You have a piece of farmland where you think there may be diamonds. You have to decide whether to farm there or start mining. If you decide to farm, you can either plant cocoa for export or you can grow various produce for your own use and to sell locally. If you want to dig for diamonds, you can either get a geologist in to test for diamonds or just start digging. The probability of a good outcome from deciding on diamonds and getting a geologist is 0.25. The value of this outcome is 1,000,000 and the value of a poor outcome is 40,000. The cost involved with a geologist is 200,000. The value of a positive outcome without a geologist is also 1,000,000 and the probability of a good outcome is 0.05. The value of a poor outcome is 20,000. With cocoa, the costs are 300,000 and the probability of success is estimated at 0.6. The 1 value of success here is 600,000. The value of no success here is 20,000. With produce, the costs are 40,000 and the probability of success is 0.9, with a final value of 600,000. The value of an unsuccessful outcome is 30,000. Use a decision tree to analyse the situation. Explain your final decision and justify the course of action you will take. [10]

Answer:

a)219.8

b)3846.5

Step-by-step explanation:

a) circumference is pi*diameter, so 3.14*70 is 219.8

b) area is pir^2, and radius is 1/2 of diameter, it would be 3.14*35^2, so 3.14*1225, so 3,846.5 in^2.

Answer:

lol

Step-by-step explanation:

h

The graphical representation that would be the best for this data would be a circle graph. That is option C.

A circle graph, which is also called a pie chart, is defined as a type of data representation where by the information concerning a data set is displayed in a circular form and in a way that the various information displayed is a percentage of the total data set involved.

Now, the number of students that were surveyed = 100 students.

The number of subjects that are preferred by the students would be represented as x,y,z.

Therefore to represent the number of students that preferred a particular subject on the circle graph the following is carried out;

For subject x = Number of X/100 × 360/1

Learn more about histogram here:

https://brainly.com/question/30764929

#SPJ1

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The area is 28 square feet.

The formula to find the area of a trapezoid is (base1 + base2) * height / 2. In this case, the base lengths are 6 feet and 8 feet, and the height is 4 feet. So, we can substitute these values into the formula.

Using the formula, we get:
Area = (6 + 8) * 4 / 2
      = 14 * 4 / 2
      = 56 / 2
      = 28 square feet

Therefore, the area of the trapezoidal tabletop is 28 square feet.

A trapezoid is a quadrilateral with one pair of parallel sides. The bases of a trapezoid are the parallel sides, and the height is the perpendicular distance between the bases. To find the area of a trapezoid, we multiply the sum of the bases by the height, and then divide by 2.

In this case, the sum of the bases is 6 + 8 = 14. Multiplying 14 by the height of 4 gives us 56. Dividing 56 by 2 gives us the final answer of 28 square feet.

Know more about trapezoid here:

https://brainly.com/question/31380175

#SPJ11

Answer:

After Douglass' attempt to escape slavery two years prior was betrayed by a fellow slave, he had been jailed, sent to Baltimore by his master, and hired out to work in the city's shipyards. Undeterred, Douglass vowed to try to escape again on September 3, 1838, although he knew the risk.

Step-by-step explanation: Hope this Helps

Answer:

he risked his life I think. I havent learned about this in a while.

Step-by-step explanation:

The value of x is 7

A triangle's midsegment is the section that links the midpoints of its two sides.

The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.

Given:

According to Midsegment theorem

The line joining the midpoint is equal to half the length of the third side.

Thus, 29 = 1/2 (6x+ 4)

29 = 3x + 2

3x = 39-2

3x= 27

x= 27/3

x= 9

Learn more about Midsegment theorem here:

https://brainly.com/question/30261975

#SPJ1

Answer:

is it like this?

Step-by-step explanation:

(2x-5)(2x-1)

2x(2x-1)-5(2x-1)

4x²-2x-10x-5

4x²-12x-5

that is the final answer

Given, expression is not trinomial.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

To express the expression (2x-5)(2x-1) as a trinomial,

we need to multiply the two binomials together using the distributive property.

We can use the FOIL method to do this:

(2x-5)(2x-1) = 2x(2x) + 2x(-1) - 5(2x) - 5(-1)

Simplifying this expression, we get:

(2x-5)(2x-1) = 4x² - 2x - 10x + 5

Combining like terms, we get:

(2x-5)(2x-1) = 4x² - 12x + 5

Since, trinomial is ax³ +bx² +cx +d in standard form where a can not be zero.

Therefore, the binomial form of (2x-5)(2x-1) is 4x^2 - 12x + 5, and given, expression is not trinomial.

Learn more about Polynomials here:

https://brainly.com/question/11536910

#SPJ2

Answer:

The requested ratios in words, colon form, and fraction form are:

1. strawberry bars to blueberry bars  = 3 : 5 = 3/5

2. apple bars to blueberry bars  = 2 : 5 = 2/5

3. strawberry bars to total bars  = 3 : 10 = 3/10

4. apple bars to total bars  = 2 : 10 = 2/10= 1/5

5. blueberry bars to total bars  = 5 : 10 = 5/10 = 1/2

6. apple bars to strawberry bars =2 : 3 = 2/3

Step-by-step explanation:

Let's start by doing an inventory of what Nina has:

Apple bars =  2

Blueberry bars = 5

Strawberry bars = 3

Total bars = 10

The requested ratios then are:

1. strawberry bars to blueberry bars  = 3 : 5 = 3/5

2. apple bars to blueberry bars  = 2 : 5 = 2/5

3. strawberry bars to total bars  = 3 : 10 = 3/10

4. apple bars to total bars  = 2 : 10 = 2/10= 1/5

5. blueberry bars to total bars  = 5 : 10 = 5/10 = 1/2

6. apple bars to strawberry bars =2 : 3 = 2/3

Answer:

q= -4

Step-by-step explanation:

First, simplify 4x+2y=5

2y=-4x+5

y=-2x+5/2

q+2 has to equal to -2

q = -4

Answer: I believe it is -144

Answer:

Step-by-step explanation:divide both sides by the coefficient of x that is the number beside x and in inequality, when dividing with a negative sign the sign would change to its opposite sign.

-6<-2x

-6/-2>-2x/-2

3>x

X<3 this is the answer.

Approximately 114.29% of the growth came from higher productivity.

To determine the percent of growth that came from higher productivity, we need to compare the change in output (Y) with the change in inputs (K and L). Here's how we can calculate it:

In the first year:

Initial output (Y₁) = 18

Initial inputs (K₁, L₁) = (4, 9)

In the second year:

Final output (Y₂) = 26

Final inputs (K₂, L₂) = (4, 16)

Change in output = Y₂ - Y₁ = 26 - 18 = 8

Change in inputs = (K₂ + L₂) - (K₁ + L₁) = (4 + 16) - (4 + 9) = 7

Now, let's calculate the percent of growth that came from higher productivity:

Percent of growth from higher productivity = (Change in output / Change in inputs) * 100

= (8 / 7) * 100 ≈ 114.29

Therefore, approximately 114.29% of the growth came from higher productivity.

Learn more about approximately from

https://brainly.com/question/27894163

#SPJ11

In The Country Of Mordor, Y = AVK* VL . In the first year, Y=18 and K=4 and L=9 In the second year, Y=26 and K=4 and L=16 What percent of this growth came from higher productivity? Careful: don't calculate the percent that came from inputs, you have to do an extra step once you've done that. If you think the answer was 31%, write 31 , not 31%. If you think the answer is zero, write 0 , not 0.

According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

Probability is the study of random events in mathematics, and it can be classified into four main categories: axiomatic, classical, empirical, and subjective.

So, we must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value:

P(0.3<z<3.2)=0.9993−0.6179

Simplify as follows:

P(0.3<z<3.2)=0.3814

Therefore, according to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

Know more about probability here:

brainly.com/question/24756209

#SPJ4

The correct answer is option 3. \(4x^2 + 17\) expressions represent the total perimeter of her sandwich, and if x = 1.2, the approximate length of the crust is 21.8 centimeters.

The first expression, \(4x^2 + 17\) , represents the total perimeter of the sandwich. When x = 1.2, the expression evaluates to\(4 * 1.2^2 + 17 = 21.8\).

So the total perimeter of the sandwich is 21.8 cm. However, this length is not the length of the crust, since the length of the crust would only be a portion of the total perimeter.

The expression \(4x^2 + 17\) represents a mathematical formula for the total perimeter of the sandwich. The variable x represents the thickness of each slice of bread. The expression \(4x^2\) represents the total length of the four edges of the bread slices, and the 17 represents the total length of the filling. When x = 1.2, the expression evaluates to 21.8, which represents the total perimeter of the sandwich.

Learn more about Perimeter here:

https://brainly.com/question/397857

#SPJ4

well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

Answer:

Step-by-step explanation:

Jarred drew the model below of his backyard. The perimeter of the backyard is 40 feet, and the backyard is 8 feet wide.

his backyard is in rectangle shape and breadth =8

perimeter = 40

but perimeter = 2(l+b)

so

2(l+8)=40

l+8=20

l=12 feet

Answer:

A more appropriate domain would be all real numbers except x = 5.5

Step-by-step explanation:

Given that the domain of a rational function consists of the set of real numbers but excluding those real numbers that results in a zero in the denominator

The given graph of the function has a vertical asymptote at s = 5.5 which indicates a value for which the function is not defined and at x = 5.5, and as such the value (5.5) of the asymptote is not a member of the function's domain

The values of the domain of a function consisting of a reciprocal must exclude does that result in a zero denominator.

The domain of the function that represents Jada's trip is the set of input value the function can take

The appropriate domain is: all real numbers except x = 5.5

From the graph, we can see that:

This means that the input of the graph cannot be 5.5

Hence, an appropriate domain would be: \(\mathbf{x \ne 5.5}\)

Read more about domains at:

https://brainly.com/question/21853810

Answer:

fvg bvgcjvtfjocfrx

Step-by-step explanation:

kjn

jkm

'knlnkm

kl

j

kl;n

;kn

Ed must give Fay a total of £45 for both to have the same amount of money.

Total = £330

= 11

Ed share = 7/11 × 330

= £210

Fay share = 4/11 × 330

= £120

For Ed and Fay to have the same amount of money, their share must be exactly half of £330.

That is, they must each have £330/2

= £165

Fay:

£165 - £120 = £45

Therefore, Ed must give Fay a total of £45 for both to have the same amount of money.

Learn more about ratio:

https://brainly.com/question/2784798

#SPJ1

Joe's Bamboo Hut Kitchen and Seafood, Patong: See 5 unbiased reviews of Joe's Bamboo Hut Kitchen and ... Traditional Thai food with an amazing variety including fresh seafood all at an extremely affordable price and .

Answer:

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

Step-by-step explanation:

$2.56 for 32 oz is a unit price of $2.56/(32 oz) = $0.08/oz

$0.48 for 6 oz is a unit price of $0.48/(6 oz) = $0.08/oz

The unit prices are equal, so the cost of both sizes are proportional.

If x is the weight in oz, multiply the weight by 0.08 to get the cost, y, in dollars.

y = 0.08x

The ratios 2.56/32 and 0.48/6 are equivalent; y = 0.08x.

The expressions that are result of decreasing x by 80% are given as (20x / 100) and [x - (80x / 100)].

When an unknown number 'x' is decreased by 80%, the resultant number can be obtained using the mathematical formula given below:

Percentage decrease = [(initial value - final value)/ initial value] x 100

Since the initial value would be 100 percent of any number and final value is given by reduction of 80 percentage, then the expression would be:

80x /100 = [(100 - x)/ 100] * 100

Upon rearranging the terms, we get;

[x - (80x / 100)]

On further solving the above equation, we get;

(100x - 80x)/ 100 = 20x/100

Thus, the expressions that are the result of decreasing x by 80% are (20x / 100) and [x - (80x / 100)].

Learn more about Percentage at:

brainly.com/question/1053881

#SPJ9

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

To know more about  Spherical harmonics visit

https://brainly.com/question/23067012

#SPJ11

Answer:

Interest to be paid will keep on reducing each month

Step-by-step explanation:

due to reduction of the principal amount. As a result the net interest output will be higher for a borrower who carries balance for the whole year compared to one who pays offs monthly.

Answer:

Who is paying is not as important as the interest rate. Either way, a lower rate will benefit the person who has the bill.

Step-by-step explanation:

Answer:

a = 1,450,000

b = 290,000

Step-by-step explanation:

A: 1,740,000 = x*1.20

1,740,000/1.2 = x1.20/1.20

1,450,000 = x

B: 1,740,000 - 1,450,000 = 290,000

The correct transformations:

1) 3 x Equation [A2] + Equation [A1] → Equation [B1]

2). 1/11 x Equation [B1} → Equation [C1]

The correct options are D and A respectively.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Given:

We have three systems of linear equations.

To transform system A into system B:

Multiply 3 to the equation A2 and then add to equation A1,

we get,

-7x +18x -6y + 6y = 10- 54

11x = -44

equation B1.

To transform system B into system C:

Multiply 1/11 to equation B1,

we get,

x = -4

equation C1.

Therefore, the transformations are given above.

To learn more about the system of equations;

brainly.com/question/13729904

#SPJ1

7) The given distribution of data is:

19, 17, 18, 21, 14, 17, 16, 22, 14, 22, 16

This can be rearranged as:

14, 14, 16, 16, 17, 17, 18, 19, 21, 22, 22

The frequency distribution table is drawn below

The dot plot is drawn right after the frequency table

Answer:

a,b,d

Step-by-step explanation:

a constant rate means it is constantly/repeatedly changing the same amount over time a,b,d keeps on changing (a is by 12% each year) (B is by 3 points each decade) (D is by 2.5% each year) C on the other hand changes every six months but stops at the end of the second year. therefore the answers are A,B and D

The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

Learn more about maximum likelihood estimator click;

https://brainly.com/question/32608862

#SPJ4