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2 years ago

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Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures televisions can be mo

deled by the polynomial 3x2 + 180x. The cost, in dollars, of producing the televisions can be modeled by 3x2 – 160x + 300. The variable x is the number of televisions sold.
If 150 televisions are sold, what is the profit?

2 answers:

-Dominant- [34]2 years ago

7 0

Answer:

The answer is C. - $50,700

Step-by-step explanation:

Doss [256]2 years ago

3 0

$\bf \stackrel{\mathbb{P~R~O~F~I~T}}{\stackrel{Revenue}{(3x^2+180x)}~~~~-~~~~\stackrel{Costs}{(3x^2-160x+300)}}\implies 20x+300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{profit equation}}{P(x)=20x+300}\implies \stackrel{\textit{150 televisions sold, x = 150}}{P(150)=20(150)+300}\implies P(150)=3300$

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The temperature at a point (x, y) on a flat metal plate is given by T(x, y) = 88/(2 + x2 + y2), where T is measured in °C and x,

-Dominant- [34]

Answer:

$D_uT(3,1)=-\frac{44}{9}*\frac{1}{\sqrt{2} } \approx-3.46$

Step-by-step explanation:

To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:

$D_uT(x,y)=T_x(x,y)i+T_y(x,y)j$

Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:

$i=\frac{1}{\sqrt{2} }$

$j=\frac{1}{\sqrt{2} }$

So, we need to find the partial derivative with respect to x and y:

In order to do the things easier let's make the next substitution:

$u=2+x^2+y^2$

and express T(x,y) as:

$T(x,y)=88*u^{-1}$

The partial derivative with respect to x is:

Using the chain rule:

$\frac{\partial u}{\partial x}=2x$

Hence:

$T_x(x,y)=88*(u^{-2})*\frac{\partial u}{\partial x}$

Symplying the expression and replacing the value of u:

$T_x(x,y)=\frac{-176x}{(2+x^2+y^2)^2}$

The partial derivative with respect to y is:

Using the chain rule:

$\frac{\partial u}{\partial y}=2y$

Hence:

$T_y(x,y)=88*(u^{-2})*\frac{\partial u}{\partial y}$

Symplying the expression and replacing the value of u:

$T_y(x,y)=\frac{-176y}{(2+x^2+y^2)^2}$

Therefore:

$D_uT(x,y)=(\frac{1}{\sqrt{2} } )*(\frac{-176x}{(2+x^2+y^2)^2} -\frac{176y}{(2+x^2+y^2)^2})$

Evaluating the point (3,1)

$D_uT(3,1)=(\frac{1}{\sqrt{2} } )*(\frac{-176(3)-176(1)}{(2+3^2+1^2)^2})=(\frac{1}{\sqrt{2} })* (-\frac{704}{144})=(\frac{1}{\sqrt{2} }) ( - \frac{44}{9})\approx -3.46$

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2 years ago

On the island of liars each inhabitant lies with probability 2/3. You overhear an inhabitant making a statement. Next you ask an

bonufazy [111]

Answer:

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

Step-by-step explanation:

Let A be the event 'the first inhabitant speaks the truth' and B the event the person you asked speaks the truth'

We have that

P(A) = P(B) = 1/3

The second person will say that the first person speaks the truth if:

- Both are lying

- Both are saying the truth

The probability that both inhabitants lies is 2/3 * 2/3 = 4/9

The probability that both inhabitants speaks the truth is 1/3² = 1/9

Therefore, in this problem, we want to know P(A ∩ B | (A∩ B) ∪ (A^c ∩ B^c) )

(note that, since the second persons says that A didnt lie, then in order for it to be true then the second person have to also say the truth).

We know that P(A ∩ B) = 1/9 and P((A∩ B) ∪ (A^c ∩ B^c)) = 4/9 + 1/9 = 5/9. Using the bayes formula we have

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) ) = P((A∩ B) ∪ (A^c ∩ B^c) | A ∩ B) * P(A∩ B)/ P((A∩ B) ∪ (A^c ∩ B^c))

Note that P((A∩ B) ∪ (A^c ∩ B^c) | A∩B) = 1 because the condition is more restrictive than the probability we are asking for, therefore

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) ) = P(A∩ B)/P((A∩ B) ∪ (A^c ∩ B^c)) = (1/9) / (4/9) = 1/4.

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

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2 years ago

In a survey of students, 80% were girls and 20% were boys. of the girls surveyed, 40% were wearing sneakers. if a surveyed stude

prisoha [69]

Answer:

$\frac{8}{25}$

Step-by-step explanation:

probability of selecting a girl from students is $\frac{4}{5}$

probability of girl wearing sneaker from girls is $\frac{4}{10}$ or $\frac{2}{5}$

hence, probability of selecting a girl wearing a sneaker will be,

⇒ probability = probability of delecting a girl from students × probability of girl wearing sneakers from girls

⇒ probability = $(\frac{4}{5})( \frac{2}{5})$

⇒ probability = $\frac{8}{25}$

3 0

2 years ago

The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given b

kondor19780726 [428]

H = V / B
<span>= 10x3 + 46x2 – 21x – 27 / 2x^2 + 8x - 9
</span>= 5x + 3

8 0

2 years ago

Read 2 more answers

a shopkeeper sold goods for rs 2400 and made a profit of 25% in the process. find his profit per cent if he had sold his goods f

miv72 [106K]

case 1,

Let the CP be ₹x,

SP = ₹2400

Profit = SP – CP

= 2400 – x

Profit % = {(2400–x)/ x} × 100%

According to the question,

{(2400–x)/ x} × 100 = 25

=> (2400–x)/ x= 25 /100

=> 100(2400–x) = 25x [ cross multiplication]

=> 240000 – 100x = 25x

=> 240000 = 25x + 100x

=> 240000 = 125x

=> 240000/125 = x

=> x = 1920

So, CP = ₹1920

case 2,

SP = ₹2040

Profit = SP – CP

= 2040 – 1920

= ₹120

profit % = 120/1920 × 100%

= 16%

<h3>Thus, his profit would be 16% if he had sold his goods for ₹2040.</h3>

6 0

2 years ago