Melissa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Melissa drove home, there was notraffic and the trip only took 5 hours. If her average rate was 21 miles per hour faster on the trip home, how far away does Melissa live from the mountains?Do not do any rounding.

Answer:

500

Step-by-step explanation:

125x4=500

(125+125+125+125)  

Sorry if it's blurry, I can retake the picture

\(\color{plum}\tt\bold{(C) \: 500 \: mi}\)

Scale of a map :

=> 1 inch = 125 miles

Distance between two cities in map = 4 inches

Actual distance between the two cities :

\( =\tt 125 \times 4\)

\( =\color{plum}\tt 500 \: miles\)

Thus, the actual distance between the two cities = 500 miles

Therefore, the correct option is (C) 500 mi

Answer:

1

\(2 \times 2 \times 4 \times 1 \times \)

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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Answer:

4x+24

Step-by-step explanation:

4*x+4*6

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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Answer:

Step-by-step explanation:

The mountain in "The Negro Artist and the Racial Mountain" is considered as an obstacle for Negro artists who wish for others to recognize their work. This isn't just part of their job, but it's part of a racial dispute because of their color. Langston Hughes, the author, describes these Negro artists as very talented people. These are also people who believe they can make it big as artists, but they wish to be white to do so. Black artists think they can't be accepted as people, let alone artists. So the mountain in the essay represents a huge obstacle these people have to achieve. That obstacle is being accepted by everyone else, and that includes them looking past their color before appreciating their art.

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An inverse relationship can not direct.

We know that an inverse proportion represents inverse or indirect relation between two quantities.

In inverse relationship, one value increases while the other value decreases, and vice versa.

But in case of direct relationship, if one quantity increases , the other quantity also increases, and  if one quantity decreases , the other quantity also decreases.

When two quantities 'm' and 'n' are inversely proportional to each other, it means when the value of m increases while the value of quantity  'n' decreases, and vice versa.

Also, an inverse relationship always has a negative slope.

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Answer:

Step-by-step explanation:

The white-gloved etiquette mavens at the Emily Post Institute in Vermont say that restaurant tips should be 15% to 20% of the bill's pretax total. The Etiquette Scholar website agrees that you should “tip on the pretax amount of the bill, not on the total.”

Answer:

\(log_4(\frac{1}{4^5}) = -5\)

Step-by-step explanation:

\(log_b(a) = c\) ↔ \(b^c = a\)

You are given \(b\) = 4

You re also given \(c\) = -5

To find a, use the exponential form:

\(b^c = a\)

\(= (4)^{-5} = \frac{1}{4^5} = a\)

Then you can convert into a logarithm.

\(log_4(\frac{1}{4^5}) = -5\)

Answer:

There are multiple ways of writing this:

\(\sf -5log_4(4)=log_4(4^{-5})=log_4\left(\dfrac{1}{4^5}\right)=log_4\left(\dfrac{1}{1024}\right)\)

Step-by-step explanation:

Log rule:  \(\sf log_a(a)=1\)

\(\sf \implies log_4(4)=1\)

\(\sf \implies -5log_4(4)=-5\)

Log rule:  \(\sf c \cdot log_ab=log_a(b^c)\)

\(\sf \implies -5log_4(4)=log_4(4^{-5})\)

                       \(\sf = log_4\left(\dfrac{1}{4^5}\right)\)

                       \(\sf = log_4\left(\dfrac{1}{1024}\right)\)

Answer:

x = 27

Step-by-step explanation:

3x-4y = 65

Let y = 4

3x - 4*4 = 65

3x -16 = 65

Add 16 to each side

3x-16+16 = 65+16

3x  = 81

Divide each side by 3

3x/3 = 81/3

x = 27

The probability that the specific engineer Jane and the specific manager Mary are on the committee is 0.012.

The probability that the most experienced and least experienced engineers are on the committee is 0.1442.

To calculate this probability, we need to find the number of favorable outcomes (combinations where Jane and Mary are selected) and divide it by the total number of possible outcomes. Since we are selecting without replacement, the number of favorable outcomes is 1 (since there is only one Jane and one Mary). The total number of possible outcomes can be calculated using combinations: C(9, 2) * C(16, 4). Dividing the number of favorable outcomes by the total number of possible outcomes gives us the desired probability of 0.012.

To calculate this probability, we need to consider the arrangements where the most experienced and least experienced engineers are selected. There are 16 engineers, and we need to select 4 engineers for the committee. The most experienced engineer and the least experienced engineer are fixed, so we have to select the remaining 2 engineers from the remaining 14 engineers. The total number of possible outcomes is C(14, 2). Dividing this by the total number of possible outcomes (C(16, 4)) gives us the desired probability of 0.1442.

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Answer: I think it’s 5

Step-by-step explanation:

Well if you go on calculator 16 * 5 which would represent m - 0.4 would give you the answer 0.4.

The differential dy when x = 1 and dx = 0.3 is approximately 8.901.

When evaluating the differential dy of the function y = tan(5x + 3), we can use the formula dy = f'(x) * dx, where f'(x) represents the derivative of the function with respect to x. In this case, the derivative of tan(5x + 3) can be found using the chain rule, resulting in f'(x) = 5sec^2(5x + 3).

Substituting the given values into the formula, we have f'(1) = 5sec^2(5*1 + 3) = 5sec^2(8).

Evaluating sec^2(8) gives us a numerical value of approximately 9.867.

Multiplying f'(1) by the given dx of 0.3, we get dy = 5sec^2(8) * 0.3 ≈ 8.901.

To find the differential dy in this case, we applied the chain rule to differentiate the given function. The chain rule is a fundamental concept in calculus used to find the derivative of composite functions. By applying the chain rule, we were able to find the derivative of the function tan(5x + 3) and subsequently evaluate the differential dy. Understanding the chain rule is essential for solving problems involving derivatives of composite functions.

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Answer:

y = (7/4)x + 3

Step-by-step explanation:

(isolate the y variable by moving 7x) 4y = 7x + 12

(divide by 4 to get y by itself) y = (7/4)x + 3

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Option(C),  the approximate standard deviation of X is 7.59. The sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

To find the approximate standard deviation of X, we can use the formula:
σ = √(np(1-p))
Where n is the sample size (1500 in this case), p is the probability of success (0.04 in this case), and (1-p) is the probability of failure (0.96 in this case).
Substituting the values, we get:
σ = √(1500 x 0.04 x 0.96)
σ = √57.6
σ ≈ 7.59
Therefore, the approximate standard deviation of X is 7.59. Option C is the correct answer.
The standard deviation is a measure of how spread out a set of data is from the mean. In this case, the standard deviation of X represents how much the number of people who support the increase in the state sales tax varies from sample to sample.
As per the given information, 4% of all adults in Ohio support the increase. We can assume that this is the population proportion. Since we are dealing with a sample of 1500 adults in Ohio, we need to calculate the standard deviation of the sample proportion (X), which is an estimate of the population proportion.
Using the formula σ = √(np(1-p)), we find that the standard deviation of X is approximately 7.59. This means that if we were to take multiple random samples of 1500 adults from Ohio and ask them about their support for the sales tax increase, we can expect the number of supporters to vary by about 7.59 on average.
It's important to note that this is only an estimate, and the actual standard deviation of X may differ slightly from 7.59 due to sampling error. However, as the sample size increases, the standard deviation of X will decrease, making it a more reliable estimate of the population proportion.

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-7c^3d is a polynomial.

To determine the prices that maximize ACME's weekly profit, we need to set up the profit function and find its maximum point.

The profit function, denoted as Π, is given by:

Π = Revenue - Cost

Revenue = (p₁ * q₁) + (p₂ * q₂)

Cost = 28q₁ + 36q₂ + 1500

Substituting the demand equations into the revenue equation, we have:

Revenue = (120 - 1.5p₁ + p₂) * q₁ + (100 + 2p₁ - 3p₂) * q₂

Now, let's express the profit function in terms of p₁ and p₂:

Π(p₁, p₂) = (120 - 1.5p₁ + p₂) * q₁ + (100 + 2p₁ - 3p₂) * q₂ - (28q₁ + 36q₂ + 1500)

To maximize the profit, we need to find the critical points of the profit function. We can do this by taking partial derivatives with respect to p₁ and p₂ and setting them equal to zero.

∂Π/∂p₁ = -1.5q₁ + 2q₂ = 0

∂Π/∂p₂ = q₁ - 3q₂ = 0

Solving these two equations simultaneously, we find:

q₁ = 4q₂

Now, we can substitute this relationship back into one of the demand equations to find the corresponding prices:

91 = 120 - 1.5p₁ + p₂

92 = 100 + 2p₁ - 3p₂

Substituting q₁ = 4q₂ into the second demand equation, we get:

92 = 100 + 2p₁ - 3(4p₁/4)

92 = 100 + 2p₁ - 3p₁

92 = -p₁

From this, we can determine the prices:

p₁ = -92

Substituting p₁ = -92 into the first demand equation, we find:

91 = 120 - 1.5(-92) + p₂

91 = 120 + 138 + p₂

p₂ = -167

Therefore, the prices that ACME should set to maximize their weekly profit are p₁ = -92 and p₂ = -167, and their maximum weekly profit can be calculated by substituting these prices into the profit function Π(p₁, p₂).

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Answer:

many

a = 0.2

b = 0.7

Step-by-step explanation:

if a÷b is less than 1, then a must be smaller than b, so you can use any two decimals as long as a is the smaller of the two.

The given differential equation is not exact. To check if the differential equation is exact, we need to take partial derivatives of each term with respect to x and y and check if they are equal.

Since the partial derivatives are not equal, the differential equation is not exact.

To solve this equation, we need to use an integrating factor, a function that multiplies the entire equation to make it exact. The integrating factor for this equation is e^x:

Multiplying both sides of the equation by e^x, we get:

Now, if we take partial derivatives of each term with respect to x and y, we find that they are equal:

Since the partial derivatives are equal, the differential equation is now exact.

To solve the equation, we can integrate each term with respect to its corresponding variable. The solution is given by:

where C is the constant of integration.

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The paint needed is the surface area of the cylinder and he answer is approximately 296.73 cm².

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the notion of surface areas include wrapping, painting, and finally constructing things to get the greatest potential design.

The area of the lateral surface (the curved portion) and the areas of the top and bottom circles must be added to get the soup can's surface area.

The lateral surface area is calculated by dividing the can's height by its circumference (the distance around the circular base). The diameter is multiplied by to determine the circumference.

The area of the lateral surface (the curved portion) and the areas of the top and bottom circles must be added to get the soup can's surface area.

The lateral surface area is calculated by dividing the can's height by its circumference (the distance around the circular base). The diameter is multiplied by to determine the circumference.

Circumference = diameter × π = 7 cm × 3.14 = 21.98 cm

Lateral surface area = height × circumference = 10 cm × 21.98 cm = 219.80 cm²

The area of each circular top/bottom is given by:

Area of circle = π × radius²

The radius is half of the diameter, which is 7/2 = 3.5 cm.

Area of each circle = π × (3.5 cm)² = 38.48 cm²

The total surface area of the soup can is the sum of the lateral surface area and the two circular areas:

Total surface area = Lateral surface area + 2 × Area of each circle

Total surface area = 219.80 cm² + 2 × 38.48 cm²

Total surface area = 296.76 cm²

Therefore, the answer is approximately 296.73 cm².

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Answer:

?

Step-by-step explanation:

The density of rubbing alcohol is greater than the density of the block of wood.

What is Density?

Density is a physical property of matter that describes how much mass is contained within a certain volume of a substance. It is expressed in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per liter (kg/L). The formula for density is:

Density = mass / volume

Where mass is the amount of matter in a substance, typically measured in grams (g) or kilograms (kg), and volume is the amount of space the substance occupies, typically measured in cubic centimeters (cm³) or liters (L).

Density is defined as the mass of a substance per unit volume. In order to determine which material has the greater density, we need to calculate the density of each material using the given information.

The density of rubbing alcohol is given by:

Density = mass / volume = 4.0 g / 5.0 mL = 0.8 g/mL

The density of the block of wood is given by:

Density = mass / volume = 5.6 g / 8.0 cm³ = 0.7 g/cm³

Comparing the two densities, we can see that the density of rubbing alcohol is greater than the density of the block of wood. Therefore, rubbing alcohol has the greater density of the two materials.

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Answer:

5.625

Step-by-step explanation:

Answer:

$8.75

Step by Step Explanation:

10.00 - 1.25= $8.75

Answer:

Sum of Interior Angles = (Number of Sides -2) • 180 degrees

Sum = (12 -2) * 180

Sum of the interior angles = 1,800 degrees

Source:  http://www.1728.org/polygon.htm

Step-by-step explanation:

Answer:

Use the slope formula to find the slope  m.

 m = 0

Step-by-step explanation:

The slope of the line is zero (0).

Given the following points:

To find the slope of the line, we would use the following formula;

\(Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substituting the points into the formula, we have;

\(Slope. \;m = \frac{5 - 5}{-9 - 8}\\\\Slope. \;m = \frac{0}{-17}\\\\Slope. \;m = \frac{0}{-17}\)

Slope, m = 0

Therefore, the slope of the line is zero (0).

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24 students received an A on the test.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

If 80% of 120 students passed the test, the number of students who passed is 120 * 80% = 96 students.

If (1)/(4) of these students received an A on the test, the number of students who received an A is (1)/(4) * 96 = 24 students.

Therefore, 24 students received an A on the test.

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Answer:

a)7

b)x=6

Step-by-step explanation:

Answer:

z = 4, x = 6

Step-by-step explanation:

(a)

\(\frac{5z+1}{3}\) = 7 ( multiply both sides by 3 to clear the fraction )

5z + 1 = 21 ( subtract 1 from both sides )

5z = 20 ( divide both sides by 5 )

z = 4

(b)

\(\frac{5x}{3}\) + 3 = x + 7 ( multiply through by 3 to clear the fraction )

5x + 9 = 3x + 21 ( subtract 3x from both sides )

2x + 9 = 21 ( subtract 9 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Answer:

the last one

Step-by-step explanation: