The market research department of a company recommended to management that the company manufacture and market a promising new product. After extensive surveys, the research department backed up the recommendation with the demand equation: x = f (p) = 6000 - 30p where x is the number of units that retailers are likely to buy per month at $p per unit. From the financial department, the following cost equation was obtained: C = g(x) = 72,000 + 60x where $72,000 is the fixed cost (tooling and overhead) and $60 is the variable cost per unit (materials, marketing, transportation, storage, etc.). a. Find the break-even points. b. Find the price that produces the maximum revenue. c. Find the price that produces the maximum profit.

Answer:

z = (3/√2) + (1/√2)î = (1/√2) [3 + i] = (2.1213 + 0.7071i)

OR

z = -(3/√2) + i(1/√2) = (1/√2) [-3 + i] = (-2.1213 + 0.7071i)

p = (3/√2) = 2.1213

q = (1/√2) = 0.7071

OR

p = (-3/√2) = -2.1213

q = (1/√2) = 0.7071

Step-by-step explanation:

z = √(4 + 3i)

Let the complex number z be equal to

z = p + qi

So, we can write

z = p + qi = √(4 + 3i)

p + qi = √(4 + 3i)

Square both sides

(p + qi)² = [√(4 + 3i)]²

p² + pqi + pqi + (qi)² = (4 + 3i)

p² + 2pqi + q²i² = 4 + 3i

note that i² = -1

p² + 2pqi - q² = 4 + 3i

(p² - q²) + 2pqi = 4 + 3i

Comparing both sides, and them equating the real parts on both sides to each other and the complex parts to each other

(p² - q²) = 4 (eqn 1)

2pq = 3 (eqn 2)

From eqn 2

p = (3/2q)

p² = (9/4q²)

Substituting this into eqn 1

(9/4q²) - q² = 4

multiplying through by 4q²

9 - 4q⁴ = 16q²

4q⁴ + 16q² - 9 = 0

let q² = x, q⁴ = x²

4x² + 16x - 9 = 0

Solving the quadratic equation

x = 0.5 or -4.5

q² = 4

q² = 0.5 or q² = -4.5

q = √0.5 or √-4.5

q = (1/√2) = (√2)/2 = 0.7071

Or q = i(3/√2) = i(3√2)/2 = 2.1213I

p = (3/2q)

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = p + qi

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

z = (3/√2) + (1/√2)î = (1/√2) [3 + i]

= 2.1213 + 0.7071i

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = i(1/√2) + [i(3/√2) × i]

z = i(1/√2) - (3/√2)

z = -(3/√2) + i(1/√2)

z = (1/√2) [-3 + i]

z = -2.1213 + 0.7071i

Hope this Helps!!!

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

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Answer:

D 100% d

Step-by-step explanation:

The area of the given parallelogram will be 6.5 square cm.

The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle and a parallelogram.

Given that the measure of the parallelogram is,

a = 7 cm

b = 6 cm

h = 1 cm

The area of the parallelogram is calculated by the formula given below as,

Area = (1/2) ( a + b ) x h

Area = (1/2) ( 7 + 6 ) x 1

Area = 6.5 square cm

Therefore, the parallelogram will have an area of 6.5 square cm.

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The equation z = 30x represents a direct variation the two variables, z and x, are directly proportional to each other. a.

Direct variation can be defined as a relationship between two variables where their values increase or decrease at the same rate.

In the case of the given equation, as x increases, z also increases proportionally.

Similarly, if x decreases, z will also decrease proportionally.

Direct variation can be represented as y = kx, where y and x are the variables, and k is the constant of variation.

In the given equation, we can see that z is the dependent variable, and x is the independent variable.

We can rewrite the equation as z = kx, where k = 30.

To understand how direct variation works, let's consider an example. Suppose we have an equation y = 5x, where y represents the cost of buying x apples at $5 per apple.

Here, the cost of buying apples is directly proportional to the number of apples purchased.

For instance, if we buy 10 apples, the total cost will be 10 × $5 = $50.

Similarly, if we buy 20 apples, the total cost will be 20 × $5 = $100.

Thus, we can see that the cost increases as the number of apples purchased increases, and vice versa.

The given equation z = 30x represents a direct variation is a type of relationship between two variables where their values increase or decrease proportionally.

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Using distributive property, the solution to the given expression is: 50v - 40w + 20

The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

4(3 + 5)

According to the distributive property, you first have to multiply out the bracket to get:

4*3 + 4*5 = 12 + 20

= 32

Thus:

5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)

= 50v - 40w + 20

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Answer:

Step-by-step explanation:

Let total mass be x

(3/4)*x=15

on solving

x=20

now,

mass of 2/5 of piece of metal is-

=> (2/5)*20

=> 8

Ans- 8kg

Answer:

[3,∞)

Step-by-step explanation:

[3,∞)

Hope that helps

Answer:

B that's the answer for that

Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Answer:

99685/ 112

or

890  5/112

Step-by-step explanation:

Answer:

60.5

Step-by-step explanation:

Ehhh 52.07+8.43=60.5?

Answer:

Step-by-step explanation:

To find the price that maximizes the country's revenue, we need to consider the relationship between price, sales, and revenue.

Let's start by calculating the current revenue for the country:

Revenue = Price × Sales

Revenue = $80/barrel × 7 million barrels/day

Revenue = $560 million/day

Now let's consider the effect of a price increase on sales. According to the problem, a $1 increase in price will result in a decrease of 100,000 barrels/day in sales. This means that the new sales rate at a price of $81/barrel will be:

New sales = 7 million barrels/day - 100,000 barrels/day per $1 increase × (81 - 80)

New sales = 6.9 million barrels/day

The new revenue at a price of $81/barrel will be:

New revenue = $81/barrel × 6.9 million barrels/day

New revenue = $559.9 million/day

We can repeat this process for a range of prices to see how revenue changes:

Price Sales (million barrels/day) Revenue (million $/day)

 80                            7.0                             560.0

 81                            6.9                             559.9

 82                            6.8                             544.0

 83                            6.7                             534.1

 84                            6.6                             528.0

 85                            6.5                             520.0

From this table, we can see that the price that maximizes revenue is $84/barrel. At this price, the country will sell 6.6 million barrels/day, and generate revenue of $528 million/day.

Therefore, the price that will maximize the country's revenue is $84/barrel, and it will sell 6.6 million barrels/day at that price.

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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\(\\ \sf\longmapsto 5x+5+4x-5=180\)

\(\\ \sf\longmapsto 5x+4x+5-5=180\)

\(\\ \sf\longmapsto 9x=180\)

\(\\ \sf\longmapsto x=\dfrac{180}{9}\)

\(\\ \sf\longmapsto x=20\)

Step-by-step explanation:

hope this helps u ✌️✌️

Make mister as brainliest

The width of the path is approximately 7.45 meters.

What is meant by width?

The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.

What is meant by meters?

Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.

According to the given information

The area of the pool is given by the product of its length and width:

18 × 30 = 540 square meters

The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:

(18 + 2x) × (30 + 2x)

Expanding this expression, we get:

540 + 36x + 60x + 4x²

Simplifying, we get:

4x² + 96x + 540

We are given that the area of the entire region is 1900 square meters:

4x² + 96x + 540 = 1900

Subtracting 1900 from both sides, we get:

4x² + 96x - 1360 = 0

Dividing both sides by 4, we get:

x² + 24x - 340 = 0

We can use the quadratic formula to solve for x:

x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)

Simplifying, we get:

x = (-24 ± √(1216)) / 2

x ≈ -17.45 or x ≈ 7.45

Since the width of the path cannot be negative, we can ignore the negative solution.

Therefore, the width of the path is approximately 7.45 meters.

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the rectangle is

the dimension are 3x7 because the multipliation is 21

Answer:

D

Step-by-step explanation:

You can infer to the solution of this problem by looking at the choices. Hope this helped :)

Answer:

13 and 5

Step-by-step explanation:

x - y = 8

x = 3y - 2

This is a system of equations, solve by substitution.

(3y - 2) - y = 8

2y - 2 = 8

2y = 10

y = 5

Then solve for x

x = 3y - 2

x = 3(5) - 2

x = 15 - 2

x = 13

1.The probability of winning $20 is 1/200.

2.The probability of winning $1500 is 1/7500.

3.The probability of winning $20000 is 1/200000.

4. the probability of not winning anything is 0.9989375

1.The probability of winning $20 is

P(winning) = p(winning chance)/total

                   =1/200.

2.The probability of winning $1500 is

P(winning 1500) = p(winning chance)/total

                           = 1/7500.

3.The probability of winning $20000 is

P(winning) = p(winning chance)/total

                    =1/200000.

4.To find the probability of not winning anything, you can subtract the sum of the probabilities of winning $20, $1500, and $20000 from 1. This is 1 - (1/200 + 1/7500 + 1/200000) = 1 - 0.0010625 = 0.9989375

Probability is a mathematical concept used to measure the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. A probability of 0.5, for example, means that there is an equal chance of an event happening or not happening. In general, the probability of an event can be calculated as the number of favorable outcomes divided by the number of possible outcomes.

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Answer: likely

Step-by-step explanation:

B) Likely

Step-by-step explanation:

i just just answered the question on e d g e n u i t y

i hope this helps <3

Answer:

the 19%

Step-by-step explanation:

we can convert each to a percentage, decimal, or fraction to solve. i used decimals:

1/5 = 2/10 = 0.2

0.22 is a decimal

19% = 19/100 = .19

then we compare

.22 > .2 > .19

The simplified expression can be written as:

\((-\sqrt{6} )*(-2*\sqrt{-42} ) = \sqrt{-1,008}\)

Here you need to remember the property:

\(\sqrt{x} *\sqrt{y} = \sqrt{x*y}\)

Now we have the expression:

\((-\sqrt{6} )*(-2*\sqrt{-42} )\)

First, we can cancel the two first negative signs to get:

\((\sqrt{6} )*(2*\sqrt{-42} )\)

Now we can write the 2 as the square root of 4.

\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} )\)

Finally, we can use the above property to get:

\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} ) = \sqrt{6*4*(-42)} = \sqrt{-1,008}\)

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Answer: 102 dollars/4.5x+75

Step-by-step explanation: Your question isn't really straightforward, x x snacks for everybody to share? Please elaborate, and are they talking about the total cost, or just the cost of 6 snacks?

First, we have to take into account that if SADIE is taking her FOUR kids, there will be 5 people.

Cost of tickets is equal to $15 per one, and

5x (where x=15, per 5)

5(15)=75, and now onto the snacks

4.5x2=9, and 6/2=3, so 9x3=27, or 4.5x6=27

75+27=102

then for x snacks, if 1 snack costs 4.5 dollars than it'd be 4.5x (x number of snacks)+75 to find the total cost with tickets and all.

Answer:

60

Step-by-step explanation:

the question is based on similarity and enlargement

firt thing put the velues to ratio form;8;20

simplify to obtain2:5 as your linear scale factor...

if 5:150

2=?

2*150/5=60

Answer:

12

Step-by-step explanation:

Your problem can be described in the following equation

$139 + $15x = $319

139 dollars + 15 dollars (times x (the number of weeks)) = 319

319 - 139 = 180

180 / 15 = 12

x = 12

Chow,...!

The blank spaces in the statements area. S, R, and Q  are distinct points that are collinear: b. TX and QS are distinct lines that intersect. c. Point Y and line QS are coplanar. d. Another name for plane P is: plane QSY.

Points that lie on the same straight line are collinear points.

If two lines are lie on the same plane, they are referred to as coplanar lines.

(a.) S, R, and Q are on a straight line. Therefore S, R, and Q  are distinct points that are collinear.

b. TX and QS are distinct lines that intersect.

c. Point Y and line QS are on the same plane. Therefore:

Point Y and line QS are coplanar.

d. Another name for plane P is: plane QSY.

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Answer:

A business person will use algebra to determine whether a piece of equipment does not lose its worth if it is in stock.

Step-by-step explanation:

Answer:

x=32

Step-by-step explanation: