Un comerciante compra 320 kg de azúcar en $784.00 en cuanto debe vender el kg. Para ganar el 18% sobre el precio de compra

The area of the rectangle EFHG with vertices E(-13, 7), F(-5, -1), G(-8, -4), and H(-16, 4) is 24 square units.

To calculate the area of rectangle EFHG, we need to find the length and width of the rectangle first.

One way to do this is to use the distance formula to find the length of one side of the rectangle and the width of the rectangle, and then multiply the length and width to find the area.

Length of the rectangle = distance between points E and H

= √[\((-13 - (-16))^2 + (7 - 4)^2\)]

= √(\(3^2 + 3^2\))

= 3√2

Width of the rectangle = distance between points E and F

= √[\((-13 - (-5))^2 + (7 - (-1))^2\)]

= √(\(8^2 + 8^2\))

= 8√2

Now that we know the length and width of the rectangle, we can calculate its area:

Area of rectangle EFHG = Length x Width

= 3√2 x 8√2

= 24

Therefore, the area of rectangle EFHG is 24 square units.

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Answer:

Angle P is congruent to itself due to the reflexive property.

Explanation:

Angle P must be congruent to angle S through corresponding angle theory.

Otherwise, it wouldn't prove ΔPQR is similar to ΔSTR.

Answer:

Angle P is congruent to itself due to the reflexive property.

Step-by-step explanation:

The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

A

Step-by-step explanation:

A is the most simplifiest form between the numbers.

Hey there! :)

Answer:

Last option. (-1, 0) and (0, 6).

Step-by-step explanation:

Solve this system by setting the two equations equal to each other:

6x + 6 = -x² + 5x + 6

Rearrange the equation:

x² + 6x + 6 - 5x - 6 = 0

Combine like terms:

x² + x = 0

Factor out x:

x(x + 1) = 0

Set each factor equal to 0:

x = 0

x + 1 = 0

x = -1

These are the x values of the solutions. Plug these into an equation to solve for y:

y = 6(0) + 6

y = 6

-------

y = 6(-1) + 6

y = -6 + 6

y = 0

Therefore, the solutions to the equation are (-1, 0) and (0, 6).

The requreid,
(a) Approximate values of the given numbers are π ≈ 3.1, √6 ≈ 2.4, 2√6 ≈ 4.8, and √7 ≈ 2.6.
(b) √6  < √7 <  π  < 2√6

(a)

π ≈ 3.1 (since π is between 3 and 4, and is closer to 3.1 than to 3.2)

√6 ≈ 2.4 (since 6 is between 4 and 9, and the square root of 6 is closer to 2.4 than to 2.5)

2√6 ≈ 4.8 (since 2√6 is approximately twice the value of √6, which is 2.4)

√7 ≈ 2.6 (since 7 is between 4 and 9, and the square root of 7 is closer to 2.6 than to 2.7)

(b)

Order from least to greatest:

√6  < √7 <  π  < 2√6

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Answer:

(a) \(x < \frac{9}{11}\)

(b) \(y> 2\)

Step-by-step explanation:

(1):

\(x - 15 > 4(-6+3x)\)

Open bracket

\(x - 15 > 4*-6+4*3x\)

\(x - 15 > -24+12x\)

Collect Like terms

\(x - 12x > 15 - 24\)

\(-11x > 15- 24\)

\(-11x > -9\)

Divide both sides by -11

\(x < \frac{-9}{-11}\)

\(x < \frac{9}{11}\) --- See first attachment for graph

(2):

\(6y-7>y+3\)

Collect Like Terms

\(6y-y>7+3\)

\(5y > 10\)

Divide both sides by 5

\(y > \frac{10}{5}\)

\(y> 2\) --- See second attachment for graph

Answer:

1.7 everyday

Step-by-step explanation:

The possible values of V is E. -9, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

To find the possible values of V, we need to consider the maximum and minimum number of pumps in use at the two stations. Let's call the maximum number of pumps used at either station as M, or the minimum number of pumps used as m. Then, the possible values of V would be from -(M-m) to (M-m).

Since each gas station has nine pumps, the maximum number of pumps in use at either station can be 9, and the minimum number of pumps in use at either station can be 0 (if all pumps are idle). Therefore, the possible values of M-m can range from 0 to 9, which means the possible values of V can range from -9 to 9.

The correct answer is E. -9, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

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The total number of different signals consisting of flags is 216

Given data ,

The number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags can be calculated using combinatorial principles.

There are 3 choices for the top flag (white, red, or blue), 2 choices for the second flag (since we've already used one color for the top flag), and 1 choice for the third flag.

Similarly, there are 3 choices for the fourth flag, 2 choices for the fifth flag, and 1 choice for the sixth flag. Finally, there are 3 choices for the seventh flag, 2 choices for the eighth flag, and 1 choice for the ninth flag.

Using the multiplication principle, we can multiply the number of choices at each step to get the total number of different signals:

3 × 2 × 1 × 3 × 2 × 1 × 3 × 2 × 1 = 3! × 3! × 3!

where "!" represents the factorial operation, which is the product of all positive integers up to a given number.

So, the total number of different signals consisting of 9 flags that can be made using 3 white flags, 3 red flags, and 3 blue flags is:

3! × 3! × 3! = 6 × 6 × 6 = 216

Hence , the number of signals is 216

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Answer:

0.0071% or 1/14000

Step-by-step explanation:

5/70,000 is approximately 0.00007142857 which is approximately 0.000071 which is 0.0071%

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

The maximum amount you can finance is $896.

We are given that;

The monthly gross income = $3,200

Now,

28% of your gross monthly income on your mortgage, including taxes and insurance

The percentage = 28%

3200* 28/100

=32*28

=896

Therefore, by percentage the answer will be $896.

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Answer:

830

Step-by-step explanation:

7470/9 = 830

Answer:

900% of 7470=67230

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 7470 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 7470 is 100%, so we can write it down as 7470=100%.

4. We know, that x is 900% of the output value, so we can write it down as x=900%.

5. Now we have two simple equations:

1) 7470=100%

2) x=900%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

7470/x=100%/900%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 900% of 7470

7470/x=100/900

(7470/x)*x=(100/900)*x       - we multiply both sides of the equation by x

7470=0.11111111111111*x       - we divide both sides of the equation by (0.11111111111111) to get x

7470/0.11111111111111=x

67230=x

x=67230

now we have:

900% of 7470=67230

Answer/Step-by-step explanation:

A1. Reference angle = 41°

Hypotenuse = x

Adjacent = 7

Thus, applying trigonometric ratio, we would have:

Cos 41 = 7/x

Multiply both sides by x

x × cos 41 = 7

Divide both sides by cos 41

x = 7/cos 41

x = 9.3 (nearest tenth)

A2. Reference angle = 65°

Hypotenuse = 6

Opposite = y

Thus, applying trigonometric ratio, we would have:

Sin 65 = y/6

Multiply both sides by 6

6 × sin 65 = y

5.4 = y (nearest tenth)

y = 5.4

A3. Reference angle = 50°

Hypotenuse = z

Opposite = 8

Thus, applying trigonometric ratio, we would have:

Sin 50 = 8/z

Multiply both sides by z

z × sin 50 = 8

Divide both sides by sin 50

z = 8/sin 50

z = 10.4 (nearest tenth)

B1. Reference angle = 49°

Hypotenuse = x

Opposite = 7

Thus, applying trigonometric ratio, we would have:

Sin 49 = 7/x

Multiply both sides by x

x × sin 49 = 7

Divide both sides by sin 49

x = 7/sin 49

x = 9.3 (nearest tenth)

B2. Reference angle = 25°

Hypotenuse = 6

Adjacent = y

Thus, applying trigonometric ratio, we would have:

Cos 25 = y/6

Multiply both sides by 6

6 × cos 25 = y

y = 5.4 (nearest tenth)

B3. Reference angle = 40°

Hypotenuse = z

Adjacent = 8

Thus, applying trigonometric ratio, we would have:

Cos 40 = 8/z

Multiply both sides by z

z × cos 40 = 8

Divide both sides by cos 40

z = 8/cos 40

z = 10.4 (nearest tenth)

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

The graph of y = 3 x 2^x passes through the coordinate points (2,12) and (3,24).

To write a question in the form of y=a x b^x that passes through the coordinate points (2,12) and (3,24), we need to solve for the values of a and b.

First, let's substitute the coordinates (2,12) into the equation:
12 = a x b^2

Next, let's substitute the coordinates (3,24) into the equation:
24 = a x b^3

We now have two equations with two unknowns (a and b), which we can solve using algebra.

From the first equation, we can solve for a:
a = 12 / b^2

We can then substitute this value of a into the second equation:
24 = (12 / b^2) x b^3

Simplifying this equation, we get:
2 = b

We can then substitute this value of b back into the equation for a:
a = 12 / 2^2
a = 3

Therefore, the equation of the graph that passes through the coordinate points (2,12) and (3,24) is:
y = 3 x 2^x

We can check that this equation is correct by plugging in the coordinates:
When x = 2: y = 3 x 2^2 = 12
When x = 3: y = 3 x 2^3 = 24
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the smallest angle formed by cables AD and AB in terms of the height of the tower and the distance between points A and B. We can plug in the values given in the problem to get a numerical answer.

In order to determine the smallest angle formed by cables AD and AB, we need to use trigonometry. Let's first draw a diagram of the situation:

            A

           /|\

          / | \

         /  |  \

        /   |h  \

       /    |    \

      /     |     \

     D------C------B

Here, A represents the top of the tower, and D, C, and B represent the points where the cables are attached. The height of the tower is given as h = 60 m. We want to find the smallest angle formed by cables AD and AB.

To do this, we can use the sine function. The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side of the angle we want to find is h, and the hypotenuse is AB. Therefore:

sin(theta) = h/AB

To solve for theta, we can take the inverse sine (also known as the arcsine) of both sides:

theta = arc sin(h/AB)

Now, we need to find the length of AB. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have a right triangle with sides AD, AC, and CD. Therefore:

AC{power}2 + CD{power}2 = AD{power}2

We know that AC = AB and CD = BC, so we can substitute:

AB{power}2 + BC{power}2 = AD{power}2

We also know that BC = h, so we can substitute again:

AB{power}2 + h{power}2 = AD{power}2

We want to solve for AB, so we can isolate it on one side:

AB{power}2 = AD{power}2 - h{power}2

AB = sqrt(AD{power}2 - h{power}2)

Now, we can substitute this expression for AB into the equation we derived for theta:

theta = arc sin(h/sqrt(AD{power}2 - h{power}2))

This gives us the smallest angle formed by cables AD and AB in terms of the height of the tower and the distance between points A and B. We can plug in the values given in the problem to get a numerical answer.

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Answer:

d. 48 inches

Step-by-step explanation:

We assume the mirror is a rectangle

We solve for the length of a diagonal using Pythagoras Theorem

a² + b² = c²

c = √a² + b²

Where c = diagonal

a = 30 inches

b = 38 inches

c = √30² + 38²

c = √2344

c = 48.414873748 inches

Approximately = 48 inches

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Answer:

$282

Step-by-step explanation:

if one telephone costs $47 and you want to find the cost of six telephones, you multiply 47 x 6 = 282.

Answer:

If two angles are complementary, then they add up to 90 degrees. Therefore, we can set up an equation to solve for the value of p:

3p + 10 + 5p = 90

Solving for p, we get p = 16. Therefore, the value of p is 16.

Answer:

10

Step-by-step explanation:

8p+10=90

8p=80

p=10