A farmer created a crop circle that is a square inside a circle. The square contains the crop of​ wheat, and the part outside the square is flat. The circle has a radius of 25​meters, and the square has a side length of 35 meters. What is the area of the flat region within this crop​ circle? Use 3.14.

The area of the rectangle is 13, 950 square unit.

We have,

length = 150

width= 93

So, Area of rectangle

=  length x width

= 150 x 93

= 13950 square unit.

Thus, the required Area is 13, 950 square unit.

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The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1

If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.

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The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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The length of time for one individual to be served at a cafeteria follows an exponential distribution with a mean of 4 minutes.

In an exponential distribution, the probability density function (PDF) is given by:

f(x) = (1/μ) * e^(-x/μ)

Where μ is the mean of the distribution. In this case, the mean is 4 minutes. Therefore, the PDF for the length of time for one individual to be served at the cafeteria can be expressed as:

f(x) = (1/4) * e^(-x/4)

The exponential distribution is commonly used to model the time between events in a Poisson process. In this case, it represents the time it takes for an individual to be served at the cafeteria, with an average of 4 minutes.

The exponential distribution is characterized by the property of memorylessness, which means that the probability of an event occurring in the next interval of time is independent of how much time has already elapsed. In the context of the cafeteria, this property implies that the probability of an individual being served in the next minute is the same, regardless of how much time has already passed.

It's important to note that the exponential distribution is only valid for non-negative values of x, as it represents a continuous random variable. The distribution is skewed to the right, with a longer tail on the positive side. The mean (μ) and standard deviation (σ) of the exponential distribution are equal and can be calculated as 1/λ, where λ is the rate parameter of the distribution.

In summary, the length of time for one individual to be served at the cafeteria follows an exponential distribution with a mean of 4 minutes. The probability density function (PDF) for this distribution is given by f(x) = (1/4) * e^(-x/4), where x represents the time in minutes.

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Answer:

Below

Step-by-step explanation:

48 ft /  4.5 ft/piece = 10 2/3 =     ~ 10    pieces with   2/3 ft left over

The factored form of the quadratic equation 2x² + 25x + 50 is (2x + 5)(x + 10)

Factoring quadratics is a method of expressing the quadratic equation ax² + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax² + bx + c = 0.

Therefore, let's factor the equation 2x² + 25x + 50.

2x² + 25x + 50

The two numbers one can multiply and add to get 100 and 25 respectively are 20 and 5.

Therefore,

2x² + 20x + 5x + 50

2x(x + 10)+ 5(x + 10)

Therefore,

(2x + 5)(x + 10)

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Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

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Answer: 3

Step-by-step explanation: First, solve with the parenthesis. Next, solve the square brackets.  Then, solve the quote brackets. And finally, solve the them after solving the brackets.

Answer:

Step-by-step explanation:

17-[4[-1(-3)2]

17-[4+3(2)]

17-[4+6]
17-10

7

Answer:

4x^2 + 9x + 23

Step-by-step explanation:

just factor the last equation and combine them all.

For the bell-shaped graph of the normal distribution of weights of Hershey kisses, the area under the curve is 1, the value of the median and mode both is 4.5338 G and the value of variance is 0.0108.

In the given question,

The weight of the chocolate and Hershey Kisses are normally distributed with a mean of 4.5338 G and a standard deviation of 0.1039 G.

We have to find the answer of many question we solve the question one by one.

From the question;

Mean(μ) = 4.5338 G

Standard Deviation(σ) = 0.1039 G

(a) We have to find for the bell-shaped graph of the normal distribution of weights of Hershey kisses what is the area under the curve.

As we know that when the mean is 0 and a standard deviation is 1 then it is known as normal distribution.

So area under the bell shaped curve will be

\(\int\limits^{\infty}_{-\infty} {f(x)} \, dx\)= 1

This shows that that the total area of under the curve.

(b) We have to find the median.

In the normal distribution mean, median both are same. So the value of median equal to the value of mean.

As we know that the value of mean is 4.5338 G.

So the value of median is also 4.5338 G.

(c) We have to find the mode.

In the normal distribution mean, mode both are same. So the value of mode equal to the value of mean.

As we know that the value of mean is 4.5338 G.

So the value of mode is also 4.5338 G.

(d) we have to find the value of variance.

The value of variance is equal to the square of standard deviation.

So Variance = \((0.1039)^2\)

Variance = 0.0108

Hence, the value of variance is 0.0108.

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with 4 df.

The correct answer is d. Two-sample t test with 9 df.

Answer:

1/12

Step-by-step explanation:

The probality of getting a 3 on a die is ⅙ since they is only one 3 on the 6 sided die. So that will mean there is a 1 in 6 chance to get a 3.

Then the probability of getting tails on a coin is ½ because a coin on has 2 sides.

The probability of getting the 3 on the die and a tail on a coin will be the probability of getting the 3 on the die times the probability of getting the tails on the coin.

⅙×½=1/12

The maximum utility is $562,500 and the company incurred a loss of $202,500.

a) To find the maximum utility, we need to determine the maximum value of the function U(x) = -x² + 1500x.

The function U(x) is a quadratic function with a negative coefficient for the x² term, which means it has a downward-facing parabola.

The maximum value of the function occurs at the vertex of the parabola.

The x-coordinate of the vertex can be found using the formula:

x = -b / (2a), where a is the coefficient of the x² term (-1 in this case) and b is the coefficient of the x term (1500 in this case).

So, substituting the values into the formula, we have:

x = -1500 / (2 × (-1)) = -1500 / -2 = 750

The maximum utility occurs when 750 items are produced.

To find the maximum utility,

Substitute x = 750 into the utility function:

U(750) = -(750)²  + 1500 × 750

U(750) = -562,500 + 1,125,000

U(750) = 562,500

Therefore, the maximum utility is $562,500.

b) If 1200 items are manufactured, we need to calculate the profit and determine if it's a gain or loss.

To do that, substitute x = 1200 into the utility function:

U(1200) = -(1200)² + 1500 × 1200

U(1200) = -1,440,000 + 1,800,000

U(1200) = 360,000

The utility is $360,000 when 1200 items are produced.

To determine if it's a gain or loss, compare the utility (profit) to the maximum utility:

360,000 < 562,500

Since 360,000 is less than 562,500, it means the company incurred a loss of $562,500 - $360,000 = $202,500 when 1200 items were manufactured.

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Translated question =

Under certain conditions a company finds that the daily profit in thousands of dollars when producing x items of a certain type is giving by: U(x) = -x^2 + 1500x. a) What is the maximum utility? b) If 1200 items are manufactured, is it won or lost and how much?

Answer:

I have to show the work gimme a sec

Step-by-step explanation:

When graphing an exponential function, a T-chart is commonly used to determine the values. The correct answer is option A.

The T-chart employs positive real numbers since this is the most typical form of exponential function.

Exponential functions are utilized to represent processes that increase or decrease exponentially, as well as to model phenomena in many different disciplines, including science, economics, and engineering.

The exponential function can be represented by the following equation:

\(y=a^x\), where a is the base, x is the exponent, and y is the outcome.

When a is a positive number greater than one, the function is called exponential growth, while when a is a fraction between 0 and 1, the function is called exponential decay.

The T-chart is used to determine the values to use in the graph and connect the dots as required. Positive real numbers are used as the values in the T-chart in order to effectively graph the exponential function.

Therefore, the correct answer is option A.

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⇒ To find the equation of the straight line we have to first calculate the slope/gradient of the line .

⇒To calculate the slope of the line you use the gradient formula below:

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

⇒Calculating the slope of the line let us  plug in the points of our choice from the graph and simplify.

\(m=\frac{4-1}{8-4} \\m=\frac{3}{4\\} \\m=\frac{3}{4}\)

⇒Note m is just a a letter of alphabet that represents the slope of the line.

⇒The slope of the line is \(\frac{3}{4}\)

⇒ The general equation to calculate the straight line equation is

y=mx+c where y is the y coordinate

x is the x-coordinate

m is the slope

c is the y-intercept.

I will use any point (x,y) ,note you can use any point as you will still get the same value c

I will use the point (4,1) from the graph.

\(1=4(\frac{3}{4} )+c\\1=3+c\\1-3=c\\c=-2\)

∴From the known values of the general equation

\(y=\frac{3}{4} x-2\)  is our equation.

Answer:

90 degrees

Step-by-step explanation:

Answer:

(0,2) - (2,0) - (4,-2)

Step-by-step explanation:

You have the following straight line:

\(y=-x+2\)   (1)

You can plot the y-intercept point, the x-intercept point and another one.

The y-intercept is obtained by doing x=0:

y=-+2=2

y-intercept = 2

the x-intercept is obtained by doing y=0 and solving for x:

0=-x+2

x=2

x-intercept = 2

another point can be for x = 4:

y=-4+2=-2

Then, the points to plot are

(0,2) - (2,0) - (4,-2)

The graph is attached in the image below.

Answer:

x=36

Step-by-step explanation:

5x=180

x=180/5=36

Answer:x=36

Step-by-step explanation:

Took the test and got it right!

For both problems, we can use the section formula.

1) \(P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}\)

2) \(Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}\)

Answer:

.................................

Step-by-step explanation:

Answer:

5/3

Step-by-step explanation:

multiply the whole thing by y to get 3y/x=5 and then divide by 3 to get y/x=5/3

Answer:

y/x=5/3

Step-by-step explanation:

3/x=5/y ⇒ y/x=5/3  replacing y with 3

Answer:

The change in latitude, Δφ, from Liverpool to Melbourne is 91.22° south

The change in longitude, Δλ, from Liverpool to Melbourne is 147.95° East

Step-by-step explanation:

The parameters given are;

The latitude of Liverpool is 53.41°

The longitude of Liverpool is -2.99°

The latitude of Melbourne is -37.81°

The longitude of Melbourne is 144.96°

The change in latitude from Liverpool to Melbourne = Δφ

Δφ = 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

The change in latitude, Δφ, from Liverpool to Melbourne = 91.22° south

The change in longitude from Liverpool to Melbourne = Δλ

Δλ = -2.99° - 144.96°  = -147.95°

Therefore the change in longitude from Liverpool to Melbourne = 147.95° East.

Answer:

the difference in latitude is 91.22°

the difference in longitude is 147.95°

Explanation:

For Liverpool, London. The latitude is 53.41°, longitude is -2.99°

For  Melbourne, Australia. The latitude is -37.81°, longitude is 144.96°

The negative or positive magnitude of their values shows their position on either sides of the origin of the latitude (equator) and the origin of the longitude (prime meridian).

The latitude measures the relative position of a point, north or south of the equator (latitude 0°). The longitude measures the relative position, east or west of the prime meridian (longitude 0°)

the difference in latitude is 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

the difference in longitude = 144.96° - (-2.99°) = 144.96 + 2.99 = 147.95°