you will build a rectangular sheep pen next to a river. there is no need to build a fence along the river, so you only need to build three sides. you have a total of 420 feet of fence to use. find the dimensions of the pen such that you can enclose the maximum area.

Answer:

Step-by-step explanation:

Since ∠S and ∠Y are complementary, we have:

∠S + ∠Y = 90°

We also know that:

m∠S = 2(m∠Y) − 30°

Substituting the second equation into the first equation, we get:

2(m∠Y) − 30° + ∠Y = 90°

Combining like terms:

3(m∠Y) = 120°

Dividing both sides by 3:

m∠Y = 40°

Therefore, m∠Y is 40 degrees.

In this conversion, we assume that θ is not equal to 0 or any multiple of π, as csc(θ) is undefined for those values.

In rectangular coordinates, the equation r = 2csc(θ) can be expressed as:

x = 2cos(θ)

y = 2sin(θ)

To convert the polar equation r = 2csc(θ) to rectangular coordinates, we need to express the equation in terms of x and y.

In polar coordinates, r represents the distance from the origin (0,0) to a point (x, y), and θ represents the angle between the positive x-axis and the line segment connecting the origin to the point.

To convert r = 2csc(θ) to rectangular coordinates, we can use the following relationships:

x = r * cos(θ)

y = r * sin(θ)

First, let's express csc(θ) in terms of sin(θ):

csc(θ) = 1 / sin(θ)

Now, substitute r = 2csc(θ) into the equations for x and y:

x = (2csc(θ)) * cos(θ)

y = (2csc(θ)) * sin(θ)

Using the relationship between csc(θ) and sin(θ), we can rewrite the equations as:

x = (2/sin(θ)) * cos(θ)

y = (2/sin(θ)) * sin(θ)

Simplifying further:

x = 2cos(θ)

y = 2sin(θ)

Therefore, in rectangular coordinates, the equation r = 2csc(θ) can be expressed as:

x = 2cos(θ)

y = 2sin(θ)

Note: In this conversion, we assume that θ is not equal to 0 or any multiple of π, as csc(θ) is undefined for those values.

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Correct question- How do you convert the polar equation  r = 8cscθ into rectangular form?

We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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The probability is 0.421 that the mean time spent commuting from home to work by a sample of 12 employees.

Empirical states that if most of the values or observations of a data set fall within the 3-population standard deviation, then the distribution of the data said to be a normal otherwise non-normal. It is also known by the name of the three-sigma rule.

We have the following information from the question is:

Sample size (N) = 12,

standard deviation (σ) = 8.1

and  mean (μ) = 42.7

The probability mean time spent commuting from home to work by a sample of 12 employees will be between 43.26 and 49.35 minutes is:

\(p[43.26 < x(bar) < 49.35]\)

\(p[\frac{43.26-43.7}{\frac{8.1}{\sqrt{12} } } < z < \frac{49.35-43.7}{\frac{8.1}{\sqrt{12} } }]\)

=> -0.18 < z < 2.41

=> p[z ≤ 2.41] - p[z ≤ 0.18] = 0.992 - 0.571

                                         = 0.421

Therefore, the probability 0.421 (rounded to three decimal places)  

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cos 48° = b / √(a²+b²)

tan 48° = a/b

sin 48° = a / √(a²+b²)

Answer:

D. 54.898

Step-by-step explanation:

Answer: 50/109

Step-by-step explanation:

Answer:

y  =  \(-\frac{1}{2}\) x + 9

Step-by-step explanation:

Given parameters:

  Coordinates = (-2,8)

Equation of the line  y  = 2x + 5;

Unknown:

Linear equation of a line perpendicular = ?

Solution:

From the given expression, a line perpendicular will have a negative inverse of the slope given.

           y  = 2x + 5

Equation of a line  is y = mx + c;

y and x are the coordinates

  m is the slope

   c is the intercepts

    y  = 2x + 5 ;

 The slope is 2;

  A line perpendicular will have a slope of \(-\frac{1}{2}\)  

 Since y = 8 and x  = -2, let us find c;

     8  = 2 x \(-\frac{1}{2}\)  + c

    8 = -1 + c

     c  = 8+1 = 9

The equation of the line is;

       y  =  \(-\frac{1}{2}\) x + 9

Answer:

10 root 2

Step-by-step explanation:

Refer to attachment.

Hope it helps.

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

The students rented 3 small cars and 6 large cars.

Step-by-step explanation:

Since a group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip, and each small car can hold 4 people and each large car can hold 6 people, and the students rented twice as many large cars as small cars, which altogether can hold 48 people, to determine the number of small cars rented, X, and the number of large cars rented, Y, the following calculation must be performed:

4X + 6Y = 48

4x4 + 6x8 = 16 + 48 = 64

4x3 + 6x6 = 12 + 36 = 48

Thus, the students rented 3 small cars and 6 large cars.

A disk with a radius of 0.1 m is spinning about its center with a constant angular speed of 10 rad/sec. The speed of the bug is equal to the tangential speed of a point on the rim of the disk, which can be given by: v = rωWhere:r = 0.1 m (the radius of the disk)ω = 10 rad/sec (the angular speed of the disk)Therefore, the speed of the bug is: v = rω= 0.1 m x 10 rad/sec= 1 m/s

The acceleration of the bug can be given by: a = rαWhere:α = α (angular acceleration)The angular acceleration is zero because the disk is spinning at a constant angular speed. Hence, the acceleration of the bug is zero or a = 0 m/s². Therefore, the correct option is option 2) 1 m/s and 0 m/s² (Disk spins at a constant speed).

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Answer:

140 mile

Step-by-step explanation:

\(d_{1} +d_{2} =220\\2(2x-10+x)=220\\x=40\\d_{1}=2*(2*40-10)=140mile\)

While x is the speed of the second train.

The speed of the first train is 50 miles per hour while the second train is at 60 miles per hour.

Speed is the ratio of total distance to total time taken. It is given by:

Speed = distance / time

Let a represent the speed of the first train. In two hours:

a = d₁/2

d₁ = 2a

a + 10 = d₂/2

d₂ = 2a + 20

d₁ + d₂ = 220

2a + 2a + 20 = 220

4a = 200

a = 50 miles per hour

The speed of the first train is 50 miles per hour while the second train is at 60 miles per hour.

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The prices in order from greatest to least unit rate is Price A>Price C>Price B.

Given a table that showing different prices for cans of soup as shown in attached image.

Here, we will calculate the price of 1 quantity of each type of soup.

The Price of 3 quantities of soup price A=$3.87

Now, we will find the price of soup A for the 1 quantity.

The Price of 1 quantity of soup price A=$3.87/3=$1.29

The Price of 2 quantities of soup price B=$2.38

Now, we will find the price of soup B for the 1 quantity.

The Price of 1 quantity of soup price B=$2.38/2=$1.19

The Price of 7 quantities of soup price C=$8.75

Now, we will find the price of soup C for the 1 quantity.

The Price of 1 quantity of soup price C=$8.75/7=$1.25

Hence, the prices in order, from greatest to least unit rate from the given table which is shown in attached image is Price A>Price C>Price B or $1.29>$1.25>$1.19.

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Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

Answer:

The correct answer is: 23.39%

Step-by-step explanation:

To determine the percentage of underclassmen interested in taking a Mandarin course next year, we need to calculate the ratio of the number of underclassmen interested in Mandarin (145) to the total number of underclassmen (620) and then multiply by 100 to get the percentage.

(145 / 620) * 100 ≈ 23.39%

Therefore, approximately 23.39% of the underclassmen have an interest in taking a Mandarin course next year.

Answer:

the 3x +7 I think?

Step-by-step explanation:

correct me if I'm wrong

The rate of change of the probability of having an accident with respect to BAC level at b = 0.08 is approximately 9.3707% per unit.

To evaluate P(0.08), we substitute b = 0.08 in the equation P(b) = e^(21.5b):

P(0.08) = e^(21.5*0.08) ≈ 0.4405

Therefore, the probability of having an accident at a BAC level of 0.08 is approximately 44.05%.

To evaluate P'(0.08), we take the derivative of P(b) with respect to b and then substitute b = 0.08:

P'(b) = 21.5e^(21.5b)

P'(0.08) = 21.5e^(21.5*0.08) ≈ 9.3707

Therefore, the rate of change of the probability of having an accident with respect to BAC level at b = 0.08 is approximately 9.3707% per unit increase in BAC level. In other words, if a person's BAC level increases by 1%, the probability of having an accident at b = 0.08 would increase by approximately 9.3707%.

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Answer:

either 1/3 chance or 1/6 chance

Step-by-step explanation:

not exactly sure...

The complete question should be: What is the per capita personal income for a given state in 2004, represented by the value [?] on the vertical axis of the state table?

The missing value on the vertical axis represented by [?] must be $21,200.

In order to determine the missing value on the vertical axis represented by [?], we need to consider the per capita personal income for each of the states listed in the table. The states are listed in order from highest income to lowest income. The highest-earning state is listed first with a per capita personal income of $52,000. The next-highest-earning state has a per capita personal income of $21,200. Therefore, the missing value on the vertical axis represented by [?] must be $21,200.

To enter this answer, first identify the numerical keypad on the calculator. Then, enter the numerical value of $21,200 (21200) using the keypad. Finally, press the “enter” or “equals” key to submit the answer. This will cause the missing value on the vertical axis to be displayed on the calculator screen.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

Step-by-step explanation:

i did it

Answer:

C B E

Step-by-step explanation:

The exponential function f, whose graph is given below, can be written as f(x)=4.7ˣ.

In mathematics, a function is a rule that maps each element (or input) of a set, called the domain, to a unique element (or output) of another set, called the range. Functions are often represented using function notation, such as f(x), where "f" is the name of the function and "x" is the input variable. The value of f(x) is the output or image of x under the function f.

Here,

If the exponential function f can be written as f(x) = a ⋅ b^x, where a and b are constants, then the graph of f will have the following characteristics:

The y-intercept of the graph will be a, which is the value of f(0).

The base of the exponential function, b, determines the rate of growth or decay of the function. If b > 1, the function grows as x increases. If 0 < b < 1, the function decays as x increases. If b = 1, the function is constant.

The graph of f will be increasing if b > 1 and decreasing if 0 < b < 1. The rate of increase or decrease will be determined by the magnitude of b.

The graph of f will never cross the x-axis, but it will approach the x-axis as x becomes very negative (if b > 1) or very positive (if 0 < b < 1).

Note that the graph of an exponential function can also be characterized by its asymptote, which is a horizontal line that the function approaches but never crosses. The asymptote is the line y = 0 if 0 < b < 1, and the line y = a if b > 1.

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Area = 19.63cm²

A=πr2=π·2.52≈19.63495cm²

The expected change in m if GDP increases by 4% is approximately -2%.

The given equation is a logarithmic regression model that relates the quantity of (real) money (m) to the value of (real) gross domestic product (GDP) and the nominal interest rate (R). The equation is expressed as ln(m) = β0 + β1ln(GDP) + β2R, where β1 = 2.78 and β2 = -0.09.

To determine the expected change in m when GDP increases by 4%, we need to substitute the new GDP value into the equation and calculate the resulting change in m.

Let's consider the scenario where the initial GDP increases by 4%. We can calculate the change in m by plugging the new GDP value into the equation:

ln(m') = β0 + β1ln(GDP') + β2R,

where m' represents the new quantity of money and GDP' is the new GDP value.

Since we are interested in the change in m, we subtract the initial equation from the new equation:

ln(m') - ln(m) = β0 + β1ln(GDP') + β2R - β0 - β1ln(GDP) - β2R,

Simplifying the equation:

ln(m'/m) = β1(ln(GDP') - ln(GDP)),

Using the property of logarithms, ln(a) - ln(b) = ln(a/b):

ln(m'/m) = β1ln(GDP'/GDP).

Now, we know that GDP increased by 4%, so GDP'/GDP = 1 + 0.04 = 1.04. Substituting this value into the equation:

ln(m'/m) = β1ln(1.04),

Since ln(1.04) is a constant, we can multiply both sides by β1:

ln(m'/m) * β1 = \(β1^2\) * ln(1.04),

ln(m'/m) * β1 = 2.78 * ln(1.04),

Finally, we can solve for ln(m'/m) by dividing both sides by β1:

ln(m'/m) = 2.78 * ln(1.04) / β1.

Using the given values, β1 = 2.78 and β2 = -0.09, we can calculate the approximate change in m by exponentiating both sides:

m'/m = \(e^(^2^.^7^8^ *^ l^n^(^1^.^0^4^)^ /^ β^1^)\).

Substituting the values, we find:

m'/m ≈ \(e^(^2^.^7^8^ * ^l^n^(^1^.^0^4^)^ / ^2^.^7^8^)\) ≈ \(e^l^n^(^1^.^0^4^)\) ≈ 1.04.

This means that the expected change in m, when GDP increases by 4%, is approximately 1.04. To express this as a percentage change, we subtract 1 and multiply by 100:

Percentage change = (1.04 - 1) * 100 ≈ 4%.

Therefore, the expected change in m, when GDP increases by 4%, is approximately -2% (rounded to the nearest integer).

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Answer:

There are several different sorts of pacifism, but they all include the idea that war and violence are unjustifiable, and that conflicts should be settled in a peaceful way.

...

Pacifism

religious faith.

non-religious belief in the sanctity of life.

practical belief that war is wasteful and ineffective

Step-by-step explanation:

A; The distance between the starting point to Obstacle 2 is  13 meters

B; There are 10 meters around one lap of course.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Part A;

Starting point: (-12, 5); Obstacle 2: (0, 0)

(x₁, y₁) and (x₂, y₂)

Therefore,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

B. Starting point: (-12, 5); Obstacle 2: (0, 0);

Obstacle 1: (-12, 0)

(Starting Point + Obstacle 2)

Now,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

Therefore, (Starting Point + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - (-12))² + (0 - 5)²

d = √(0)² + (-5)²

d = √25

d = 5 meters

(Obstacle 2 + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - 0)² + (0 - 0)²

d = √(-12)² + (0)²

d = √144

d = 12 meters

Total = 12m + 5m + 13m = 30

30 ÷ 3 = 10 meters

we can conclude that 10 meters around one lap of course.

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Answer:

△ABCtriangle and △CDAtriangle, by side-angle-side

Step-by-step explanation:

The amount of money in the account after 18 years will be $449.5.  

Given is a parallelogram as shown in the image.

In order to prove ABCD as a parallelogram, we can prove ΔABE and ΔCDE congruent to each other by Angle - Angle - Side congruent property as -

∠BAE = ∠DCE     {Alt. int. angles}

∠ABE = ∠CDE     {Alt. int. angles}

AB = CD    {Given}

Therefore, she can prove ABCD as a parallelogram by proving -

ΔABE ≅ ΔCDE using AAS criteria.

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