you are to build a rectangular pen with three parallel partitions using 500 feet of fencing. what dimensions will maximize the total area of the pen?

Answer:

x = -7

Step-by-step explanation:

Given parameters:

Slope of the line = \(\frac{4}{3}\)

 Coordinates =  (5,x) and (2,-3)

Unknown:

X= ?

Solution:

  To find slope, use the expression below;

   Slope  = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

y₂ = -3  y₁ = x

x₂ = 2   x₁ = 5

   \(\frac{4}{3}\)  = \(\frac{-3 - x}{2 - 5}\)

           3(-3-x) = 4(-3)

            -9 -3x = 12

                -3x = 21

                  x = -7

Answer:

Yeup, youre correct

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

multiply 350 by .30(30%) and that will tell you how many goldfish there are

Answer:

105 fish my dear

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sides r, 10 and 20 are parallel to each other as all three are perpendicular  to same line.

The triangles are similar as two sides are on same lines and another one is parallel as described above.

Work out the value of r using ratios of corresponding sides:

Now, find the distance x from the bottom of the cone to the base of the smallest ball, using same method as above:

Answer:1493.1

Step-by-step explanation:

The rent of the apartment during the 8th year of living in the apartment is $1,605.13.

Given that, you rent an apartment that costs $900 per month during the first year, but the rent is set to go up 7.5% per year.

We need to find What would be the rent of the apartment during the 8th year of living in the apartment.

The formula to find the rent of the apartment during the 8th year of living in the apartment is Amount \(=P(1+\frac{r}{100} )^{n}\)

Where, P=principal, r=rate of interest and n=number of years.

Now, amount=\(=900(1+\frac{7.5}{100} )^{8}\)

\(=900(1.075)^{8}\)

=900×1.78347782556

=1,605.13

Therefore, the rent of the apartment during the 8th year of living in the apartment is $1,605.13.

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Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

El costo de los lentes de sol es de $85 y el costo de las sandalias es de $79.

Para determinar el costo de los lentes de sol y las sandalias, podemos plantear un sistema de ecuaciones basado en la información proporcionada. Sea "x" el costo de un par de lentes de sol y "y" el costo de un par de sandalias.

De acuerdo con los datos, tenemos la siguiente ecuación para Teresa:

x + y = 164.

Y para Gaby, tenemos:

2x + y = 249.

Podemos resolver este sistema de ecuaciones utilizando métodos de eliminación o sustitución. Aquí utilizaremos el método de sustitución para despejar "x".

De la primera ecuación, podemos despejar "y" en términos de "x":

y = 164 - x.

Sustituyendo este valor de "y" en la segunda ecuación, obtenemos:

2x + (164 - x) = 249.

Simplificando la ecuación, tenemos:

2x + 164 - x = 249.

x + 164 = 249.

x = 249 - 164.

x = 85.

Ahora, podemos sustituir el valor de "x" en la primera ecuación para encontrar el valor de "y":

85 + y = 164.

y = 164 - 85.

y = 79.

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A given linear model shows negative correlation.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

Given that, a researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29.

Here, a linear model shows negative, or inverse, correlation.

Therefore, a given linear model shows negative correlation.

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Answer: 24/10

Answer: 24/10Step-by-step explanation:

1) 1*1÷10 +1*1÷5+2÷20

2)(1*10+1)/10+(1*5+1)/5+2/20 3)11/10+6/5+2/20

4)11/10+6/5+1/10

5)11/10+12/10+1/10

6)(11+12+1)/10

7)24/10

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We use integration by parts with the formula:

∫u dv = uv - ∫v du

In this case, we choose:

u = ln(x), dv = x^4 dx

Then we have:

du = (1/x) dx

v = ∫x^4 dx = (1/5)x^5 + C

where C is the constant of integration.

Using the formula, we get:

∫x^4 ln(x) dx = u v - ∫v du

= ln(x) [(1/5)x^5 + C] - ∫[(1/5)x^5 + C] (1/x) dx

= ln(x) [(1/5)x^5 + C] - (1/25)x^5 - C ln(x) + C

= (1/5)ln(x) x^5 - (1/25)x^5 + C

Therefore, the integral of x^4 ln(x) dx is (1/5)ln(x) x^5 - (1/25)x^5 + C.

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Answer:

The most important characteristic of a correlation coefficient is the absolute value.

The absolute value of a correlation coefficient represents the strength of the relationship between two variables, regardless of the direction of the relationship. A correlation coefficient can range from -1 to +1, where a value of -1 indicates a perfect negative correlation (i.e., as one variable increases, the other decreases), a value of +1 indicates a perfect positive correlation (i.e., as one variable increases, the other also increases), and a value of 0 indicates no correlation (i.e., there is no relationship between the variables).

The most important characteristic of a correlation coefficient is the absolute value.

The absolute value of the correlation coefficient represents the strength of the relationship between two variables, regardless of its direction. It indicates the degree to which the variables are associated with each other.

By focusing on the absolute value, we can assess the magnitude of the correlation without being influenced by whether it is positive or negative. For example, a correlation coefficient of -0.8 or +0.8 both indicate a strong relationship, while a correlation coefficient of 0 suggests no relationship.

The number of variables included is not a characteristic of the correlation coefficient itself, but rather a consideration in the analysis. One-tailed and two-tailed refer to the type of hypothesis being tested and are relevant in statistical testing. However, the absolute value of the correlation coefficient is crucial in determining the strength of the relationship between variables, making it the most important characteristic to assess in correlation analysis.

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The quadrilateral with no pair of parallel sides is trapezium

Given data ,

A = a quadrilateral with no pair of parallel sides

This type of quadrilateral is called a trapezium. In some countries, a trapezium is defined as having exactly one pair of parallel sides, while in other countries, a trapezium is defined as having at least one pair of parallel sides.

In any case, a quadrilateral with no pair of parallel sides is not considered a trapezium. Instead, it is known as a general quadrilateral.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

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Answer: The answer is triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

Step-by-step explanation: The reason this would be is that both triangles are equilateral, so all the sides are the same.

Now that we know that the triangles are similar to each other, then we can eleminate the last two answers. The best possible answer would be triangle ABC ~ triangle EDC because m<3=m<4 and m<1=m<5.

Using the t-distribution, as we have the standard deviation for the sample, it is found that:

The confidence interval is:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797.

The other parameters are given as follows:

\(\overline{x} = 18, s = 1.2, n = 25\).

Hence, the bounds of the interval are given by:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 18 - 2.797\frac{1.2}{\sqrt{25}} = 17.33\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 18 + 2.797\frac{1.2}{\sqrt{25}} = 18.67\)

The 99% interval estimate of the population mean is (17.33, 18.67).

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Answer:

12 less than a number means to subtract 12 from that number. So, 12 less than 20 is 8 , because is 20−12 , 12 less than 12 is 0 , because it's 12−12 , and so on. But since you don't know which number you need to subtract from, it's a variable, and you can call it as you like, usually x .

Answer:

A

Step-by-step explanation:

The solution to the initial value problem dy/dx = x⁵(y-2), y(0) = 9 is y = (1/6)x⁶ + 2.

To solve the given initial value problem, we can use the method of separation of variables. Rearranging the equation, we have dy/(y-2) = x⁵dx.

Integrating both sides, we get ∫dy/(y-2) = ∫x⁵dx. The integral on the left side can be evaluated as ln|y-2|, and the integral on the right side can be evaluated as (1/6)x⁶ + C, where C is the constant of integration.

Applying the initial condition y(0) = 9, we can substitute x = 0 and y = 9 into the solution. This gives us ln|9-2| = (1/6)(0⁶) + C. Simplifying, ln|7| = C.

Therefore, the final solution to the initial value problem is ln|y-2| = (1/6)x⁶ + ln|7|. By exponentiating both sides, we obtain |y-2| = 7e^(x⁶/6). Taking the positive and negative values, we have y - 2 = ±7e^(x⁶/6). Finally, solving for y, we get y = (1/6)x⁶ + 2 as the solution to the initial value problem.

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Answer:

IT's d!!!!!

Step-by-step explanation:

We have proven the identity **sec(-x) sin(-x) - 2 tan(x) csc(-x) cos(-x) = -3 tan(x)**.

To prove the given identity, we have:

sec(-x) sin(-x) - 2 tan(x) csc(-x) cos(-x)

Using the reciprocal identities, we can rewrite sec(-x) as 1/cos(-x), sin(-x) as -sin(x), csc(-x) as -1/sin(x), and cos(-x) as cos(x):

(1/cos(-x)) (-sin(x)) - 2 tan(x) (-1/sin(x)) cos(x)

Simplifying further:

(-sin(x)/cos(-x)) - 2 tan(x) (-1/sin(x)) cos(x)

Since cos(-x) is equal to cos(x), we can substitute it:

(-sin(x)/cos(x)) - 2 tan(x) (-1/sin(x)) cos(x)

Now, let's simplify each term:

- tan(x) - 2 tan(x) cos(x)/sin(x)

Using the identity tan(x) = sin(x)/cos(x), we can rewrite the expression:

- sin(x)/cos(x) - 2 (sin(x)/cos(x)) (cos(x)/sin(x))

Simplifying further:

- sin(x)/cos(x) - 2 sin(x)/cos(x)

Combining the terms:

(- sin(x) - 2 sin(x))/cos(x)

Simplifying the numerator:

- 3 sin(x)/cos(x)

Using the identity sin(x)/cos(x) = tan(x), we have:

- 3 tan(x)

Therefore, we have proven the identity **sec(-x) sin(-x) - 2 tan(x) csc(-x) cos(-x) = -3 tan(x)**.

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Answer: f(-4) = -7

Step-by-step explanation:

    Since -4 is less than -1, we will be substituting x = -4 into the top equation of the piecewise function.

 Given:

 \(\displaystyle \frac{3}{4}x -4\)

 Substitute:

 \(\displaystyle \frac{3}{4}(-4) -4\)

 Multiply:

 -3 - 4

 Subtract:

 -7

Answer:

the question is blurry and it has a glare

Answer:

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The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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Answer:

Step-by-step explanation:

Radius is 1/2 of the diameter

or

Diameter is 2 of the radius

Answer:D. y = 3/4x + 1

The additional time it will take for the liquid's temperature to decrease from 64°F to 32°F is 2 minutes, considering a rate of temperature decrease of 16°F per minute.

To find the additional time it will take for the liquid's temperature to decrease from 64°F to 32°F, we can consider the rate at which the temperature is decreasing.

From the given information, we know that the liquid's temperature decreases from 160°F to 64°F in 6 minutes. This means that the temperature decreases by 160°F - 64°F = 96°F in 6 minutes.

Therefore, the rate of temperature decrease is 96°F / 6 minutes = 16°F per minute.

To find the additional time it will take for the temperature to decrease from 64°F to 32°F, we can calculate the difference in temperature and divide it by the rate of temperature decrease

Temperature difference = 64°F - 32°F = 32°F

Additional time = Temperature difference / Rate of temperature decrease

Additional time = 32°F / 16°F per minute = 2 minutes

Therefore, it will take an additional 2 minutes for the temperature to decrease from 64°F to 32°F.

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Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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