la quema de gasolina en un automóvil libera aproximadamente 3x104 kcal/gal. si un automóvil promedia 38 km/gal cuando se conduce a 95 km/h, lo que req

The total quantity demanded, q = q1 + q2, should be set such that the total cost is minimized and the price is maximized. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.

To maximize the company's profit, we must find the optimal quantity of q1 and q2 that minimizes the total cost and maximizes the price. We start by finding the total quantity demanded, q: q = q1 + q2. We can then use this equation to relate the price, p, and the total quantity, q, by substituting the equation for q into the equation for price: p = 50 - 0.04q. Next, we use the cost functions for each plant to find the total cost: C = C1 + C2. We can then use calculus to find the minimum total cost by taking the partial derivatives of C with respect to q1 and q2 and setting them equal to zero.Finally, we can use the equations for price and total cost together to find the optimal values for q1 and q2 that maximize the company's profit. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.

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We need to roll a die at least 3 times and a coin should be tossed at least 2 times.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given this, Becca repeatedly tosses a fair coin until she gets a head.

The probability of getting a head P(H) is = 1/2.

The probability of getting a number 3 or higher is,

P(3) + P(4) + P(5) + P(6).

= 1/6 + 1/6 + 1/6 + 1/6.

= 4/6.

= 2/3.

So, to get a number 3 or higher we need at least 3 rolls, and to get a head we need at least 2 tosses.

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-8

it is -8 because it is 8 blocks away, but since it os - it will be -8 your welcome

The number of nonempty sets of letters that can be formed from four a's and eight b's is 4096.

A set is a collection of distinct objects, called elements or members, that have some property or characteristics in common. Sets are used in mathematics to model and study the properties of objects and the relations between objects.

In set theory, sets are defined as unordered collections of elements that are well-defined and have certain properties.

We have,

The number of letters.

4 a's and 8 b's

This means,

a, a, a, a, b, b, b, b, b, b, b, b

Now,

The number of non-empty sets we can form is given by the formula.

= [tex]2^{n}[/tex]

Where n is the number of letters.

For example,

S = {1, 2, 3}

The number of nonempty sets.

[tex]2^{3}\\ =8[/tex]

= { {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}, Ф }

Similarly,

The number of nonempty sets from 4 a's and 8 b's.

= [tex]2^{12}[/tex]

= 4096

Therefore, The number of nonempty sets that can be formed from 4 a's and 8 b's is 4096.

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The purpose of converting a random variable to a z-value is to Compare a normal distribution to a standard normal distribution and Express the distance from the mean in terms of the standard deviation.

The purpose of converting a random variable to a z-value is to:

Compare a normal distribution to a standard normal distribution: By converting a random variable to a z-value, it can be compared to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. This allows for the calculation of probabilities and the interpretation of the results in a standard way.

Express the distance from the mean in terms of the standard deviation: The z-value expresses the distance of the random variable from the mean in terms of the standard deviation. This standardization makes it easier to compare values and to perform statistical analysis.

Converting a normal distribution to a z-value does not convert it to a uniform distribution or ensure that the sum of the probabilities is one. The sum of the probabilities in a normal distribution does not equal one, but rather approaches one as the values approach infinity.

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The maximum value of the expression ax² + 10x + c is 7, which means that the parabola represented by this equation opens upwards and its vertex is at the highest point.

The vertex of a parabola represented by the equation ax² + 10x + c is given by (-b/2a, f(-b/2a)), where b is the coefficient of x, a is the coefficient of x² and f(x) is the function.

Therefore the vertex of this parabola is (-10/2a, 7 - c)

Since the vertex is the highest point, the y-coordinate of the vertex is the maximum value of the expression.

7 - c = 7

therefore c = 0

We also know that the x-coordinate of the vertex is -10/2a, this means that the x-coordinate of the vertex is -5/a

There are many possible combinations of a and c that work for this question, some possible combinations are:

   a=1, c=0

   a=2, c=0

   a=-2, c=0

Another way to find a and c is by expanding the equation:

ax² + 10x + c = a(x²+ 10/a x) + c = a(x²+ 10/a x + (100-100a)/(4a²)) + c = a(x+5/a)² + c -25/a + 7

So, when a=1, c=0 and a=2, c=0 will give you the maximum value of 7, where it's a parabola that opens upwards and it's vertex is at the highest point.

Salut/Hello!

Answer: 133 km/h

Step-by-step explanation:
We need to first find out the distance travelled in 3 hours and 20 minutes.
We can say that 3 and 20 minutes is 3.20 by knowing that 100 km/h results that the distance travelled is 320 km

The same distance in 2 hours and 40 minutes:
We can say 2 hours and 40 minutes is 2,40 and we know our distance is 320 km results that the speed will be approximately 133 km/h

I hope it was useful! :]

The composite function g(x) is g(x) = 12x/(2x - 1)

From the question, we have the following parameters that can be used in our computation:

f(x) = x/(x - 6)

f(g(x)) = 2x

This means that

f(g(x)) = g(x)/(g(x) - 6)

So, we have

g(x)/(g(x) - 6) = 2x

Rewrite as

y/(y - 6) = 2x

This gives

y = 2x(y - 6)

Open brackets

y - 2xy = -12x

This gives

y = -12x/(1 - 2x)

So, we have

y = 12x/(2x - 1)

Hence, the function g(x) = 12x/(2x - 1)

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Answer:

To calculate the minimum thickness of the book, we need to add the thickness of the front and back covers to the thickness of all the pages.

Step 1: Calculate the thickness of the front and back covers:

2 * 0.9 mm = 1.8 mm

Step 2: Calculate the thickness of all the pages:

400 pages * 0.13 mm/page = 52.0 mm

Step 3: Add the thickness of the front and back covers to the thickness of all the pages:

1.8 mm + 52.0 mm = 53.8 mm

Answer:

The minimum thickness of the book is 53.8 mm.

Answer: 100

Step-by-step explanation:

(3*12)+2 = 38

(5*12)+2 = 62

38+62 = $100

Answer:

One possible exponential function that goes through points (0, 15) and (2, 240) is y = 15 * (2^x)

Another possible exponential function that goes through the points (0,15) and (2,240) is y= 15*(5^x)

Step-by-step explanation:

The rectangle volume is = 36000[tex]l[/tex] , where height = 6m, width = 4m , depth = 3m

The volume, V , of any rectangular volume solid is the product of the length, width, and height. We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, B , is equal to length × width.

Given that,

Rectangle height (h) = 6m

Rectangle width(w) = 4m

Rectangle depth(l) = 3m

Volume = [tex]l*w*h[/tex]

Volume = 6m * 4m * 3m

Volume = 72[tex]m^{3}[/tex]

In this example the depth will be 10 inches. Insert the measurements into the formula. Multiply the length (L) times the width (W) times the height (H). The formula looks like this: [tex]l*w*h[/tex] For this example, to calculate the volume of the object the formula would be 10 x 10 x 10 = 1,000 cubic inches.

Then the,

Volume = 72/2

Volume = 36[tex]m^{3}[/tex]

1[tex]m^{3}[/tex] = 1000[tex]l[/tex]

36[tex]m^{3}[/tex] = (36*1000)[tex]l[/tex]

= 36000[tex]l[/tex]

Therefore,

The rectangle volume is = 36000[tex]l[/tex] , where height = 6m, width = 4m , depth = 3m

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The average speed can be calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, Marjorie's average speed can be calculated by dividing the distance from her house to school (2 miles) by the time it takes her to get there (20 minutes).

To convert minutes to hours, we need to divide the minutes by 60. So, 20 minutes is equal to 20/60 = 0.33 hours.

Next, we divide the distance (2 miles) by the time in hours (0.33 hours) to find Marjorie's average speed:

2 miles / 0.33 hours = 6 miles/hour

Therefore, Marjorie's average speed is 6 miles per hour, making the correct answer (c) 60 mi/h.

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0, no solutions

that is the answer

The area of the rectangle whose length is twice its width, having a perimeter of 24√3 - 6√2 is 100 - 16√6.

The perimeter and area of a rectangle are expressed as;

Perimeter = 2( length + Width )

Area = Length × Width

Let the width be represented by 'x'.

Plug the given values in the formula above and solve for x.

Perimeter = 2( length + Width )

24√3 - 6√2 = 2( 2x + x)

24√3 - 6√2 = 2( 3x )

24√3 - 6√2 = 6x

6x = 24√3 - 6√2

x = ( 24√3 - 6√2 ) / 6

x = 4√3 - √2

Hence;

Width = x = 4√3 - √2

Length = 2x = 2(4√3 - √2) = 8√3 - 2√2

Now, we determine the area;

Area = Length × Width

Area = (8√3 - 2√2) × (4√3 - √2)

Expand using FOIL Method

Area = 8√3(4√3) + 8√3(-√2) - 2√2(4√3) - 2√2(-√2)

Area = 100 - 16√6

Therefore, the area is 100 - 16√6.

Option A) 100 - 16√6 is the correct answer.

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Answer:

To find the sum of all the numbers in the list, we can add each number together:

-45 + -21 + -16 + 12 + 33 + 40 = 59

So the sum of all the numbers in the list is 59.

The absolute maximum and minimum of f(x) = [tex]\frac{4x}{x^2+1}[/tex] on the interval [−4,0] are at x = 0 and -1, respectively.

The function is f(x) = [tex]\frac{4x}{x^2+1}[/tex] .

The interval is [−4,0].

To find the value of x we differentiate the function using the u/v formula.

[tex]\frac{d}{dx}\frac{u}{v}=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]

According to formula

f'(x) = [tex]\frac{(x^2+1)\frac{d}{dx}4x-4x\frac{d}{dx}(x^2+1)}{(x^2+1)^2}[/tex]

f'(x) = [tex]\frac{4(x^2+1)-4x(2x)}{(x^2+1)^2}[/tex]

f'(x) = [tex]\frac{4(x^2+1)-8x^2}{(x^2+1)^2}[/tex]

To determine the value of x equating f'(x) = 0

[tex]\frac{4(x^2+1)-8x^2}{(x^2+1)^2}[/tex] = 0

4(x^2 + 1) - 8x^2 = 0

4x^2 + 4 - 8x^2 = 0

4 - 4x^2 = 0

Add 4x^2 on both side, we get

4x^2 = 4

Divide by 4 on both side, we get

x^2 = 1

Taking square root on both side, we get

x = -1, 1

The value of x = 1 doesn't lie between the interval [-4, 0]. So we cannot consider 1.

Now evaluating the value of f(x) at -4,-1,0.

At x= -4, f(x) = -16/17

At x = -1, f(x) = -2

At x = 0, f(x) = 0

Therefore, the absolute maximum and minimum are at x = 0 and -1, respectively.

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The complete question is:

Determine where the absolute extrema of f(x) = [tex]\frac{4x}{x^2+1}[/tex] on the interval [−4,0] occur.

Answer:1.25/

Step-by-step explanation:

Answer:

The solid formed by rotating the above rectangle around the horizontal axis shown is best described as a cylinder with radius 3cm and height 6cm. The volume of this solid is 108 cubic centimeters, which can be calculated as follows: V = πr2h, where r is the radius and h is the height. In this case, r = 3cm and h = 6cm, so the volume is π x (3 cm)2 x 6 cm = 108 cubic centimeters.

The standard deviation of the given data is  4.35.

The variance of data can be expressed as the expectation of  as

σ²[tex]= E(X^{2} ) - (E(X))^{2}[/tex]

      [tex]E(X) = \frac{12 +18+ 19 + 22 + 25}{5}[/tex] [tex]= \frac{96}{5} = 19.2[/tex]      ⇒ [tex](E(X))^{2} = 368.64[/tex]

Now we have,

        [tex]E(X)^{2} = \frac{12^{2} +18^{2} +19^{2} + 22^{2} +25^{2} }{5}[/tex] = 387.6

From the above values we get the variance,

σ² = 387.6 - 368.64 = 18.96

σ = 4.35

Hence, the standard deviation of the given data is  4.35.

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The measure of side EF in triangle DEF is 5.34 units when angle D measures 40° and its adjacent side measures 7.6 units.

To get this answer, use the Pythagorean Theorem:

a2 + b2 = c2,

where a and b are the lengths of the sides adjacent to the right angle, and c is the length of the hypotenuse.

In this case, a = 7.6 and b = 5.34, so c = 8.93. Round this to the nearest hundredth and you get 5.34.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides adjacent to the right angle is equal to the square of the hypotenuse.

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Answer:

a

Step-by-step explanation:

because as time increases by 1 hr, the number of arrangements increases simultaneously by 3. so I can conclude that a=3hrs

The scatter plot for the correlation of weight and intelligence scores for 250 students would likely be very close to the origin, meaning that the majority of the points would be clustered around the point (0,0), with a very small range of points scattered further away.

This would indicate that there is no correlation between the two variables, which is reflected in the computed correlation coefficient of .00.

A scatter plot is a type of plot that displays data points on a two-dimensional graph. The data points are represented as dots or circles on the graph and show the relationship between two variables. The location of each data point is determined by the value of the two variables for that point. Scatter plots can be used to identify patterns in data, such as clusters, linear relationships, or nonlinear relationships. They can also be used to identify outliers or unusual data points.

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The function defined by M(t) = 2t + 1 has no maximum value on the interval [0,4) as the derivative of m(t) is not equal to zero.

The maxima of the function can be calculated by the derivative of the function. The derivative is equated to 0 to calculate the critical points. If the second derivative is negative at this critical point then a maximum exists at this point.

The function is M(t) = 2t + 1 . Differentiate the function with respect to t. Now equate the derivative to 0. This will give the critical point. Since 2 is not equal to 0, the critical point does not exist on the curve of the function. Therefore, the function M(t) = 2t + 1does not have a maxima.  M(t) = 2t + 1

   d/dt M(t) = d/dt 2t + 1

                  = 2

d/dt m'(t) = 0

2 not equal to 0

The function does not have a critical point. Therefore, the maxima do not exist for the function.

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The formula "3y + 8.6 = 24" can be expressed as "8.6 greater than for the combination of 3 and just a number y."

Mathematical operators like addition, deletion, multiply, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.For instance, the mathematical equation for "4 increased to 2" will be 2+4.

A mathematical expression is formed of a statement, at least two integers or variables, and one or more arithmetic. This mathematical operation enables the multiple, division, modification, or subtraction of numbers. The the above is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

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The exchange rate is the value of a country's currency in terms of another country's currency.

The exchange rate is the cost of a country's currency in respect to another currency. If the exchange rate between the U.S. dollar (USD) and the Japanese yen (JPY) is 120 yen for every dollar, then one dollar may be exchanged for 120 yen in the foreign exchange market.

From the above definition, it is clear that the complete definition of the exchange rate is given as the exchange rate is the value of a country's currency in terms of another country's currency.

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The solution to the system of linear inequalities x ≥ 3 and y≤ 2.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

This is represented on a coordinate plane, is a region that satisfies both inequalities. It is the half-plane formed by the line x= 2 and above the line y= 3 .

x ≥ 3

y ≤ 2.

It can be represented on a coordinate plane as a region that satisfies both inequalities.

To graph the solution, we first plot the line x = 2 on the coordinate plane. Since x <= 2, this line represents the boundary of the solution. Everything to the left of the line x = 2 is included in the solution.

Next, we plot the line y = 3. Since y less than 3, everything above the line y = 3 is included in the solution.

The solution set is x ≥ 3 and y≤ 2

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Answer:

Step-by-step explanation:

869 of the 800 surveyed volunteers were either tour guides or retirees. 539 were tour guides, and 430 were retirees, with 310 of the tour guides also being retirees.

Surveys are a type of data collection method in which individuals or organizations are asked to provide information about a particular topic or issue. Surveys can be used to collect information about people's opinions, behaviors, and preferences.

They can also be used to gather data on a particular population or group, such as demographics, employment, health, or other topics. Surveys are often used in research studies and can help to provide valuable insights into a variety of topics.

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Answer:

2b^2+10b+12 = 2(b^2+5b+6) = 2(b+3)(b+2)

4x^2+4x-3 = 4(x^2+x-3/4) = 4(x+3/2)(x-1/2)

6m^2+7m-3 = 6(m^2+m-1/2) = 6(m+1/2)(m-1/2)

10x^2-9x+6 = 10(x^2-x+6/10) = 10(x-1/2)(x-3/2)

18h^2+15h-18 = 18(h^2+5/6h-1) = 18(h+3)(h-2)