2. A client has approached a stockbroker with the following request: Invest $100,000 for maximum annual income under these conditions: • Spread the investment over no more than three different stocks • Put no more than 40 percent of the money into anyone stock • Put a minimum of $10,000 in to oil stock. The broker has identified three stocks for investing the funds. Their estimated annual returns and price per share are shown in the following table: Stock Price Per share Estimated annual return per share Oil $120 $11 Auto 52 4 Health 18 2 Required: Formulate an LPM for the problem. 1. Given this summarized linear programming model: Maximize: Subject to: 1. 2. 3. i) Graph the model ii) Find the optimal point on the graph using the extreme point approach iii) Use simultaneous equations to determine the optimal value of iv) Determine the amount of slack for each constraint

Answer:

Step-by-step explanation:

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force.

If you are standing on separate sheets of paper and start running, your body will experience a forward motion. However, the sheets of paper under your feet will initially resist the motion due to friction. The force of friction will create an equal and opposite force, causing the sheets of paper to slide backwards. As you continue to run, the friction between your feet and the paper will decrease, and the sheets of paper may eventually stop sliding and you will continue running with a constant velocity.

This is an example of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force you apply to the ground when running is the action, and the force of the ground pushing back on you is the reaction.

The solution is, x²-14x+24

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

Given:

x=12, x=2

Solution:  In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.

Move the integers

Solution #1

x-12 = 0

Solution #2

x-2=0

Create and expression and distribute

(x-12)(x-2)=0

solving we get,

x²-14x+24 = 0

Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.

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This graph shows how far Han is from his house as he drives. (0, 10) is the Y Vertical intercept. Han is therefore originally located 10 miles from his house.Horizontal intercept of X (10,0) It indicates that it takes 10 minutes to reach.

The point where the graphs of a function and relation meets the y-axis of the coordinate system is known as a y-intercept, also referred to as a vertical intercept. Analytic geometry is used for this, with the widely accepted standard that the variable y is represented by the vertical axis and the variable x by the horizontal axis.

Anything straight to the horizon is said to as horizontal. Since the vertical is the polar opposite of the horizontal, everything that intersects it at a right angle of 90 degrees is known as vertical. Hence, the line that runs form left to center is seen as being horizontal.

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The value of y is given as follows:

y = 4.3 cm.

The value of y is obtained applying the two secant segment theorem, which means that the following equation will hold true:

3(3 + y) = 2(2 + 9).

(a secant is a segment that crosses the circumference of the circle twice, and the product has to be equal for each).

Then we apply the distributive property to each side of the equality, and then isolate the variable y, as follows:

9 + 3y = 22

3y = 13

y = 13/3

y = 4.3.

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The real GDP per capita increased by 28% from 2012 to 2013.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

The table with GDP deflator and population

Now,

i. The percentage change in nominal GDP from 2012 to 2013 can be calculated as follows:

[(Nominal GDP in 2013 - Nominal GDP in 2012) / Nominal GDP in 2012] x 100

= [(112 - 75) / 75] x 100

= 49.33%

Therefore, nominal GDP grew by 49.33% from 2012 to 2013.

ii. Real GDP is nominal GDP adjusted for inflation. To find real GDP, we need to use the GDP deflator:

Real GDP (in billions) = Nominal GDP (in billions) / (GDP Deflator / 100)

In 2012: Real GDP = 75 / (50 / 100) = £150 billion

In 2013: Real GDP = 112 / (54 / 100) = £207.41 billion

iii. The percentage change in real GDP from 2012 to 2013 can be calculated as follows:

[(Real GDP in 2013 - Real GDP in 2012) / Real GDP in 2012] x 100

= [(207.41 - 150) / 150] x 100

= 38.27%

Therefore, real GDP grew by 38.27% from 2012 to 2013.

iv. To determine if the growth in nominal and real GDP increased the standard of living, we need to look at the change in real GDP per capita. Real GDP per capita is calculated by dividing real GDP by the population:

Real GDP per capita in 2012 = 150 / 50 = £3 billion

Real GDP per capita in 2013 = 207.41 / 54 = £3.84 billion

The percentage change in real GDP per capita can be calculated as follows:

[(Real GDP per capita in 2013 - Real GDP per capita in 2012) / Real GDP per capita in 2012] x 100

= [(3.84 - 3) / 3] x 100

= 28%

Therefore, by the percentage the answer will be 28% from 2012 to 2013.

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Therefore, it will take approximately 4.2 years for the television set to be worth half of its original value.

All of your revenues and expenses are listed in your profit and loss statements. They also show whether operating expenses have been covered by profits earned by your business. In that case, you could claim that your business has made money. The profit and loss statement displays the profitability of a company.

We can start solving this problem by setting up an equation for the value of the TV over time. Let V be the value of the TV in dollars and t be the time in years. Then, we have:

V(t) = 1900 - 225t

We want to find the time it takes for the TV to be worth half of its original value, which means we want to find t when V(t) = 950. So, we can set up the following equation:

950 = 1900 - 225t

Solving for t, we get:

t = (1900 - 950) / 225

t = 4.22 years (rounded to two decimal places)

Therefore, it will take approximately 4.2 years for the television set to be worth half of its original value.

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Using the given restrictions we can see that there are 37 balls on the box.

Let's assume that the total number of balls is B.

We know that in the box there are more than 25 and fewer than 40 tennis balls, so we have the inequality.

25 < B < 40

If we count in 3's, then there is one left over, so we can write:

B = 3*n + 1   (where n is an integer number)

And if we count in 5's there are 2 leftovers:

B = 5*m + 2  (where m is an integer, from this we conclude that the number ends in a 2 or a 7)

Then we have 3 restrictions:

25 < B < 40

B = 3*n + 1

B = 5*m + 2

notice that if n = 12

B = 3*12 + 1 = 37

if m = 7

B = 5*7 + 2 = 37

and 37 is a solution of the inequality, then we conclude that there are 37 balls on the box.

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Total snacks

15

Initially, cashews are 2x the amount of almonds

After 10 cashews are eaten, there are still 5 more cashews than almonds.

this gives us an insight into the amount eaten before they are equal

cashew eaten = 10

cashews left = almonds + 5

Therefore the almondds are 10 + 5 = 15

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The value of the transformed function after a vertical stretch in the y direction is h ( x ) = k ( | x | - 3 ) , where k is the scale factor

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = ( | x | - 3 )   be equation (1)

Now , when the function is stretched in the y direction , we get

Vertical stretch by a factor k: y = k × f(x)

On simplifying , we get

Let the transformed function be represented as h ( x )

where the value of h ( x ) is

Let the scale factor of stretching be k

h ( x ) = k ( | x | - 3 )

Hence , the transformed function is h ( x ) = k ( | x | - 3 )

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Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = previous balance + new charge

Current balance = $319 + $170

Current balance = $489

The minimum payment is 6% of the current balance:

Minimum payment = 6% x current balance

Minimum payment = 6% x $489

Minimum payment = $29.34

Therefore, the minimum payment on the credit card would be $29.34.

Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = $319 + $170 = $489

Minimum payment = 6% x $489 = $29.34

The minimum payment on the credit card would be $29.34.

Hope this helped, have a GOOD DAY!!!!!

Answer:

x = -3/5

Step-by-step explanation:

Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]

Solve for the variable x by isolating x-term, first move subtract both sides by 3x:

[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]

Subtract both sides by 9:

[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]

Therefore x = - 3/5

Answer:

x = -3/5 (or) x = -0.6

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 8x + 9 = 3x + 6

Then the value of x will be,

→ 8x + 9 = 3x + 6

→ 8x - 3x = 6 - 9

→ 5x = -3

→ x = -3 ÷ 5

→ [ x = -3/5 ]

Hence, the answer is -3/5.

Answer:

15. x = -3.

16. x = -2.

17 x = 2.

Step-by-step explanation:

To solve the equation 7x + 5 = 12x - 10, we want to isolate the variable x on one side of the equation. We can do this by adding or subtracting terms from both sides of the equation until we have x by itself.

First, let's simplify both sides of the equation by combining like terms:

7x + 5 = 12x - 10

-7x -7x (subtracting 7x from both sides)

5x + 5 = -10

Next, let's isolate the term with x by subtracting 5 from both sides of the equation:

5x + 5 = -10

-5 -5 (subtracting 5 from both sides)

5x = -15

Finally, let's solve for x by dividing both sides of the equation by 5:

5x = -15

x = -3

Therefore, the solution to the equation 7x + 5 = 12x - 10 is x = -3.

26 = 24 - x

-24 -24 (subtracting 24 from both sides)

2 = -x

Next, let's isolate the variable x by multiplying both sides of the equation by -1:

2 = -x

-1 -1 (multiplying both sides by -1)

-2 = x

Therefore, the solution to the equation 26 = 24 - x is x = -2.

2(6x - 7) = 10

12x - 14 = 10

Next, let's isolate the term with x by adding 14 to both sides of the equation:

12x - 14 = 10

+14 +14 (adding 14 to both sides)

12x = 24

Finally, let's solve for x by dividing both sides of the equation by 12:

12x = 24

x = 2

Therefore, the solution to the equation 2(6x - 7) = 10 is x = 2.

Answer:

y = 4x + 3

Step-by-step explanation:

See picture below :)

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

The surface area of the solid is 28 square inches.

The surface area of a given object is the sum or total area of all shapes forming its external surfaces. This implies calculating the area of each surface and adding them up.

In the given question, the net has a surface area of;

Area of a square = length*length

                    = 2*2

Area of the square base = 4 [tex]in^{2}[/tex]

Area of a triangle = 1/2 base*height

              = 1/2*2*6

Area of each triangular surface = 6 [tex]in^{2}[/tex]

Surface area of the solid = (4*6) + 4

                                   = 24 + 4

                                   = 28

Surface area of the solid is 28 [tex]in^{2}[/tex].

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Answer:

Surface area of the solid is 28 .

Step-by-step explanation:

Answer:

x = [tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]7-2(3-8x)=7-6-16x[/tex]

Add/subtract like terms

[tex]5(3-8x)=1-16x[/tex]

Distribute 5

[tex]15-40x=1-16x[/tex]

Simplify

[tex]-40x+15=-16x+1[/tex]

Add -16x to both sides

[tex]-24x+15=1[/tex]

Subtract 15 on both sides

[tex]-24x=-14[/tex]

Divide by -24

[tex]x=\frac{7}{12}[/tex]

The values of x are 3 or 0. 3 and 0 will satisfy the equation |2x-3| +7 =10.

What is an absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The parent function with an absolute value is defined as f(x)=| x |.

Given equation is

|2x-3| +7 =10

Subtract 7 from both sides:

|2x-3| +7 - 7 = 10 - 7

|2x-3| = 3

Applying absolute function:

Either, 2x-3 = 3         or, 2x-3 = -3

Add 3 on both sides:

2x = 6                         2x = 0

Divide both sides by 2:

x = 3      or     x = 0

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Answer:

So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.

Step-by-step explanation:

To find out how many feet of fabric Fatima's curtain company needs, we first need to calculate the total length of fabric required for all 62 curtains.

Each curtain is 48 inches long, so the total length of fabric required for one curtain is:

48 inches = (48/12) feet = 4 feet

Therefore, the total length of fabric required for 62 curtains is:

62 curtains x 4 feet/curtain = 248 feet of fabric

So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.

The Standard deviation of the given data is 989.615.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have data as

$54,410, $51,991, $51,730, $51,300, $51,196, $51,190, $51,122, $51,115, $51,037 and $50,875.

Also we have

Count, N: 10

Sum, Σx: 515966

Mean, μ: 51596.6

Now, using the formula of Standard Deviation

= √1/ N[tex]\sum_{i=1}^n (x_i- \mu)[/tex]²

= (54410 - 51596.6)² + (51991 - 51596.6)² +(51730 - 51596.6)² + (51300 - 51596.6)²+ (51122- 51596.6)² + (51115- 51596.6)² + (51037- 51596.6)² + (50875 - 51596.6)² / 10

= √9793384.4 /10

= √979338.44

= 989.615

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An expression for e[z] by the given data is  E[z] = (n-1)/n * H_n-1.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_nT_{n+1} - T_n

for all positive integer values of n.

We are given that;

Balls are thrown uniformly and independently in all bins

Now,

We can express z as the sum of these binary random variables:

[tex]z = z_1 + z_2 + ... + z_{n-1}[/tex]

The random variables z_i are not independent, since the probability of throwing a ball into a bin that already has at least one ball in it depends on the number of balls already in the bin.

However, we can still use the linearity of expectation to calculate the expected value of z:

[tex]E[z] = E[z_1 + z_2 + ... + z_{n-1}][/tex]

By the linearity of expectation, we can distribute the expectation over the sum:

[tex]E[z] = E[z_1] + E[z_2] + ... + E[z_{n-1}][/tex]

Using these probabilities, we can calculate the expected value of each z_i:

[tex]E[z_i] = 1 * P(z_i=1) + 0 * P(z_i=0)= P(z_i=1)[/tex]

= (i-1)/n-i+1

Substituting this into the expression for E[z], we get:

[tex]E[z] = (1-1/n) + (2-1/n-1) + ... + (n-1-1/2)= (n-1)/n + (n-1)/n-1 + ... + 1/2[/tex]

This is a finite arithmetic series with n-1 terms, with first term (n-1)/n and common difference -1/n. Using the formula for the sum of an arithmetic series, we get:

[tex]E[z] = (n-1)/n + (n-2)/n + ... + 1/n= (n-1)/n * (1 + 1/2 + ... + 1/(n-1))[/tex]

This sum is known as the n-th harmonic number, denoted H_n.

Therefore, by arithmetic sequence the answer will be E[z] = (n-1)/n * H_n-1

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It is found that the distance between the two memorials is of 1,42 miles.

The distance between two points (x1 , y1) and (x2 , y2) is of:

Distance formula = [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

One memorial is at point (3,-1).

The other is at point (7, -5).

Thus, in the coordinate grid, the distance is of:

D = 5.66

In the coordinate, the distance is of 5.66 units. Each unit is worth 0.25 miles, thus:

D = 5.66 units

The distance between the two parks is of 1.42 miles.

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Answer:

11° 33'

Step-by-step explanation:

[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]

Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]

[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]

Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]

Subtract the whole numbers:
49 - 38 = 11

Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]

So

50°21' - 38°48' = 11° 33'

Therefore , the solution of the given problem of domain comes out to be the appropriate domain for p(w) would be [1, 1000]

The domain of a function is the range of possible arguments that it can accept. The cross of the an f-like functional is represented by these numbers (x). The range of potential values to which a function can be applied is known as its domain. The value that the procedure returns after inserting the x value is part of this set. An equation for a function is Y = f, where y and x are predictor variables (x). When a given value of x can produce a single value of y, a parameter is said to be in the scope of a function.

Here,

Given :

1 kilogram to 1000 kilograms.

He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

So,

The appropriate domain for p(w) would be [1, 1000]

since

Aiden sells any amount of cumin seeds from 1 kilogram to 1000 kilograms.

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The complete question is "Aiden is a spice trader. He sells any amount of cumin seeds from 1 kilogram to 1000 kilograms. He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

p(w) models the price (in dollars) of w kilograms of cumin seeds in Aiden's shop. What's the appropriate domain?"

Answer:

6

Step-by-step explanation:

Simplifying the expression (2+1)2, we can first perform the operation within the parentheses, which gives us:

(2+1)2 = 3 x 2

Then, we can multiply 3 by 2, which gives us:

3 x 2 = 6

Therefore, the simplified expression for (2+1)2 is 6

The probability of a rejected part, knowing that it came from a known shift can be calculated as follows:

Shift 1: (51/600) x 100% = 8.5%

Shift 2: (72/850) x 100% = 8.5%

Shift 3: (50/650) x 100% = 7.7%

Shift 4: (57/510) x 100% = 11.2%

The probability that a randomly selected part is defective is (1287/19500) x 100% = 6.6% (rounded to one decimal place).

The probability that a randomly selected part is not defective is (18213/19500) x 100% = 93.4% (rounded to one decimal place).

The probability that a part came from Factory A is (3500/19500) x 100% = 17.9% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory A is (120/3500) x 100% = 3.4% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory B is (125/2700) x 100% = 4.6% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory C is (210/5000) x 100% = 4.2% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory D is (712/4700) x 100% = 15.1% (rounded to one decimal place).

The probability of a defect, knowing the part came from Factory E is (120/3600) x 100% = 3.3% (rounded to one decimal place).

Based upon these probabilities, Factory D should be investigated more as it has the highest probability of a defective part among all the factories.

The probability of a defect for the flagged factory is (230/2610) x 100% = 8.8% (rounded to one decimal place).

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Imagine you draw a straight line down the middle of a piece of paper. This line is the line of symmetry. Anything you draw on one side of the line is going to have a mirror image on the other side of the line that looks exactly the same.

Now, if you have a point on the line of symmetry, that means the point is exactly in the middle of the line. And since the line is the same on both sides, that means the point is going to be the same on both sides too! So, the point on the line of symmetry stays in the same place and looks the same on both sides of the line.

- Dante

Answer:

A

Step-by-step explanation:

hope this helps

Answer:

3. Initial cost = 99 dollars.  Each hour (h) is 19 dollars. The total value will be initial cost + hours*(cost per hour)=> t=99+19h.

4. She will be using the car for 3 days. Each day costs 29.99. There is no initial cost, so her total cost will be 29.99*3=89.97 dollars.

All the probabilities are solved and are mentioned below.

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value

Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -

Pr(X = 0) = 0.55

Pr{X = 1) = 0.22

Pr(X = 2) = 0.13

Pr(X = 3) = 0.08

Pr(X = 4) = 0.02

We can find the probabilities as -

{ 1 } - the probability that two or fewer bits are transmitted in error :

P{E} = P(0) + P(1) + P(2)/∑P{n}

P{E} = 0.9/1

P{E} = 0.9

{ 2 } - the probability that at least one bit is transmitted in error -

P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}

P{E} = 0.45/1

P{E} = 0.45

{ 4 } - the expected value of the number of bits transmitted in error -

n = 0 + 1 + 2 + 3 + 4

n = 10

{ 4 } - the standard deviation of the number of bits transmitted in error -

σ = 1.0677

Therefore, all the probabilities are solved and are mentioned above.

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