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Answer:

In order to maximize profit, each widget should sell for $26.70.

Step-by-step explanation:

The total amount of profit y given by the selling price of each widget x is given by:

[tex]y=-15x^2+801x-5900[/tex]

And we want to determine the price of each widget such that is yields the maximum profit.

Since the equation is a quadratic, the maximum profit will occur at the vertex of our parabola.

The vertex of a quadratic is given by:

[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]

So, let's find the vertex. In our equation, a = -15, b = 801, and c = -5900.

Therefore, the price that maximizes profit is:

[tex]\displaystyle x=-\frac{801}{2(-15)}=\$26.70[/tex]

Therefore, in order to maximize profit, each widget should sell for $26.70.

Notes:

Then substituting this back into the equation, the maximum profit is:

[tex]y_{\text{max}}=-15(26.7)^2+801(26.7)-5900=\$ 4793.35[/tex]

Answer:

(5.4582 ; 6.8618)

Step-by-step explanation:

Given the data:

6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5

Sample mean, xbar = Σx / n

n = sample size = 50

ΣX = 308

xbar = 308 / 50 = 6.16

Using a Calculator :

The sample standard deviation, s = 2.469

Confidence interval = xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 95% ; df = 50 - 1 = 49

Tcritical = 2.010

Hence,

Margin of Error= 2.010 * (2.469/sqrt(50)) = 0.7018

Lower boundary : (6.16 - 0.7018) = 5.4582

Upper boundary : (6.16 + 0.7018) = 6.8618

(5.4582 ; 6.8618)

Answer:

[tex](7 \times 2 + 8) - ( {x}^{2} - 2) \\ (14 + 8) - ( {x}^{2} - 2) \\ 14 + 8 - {x}^{2} + 2 \\ 22 + {x}^{2} + 2 \\ 24 + {x}^{2} [/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

Answer:

The first one.

Step-by-step explanation:

Answer:

(-∞,3/2),{xIx<3/2}

Step-by-step explanation:

Using inverse function concepts, the correct option is:

B. Domain: x < -2 Range: y> 3

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in

here, we have,

we know that,

The domain of a function is the set that contains all possible input values.

The range of a function is the set that contains all possible output values.

In the inverse function, input and output are exchanged, thus, domain and range are also exchanged.

For the original function, the domain is x > 3 and the range is y < -2.

Thus, for the inverse function, the domain is x < -2 and the range is y > 3, which means that option B is correct.

learn more on domain at :

brainly.com/question/24603090

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Complete question:

The domain of a function h(x) is x > 3, and the range is y2 -2. What are the domain and range of its inverse function, h-1(x)?

A. Domain: x>3 Range: y2 -2

B. Domain: x2 -2 Range: y> 3

C. Domain: x>-2 Range: y> 3

D. Domain: x2 3 Range: y> -2 ​

i hope this helps- im not sure if its correct or not

Answer:

b is the answer

Step-by-step explanation:

a triangle equals up to 180 degrees and 75+43+62 equals 180

Answer:

24 square units is the answer

Answer:

the area is 32.5

Step-by-step explanation:

Answer:

24 different options

Step-by-step explanation:

3 cake type options

2 frosting options

4 radius sizes

3 * 2 * 4 = 24 different options

Answer:

Note  that  ABC   is  a 6 - 8 -10   right triangle  with AB  = 10

Also note  that triangle ADC  is similar to triangle  ACB

Therefore

AD/ AC =  AC / AB       so

AD / 6  = 6/ 10           cross-multiply

10*AD  =  6 * 6

810*AD   = 36

AD  = 36 /  10  =    3.6  =  x

I hope this helps a little bit.

She has 36 shells

9+(9*3)

9+27

=36

Please mark as brainliest. :)

Answer:

hewo nice to meet ya

Step-by-step explanation:

hi hello

Answer:

Hola!

*Spanish*

Gracias por los puntos!

Answer:

y = 3,254.3 yd

Step-by-step explanation:

Lets denote with 'x' and 'y' the distances we need to find.

Using the Law of Sines we can write:

x/(sin 76) = 1175/(sin(180 - (83 + 76))

x/(sin 76) = 1175/(sin 21)

x = 3,181.4 yd

y/(sin 83) = 1175/(sin(180 - (83 + 76))

y/(sin 83) = 1175/(sin 21)

y = 3,254.3 yd

The platform is 3,181.4 yards far from one end of the beach and 3,254.3 yd far from the other.

The distance of the oil​ platform is 3708.82 yards, from each end of the beach.

Given that,

The figure shows a 1300​-yard-long sand beach and an oil platform in the ocean.

The angle made with the platform from one end of the beach is 84 degrees and from the other end is 76 degrees.

We have to determine,

The distance of the oil​ platform, to the nearest tenth of a​ yard, from each end of the beach.

According to the question,

Let x be the distance of the sand beach,

And y be the distance of oil platform.

The distance of the oil​ platform of a​ yard, from each end of the beach, is determined by using the sin rule,

[tex]\rm \dfrac{x}{sina} = \dfrac{y}{sinb}\\\\ \dfrac{x}{sin76} = \dfrac{1300}{sin(180-(84+76))}\\\\ \dfrac{x}{0.97} = \dfrac{1300}{sin(180-160)}\\\\\dfrac{x}{0.97} = \dfrac{1300}{sin20}\\\\\dfrac{x}{0.97} = \dfrac{1300}{0.34}\\\\ \dfrac{x}{0.97}= 3823.52 \\\\ x = 3823.52 \times 0.97\\\\x = 3708.82[/tex]

Hence, The distance of the oil​ platform is 3708.82 yards, from each end of the beach.

For more details refer to the link given below.

https://brainly.com/question/18188038

Answer:

the diameter is 18 inches

Answer: <A and <F

Step-by-step explanation: Verticle angles are angles that are on opposite sides of each other therefore having the same angle.

Answer:

D (6)

Step-by-step explanation:

you must place a number on a number line starting from the smallest (negative number ) to the bigger number (positive number ).

the number that is represented by J is 6

Answer:

2

Step-by-step explanation:

Since with every 10 seconds, the distance increase by 20 meters

hence, 20/10 = 2

Answer:

[tex]7\frac{7}{15}[/tex]

Step-by-step explanation:

Mark as Brainllest plz

The area of the garden be  after he doubles the length and width is 160 square feet.

Given that,

Based on the above information, the calculation is as follows:

We know that

Area = (length) (width)

Now if the area is doubled

So,

= (2) (length)  (2) (width)

= 4(length) (width)

= 4 (40)

= 160

Therefore, we can conclude that option b is correct.

Learn more: brainly.com/question/24169758

Answer:

-5(k2-4k+6)

Step-by-step explanation:

I think is -5(k2-4k+6)

I think that it's 5(k2 − 4k + 6)

Answer:

It is x = 7 1/3

Step-by-step explanation:

2 feet is being used in the scale factor and 2 x 3 2/3 is 7 1/3.

Please mark as brainliest

Answer:

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

we have:

[tex]scale \: factor = \frac{smaller \: length}{larger \: length} [/tex]

let the length be x.

we have

[tex]2 = \frac{x}{3 \frac{2}{3} } [/tex]

[tex]x = 2 \times \frac{11}{3} [/tex]

[tex]x = 7 \frac{1}{3} [/tex]

so.

C .[tex]x = 7 \frac{1}{3} [/tex] is your answer

Answer:

log3x

Step-by-step explanation:

i think it would be y=log3x

Answer:Answer: 26 ft.

Step-by-step explanation:

Answer:

We have to flip the coin 78 times.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

We suspect that the coin is fair.

This means that [tex]\pi = 0.5[/tex]

96.5% confidence level

So [tex]\alpha = 0.035[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.035}{2} = 0.9825[/tex], so [tex]Z = 2.108[/tex].

How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?

n times, and n is found when M = 0.12. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.12\sqrt{n} = 2.108*0.5[/tex]

[tex]\sqrt{n} = \frac{2.108*0.5}{0.12}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.108*0.5}{0.12})^2[/tex]

[tex]n = 77.1[/tex]

Rounding up

We have to flip the coin 78 times.

Answer:

x=7°      y=4°

Step-by-step explanation:

7x+131=180

7x=180-131=49

x=49/7=7°

11x+y+99=180

77+y+99=180

y=180-99-77

y=4°

Answer:

Step-by-step explanation:

the concepts are confusing of what a function is.   f(x)  seems mysterious , huh

it's just a way to give a label to some set of terms.  Just think of it as a name of a person, but in a generic sense, like   hey "guy"   or hey "gal"  you can address many people that way.  f(x) is doing that same thing addressing by a name,  a set of math terms.  

a)  

in a)  we are addressing the g(x) function and we are also sending that function the number -2 as an input. so find the g(x) function and put in (-2) everywhere that there is an "x" , so

g(x)=[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11

g(-2) = [tex](-2)^{3}[/tex]-3[tex](-2)^{2}[/tex]+2(-2)+11

g(-2) = -8 -3(4) - 4 +11

g(-2) = -8 -12 -4 + 11

g(-2) = -24 + 11

g(-2) = -13

b)  

h(-1)  find the h(x) function and input a negative 1 where ever there is an x

h(x) =

h(-1) = [tex](-1)^{2}[/tex] - 3

h(-1) = 1 - 3

h(-1) = -2

c)

for c)  just combine like terms of the two given functions

g(x) - h(x)  =  [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - ([tex]x^{2}[/tex] - 3)

g(x) - h(x)  = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - [tex]x^{2}[/tex] + 3

g(x) - h(x)  = [tex]x^{3}[/tex]-4[tex]x^{2}[/tex]+2x + 14

d)

-2f(x) - h(x) = -2(3x + 2) - ([tex]x^{2}[/tex] - 3)

-2f(x) - h(x) = -6x - 4 - [tex]x^{2}[/tex] + 3

-2f(x) - h(x) = -6x - 1 - [tex]x^{2}[/tex]

-2f(x) - h(x) = - [tex]x^{2}[/tex] - 6x - 1

e)

f(h(x))  this gets a bit more confusing b/c it's  a composition of functions,  that's just a fancy way of saying the functions are nested. one inside the other.

f(x) = 3x + 2

h(x) = [tex]x^{2}[/tex] - 3

plug h(x) in to f(x) where ever there is an x in f(x)   , luckily there is only one x in f(x)  :)

f(h(x)) = 3([tex]x^{2}[/tex] - 3) + 2

f(h(x)) = 3[tex]x^{2}[/tex] - 9 + 2

f(h(x)) = 3[tex]x^{2}[/tex] - 7

f(h(x)) = 3[tex]x^{2}[/tex] + 0x + (-7)  

f)

f(x) = 3x + 2

g(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11

f(g(x)) = 3([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11) + 2

f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 33 + 2

f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 35

Hope that helps :)

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]x + 4y < 4[/tex]

The question is incomplete, as what is to be done is not stated.

However, possible sub-questions could be to determine the slope and the y-intercept for the boundary line.

To calculate slope, we have:

[tex]x + 4y < 4[/tex]

Solve for 4y

[tex]4y < - x + 4[/tex]

Solve for y

[tex]y < -\frac{x}{4} + \frac{4}{4}[/tex]

[tex]y < -\frac{1}{4}x + 1[/tex]

A linear inequality is represented as:

[tex]y <mx + b[/tex]

Where [tex]m =slope[/tex] and [tex]b = y\ intercept[/tex]

So:

By comparison:

[tex]mx = -\frac{1}{4}x[/tex]

[tex]m = -\frac{1}{4}[/tex]

and

[tex]b = 1[/tex]

So:

[tex]Slope = -\frac{1}{4}[/tex]

[tex]y\ intercept = 1[/tex]

Also, see attachment for graph