Suppose the demand for Volkswagen Beetles in Mexico is described by the function D=33.000-2P. where D is the quantity of Beetles that will be demanded when the price is P dollars. Suppose further that the supply S of Volkswagen Beetles follows the functional relationship S = 6000 + P Solve for the equilibrium price P which is the value of at which demand would equal supplyi.e. at which D = S

Answer:

  x = 25

Step-by-step explanation:

The measure of an inscribed angle in a circle is half the measure of the arc it subtends. The acute angles in a right triangle are complementary.

__

Inscribed angle CAD is half the measure of arc CD, so is 80°/2 = 40°.

Acute angle 2x° is the complement of angle CAD in the right triangle shown, so we have ...

  2x° = 90° -40° = 50°

  x = 25 . . . . . . . . . . . . divide by 2°

Answer:

1,498.32

Step-by-step explanation:

1,894.32 - 396.00 = 1,498.32 You subtract 396 from 1,894.32

Answer:

55

Step-by-step explanation:

Since whole numbers do not include fractions and decimal values, 55 is the answer

The concavity of the function in this problem is classified as follows:

Hence the intervals are given as follows:

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Answer:

64

Step-by-step explanation:

16/10=1.6 and 1.6x40=64

Answer: y = 64

Step-by-step explanation:

[tex]$$Given, \\$y$ is directly proportional to $x$ \\$\Rightarrow y \propto x$ (Note: ' $\alpha$ ' be proportion/various sign) \\$\Rightarrow y=k x$ ( $k$ be the constant) \\$\therefore y=k x-$ (1)[/tex]

[tex]$$Given $y=40$ when $x=10$.So, substitute $y=40 \ \& \ x=10$ in (1) we get,$$\begin{aligned}&\Rightarrow 40=k(10) \\&\Rightarrow 10 k=40 \\&\Rightarrow k=\frac{40}{10} \text { (divide '10' both sides) } \\&\Rightarrow k=4\end{aligned}$$[/tex]

[tex]$$Put $k=4$ in (1) we get,$$y=4 x$$We substitute $x=16$ in (2) we get$$\begin{aligned}y &=4(16) \\\Rightarrow y &=64 \\\end{aligned}$$[/tex]

Answer:

10

explanation:

Answer:

57 ounces

Step-by-step explanation:

He needs 28 oz of oil for every 44 cups. Multiply both to get 56 oz of oil for 88. Since there is one more cup of flour, you will need one more ounce of oil.

Answer:

dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x

Step-by-step explanation:

We use the Product Rule:

y= (x²-3)³cos2x

dy/dx =   (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx

=   (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x

= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)

=  6x(x²-3)cos2x - 2(x²-3)³sin2x

Answer:

sorry I haven't learned this yet

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

Step-by-step explanation:

We are given the options,

(a) The number of accidents was reduced by 0.67 per month for every additional 100 drivers in the program.

(b) The number of accidents was reduced by 0.67 per month every month.

(c) The number of accidents increased by 0.67 per month for every additional 100 drivers in the program.

(d) There were 0.67 accidents per month.

We can eliminate option 'c' because the accidents are obviously not increasing, but rather, decreasing. We can also eliminate option 'd' (which to a certain extent is rather vague) because there is a trend in the data. If there were only 0.67 accidents per month (which is impossible anyway), then the graph would be that of [tex]y=0.67[/tex] which is indeed a straight line. Finally, we can eliminate option 'b' because the x-axis isn't in terms of months, but drivers in the program. This leaves 'a' as the only logical answer, which we can see is true because the graph trends downward (hence the negative slope) by about 0.67 per 100 drivers. With a bit of understanding about the problem, we can eliminate the illogical answers to find the correct one!

Note: you may be wondering why the slope isn't just -0.67, but that is because then it would go down by 0.67 for each driver in the program. Therefore, the slope was divided by 100 to yield us a slope of -0.0067 which makes it go down 0.67 per 100 drivers instead of only 1 driver.

Analyzing the information, it is clear that to find the solutions of the problems it is necessary to perform the calculation of mathematical arrangements.

Correspond to a case of permutations, they are groupings that are formed with a number p of elements from a set of n elements. The elements of p must occupy ordered positions, where p ≤ n. The formula is:

So, to solve the problems we do the following calculations:

A) 2^n =

2^8 = 256

B) We must pay attention to the statement, which asks for the minimum number of condiments required to prepare 1000 different sandwiches, so:

2^n [tex]\geq[/tex] 1000

n = 3

2^3 = 8

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Answer:

y = -1/2 x + 4

Step-by-step explanation:

y = 2x + 4    

Since this equation is in slope-intercept form, the slope of the line is 2.  Perpendicular lines have slopes that are negative reciprocals of each other.  Thus, the slope of a line perpendicular to this line would be -1/2.

So, any equation of the form y = -1/2 x + b

it does not matter what the y-intercept of either line is. They will remain perpendicular as long as their slopes are negative reciprocals.

Step-by-step explanation:

the lateral area of the cone is, well, the lateral area.

the total surface area of the cone is the lateral area plus the area of base circle.

so, the difference between both is the area of the base circle :

120pi - 70pi = 50pi

the area of a circle is

pi×radius²

and that is in our case

pi×radius² = 50pi

radius² = 50

radius = sqrt(50) = 7.071067812... ≈ 7.1 units

therefore, C is the right answer.

Answer:

Step-by-step explanation:

3 1/3 is 10/3. 1 1/5 is 6/5. KCF, Keep Change Flip.

10/3 divided by 6/5 becomes 10/3 multiplied by 5/6, or 50/18.

50/18 becomes 25/9, or 2 7/9.

Hey there!

[tex] \displaystyle{ \red{ \boxed{ \green{ \bold{m = - 1}}}}}[/tex]

[tex] \\ [/tex]

To find the slope of a line using two points [tex] \displaystyle{(x_1 , y_1)} [/tex] and [tex] \displaystyle{(x_2 , y_2)} [/tex] , we can use the slope formula.

This formula corresponds to the quotient of the change in y [tex] \: [/tex] over [tex] \: [/tex] the change in x :

[tex] \displaystyle{m = \frac{ \blue{y_2} - \orange{y_1}}{ \green{x_2} - \red{x_1} }}[/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow [/tex] We are given the points (-2 , 3) and (-5 , 6) where:

[tex] \\ [/tex]

[tex]\displaystyle{ \hookrightarrow m = \frac{\blue{6} - \orange{3}}{\green{-5} - \red{(-2)}}} \\ \\ \displaystyle{\implies m=\frac{3}{-3}} \\ \\ \displaystyle{\purple{\implies} \boxed{\bold{m=-1}}}[/tex]

Therefore, the slope of the line is -1.

[tex] \\ [/tex]

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Answer: (10x + 9) (x - 3)

Step-by-step explanation:

Factor by grouping

Answer:

The area of the circle is approximately 154 square meters

Step-by-step explanation:

Area of a circle formula: [tex]A = \pi r^{2}[/tex]

given:

- diameter = 14m

- pi = 22/7

[tex]radius (r) = diameter/2 = 14/2 = 7\\A = 22/7*(7)^2\\A = 22/7*(49)\\A = 154[/tex]

Answer

All real numbers or (-∞, ∞)

Step-by-step explanation:

There aren't any X values that can make this linear equation output an invalid results, so we can deduce that the domain is all x values.

Answer:

All Real Numbers

Step-by-step explanation:

The Domain for a function simply is all the possible x values.

When graphing this function, you'll realize that it's continuous and passes all x values.

Additionally, when looking at it, you'll realize you can input any number of your choosing.

When trying to evaluate the domain of other functions, you can look at if any values of x will create an undefined value.

For example, some functions may have x in the denominator, and since the denominator can not be 0, there will be a discontinuity.

Other examples where the domain wouldn't be all real numbers would be if x was under a square root and couldn't be negative, or if the function was a vertical line.

Hope that helps, please let me know if you have any queries.

Answer:

SEE BELOW IN BOLD.

Step-by-step explanation:

a.

h = -16t^2 + 50t

h = 20 t

When the height is the same:

-16t^2 + 50t = 20t

-16t^2  + 30t = 0

t(-16t + 30) = 0

t = 0 or  -16t + 30 = 0, so:

t = 0 or -30/-16 = 1.875

So the answer is 1.88 seconds to the nearest hundredth.

b.

For the ball

h = -16t^2 + 50t

Finding the derivative and equating to zero:

dh/dt = -32t + 50 = 0

t = -50/-32 = 1.563

Maximum height after 1.56 seconds to nearest hundredth

c.

When the ball hits the ground h = 0 so

-16t^2 + 50t = 0

-16t(t - 50/16)= 0

T = 3.13 SECONDS TO THE NEAREST HUNDERDTH

Answer:

a = 10

a = 2

a = 8

Step-by-step explanation:

  The inequality:

11 ≥ a

   We will go through all the options:

-> In short, all values less than or equal to 11 will be solutions.

a = 10

11 ≥ a

11 ≥ 10 ✓

-

a = 2

11 ≥ a

11 ≥ 2 ✓

-

a = 8

11 ≥ a

11 ≥ 8 ✓

-

2 = 3

N/A, no 'a' variable given.

Answer:

Step-by-step explanation:

2x^2 + 9x + 4=0

2x^2+8x+x+4=0

2x(x+4) +1 (x+4) =0

2x+1 = 0

x+ 4 =0

2x= -1

x= -1/2

x=-4

Therefore x = -4 and x = -1/2

Answer:

C) f(x) = (x - 1)(x - 1)(x-6)

Explanation:

Multiplicity means number of times a factor appears in a particular equation.

For example, a root of 3 has multiplicity of 3 then = (x - 3)(x - 3)(x - 3)

Breakdown for this question:

If a polynomial where root of 1 has multiplicity of 2, then it means (x - 1)²

Where polynomial of root of 6 has multiplicity of 1, then it means (x - 6)

Joining them together:

(x - 1)²(x - 6) = (x -1)(x - 1)(x - 6) Hence option C is correct.

Answer: {x | x is a season}

Step-by-step explanation:

Spring, summer, autumn, and winter are all seasons.

The best pairing to complete the task in the shortest amount of time is You and Aunt 1 and it would take them 30 minutes.

This represents the fastest time it takes for a person to execute a task.

The time needed for all tasks for You is:

2.5 + 5 + 1.5 = 9 hours

The time needed for all tasks for Aunt 1 is:

1.5 + 4 + 3= 8.5 hours.

9 - 8.5 = 0.5 hours

= 30 minutes

The shortest amount of time to complete all tasks is 8.5 hours by Aunt 1

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[tex]\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}} [/tex]

4 hours 12 minutes

Step-by-step explanation:

We need to convert time in hours by diving 15 by 60

[tex] \sf 2 \frac{15}{60} \\ \\ \sf 2 \frac{1}{4} [/tex]

as it is mixed fraction we will convert into improper

[tex] \sf \frac{(2 \times 4) + 1}{4} \\ \\ \sf time = \frac{9}{4} hours[/tex]

Now we need to find distance

[tex] \sf \green {distance = speed \times time}[/tex]

Here speed is 50km/h

[tex] \sf \implies distance = 50 \times \frac{9}{4}km \\ \\ \sf \implies distance = \frac{25 \times 9}{2}km \\ \\ \sf \implies distance = \frac{225}{2} km \\ \\ \sf \implies \red {distance = 112.5km}[/tex]

Now we have to have time at new speed at 27km/h

and distance is same

[tex] \sf \pink{ time = \frac{distance}{speed} }[/tex]

Now substituting the value of speed and distance

[tex] \sf \implies time = \frac{112.5}{27} [/tex]

Now we will remove point(.) from the distance by multiplying 10 with 27

[tex] \sf \implies time = \frac{1125}{27 \times 10} \\ \\ \sf \implies time = \frac{41.6}{10} [/tex]

now we will convert it into mixed fraction

[tex] \sf \implies time = 4 \frac{1}{5} hours [/tex]

Now we will convert fraction hours into minutes by multiply with 60

[tex] \sf \implies time = 4 \: hours \: \frac{1}{5} \times 60 \: minutes \\ \\ \sf \implies \orange{ time = 4 \: hours \: 12 \: minutes}[/tex]

Answer:

(i) Breadth = 14 cm

(ii) Perimeter = 176 cm

Step-by-step explanation:

Given,

(i) Breadth = ?

We know that, Area of a rectangle = length × breadth.

Then,

[tex]1036 = 74 \times Breadth\\1036 \div 74 = Breadth\\\boxed{\bf\:14 \:cm = Breadth }[/tex]

(ii) Perimeter of a rectangle = 2 (length + breadth)

Then,

[tex]Perimeter = 2(74 + 14)\\Perimeter = 2(88)\\\boxed{\bf\: Perimeter = 176 \: cm}[/tex]

[tex]\rule{150pt}{2pt}[/tex]