + 8) = 83                          Subtract 8 from both sides

3w = 83 - 8

3w = 75                                  Divide by 3

w = 25

L = 2*25 + 8                           Find the Length

L = 50 + 8 = 58                      

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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Answer:

Step-by-step explanation:

The systems of linear equations that have no solution are:

a)

x + y + z = 1,100

x - 2y - z = -500

2x + 3y + 2z = 2,600

b)

x + y + z = 2,400

2x - 2y + 2z = 700

x + 3y + z = 2,400

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To determine which systems of linear equations have no solution, we need to check whether the system is inconsistent, i.e., there are no values of x, y, and z that satisfy all the equations simultaneously.

One way to check this is to use row reduction to put the system into row echelon form or reduced row echelon form and see if we obtain any contradictory equations.

Another way is to use determinants, but we'll use row reduction here.

a)

| 1 1 1 | 1,100 |

| 1 -2 -1 | -500 |

| 2 3 2 | 2,600 |

R2 = R2 - R1 and R3 = R3 - 2R1:

| 1 1 1 | 1,100 |

| 0 -3 -2 | -1,600 |

| 0 1 -1 | -1,800 |

R2 = -1/3 R2 and R3 = R3 + R2:

| 1 1 1 | 1,100 |

| 0 1/3 2/3 | 533.33|

| 0 0 1/3 | -933.33|

Now, we can solve for z in the last equation:

z = -2800

Substituting into the second equation gives:

y = 2666.67

But substituting into the first equation gives:

x = -566.67

So, this system has no solution.

b)

| 1 1 1 | 1,500 |

| 1 -1 -1 | -500 |

| 2 1 1 | 2,000 |

R2 = R2 - R1 and R3 = R3 - 2R1:

| 1 1 1 | 1,500 |

| 0 -2 -2 | -2,000 |

| 0 -1 -1 | -1,000 |

R2 = -1/2 R2 and R3 = R3 - 1/2 R2:

| 1 1 1 | 1,500 |

| 0 1 1 | 1,000 |

| 0 0 -1 | -500 |

Now, we can solve for z in the last equation:

z = 500

Substituting into the second equation gives:

y = 500

But substituting into the first equation gives:

x = 500

So, this system has a unique solution.

c)

| 1 1 1 | 1,400 |

| 1 -2 -1 | -500 |

| 2 2 2 | 2,700 |

R2 = R2 - R1 and R3 = R3 - 2R1:

| 1 1 1 | 1,400 |

| 0 -3 -2 | -900 |

| 0 0 0 | 0 |

The last row of the augmented matrix corresponds to the equation 0x + 0y + 0z = 0, which is always true.

Therefore, this equation is not contradictory and doesn't add any new information to the system.

We can eliminate it and rewrite the system as:

| 1 1 1 | 1,400 |

| 0 -3 -2 | -900 |

R2 = -1/3 R2:

| 1 1 1 | 1,400 |

| 0 1 2/3 | 300 |

R1 = R1 - R2:

| 1 0 1/3 | 1,100 |

| 0 1 2/3 | 300 |

Now, we can solve for z in the first equation:

z = 3,300

Substituting into the second equation gives:

y = -1,200

But substituting into the first equation gives:

x = -2,200

So, this system has a unique solution.

d)

| 1 1 1 | 1,400 |

|-0.5 -0.5 -0.5 | -900 |

| 2 3 2 | 3,000 |

R2 = 2R1 + R2 and R3 = -4R1 + R3:

| 1 1 1 | 1,400 |

| 0 1/2 1/2 | -100 |

| 0 -1 -2 | -3,600 |

R3 = -2R2 + R3:

| 1 1 1 | 1,400 |

| 0 1/2 1/2 | -100 |

| 0 0 -3 | -3,400 |

Now, we can solve for z in the last equation:

z = 1,133.33

Substituting into the second equation gives:

y = -1,066.67

But substituting into the first equation gives:

x = 2,333.33

So, this system has a unique solution.

e)

| 1 1 1 | 1,900 |

| 1 -1 -2 | -2,000 |

| 2 2 1 | 1,100 |

R2 = R2 - R1 and R3 = R3 - 2R1:

| 1 1 1 | 1,900 |

| 0 -2 -3 | -3,900 |

| 0 0 -3 | -4,100 |

Now, we can solve for z in the last equation:

z = 1,366.67

Substituting into the second equation gives:

y = -1,033.33

But substituting into the first equation gives:

x = 1,667

So, this system has a unique solution.

f)

| 1 1 1 | 2,400 |

| 2 -2 2 | 700 |

| 1 3 1 | 2,400 |

R2 = R2 - 2R1 and R3 = R3 - R1:

| 1 1 1 | 2,400 |

| 0 -4 0 | -1,100 |

| 0 2 0 | 1,000 |

R2 = -1/4 R2 and R3 = 1/2 R3:

| 1 1 1 | 2,400 |

| 0 1 0 | 275 |

| 0 1 0 | 500 |

R3 = R3 - R2:

| 1 1 1 | 2,400 |

| 0 1 0 | 275 |

| 0 0 0 | 225 |

The last equation shows that 0x + 0y + 0z = 225, which is impossible. Therefore, this system has no solution.

Thus,

The systems of linear equations that have no solution are:

a)

x + y + z = 1,100

x - 2y - z = -500

2x + 3y + 2z = 2,600

b)

x + y + z = 2,400

2x - 2y + 2z = 700

x + 3y + z = 2,400

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Answer:

6

Step-by-step explanation: