The monthly demand function for a product sold by a monopoly is
P= 3380 - (1/3) x^2
dollars, and the average cost is
C = 1000 + 15x + 3x2
dollars. Production is limited to 1000 units and x is in hundreds of units.
(a) Find the quantity that will give maximum profit.
____________ units
(b) Find the maximum profit. (Round your answer to the nearest cent.)
$___________

Using the Pythagorean's theorem we can see that length of the segment AB =is6.4 units

We can see that this is a right triangle, notice that we know two sides, these are

AC = 4

CB = 5

(to know that just count the number of squares between the given vertices)

Using Pythagorean's theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) we can write an equation that allows us to find the length of AB, the hypotenuse of the right triangle:

AB² = 4² + 5²

AB = √(16 + 25)

AB = 6.4 units.

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P(BND) = 0.65, P(B U D) = 0.65 and the probability that a student does not select a book nor a DVD is 0.35.

a.P(BND) = 0.3015

b.P(B U D) = 0.65

To find the probability of both events B and D occurring, we use the formula P(BND) = P(B) * P(D|B). Given that P(B) = 0.45 and P(D|B) = 0.67 (which is the probability of D given that B has occurred), we can calculate P(BND) as follows:

P(BND) = 0.45 * 0.67 = 0.3015.

b.P(B U D) = 0.65

To find the probability of either event B or event D or both occurring, we use the formula P(B U D) = P(B) + P(D) - P(BND). Given that P(B) = 0.45, P(D) = 0.50, and we already calculated P(BND) as 0.3015, we can calculate P(B U D) as follows:

P(B U D) = 0.45 + 0.50 - 0.3015 = 0.6485 ≈ 0.65.

P(not selecting a book nor a DVD) = 0.05

The probability of not selecting a book nor a DVD is the complement of selecting either a book or a DVD or both. Since P(B U D) represents the probability of selecting either a book or a DVD or both, the complement of P(B U D) will give us the probability of not selecting a book nor a DVD:

P(not selecting a book nor a DVD) = 1 - P(B U D) = 1 - 0.65 = 0.35 = 0.05.

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Answer:

context pls

Step-by-step explanation:

Percent of the students in Rosa's art class do not own a cat but play an instrument = 28.6%

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given,

total number of students = 35

number of students do not own a cat but play an instrument = 10

Percentage of number of students do not own a cat but play an instrument

= (number of students do not own a cat but play an instrument/ total number of students) × 100

= (10/35) × 100

= 28.6 %

Hence, 28.6% students do not own a cat but play an instrument.

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The DPMO for the first characteristic is 222, the DPMO for the other eight characteristics is 111, and the overall DPMO for the boards is 1,111.

To calculate the DPMO (Defects Per Million Opportunities) for each characteristic, we first need to find the number of opportunities for defects for each characteristic. Since we inspected 3,000 boards and there are 9 characteristics, the total number of opportunities is 27,000 (3,000 × 9).

For the first characteristic, we found 6 defects, so the DPMO is:

DPMO = (6 / 27,000) × 1,000,000 = 222

For the other eight characteristics, we found 3 defects each, so the DPMO for each is:

DPMO = (3 / 27,000) × 1,000,000 = 111

To find the overall DPMO for the boards, we need to add up all the defects and divide by the total number of opportunities:

Total defects = 6 + (8 × 3) = 30

Total opportunities = 27,000

Overall DPMO = (30 / 27,000) × 1,000,000 = 1,111

Therefore, the DPMO for the first characteristic is 222, the DPMO for the other eight characteristics is 111, and the overall DPMO for the boards is 1,111.

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The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90  angle.

To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.

Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.

Without this information, no concrete calculations can be made.

Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.

Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.

Round your answer to the nearest tenth as specified.

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

Sure, I can help you with that! The volume of a cone with a radius of 2.5 and a height of 4 is (1/3)*pi*(2.5^2)*4. This equals approximately 26.18 cubic units.

Answer:

what langue is that

Step-by-step explanation:

Answer:

Your answer should be 35 :)

Step-by-step explanation:

Hope this helps!

The unique representation of an arbitrary vector (a₁, a₂, a₃, a₄) in F as a linear combination of u₁, u₂, u₃, and u₄, can be solved by the system of equations.

To find the unique representation of an arbitrary vector (a₁, a₂, a₃, a₄) in F₄ as a linear combination of u₁, u₂, u₃, and u₄, we need to solve the system of equations:

(a₁, a₂, a₃, a₄) = x₁u₁ + x₂u₂ + x₃u₃ + x₄u₄

where x₁, x₂, x₃, and x₄ are the coefficients we need to determine.

Writing out the equation component-wise, we have:

a₁ = x₁(1) + x₂(0) + x₃(0) + x₄(0)

a₂ = x₁(1) + x₂(1) + x₃(0) + x₄(0)

a₃ = x₁(1) + x₂(1) + x₃(1) + x₄(0)

a₄ = x₁(1) + x₂(1) + x₃(1) + x₄(1)

Simplifying each equation, we get:

a₁ = x₁

a₂ = x₁ + x₂

a₃ = x₁ + x₂ + x₃

a₄ = x₁ + x₂ + x₃ + x₄

We can solve this system of equations by back substitution. Starting from the last equation:

a₄ = x₁ + x₂ + x₃ + x₄

we can express x₄ in terms of a₄ and substitute it into the third equation:

a₃ = x₁ + x₂ + x₃ + (a₄ - x₁ - x₂ - x₃)

= a₄

Now, we can express x₃ in terms of a₃ and substitute it into the second equation:

a₂ = x₁ + x₂ + (a₄ - x₁ - x₂) + a₄

= 2a₄ - a₂

Rearranging the equation, we have:

a₂ + a2 = 2a₄

2a₂ = 2a₄

a₂ = a₄

Finally, we can express x₂ in terms of a₂ and substitute it into the first equation:

a₁ = x₁ + (a₄ - x₁)

= a₄

Therefore, the unique representation of the vector (a₁, a₂, a₃, a₄) in F₄ as a linear combination of u₁, u₂, u₃, and u₄ is:

(a₁, a₂, a₃, a₄) = (a₄, a₂, a₃, a₄)

Hence, the vector (a₁, a₂, a₃, a₄) is uniquely represented as (a₄, a₂, a₃, a₄) in terms of the basis vectors u₁, u₂, u₃, and u₄.

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Answer:

Domain = {x | x is a real number}

Look at the step-by-step explanation to get a better understanding

Step-by-step explanation:

Domain = {x | x is a real number}

The function shown  f(x)=5^x-7 is an exponential function with a vertical shift  of  -7 units (shift downwards). Nevertheless, it is an exponential function.

Domain is the set of x-values that we can put into the function. Exponential functions of this type have a domain of "all real numbers". If you see the function, you can figure out that we can put any real number and still there will be no "undefined" or "division by zero" cases.

Thus, this function's domain is the set of all real numbers.

Domain = {x | x is a real number}

Hope you fond this helpful! :)

Answer:

all real numbers

Step-by-step explanation:

The correct option is (a) two factors and three levels. The design has two factors (time of day) and three levels (7 a.m., noon, and 5 p.m.).

In this research design, the factor is the time of day and it has three levels: 7 a.m., noon, and 5 p.m. The researcher is conducting an ANOVA test to measure the influence of the time of day on reaction time.

The factor is the time of day, and it has three levels: 7 a.m., noon, and 5 p.m. The ANOVA test will help determine if there are any significant differences in reaction times between these three periods throughout the day.

Therefore, the design has two factors (time of day) and three levels (7 a.m., noon, and 5 p.m.). The ANOVA test will be used to analyze the influence of the time of day on reaction time.

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Answer:

X= 82⁰

z= 82⁰

Step-by-step explanation:

for X:

we can use co-interior angles sum up to make 180 so,

x+ 98= 180

x= 180-90= 82⁰

for z, we can use either angles on a straight line or corresponding angles

98 + z= 180

z= 180-98= 82⁰

corresponding angles are always equal and can be found in the F shape diagram when lines are parallel

therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰

Answer:

V

Step-by-step explanation:

================================================

Work Shown:

M = number of miles

L = cost to rent a luxury car = 1.15M + 16.40

E = cost to rent an economy car = 0.80M+10.95

C = difference in price

C = L - E

C = (1.15M + 16.40) - (0.80M+10.95)

C = 1.15M + 16.40 - 0.80M-10.95

C = 0.35M + 5.45

Don't forget to distribute the negative to each term in the second parenthesis.

-------------------

Optional Section:

Let's say you drove M = 100 miles as an example.

The luxury car would cost L = 1.15M+16.40 = 1.15*100+16.40 = 131.40 dollars to rent.

The economy car would cost E = 0.80M+10.95 = 0.80*100+10.95 = 90.95 dollars to rent.

The difference in rental costs is L-E = 131.40-90.95 = 40.45 dollars.

Or you could say C = 0.35M+5.45 = 0.35*100+5.45 = 40.45

This means you pay $40.45 more if you go for a luxury car instead of an economy car.

The equatiοn that represents the area = 5.5x + 11. Optiοn C is the cοrrect οptiοn.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical statement that demοnstrates the equality οf twο mathematical expressiοns.

Given that the width οf tulips and lilies in a field 5. 5 meters.

The length οf the field οf tulips is 2 meters.

The length οf the field οf lilies is x meters.

The tοtal length οf the field is (x+2) meters.

The area οf a rectangle is the prοduct οf length and width.

The area οf the field is 5.5(x+2) square meters

The distributive prοperty:

Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.

Apply the distributive prοperty:

= (5.5 × x) + (5.5×2)

= 5.5x + 11

The equatiοn is Area = 5.5x + 11

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Answer:

4-x

Step-by-step explanation:

since x is a number given and it should be subtracted from 4.

Since the graph shows the population P in a small industrial city from 1950 to 2000, we can assume that x = 0 corresponds to 1950, x = 10 corresponds to 1960, x = 20 corresponds to 1970, x = 30 corresponds to 1980, and x = 40 corresponds to 1990.

(a) To find the average rate of change of P between x = 20 and x = 40, we can use the formula:

average rate of change = (change in P) / (change in x)

The change in P between x = 20 and x = 40 is:

P(40) - P(20) = 60 - 80 = -20

The change in x between x = 20 and x = 40 is:

40 - 20 = 20

Therefore, the average rate of change of P between x = 20 and x = 40 is:

average rate of change = (-20) / (20) = -1

(b) The value of the average rate of change that we found in part (a) is -1. This means that the population of the small industrial city was decreasing at an average rate of 1 unit per year between 1990 and 1970. In other words, for every year that passed during this time period, the population decreased by an average of 1 person. This rate of decline is relatively slow, but it could have significant long-term effects on the city's economy, infrastructure, and social dynamics if it continued for a prolonged period of time.

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Answer:

4v^2 + 6v + 3

Step-by-step explanation:

Answer:

Top Right

Step-by-step explanation:

The greater than or equal to sign makes the line solid, and the greater than 2 makes the shading go to the right

Answer: the graph is decreasing everywhere

Answer: x = 12

Step-by-step explanation:

Divide both sides by 10 to isolate x:

10x/10 = 120/10

x = 12

Answer:

x=12

Step-by-step explanation:

Divide each term in 10x=120 by 10 and simplify.

x=12 Is what you would get.

Term: Any expression written as a product or quotient.

Quotient: The answer to a division problem.

Hope this helps!

Answer:

-17

Step-by-step explanation:

as the picture says I have moved 21 so that the numbers are together and it's easier to solve then you move 3 to divide it on the other side and x is left alone.

cube roots of -1 lies in the region given in the best options are  A. on real axis, B. quadrant 1, F. quadrant 4.

Cube roots of -1 mean "finding solution of the equation z³ = -1 since the equation is of order 3, the equation has 3 roots in complex field."

According to the question,

Cube roots of -1 can written as \((-1)^\frac{1}{3}\)

First, write the given number in polar form

\(x = ( cos 0 - i sin 0)^\frac{1}{3}\)

Add 2kπ to the argument

\(x = (cos2k\pi - i sin 2k\pi )^\frac{1}{3}\)

Apply De Moivre's  theorem

\((cos\alpha - i sin\alpha) = cosn\alpha + i sin\alpha\)

x = \(\frac{2k\pi }{3} - i sin\frac{2k\pi }{3}\)

Put k = 0,1,2..., (n-1)                   [sin (-θ) = -sin θ, cos(-θ) = cos θ]

The three roots are

cos 0 -  sin 0, cos \(\frac{2\pi }{3}\), \(i sin\frac{2\pi }{3}\) , cos \(\frac{4\pi }{3}\),  \(i\)sin\(\frac{4\pi }{3}\)

-1, \(-\frac{1}{2} ,- i \frac{\sqrt{3} }{2}, -\frac{1}{2} , +\frac{\sqrt{3} }{2}\) ,  are the three roots of cube roots of -1

It can be seen that the three roots lies in the regions of real axis, quadrant 1 and quadrant 4.

Hence, cube roots of -1 lies in the region given in the best options are  A. on real axis, B. quadrant 1, F. quadrant 4.

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The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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The system will be consistent and will have unique solution.

Given,

Coefficient matrix of 5 equation in 5 variables.

Here,

Let A be a 5x5 coefficient matrix such that its each column has a pivot element, then

Rank A = 5, rank of augmented matrix [A|b] = 5 and number of unknowns = 5

Rank A = rank of augmented matrix [A|b] = number of unknowns = 5

Hence , System is consistent

There is a unique intersection point of all three lines, so values of variables is unique.

Hence, solution of system if unique.

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Answer:

Her mistake was subtracting twelve from both sides even though it was in the parentheses.

Step-by-step explanation:

Anita did not follow the order of operations

Anita made the mistake of subtracting 12 from both sides. WHat she should have done was multiply the five into the parentheses

5(x+12) = 2 -----------> 5x + 60 = 2

then she should have subtracted 60 from both sides

5x = -58

and lastly divided 5 from both sides

x= -58/5

Answer

Anita did not use the distributive property properly and the real answer is

x = -11.6

Step-by-step explanation:

The mistake that she did was not using the distributive property properly.

Based on the property

5(x + 12) = 2

5x + (5)(12) = 2

5x + 60 = 2

5x = 2 - 60

5x = - 58

x = \(\frac{-58}{5}\)

x = -11.6

Answer:

I think it's 3,600

Step-by-step explanation:

multiplication