What is the inequality

The company must produce and sell 350 dishwashers in order to maximize profit.

To determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.

The profit (P) is given by the equation:

P(x) = Revenue - Cost

The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):

Revenue = p * x

The cost is given by the function C(x):

Cost = C(x)

Therefore, the profit function can be expressed as:

P(x) = p * x - C(x)

Substituting the given expressions for p and C(x):

P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)

Expanding and simplifying the equation:

P(x) = 420x - 0.3x² - 5000 - 0.3x²

Combining like terms:

P(x) = -0.6x² + 420x - 5000

To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:

x = -b / (2a)

In our case, a = -0.6 and b = 420:

x = -420 / (2 * -0.6)

x = -420 / (-1.2)

x = 350

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350 dishwashers must the company produce and sell in order to maximize profit.

Maxima means a point at which the function attains the maximum value.

Given the following information:

Price per dishwasher, p = 420 - 0.3x

Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2

Profit= Total Selling price- Total Cost Price

Total Selling price of x dishwasher, S.P= xp

S.P=x(420 - 0.3x)

S.P=420x - 0.3x²

Profit= 420x - 0.3x² - ( 5000 + 0.3x²)

Profit= 420x - 0.3x² - 5000 - 0.3x²

Profit=  -0.6x²+420x-5000

So, profit, f(x)=-0.6x²+420x-5000

To determine the value of x so that maximum profit is possible:

1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.

2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.

[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]

Calculating the value of x by transposing,

x=420/1.2

x=350

To check maxima, calculating second derivative.

[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]

2nd derivative is negative, it means that x=350 is the point of maxima.

Thus, a company must produce and sell 350 dishwashers in order to maximize profit.

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Answer: Smokers pay less attention to driving while trying to light a cigarette.

Step-by-step explanation:

( A ) reasons for, why the given statement was misleading.

Following are the reasons for accidents

(i) Drunk Driving.

(ii) Driving during the night.

(iii) Smoking.

(iv) Unsafe lane changes.

(v) Driving the wrong way.

(vi) Bad weather e.g fog.

From the list above, it is shown that, smoking is also one of the major cause of car accidents on the roads.

( B.) Smokers tends to pay less attention to driving why trying to light a cigarette.

Answer:

  φ ≈ 1.19029 radians   (≈ 68.2°)

Step-by-step explanation:

There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.

We want to compare ...

  y(t) = Asin(ωt +φ)

to

  y(t) = Psin(ωt) +Qcos(ωt)

Using trig identities to expand the first equation, we have ...

  y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Matching coefficients with the second equation, we have ...

  P = Acos(φ)

  Q = Asin(φ)

The ratio of these eliminates A and gives a relation for φ:

  Q/P = sin(φ)/cos(φ)

  Q/P = tan(φ)

  φ = arctan(Q/P) . . . . taking quadrant into account

__

We can also use our equations for P and Q to find A:

  P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²

  A = √(P² +Q²)

_____

Here, we want φ.

  φ = arctan(Q/P) = arctan(5/2)

  φ ≈ 1.19029 . . . radians

Answer:

4:00 pm

Step-by-step explanation:

To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.

5:30 minus 1 hour is 4:30.

Now, subtract 30 minutes.

4:30 minus 30 minutes is 4:00.

Malik started working on his English essay at 4:00 pm.

Hope that helps.

Answer:

Hey there!

An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.

Thus, the perimeter for this equilateral triangle would be 3(12)=36

Hope this helps :)

Answer:

[tex]\boxed{Perimeter = 36 \ units}[/tex]

Step-by-step explanation:

Perimeter = sum of all sides

Perimeter = 12 +12 + 12

Perimeter = 36 units

First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.

So, let's apply this pattern to find the next number in this series.

2, 2 1/2, 1 1/2, 2, 1

The next number in this series is 1.

Hope this helps!! :)

Answer:

pleasse elaborate more

Step-by-step explanation:

Answer:

[tex]\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }[/tex]

Step-by-step explanation:

Hello,

I assume that we are working in [tex]\mathbb{C}[/tex], otherwise there is only one zero which is 1. Please consider the following.

First of all, we can notice that 1 is a trivial solution as

   [tex]p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0[/tex]

It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.

[tex]p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b[/tex]

Let's identify like terms as below.

a-1 = -5 <=> a = -5 + 1 = -4

b-a = 33

-b = -29 <=> b = 29

So

[tex]\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }[/tex]

Now, we need to find the zeroes of the second factor, meaning finding x so that:

[tex]x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: Diverging

Step-by-step explanation:

Find explanations in the attached file

Answer:

The simple pendulum should be 15.9 m long.

Step-by-step explanation:

Approximately (for small amplitudes), the period of a simple pendulum is

T = 2*pi * sqrt (L/g), L=length

using pi = 22/7, and g=9.8 m/s^2

8 = 2* 22/7 * sqrt(L/9.8)

solve for L

L = (8*7/(2*22))^2 * 9.8

= 15.874 m

That's quite a long pendulum!

Answer:

1) 18

2) P

Step-by-step explanation:

1) Multiply the top number by itself and then reverse the digits!

9*9 = 81 reversed is 18

2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.

Answer:

P

Step-by-step explanation:

2.

The number of strokes of the letter that come to an end.

The bottom of the A has two sticks that come to an end.

A = 2

The B has no sticks coming to an end.

B = 0

The C and an upper and a lower stroke coming to an end.

C = 2

D has none.

D = 0

E has 3 sticks coming to an end.

E = 3

etc.

M has 3.

N has 2.

O has 0.

P has 1 stick coming to an end.

Q has none.

R has 2.

S has 2.

T has 3.

U has 2.

V has 2.

W has 3.

X has 4.

Y has 3

Z has 2.

Of all letters after L, only P has exactly 1 stroke coming to an end.

Answer: P

Answer:

5

Step-by-step explanation:

According to the given question, the calculation of number is shown below:-

Let the number be x.

[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.

[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]

Now we will solve the above equation

[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]

x = 5

Therefore the correct answer is 5

Hence, the number based on the given information provided in the question is 5

Answer:

Simply plug in the polynomial into a graphing calc.

Step-by-step explanation:

Answer:

Optimal production = 600 gold pens

Revenue  = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000  ....................(1)   bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800  ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder)  .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4).  Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7)    [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x   [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue  = 600*7 = 4200 gold pens

Answer:

1st blank: X axis reflection

2nd blank: Y axis reflection

Step-by-step explanation:

If you drew the first triangle and then the second triangle on a piece of paper, you would notice that it would reflect across the corresponding axis.

So the solution is to just draw it out.

Answer:

reflection across the x axis and the second is a reflection across the y axis.

Answer:

  0

Step-by-step explanation:

The determinant of this matrix is zero (0).

Answer:

B y ≥ 4x + 2

Step-by-step explanation:

1. find slope of the line: (y² - y¹) / (x² - x¹)

(0, 2) and (-1, -2)

(-2 - 2) / (-1 - 0) = -4 / -1 = 4

y = 4x + 2*

*+2 because that is the y-intercept as shown by point (0, 2)

2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >

3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥

4. final equation: y ≥ 4x + 2

Answer:

The value of  annuity is [tex]P_v = \$ 32058[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 1500[/tex]

     The  interest rate  is   [tex]r = 8\% = 0.08[/tex]

     Frequency at which it occurs in a year is  n = 2 (semi-annually )

      The number of years is  [tex]t = 22 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)

 substituting values

             [tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]

             [tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]

             [tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]

            [tex]P_v = \$ 32058[/tex]

The correct statement about the line segment is,

⇒ the segment DE bisects segment AC.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

Triangle ABC is shown in figure.

Now, We can see that;

⇒ AE = EC

Hence, the segment DE bisects segment AC.

Thus, The correct statement about the line segment is,

⇒ the segment DE bisects segment AC.

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Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

Answer:

x=4

Step-by-step explanation:

5x - 17 = -x +7

Add x to each side

5x+x - 17 = -x+x +7

6x -17 = 7

Add 17 to each side

6x-17+17 = 7+17

6x =24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

4

Step-by-step explanation:

5x - 17 = -x + 7

Add x on both sides.

5x - 17 + x = -x + 7 + x

6x - 17 = 7

Add 17 on both sides.

6x - 17 + 17 = 7 + 17

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Step-by-step explanation:

Put A = 2, B = 3, C = 9 and D = 15 to the given expressions.

Use PEMDAS.

-A + C - (D : B)

-2 + 9 - (15 : 3) = -2 + 9 - 5 = 7 - 5 = 2

B × (-C) - (-D) + A

3 × (-9) - (-15) + 2 = -27 + 15 + 2 = -12 + 2 = -10

(C + D) : B + A

(9 + 15) : 3 + 2 = 24 : 3 + 2 = 8 + 2 = 10

D : B + A - C

15 : 3 + 2 - 9 = 5 + 2 - 9 = 7 - 9 = -2

Answer:

13 in.

Step-by-step explanation:

Theorem:

The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.

Each side of triangle MNK has as endpoints two midpoints of sides of triangle ABC, so each side of triangle MNK is half the length of a side of triangle ABC.

p = 26 in./2 = 13 in.

Answer:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]

[tex](f/g)(2)=-4[/tex]

Step-by-step explanation:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]  and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]

Answer:

20*

Step-by-step explanation:

Your welcome plz mark me the brainlist

Answer:

The width of the model will be  2.5 inches

Step-by-step explanation:

The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.

Step One: Determine the scale factor from the tower height.

The scale factor is obtained from the formula:

Scale factor = model size / observed size

This will be

Height of model tower/ height of the real tower.

The height of the model tower is 5 inches which is the same as 0.416667 ft

Scale factor = 0.416667 ft/ 40ft = 0.0104

Step two:  Multiply the width of the real-life tower by the scale factor to get the model width.

Width of model =20ft X 0.0104 = 0.208ft

Step three:  Convert your answer back to inches.

We will now have to convert 0.208 ft back to inches by multiplying by 12

This will be 0.208 X 12 =2.5 inches.

The width of the model will be  2.5 inches

Answer:

(1400)(1+0.029/12)3(1+0.221/12)9

Step-by-step explanation:

A p e x

Answer:

Step-by-step explanation:

Just so you know how it looks on the page