Profit, revenue and cost are related, and can be calculated from one another.
The profit function is [tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]The domain of the profit function is x > 0The profit when producing 60 items is 1650The profit when producing 70 items is 1600The cost function is given as:
[tex]\mathbf{C(x) =30x + 150}[/tex]
The revenue function is given as:
[tex]\mathbf{R(x) =-0.5(x -90)^2 + 4050}[/tex]
(a) Calculate the profit function
This is calculated using:
[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]
So, we have:
[tex]\mathbf{P(x) =-0.5(x -90)^2 + 4050 - 30x - 150}[/tex]
Evaluate like terms
[tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]
(b) The domain of the profit function
When profit is 0 or less, then it becomes no profit.
Hence, the domain of the profit function is x > 0
(c) The profit for 60 and 70 items
Substitute 60 and 70 for x in P(x)
[tex]\mathbf{P(60) =-0.5(60 -90)^2 - 30 \times 60 + 3900}[/tex]
[tex]\mathbf{P(60) =1650}[/tex]
The profit when producing 60 items is 1650
[tex]\mathbf{P(70) =-0.5(70 -90)^2 - 30 \times 70 + 3900}[/tex]
[tex]\mathbf{P(70) = 1500}[/tex]
The profit when producing 70 items is 1600
(d) Why producing 10 more units less profit
When a function reaches the optimal value, the value of the function begins to reduce.
This means that, producing 10 more units takes the profit function beyond its maximum point.
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How do I find the percent of change
Answer:
200%
Step-by-step explanation:
It increases by 3 times. Because 100% increase is a 2x increase, 200% will be a 3x increase. Therefore, your answer is 200%.
In which quadrant does the point (13 , -6) lie?
A.
Quadrant III
B.
Quadrant I
C.
Quadrant IV
D.
Quadrant II
Answer:
C
Step-by-step explanation:
i hope you'll find these useful......
Answer:
C, quadrant IV
Step-by-step explanation:
The X (13) is positive meaning the point is on the right side of the graph, and Y (-6) is negative so it's below the x axis
Order from least to greatest -0.4, -1/5, and -0.65
How many gallons of a 90% antifreeze solution must be mixed with 100 gallons of 10% antifreeze to get a mixture that is 80% antifreeze? Use the six-step method.
slope of thissss
please help
-0.66
Step-by-step explanation:
can u mark me a brainliest
cuanto es 3/5 menos 1/2
Answer:
1/10
Step-by-step explanation:
(3/5) - (1/2)
3/5 = 3*2/ 5*2 = 6/10
1/2 = 1*5/ 2*5 = 5/10
(6/10) - (5/10)
= (6-5) / 10
= 1/10
Will the answer to the subtraction problem below be odd or even?
5291 - 4070 = ?
Answer:
1221
Step-by-step explanation:
here you go ...........
A store sells 6 apples for $2.82. At that rate, how much would 1 apple cost?
Answer:
$0.46
Step-by-step explanation:
6 apples = $2.82
1 apple = 2.82 / 6
= $0.46
what is 282.74 in terms of pi
Answer:
90π
Step-by-step explanation:
282.74 / π
282.74 / 3.14159 = 90
282.74 = 90π
Help, with my homework. Please represent 2x^-5x-12 using algebra tiles
Answer:
2−4−12
Step-by-step explanation:
The scale for a map to actual distance is 2 centimeters to 100 miles. The driving distance on the map between Los Angeles and Las Vegas is 5.4 centimeters. What is the actual distance, in miles, between Los Angeles and Las Vegas?
[tex]\begin{array}{ccll} \stackrel{cm}{map}&\stackrel{mi}{actual}\\ \cline{1-2} 2&100\\ 5.4&x \end{array}\implies \cfrac{2}{5.2}=\cfrac{100}{x}\implies 2x = 520\implies x = \cfrac{520}{2}\implies x = 260[/tex]
Help please please need quick
Solve for N is this equation.
Answer:
[tex]n + (13 - 6) = 124[/tex]
[tex]n+13-6=124[/tex]
[tex]n+7=124[/tex]
[tex]n+7-7=124-7[/tex]
[tex]n=117[/tex]
Write two numbers that multiply to −33 and add to 8
Answer:
-3 and 11
Step-by-step explanation:
Waiting times to receive food after placing an order at the local Subway sandwich shop follow an exponential distribution with a mean of 66 seconds. Calculate the probability a customer waits:a. Less than 39 seconds.
Using the exponential distribution, it is found that there is a 0.4462 = 44.62% probability that a customer waits less than 39 seconds.
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this problem, mean of 66 seconds, hence, the decay parameter is:
[tex]\mu = \frac{1}{66}[/tex]
The probability that a customer waits less than 39 seconds is:
[tex]P(X \leq 39) = 1 - e^{-\frac{39}{66}} = 0.4462[/tex]
0.4462 = 44.62% probability that a customer waits less than 39 seconds.
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whoever answers ets brainliest, 5 stars, and a thanks. pls help asap!
evaluate: (5/6 + 2/3) - (3/4 + 1/12)
answer as a fraction in simplest form
Given info:- Evaluate: [(5/6 + 2/3) - (3/4 + 1/12)] and find the Evaluated form = ?
Solution:-
Given fractional expression: [(5/6 + 2/3) - (3/4 + 1/12)]
Take the LCM of denominator 3 and 6 is 6.
Again take the LCM of denominator 4 and 12 is 12.
so,
⟼ [(5+4)/6 - (9+1)/12]
⟼ [9/6 - 10/12]
Now, take the LCM of the denominator 9 and 12 is 36.
⟼ [(54-30)/36]
Now, reduce the fraction by extracting and cancaling out with 2.
⟼ [24÷2/36÷2]
⟼ 12/18
⟼ 6÷3/9÷3
⟼ 2/3
Answer↓
Therefore, Evaluated form is 2/3.
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Describe a real life example of any one of Newton's Laws. It cannot be an example already listed in this portfolio. Make sure you're adequately describing your example and how it represents the law(s). (4-5 sentences)
Newton's first law of motion states that; An object continues to be in its state of rest or uniform motion unless acted upon by an external force in which case, it acts otherwise.
An example of this law is an orange placed on a table.
In essence, the orange continues in its state of rest unless acted upon by a force of push or otherwise by an individual or perhaps wind as the case may be.
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The graph shows that the solution to 2 = 0.5^x is X = -1 What is the solution to 2 = 0.5^x - 4
Answer in Complete Sentences
Step-by-step explanation:
2 = 0.5^x - 4 is the same as
6 = 0.5^x
x is the logarithm of 6 to the base of 0.5.
which is the same as
log(6)/log(0.5) = -2.584962501...
The table shows information about some children.
Age 11
Age 12
Total
Girls
7
a
b
Boys
с
5
8
Total
d
9
e
A pupil is selected at random.
What is the probability of selecting a boy?
Give your answer in its simplest form.
I wrote this on a document in my previous years in school.
3 bombas de agua llenan una piscina en 10 días trabajando 5 horas diarias.
Si hay 5 bombas de agua, ¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?
5 bombas deben trabajar durante 4 dias para llenar la piscina.
¿cuántos días demoran en llenar la misma piscina, si trabajan 8 horas diarias?Cada bomba trabaja a un rate (razon de trabajo) R.
Sabemos que 3 bombas, trabajando 5 horas diarias por 10 días (un total de 50 horas), llena una piscina, entonces:
(3R)*50 horas= 1 piscina.
R = (1 piscina)/(150 horas).
Es decir, una sola bomba tarda 150 horas en llenar una piscina.
En el caso de que 5 bombas trabajen, tenemos que para llenar una piscina tienen que trabajar un tiempo T.
5*((1 piscina)/(150 horas))*T = 1 piscina.
(1 piscina)/(30 horas)
Resolviendo para T, obtenemos:
T = 1 piscina*(30 horas)/(1 piscina) = 30 horas.
Y sabemos que trabajan 8 horas diarias, es decir, las bombas deben trabajar durante:
30/8 = 3.75 ≈ 4 días.
5 bombas deben trabajar durante 4 dias para llenar la piscina.
Sí quieres aprender más sobre razones de trabajo.
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Decide whether the two inequalities are equivalent. Explain.
b- 12 24: bs 16
O A Yes; if you solve the first inequality for b, you will get the second inequality.
o
B. No; if you graph both inequalities on the same number line, you will cover all real numbers.
O C. No; if you solve the first inequality for b, you will end up with an inequality with a different relation symbol than the second inequality
OD. No, if you graph both inequalities on the same graph, you will get b = 16.
Answer:
D,no if you graph both inequalitiesvon thevsame geaph ,you will get b =16
what's
- 5 3/4 + (-4 5/6) in simplest form
Answer:
-(127/12)
Step-by-step explanation:
-23/4 -29/6 = -254/24
-254/24 = -127/12
John buys a computer on sale for $450.00. He
pays $50.00 less than have the original price. How
much was the original price of the computer?
Write and solve an equation
Answer:
$450+$50= X
X=$500
Step-by-step explanation:
The sale price is $450.00, so you take that amount and $50.00 which the amount he paid less and add them both. We do this because we want to see the original price of the computer. If it mentioned the original price already and the amount $50.00 and asked the sail price instead, we would have to subtract to get the answer.
Here we have to add.
450+50=500
(add the dollar sign)
$450+$50=X
X=$500
Eddie's overtime is figured on a 40-
hour work week. Last week he
worked the following hours:
Monday = 9.7
Tuesday = 8.3
Wednesday = 8
Thursday = 9.1
Friday = 8.6
=
He is paid time and a half for
overtime and makes $14.40 for
regular hours. What is Eddie's gross
pay?
Answer:
597.6 Dollars
Step-by-step explanation:
Answer:
$655.92Step-by-step explanation:
Total number of hours worked:
9.7 + 8.3 + 8 + 9.1 + 8.6 = 43.7Overtime hours:
43.7 - 40 = 3.7Gross payment:
40*14.4 + 3.7*14.4*1.5 = 655.92list all the prime numbers between 90 and 100
Im pretty sure the only prime number in between 90 and 100 is 97
Find the point on the line y=x that is closest to the point (-4,8)
Answer:
(2,2)
Step-by-step explanation:
Which expression is equivalent to 4 (5X + 3y)
Answer:
20x + 12y
Step-by-step explanation:
=> 4(5x + 3y)
=> 20x + 12y
Since we can't simplify this further, 20x + 12y is out answer.
Hoped this helped.
The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as seen from a point 47 ft farther from the pole. Find the height of the pole above the level of the observer's eyes. 10) A) 34 ft B) 86 ft C) 60 ft D) 45 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
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what is the equation of the line in the slope-intercept? write your answer in simplest form.
Answer:
y=-6x
Step-by-step explanation:
Slope intercept form is y=mx+b where b is the y intercept and m is the slope. In this particular example, the y intercept is at (0,0), the origin, so b=0. y=mx+0 or just y=mx. Now, to determine the slope, we must look at the graph. It appears the graph intersects the point (-10, 60) as well as the point (0,0). Other than just calculating it quickly in your head, the way to get slope from that is y1-y2/x1-x2. Setting that up, 60-0/-10-0, which is 60/-10, which is equal to -6. Put that into the equation and you get y=-6x
Please help! Answer if correctly only.
Answer:
f(X)= 4 and g(X)= 49 are the answers!
Answer:
f(6) = -8
g(-3) = 49
Step-by-step explanation:
So when observing a function we have to remember that the desired input value is correspondent to the function. So when looking at the first function of:
f(x) = -2x+4
we can see that we are trying to find f(6) meaning all of the values of x are 6 in the equation. When plugging in the value of x into the equation then we have:
f(6) = -2(6)+4
the next step would be to simplify. -2*6 = -12 and -12+4=-8 and thus:
f(6) = -8
Now the steps are the same with g(-3) except with the other function:
g(x) = -2x^3-5
g(-3) = -2(-3)^3-5
g(-3) = 49