A company finds that if they price their product at $ 35, they can sell 225 items of it. For every dollar increase in the price, the number of items sold will decrease by 5.


What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) $


What price will guarantee the maximum revenue? $

Answer:

Interval notation is

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Solutions:

[tex]\left(-\infty, -5\right)[/tex]

[tex]\left(0,1)[/tex]

Step-by-step explanation:

[tex]x^3 + 4x^2 - 5x < 0[/tex]

In this inequality, luckly we can easily factor it.

[tex]x^3 + 4x^2 - 5x[/tex]

[tex]x(x^2+4x-5)[/tex]

[tex]x(x-1)(x+5)[/tex]

So we have

[tex]x(x-1)(x+5)<0[/tex]

In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.

Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:

The first step to complete the table is the x value where the factor will be equal to zero.

       [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]                                                                        0

[tex]x-1[/tex]                                                                                                    0        

[tex]x+5[/tex]                      0

Then, just consider the signal:

  [tex]x<-5[/tex]       [tex]x=5[/tex]         [tex]-5<x<0[/tex]        [tex]x=0[/tex]      [tex]0<x<1[/tex]      [tex]x=1[/tex]      [tex]x>1[/tex]                                                                  

[tex]x[/tex]    -                -                       -                   0               +                 +             +

[tex]x-1[/tex]  -             -                      -                   -               -                  0             +

[tex]x+5[/tex]  -             0                     +                   +                +               +              +

[tex]x(x-1)(x+5)[/tex]    -     0       +     0      -      0     +

When [tex]x(x-1)(x+5)<0[/tex] ?

It happens when [tex]x<-5[/tex]     and when [tex]0<x<1[/tex]

The solution is

[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]

[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.375

Probability of one ripe and one unripe

=0.234375

Probability of at least one unripe

=0.625

Step-by-step explanation:

50 mangoes 20 of which are unriped in the first basket .

Riped = 50-20= 30

Probability of unripe = 20/50

Probability of unripe= 0.4

Probability of ripe = 30/50

Probability of ripe = 0.6

40 mangoes of which 15 are unripe In the second basket

Number of riped= 40-15= 25

Probability of unriped= 15/40

Probability of unriped= 0.375

Probability of riped= 25/40

Probability of riped= 0.625

probability of getting both are unripe

= 0.4*0.375

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.6*0.625

= 0.375

Probability of one ripe and one unripe

= 0.625*0375

= 0.234375

Probability of at least one unripe

= 1- probability of no unripe

= 1 - probability of both ripe

= 1-0.375

= 0.625

Answer:

Mars

Step-by-step explanation:

America

Answer: [tex]S=0.087p[/tex] .

Step-by-step explanation:

Equation for direct proportion:

y=kx

, where x= independent variable ,

y=dependent variable.

k= proportionality constant

Here, State sales tax S  is directly proportional to retail price p.

Also, dependent variable= S,  independent variable =p

Required equation: S= kp

Put S= 12.32 and x= 142

[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]

Hence, the required equation is [tex]S=0.087p[/tex] .

Answer:

try 3x=30 or 10

Step-by-step explanation:

Answer:

what do you need help with its not really clear

Answer

1. 48 2. 308

Step-by-step explanation:

Answer:

complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)

Step-by-step explanation:

90=46+5x-1

45=5x

x=9

Answer:

x = 9 Complementary

Step-by-step explanation:

The angles are compplementary cause the angle add up to 90°

Well to find x we need to make the following equation,

46 + (5x - 1) = 90

We need to simplify and combine like terms,

46 - 1 = 45

45 + 5x = 90

-45 to both sides

5x = 45

Divide 5 by both sides

x = 9

Thus,

x is 9.

Hope this helps :)

Answer:

B.77.4%

Step-by-step explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

For nay given salary X, the z-score is given by:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For X = $3.75, the z-score is:

[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]

For X = $5.00, the z-score is:

[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]

A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:

[tex]P=84.13-6.68\\P=77.45\%[/tex]

The answer is alternative B.77.4%

Answer:

The correct option is (C).

Step-by-step explanation:

The exponential function representing decay is as follows:

[tex]y=y_{0}\cdot e^{kt};\ k<0[/tex]

Here,

y = final value  

y₀ = initial value  

k = growth rate  

t = time passed

The graph represents exponential decay is:

"On a coordinate plane, a graph approaches y = 0 in quadrant 1 and curves up into quadrant 2."

Thus, the correct option is (C).

Answer:

The answer is C

Step-by-step explanation:

I  just took the test on edge

Answer:

i think its b

???

Step-by-step explanation:

im sorry if im wrong im not very confident on my answer :(

Answer:

D

Step-by-step explanation:

Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.

Answer:

C h^2  / 680 = x

Step-by-step explanation:

C=680x/h^2

Multiply each side by h^2

C h^2=680x/h^2  * h^2

C h^2=680x

Divide each side by 680

C h^2  / 680=680x/680

C h^2  / 680 = x

Answer:

Option C is the answer.

Step-by-step explanation:

here, given that;

angle XYZ=82°

we know, according to the inscribed angle theorem,

angle XYZ=1/2 of arc XZ.

or, arc XZ = 2×82°

Therefore, the value of arc XYZ is 164°.

hope it helps..

Answer: 6

Step-by-step explanation:

If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.

We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total

Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.

Now we have already included D playing every other team so we don't include any other pairings.

In total, now every team has played every other team giving a total of 6.

(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.

Answer:

6 games.

Step-by-step explanation:

The answer is the number of combinations of 2 from 4

= 4*3 / 2*1

= 6.

Answer:

h = -9

Step-by-step explanation:

5h+2(11-h)= -5

Distribute

5h +22 -2h = -5

Combine like terms

3h +22 = -5

Subtract 22 from each side

3h +22-22 = -5-22

3h = -27

Divide by 3

3h/3 = -27/3

h = -9

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

Answer:

Step-by-step explanation:

[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]

[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]

now you find the point of intersection.

then calculate the angle.

Answer:

y = 1110

Step-by-step explanation:

In the above question, we are given the cubic model

y=x³ +x² + x

We are to solve for y when x = 10

Hence,

y = 10³ + 10² + 10

y = 1000 + 100 + 10

y = 1110

Therefore, the value of y when x is 10 using the cubic model of ' y =x³ +x² + x' is 1110.

None of these options seem to be correct. You can check each result by differentiation:

[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]

[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]

[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]

[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]

But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...

Hey there! I'm happy to help!

First of all, if one bill weighs on gram, a million would weigh one million grams. Let's divide this by 1,000 to see how many kilograms it is.

1,000,000/1,000=1,000

Now, we need to convert 1,000 kilograms into pounds. We see that 1 kilogram is equal to about 2.205 pounds, so we multiply 1,000 kilograms by 2.205 to get our pounds.

1,000*2.205=2205

Therefore, one million dollar bills weigh about 2205 pounds.

Have a wonderful day! :D

Answer:

(2,0)

Step-by-step explanation:

From the information the first equation is y = 0.5 x  - 1 and the the line through (3,1) and (-5,-7) is  

y = x - 2  .   From those two equations you get

x - 2 = 0.5 x -1     and     x = 2  , y = 0.  So  it is the last point.   (2,0)

Answer:

D. (2,0)

Step-by-step explanation:

The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, the sequence is -8, -4, 0, 4, 8, ...

a = -8

d = +4

The expression for the nth term will be written as,

an = a + ( n - 1 ) d

= -8 + ( n - 1 ) 4

To know more about arithmetic progression follow

https://brainly.com/question/6561461

#SPJ5

The answer is A. Dilate circle A by a scale factor of 3

I took the test :)

Answer:

I believe the interquarrile range is 5

Answer:

no tiene mas informaion?

Step-by-step explanation:

Answer:

option 3

Step-by-step explanation:

4x+8<-16

x<-6

4x+8_>-16

x_>-1

(it's more and equal .so the circle has to be shaded and move to the right of -1)

Answer:C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length the length and breadth of the rectangle be x and y.

Area of the rectangle A = Length * breadth

Perimeter P = 2(Length + Breadth)

A = xy and P = 2(x+y)

If the area of the rectangle is 512m², then 512 = xy

x = 512/y

Substituting x = 512/y into the formula for calculating the perimeter;

P = 2(512/y + y)

P = 1024/y + 2y

To get the value of y, we will set dP/dy to zero and solve.

dP/dy = -1024y⁻² + 2

-1024y⁻² + 2 = 0

-1024y⁻² = -2

512y⁻² = 1

y⁻² = 1/512

1/y² = 1/512

y²  = 512

y = √512 m

On testing for minimum, we must know that the perimeter is at the minimum when y = √512

From xy = 512

x(√512) = 512

x = 512/√512

On rationalizing, x = 512/√512 * √512 /√512

x = 512√512 /512

x = √512 m

Hence, the dimensions of a rectangle is √512 m  by √512 m

Answer:

Option A is the correct option.

Step-by-step explanation:

[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]

Apply cross product property:

[tex]3(x - 4) = 6 \times x[/tex]

[tex]3(x - 4) = 6x[/tex]

Hope this helps...

Best regards!!

Answer:

3 * (x - 4) = 6 * x.

Step-by-step explanation:

3 / x = 6 / (x - 4)

3 * (x - 4) = 6 * x

3x - 12 = 6x

6x = 3x - 12

6x - 3x = -12

3x = -12

x = -4.

Hope this helps!

Answer:

a. (24 ln 2 − 7) / 9

b. x tan x + ln|cos x| + C

Step-by-step explanation:

a. ∫₁² x² ln x dx

Integrate by parts.

If u = ln x, then du = 1/x dx.

If dv = x² dx, then v = ⅓ x³.

∫ u dv = uv − ∫ v du

= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)

= ⅓ x³ ln x − ∫ ⅓ x² dx

= ⅓ x³ ln x − ¹/₉ x³ + C

= ¹/₉ x³ (3 ln x − 1) + C

Evaluate between x=1 and x=2.

[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]

⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C

⁸/₉ (3 ln 2 − 1) + ¹/₉

⁸/₃ ln 2 − ⁸/₉ + ¹/₉

⁸/₃ ln 2 − ⁷/₉

(24 ln 2 − 7) / 9

b. ∫ x sec² x dx

Integrate by parts.

If u = x, then du = dx.

If dv = sec² x dx, then v = tan x.

∫ u dv = uv − ∫ v du

= x tan x − ∫ tan x dx

= x tan x + ∫ -sin x / cos x dx

= x tan x + ln|cos x| + C