A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:

STATE OF NATURE

INVESTMENT GOOD ECONOMY FAIR ECONOMY POOR ECONOMY

Fund A $10,000 $2,000 –$5,000

Fund B $6,000 $4,000 0

Probability 0. 2 0. 3 0. 5

Draw the decision tree to represent this situation.


Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?


Suppose there is a question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)?

When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be 48 times.

The times he should expect the coin to land on tail based on the table will be 27 times.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be:

= 1/2 × 96

= 48

The number of times he should expect the coin to land on tail based on the table will be:

= 18/50 × 75

= 27 times

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The coordinate pair of the given system is (-1,9)

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)

Add the new equation 12x - 2y = -30 to the second equation

12x - 2y = -30, x+2y = 17, add the two equations to eliminate y

13x = -13

x = -1

Substitute -1 back into the equation x+2y = 17.

-1 + 2y = 17

2y = 18

y = 9

So the solution of the system is x = -1, y = 9

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Answer:

3.5

Step-by-step explanation:

In this problem, the line's constant of proportionality is the same as its slope.

Slope is defined as rise / run (also notated as change in y / change in x).

Using the given point, we can deduce that the line's rise (change in y) is 3.5, and its run (change in x) is 1. Putting these values into the slope formula:

3.5 / 1 = 3.5

So, the constant of proportionality of this line is 3.5.

Answer: #181000

Step-by-step explanation:

So, to solve the problem, recall these definitions:

payout - withdrawal

pay in - deposits.

Normally, deposits add money to your balance, and withdrawals take out money.

So, there is one cheque for  paying in 14,000, and two cheques for paying out 49,000 and 34,000

So, the balance is 250000 + 14000 - (49000+34000)

The balance is 181,000

1. In a triangle line parallel to one side will divides other two sides in the same ratio

2. 8/x = 12/18

   x = 12

Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b).

Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

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Answer:

20%

$18.84

Step-by-step explanation:

3.14 is what percent of 15.70?

Use the percent-to-dollar conversion (100: 15.70) :

3.14 * 100% / 15.70 =

3.14 / 15.70 * 100% =

1/5 * 100% =

100% / 5 = 20% ==> percent tip

$15.70 + $3.14 = $18.84  ==> Total cost

By considering the reflection, the coordinates of the reflected square D'E'F'G' are:

D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)

A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.

Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.

When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.

The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:

D(1,1) => D'(1-1,1) => D'(0,1)

E(1,6) => E'(1-1,6) => E'(0,6)

F(6,6) => F'(6-1,6) => F'(5,6)

G(6,1) => G'(6-1,1) => G'(5,1)

So the coordinates of the reflected square D'E'F'G' are:

D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)

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Each will get 3/5 cups of nuts by ratio and proportion concepts.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

We have to divide total nuts within 5 people.

so,

3 3/5 : 5

but first convert,

3 3/5 = 15/4

substitute,

15/4 : 5 = 15/20cups of nuts

simplify,

3/5 cups

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Using the distributive property to rewrite the expression, gives (14 x 10) + ( 14 x 2). When evaluated, the result would be 168.

According to the distributive property, it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

This means that with the formula given, 14 (10 + 2):, the distributive property makes it:

= 14 (10 + 2)

= (14 x 10) + ( 14 x 2)

The evaluation gives :

= (14 x 10) + ( 14 x 2)

= 140 + 28

= 168

In conclusion, using the distributive property gives (14 x 10) + ( 14 x 2).

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The slope of the linear equation that passes through the points (-6, -2) and (3, -2) is 0.

We can write a linear equation using the sope-intercept form as:

y = m*x + b

Where m is the slope and b is the y-intercept.

For any linear equation, if we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is given by:

m = (y₂ - y₁)/(x₂ - x₁).

In this case we know that the line passes through the points (-6, -2) and (3, -2).

Then the slope will be:

m = (-2 + 2)/(3 + 6) = 0

m = 0

The slope is zero, meaning that this is an horizontal line.

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Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.

Using the equals symbol (=), a mathematical equation appears to be a formula that connects two statements and denotes equality. A scientific assertion that supports the equality of two mathematical abstraction is known as an equation in algebra. For instance, the equal sign is present between the variables ptdc + 6 and 12 in the output obd + 6 = 12. The link between the syllable on either side of either a letter is described by a mathematical formula. In many cases, the logo and the say — are identical.

Here,

Given: A new supply of 300 spark plugs will come on Thursday,

and 520 spark plugs require 48 plugs per day.

To determine an equation to determine however many plugs will just be left at the end of Friday:

So,

where n is the no of days

=> 520 - 48*n + 300

=> 520 - 48*5 + 300

=> 520 - 240 + 300

=> 520 + 60

=> 580

Therefore , the solution of the given problem of equation comes out to be 580 spark plugs will be left.

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The length of the guy wire is 48.87 m.

To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.

To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]

Solving for b gives b = 6.78 m

Then, length of wire can be calculated as

[tex]c = sqrt(48^2 + 6.78^2)[/tex]

[tex]c = 48.87 m (approx)[/tex]

Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.

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The triangle in the figure can be proved by ASA, SAS, and AAS

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem requires the prove by ASA, SAS, and AAS to ensure that the the triangles are congruent.

Alternate angles in the figure are also equal

According to the ASA rule, two triangles are said to be congruent if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

The Angle-Angle-Side (AAS) Congruence Theorem states that two angles and a non-included side in one triangle must be congruent with two angles and the equivalent non-included side in another triangle for the triangles to be congruent.

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Answer:

A) 5

B) X-3

C) 2X+Y

step by step:

base x height = area

A Height= (5x+20) ÷ (x+4)= 5

B Base= (8x-24) ÷ 8 = x-3

C Height= (12x+6y) ÷ 6 = 2x+y

The solution is

Parallelogram A : Base = x + 4 ; Height = 5

Parallelogram B : Base = x - 3 ; Height = 8

Parallelogram C : Base = 6 ; Height = 2x + y

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be A = Base x Height

So , Substituting the values in the equation , we get

a)

Let the parallelogram be A

Now , Area = 5x + 20

Base = x + 4

So , the height = Area / Base

Height = 5

b)

Let the parallelogram be B

Now , Area = 8x - 24

Height = 8

So , the Base = Area / Height

Height = x - 3

c)

Let the parallelogram be C

Now , Area = 12x + 6y

Base = 6

So , the height = Area / Base

Height = 2x + y

Hence , the equations are solved

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Answer:

sorry, I forget how to do the other ones and I'm just as confused but for 4. AD is 20 and 5. GJ is 17

Step-by-step explanation:

4. side AD is equal to side CD so therefore its 20.

5. side are equal again so make

4x+5 = 2x+11

    -5         -5

4x = 2x+6

-2x  -2x

2x = 6

/3    /3

x = 3

2(3)+11

6+11

17

The solution for given differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)

This is a second-order linear differential equation with constant coefficients. To solve this equation, we can use the method of an auxiliary equation, which is 3r^2 + 6r + 1 = 0. This equation has two complex conjugate roots, r = -3 ± i√3. Therefore, the solution of the differential equation is y = c1e^(-x^3/3) + c2xe^(-x^3/3)cos(√3x^2/2) + c3xe^(-x^3/3)sin(√3x^2/2), where c1, c2, and c3 are arbitrary constants.

The method of an auxiliary equation is a popular way to solve second-order linear differential equations with constant coefficients. It involves finding the roots of an auxiliary equation, which is found by setting the coefficient of the second derivative equal to zero.

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Answer:

see explanation

Step-by-step explanation:

under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

C (1, 9 ) → C' (- 9, 1 )

D (4, 9 ) → D' (- 9, 4 )

E (0, 3 ) → E' (- 3, 0 )

The three equations for this problem are:

Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z

so the

let's use the third equation to get the value of x,y and z:

If you get the values and substitute, then the answer would be:

4 chocolate cakes, 5 fruit cakes, 2 sponge cakes

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To create a frequency polygon calculate the midpoint,  locate the midpoints and connect them with lines.

A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.

So, we must determine the midpoint or average of the range for each category.

0 < t < 10 = 5

10 < t < 20 = 15

20 < t < 30 = 25

30 < t < 40 = 35

2. Add a point where the data of the axis Y and X form an intersection.

3. Connect the points.

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The stem plot for the given data is 3 4 5 6.

A stem and leaf plot, also known as a stem and leaf diagram, is a technique to arrange data such that it is simple to see how frequently certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

Arranging the given data in ascending order,

30, 34, 34, 35, 35, 36, 39, 39, 40, 40, 41, 42, 42, 43, 43, 43, 44, 46, 46, 48, 49, 49, 50, 52, 53, 58, 59, 61, 66, 68

The stem plot = 3 4 5 6

Calculated Statistics:

Minimum:30

Maximum:68

Range:38

Count:30

Sum:1365

Mean:45.5

Median:43

Mode:43

Standard Deviation:9.616

Variance:92.47

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Please find attached the graph showing the translation transformation of the triangle ΔABC with vertices A(2, 1), B(-1, 2), and C(-2, -1) using the rule (x, y) → (x - 1, y - 3), to produce triangle ΔA'B'C' with vertices A'(1, -2), B'(-2, -1), and C'(-3, -4), created with MS Excel

A translation transformation is one in which the location of the points on the original figure slides by the same amount and in the same direction to form the image.

The vertices of the triangle ΔABC are; A(2, 1), B(-1, 2), and C(-2, -1)

The specified transformation is; (x, y) → (x - 1, y - 3)

Applying the specified transformation, we get;

A(2, 1) ⇒ (x, y) → (x - 1, y - 3) ⇒ A'(2 - 1, 1 - 3) = A'(1, -2)

B(-1, 2) ⇒ (x, y) → (x - 1, y - 3) ⇒ B'(-1 - 1, 2 - 3) = B'(-2, -1)

C(-2, -1) ⇒ (x, y) → (x - 1, y - 3) ⇒ C'(-2 - 1, -1 - 3) = C'(-3, -4)

The vertices of the image ΔA'B'C' of the triangle ΔABC following the transformation, (x, y) → (x - 1, y - 3) are therefore;

A'(1, -2), B'(-2, -1), C'(-3, -4)

Please find attached the graph of the triangle ΔABC and its image ΔA'B'C' after the translation (x, y) → (x - 1, y - 3), created with MS Excel

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Answer:

C. [tex]4\frac{2}{3}[/tex]

Step-by-step explanation:

One way of approaching this problem is to multiply the numbers the numerators together and then divide by the denominator to receive the quotient and the remainder.

Firstly 6 can be written as a fraction like so: [tex]\frac{6}{1}[/tex] because 6 divided by 1 is equal to 6.

To multiply two fractions together, we simply multiply the numerators and multiply the denominators:

[tex]\frac{7}{9}* \frac{6}{1} =\frac{7*6}{9*1}[/tex]

Which gives us the improper fraction of: [tex]\frac{42}{9}[/tex]

Next, we find the highest multiple of 9 which is smaller than 42. If we write out the multiples of 9 we will find that it is 36:

1x9=9, 2x9=18, 3x9=27, 4x9=36, 5x9=45

Since we know that at least 4 whole 9s go into 42 we can conclude that the coefficient of the fraction will be 4.

To find the fraction itself, we must find the remainder which we can do by subtracting 36 from 42: 42-36 = 6

The remainder is the numerator of the fraction as there are 6 ninths left over after we have divided 42 by 9.

Therefore our answer is [tex]4\frac{6}{9}[/tex]

If we divide 6 and 9 by 3 we will find that 6/9 is equivalent to 2/3 therefore our final answer is [tex]4\frac{2}{3}[/tex].

Option C is correct.

1/2

If there are 3 ponies, and 6 sheep,

the original ratio is 3/6.

However, it must be simplified down to 1/2.

Answer:

-2,2

Step-by-step explanation:

In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia

The population of the city grew from 2010 to 2020 by 13.37 %

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

Given that, In 2010, the population of a city was 237,000. From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

The population in 2015 =

A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

The population in 2015 =

A = 237,000(1+0.076)⁵

A = 341829.629

The population in 2020 =

A = P (1-r)ⁿ

A = 341829.629(1-0.047)⁵

A = 268704.047

Percent grow = 268704.047 - 237,000 / 237,000 × 100

= 31704.047 / 237,000 × 100

= 13.37 %

Hence, the population of the city grew from 2010 to 2020 by 13.37 %

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To find the midpoint of two points in a coordinate plane, you can use the midpoint formula.

The midpoint formula is the average of the x-coordinates and the average of the y-coordinates of the two given points.

The midpoint formula is:

((x1 + x2)/2 , (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

For example, if the two points are (3, 4) and (5, 8), the midpoint would be:

((3 + 5)/2 , (4 + 8)/2) = (4, 6)

So the midpoint between (3, 4) and (5, 8) is (4, 6).

It's important to note that this formula is valid for any dimension, not just 2D, and it can be used to find the midpoint of any two points in space, whether it's in 2D, 3D, 4D and so on.

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Answer:    It is not possible for me to determine which line LR is not a transversal to without more context. A transversal is a line that intersects two or more other lines at different points. In order to determine which line LR is not a transversal to, I would need to know the other lines that are involved and the points at which they intersect.

Step-by-step explanation: