The total profit (in dollars) from the sale of x calendars is given by, P(x) = 25x -0.3x2 - 350 0 SX S100. a) Find the exact profit from the sale of the 41st calendar. b) Use the marginal profit to approximate the profit from the sale of the 41st calendar.
Answers
a) Therefore, the exact profit from the sale of the 41st calendar is $170.7. b) Therefore, the approximate profit from the sale of the 41st calendar is approximately $171.1.
a) To find the exact profit from the sale of the 41st calendar, we substitute x = 41 into the profit function P(x) = 25x - 0.3x² - 350:
P(41) = 25(41) - 0.3(41)² - 350
= 1025 - 0.3(1681) - 350
= 1025 - 504.3 - 350
= 170.7.
Therefore, the exact profit from the sale of the 41st calendar is $170.7.
b) To approximate the profit from the sale of the 41st calendar using the marginal profit, we first need to find the marginal profit function. The marginal profit is the derivative of the profit function with respect to x:
P'(x) = dP/dx = 25 - 0.6x.
Now, we evaluate the marginal profit at x = 41:
P'(41) = 25 - 0.6(41)
= 25 - 24.6
= 0.4.
The marginal profit at x = 41 is $0.4.
To approximate the profit from the sale of the 41st calendar, we use the formula:
Approximate Profit = Profit at x = 41 + Marginal Profit at x = 41.
Approximate Profit = P(41) + P'(41)
= 170.7 + 0.4
= 171.1.
Therefore, the approximate profit from the sale of the 41st calendar is approximately $171.1.
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Related Questions
Angle Sum Theorem
y = ?
Answers
Answer:
140°
Step-by-step explanation:
The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)
20 + 120 = 140
Answer:
y= 140
Step-by-step explanation:
first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.
Given the following table of values, what is the slope and y-intercept?
Answers
Answer:
Y- intercept= (0, -1)
Slope = 2/3
Step-by-step explanation:
Finding the Y-Intercept is pretty much finding the Y value when X is 0
Looking at this table, when x = 0, y is -1. Which means your y intercept is (0, -1)
To find slope, you take two points (x,y) and apply it to the slope formula. We'll do the bottom 4 since those are all nice looking numbers
\(slope = \frac{y2 - y1}{x2 - x1} \)
plugging it in...
\(slope = \frac{3 - 1}{6 - 3} \)
3-1 = 2 and 6-3 = 3
Keep that in fraction form
\(slope = \frac{2}{3} \)
When is the exponential smoothing model equivalent to the naive forecasting model?
- a = 0
- a = 0.5
- a = 1
- never
Answers
Answer:
Step-by-step explanation:
a=0.5
I need help with this one please
Answers
The transformation that includes a reflection of f(x) = (x - 1)² + 1 over the y-axis is; Option C: f'(x) = (-4x - 1)² + 1
How to solve Reflection Transformation?The transformation rule for a reflection over the y -axis is given as;
(x, y) → (−x, y) .
This means that the rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the -value the same.
Now, we are given the function as;
f(x) = (x - 1)² + 1
Thus, applying the reflection rule about the y-axis gives us;
f'(x) = (-x - 1)² + 1
Now, the only correct option must have a negative sign attached to x which is option C that includes a reflection over the y-axis.
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Help me please it’s due today
Answers
Answer:
1 and 4 are correct
2, 3, and 5 are false
Hope this helps!
Factor out the coefficient of the variable term.
The expression 1/2n-1/2 factored is : ?
7th.
Answers
Given:
The expression is
\(\dfrac{1}{2}n-\dfrac{1}{2}\)
To find:
The factored form of given expression after factor out the coefficient of the variable term.
Solution:
We have,
\(\dfrac{1}{2}n-\dfrac{1}{2}\)
Here, the coefficient of variable n is \(\dfrac{1}{2}\).
It can be written as
\(=\dfrac{1}{2}\times n-\dfrac{1}{2}\times 1\)
Taking out \(\dfrac{1}{2}\) as common factor, we get
\(=\dfrac{1}{2}(n-1)\)
Therefore, the factored from of given expression is \(\dfrac{1}{2}(n-1)\).
Jaden wants to buy a BMX bike to compete in his town's extreme sports contest. He set up a lemonade and cookie stand to raise the money. Jaden sold lemonade for $1 per cup and cookies for $3 each. He sold 40 cups of lemonade and 20 cookies. How much money did he make?
Answers
Answer:
100
Step-by-step explanation:
40 x 1 = 40
20 x 3 = 60
40 + 60 = 100
hope this helps
therefore, the interval of convergence is as follows. (enter your answer using interval notation.)
I = (-13, -11)
Answers
To determine the interval of convergence for a power series, we examine the values of x for which the series converges. The interval of convergence for a given power series is (-13, -11).
To determine the interval of convergence for a power series, we examine the values of x for which the series converges. The interval of convergence is typically expressed in interval notation, [a, b), (-∞, b), (a, ∞), or (-∞, ∞), where a and b are real numbers or ±∞.
In this case, the interval of convergence is given as (-13, -11), indicating that the series converges for values of x within this interval. The inclusion of parentheses indicates that the endpoints (-13 and -11) are not included in the interval.
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Sherman has 4 cats and 1 dog.He wants to buy a toy for each of his pets.Sherman has 36$ to spend on pet toys.How much can he spend on each pet? Enter the answer as a fraction in simplest form and then as an amount in
Dollars and cents
Answers
Answer:
Sherman can buy a toy that costs at most $7.20, or $7+1/5 for each one of his pets.
Step-by-step explanation:
36/5= 7 1/5
If J=91 ,L=16 , and K=73 , list the sides of triangle JKL in order from smallest to largest
A. JL, KJ, LK
B. LK, JL, KJ
C. KJ, JL, LK
D. KJ, LK, JL
Answers
JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.
How are the angles arranged, from greatest to smallest?JKL, where K is the specified angle, is an example.Acute Angles are the smallest angles. An acute angle is a particular kind of angle that measures less than 90°.an acute angle. The planar surface typically produces obtuse angles.Straight angle. Right angle.Subtract the squares of the other sides, then calculate the square root to determine the shorter side.Reflex angle at its widest point.JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.To learn more about smallest angle refer to:
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please help me with this problem
Answers
Answer:
Step-by-step explanation:
The answer is (56+232)w_sd
your welcome
Answer:
as below
Step-by-step explanation:
use the table to put a number into f(x)
f(-3) = -3+4 = 1
f(-1) = -1+4= 3
f(2) = 2+4=6
f(11) = 2+11=13
plz help me :') im v bad at math
Answers
Answer:
D
Step-by-step explanation:
Just look at the scale and my answer and it will make sense
Answer:
\(\Large \boxed{\mathrm{\bold{D.} \ 5.50 \ g}}\)
Step-by-step explanation:
Between numbers lie in the middle of two numbers.
\(\sf \displaystyle \frac{5+6}{2} =5.5\)
The number in between 5 and 6 is 5.5.
The mass of the copper metal is 5.50 g.
Consider the expression –4b + 8c + 12 – 8b – 2c + 6. Part A Simplify the expression. b + c + Part B Factor the simplified expression using the GCF. 2(–2b + c + 3) 3(–2b + c + 3) 4(–2b + c + 3) 6(–2b + c + 3) Part C What is the value of the expression when b = 2 and c = –3?
Answers
Answer:
Step-by-step explanation:
Given the expression
-4b + 8c + 12 – 8b – 2c + 6.
To simplify, first collect the like terms
= (-4b-8b)+(8c-2c)+(12+6)
= -12b+6c+18
Factor out the GCF
The GCF is 6
On factoring out;
= 6(-2b+c+3)
If b = 2 and c = -3 the expression becomes:
= 6(-2(2)+(-3)+3)
= 6(-4-3+3)
= 6(-4+0)
= 6(-4)
= -24
Hence the value of the expression when b = 2 and c = -3 is -24
Answer:
3
Step-by-step explanation:
Finley and Booker sold candles for a school fundraiser. Booker sold 3 times as many candles as Finley. Finley sold 12 less candles than Booker. If each candle gives the seller $5.75 in profit, how much profit does each person make? Please help me I am struggling with this
Answers
Answer:
Booker: $103.50 profit
Finley: $34.50 profit
Step-by-step explanation:
b = # of candles Booker sold
f = # of candles Finley sold
1) b = 3f
2) f = b - 12 substitute b=3f into this equation to get an expression all in terms of f, then solve for f
f = 3f - 12
-2f = -12
f = -12/2 = 6 now plug this into either equation and solve for b
b = 3(6) = 18
Booker: 18 candles x $5.75 profit/candle = $103.50 profit
Finley: 6 candles x $5.75 profit/candle = $34.50 profit
What is x/-3+20=30? Can someone pls help me
Answers
Answer:
x=510
Step-by-step explanation:
You can first combine like terms to get x/17=30
The inverse operation of division is multiplication so you can multiply by 17 on both sides to get your final answer: x=510
Jasper kept track of the trick-or-treaters who came to his door and found that 1/4 were dressed as ghosts and 5/12 were dressed as witches. What fraction of the trick-or-treaters were dressed as either ghosts or witches?
Answers
Because you have to make 5/12 and 1/4 equal. 1/4=3/12. 5/12+3/12= 8/12.
Sali sells 286 cakes in the ratio small: medium: large = 9:5:12 The profit for one medium cake is three times the profit for one small cake. The profit for one large cake is four times the profit for one small cake. Her total profit is £815.76 Work out the profit for one small cake.
Answers
The profit for one small cake is approximately £0.3564.
To find the profit for one small cake, let's assign variables to represent the profits. Let's call the profit for one small cake "P_s," the profit for one medium cake "P_m," and the profit for one large cake "P_l."
Given information:
The ratio of small to medium to large cakes sold is 9:5:12.
The profit for one medium cake is three times the profit for one small cake.
The profit for one large cake is four times the profit for one small cake.
The total profit is £815.76.
We can set up equations based on the given information:
P_m = 3P_s (Profit for one medium cake is three times the profit for one small cake)
P_l = 4P_s (Profit for one large cake is four times the profit for one small cake)
Total profit = 286P_s + 286P_m + 286P_l = £815.76 (Total profit is the sum of profits for each cake sold)
Since we know the ratio of small, medium, and large cakes sold, we can express the number of each cake sold in terms of the ratio:
Let's assume the common ratio is "x," so we have:
Small cakes sold = 9x
Medium cakes sold = 5x
Large cakes sold = 12x
Now we can substitute these values into the total profit equation:
286P_s + 286P_m + 286P_l = £815.76
Substituting P_m = 3P_s and P_l = 4P_s:
286P_s + 286(3P_s) + 286(4P_s) = £815.76
Simplifying:
286P_s + 858P_s + 1144P_s = £815.76
2288P_s = £815.76
Dividing both sides by 2288:
P_s = £815.76 / 2288
P_s ≈ £0.3564
Therefore, the profit for one small cake is approximately £0.3564.
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mia is taking art and calculus courses on mondays. she is late for the art class with probability 0.5 and late for the calculus class with probability 0.4. suppose the two events are independent. what is the probability that mia is on time to exactly one of the classes?
Answers
The probability that Mia is on time to exactly one of the classes is 0.5
Given that
probability of she is late for the art class (x)= 0.5
probability of she is late for the calculus class(y) = 0.4
the probability of she is not late for the art class (z)= 1 - x = 1 - 0.5 =0.5
the probability of she is not late for the calculus class(p)= 1 - y = 1 - 0.4 = 0.6
the probability that Mia is on time to exactly one of the classes =
Probability of arriving (late for Calculus and on time for Art)) or (late for Calculus and on time for Art)
= (x × p) + (y × z)
=(0.5 × 0.6) +(0.4 × 0.5)
=0.3+0.2
= 0.5
The probability that mia is on time to exactly one of the classes = 0.5
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A square has a side length of 3 inches. What is the length of the diagonal distance across the square ?
Answers
Answer:
4.243
Step-by-step explanation:
To calculate the diagonal of a square, multiply the length of the side by the square root of 2:
d = a√2
d = 3√2=4.24264068
For any segments AB, CD, and EF, if AB = CD
and CD = EF, then AB = EF.
Select one:
0 Transitive Property
o Symmetric Property
O Reflexive Property
Answers
Answer:CD
Step-by-step explanation:not much to do
The property you are referring to is the Transitive Property.
Hence option first is correct.
Given that,
For segments AB, CD, and EF,
If AB = CD & CD = EF, then AB = EF.
The Transitive Property states that if two quantities are equal to a third quantity, then they are also equal to each other.
In this case,
if we have segments AB and CD, and AB is equal to CD, and we also have segments CD and EF, where CD is equal to EF, then by the Transitive Property, we can conclude that AB is equal to EF.
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Triangle X Y Z is shown. Angle X Y Z is 51 degrees and angle Y Z X is 76 degrees. The length of X Z is 2.6, the length of X Y is z, and Y Z is x.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
What is the value of z, rounded to the nearest tenth? Use the law of sines to find the answer.
2.7 units
3.2 units
4.5 units
5.3 units
Answers
Answer:
3.2 units
Step-by-step explanation:
Use the law of sines
z/sin 76 = 2.6/sin 51
z = 2.6 sin 76/sin 51 = 3.2
Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power
Answers
Answer:I think it’s 7x^3
Step-by-step explanation:
Apples cost 1.30 per pound.What is the cost of 6.2 pounds of apple
Answers
Answer:
That would be 8.06 lbs of apples for 6.20$.
Step-by-step explanation:
1.3 * 6.2
Which expression is equivalent to 3(2x + 4)?
A) 5x + 7
B) 6x + 7
C) 6x + 12
D) 5x + 12
Answers
Answer:
C) 6x + 12
Step-by-step explanation:
3 × 2x = 6x
3 × 4 = 12
5.
Which picture shows a rotation of the flag?
(1)
(2)
(3)
(4)
Answers
Answer:
4 my good sir
Step-by-step explanation:
A watering can dispenses water at the rate of 0.3 gallon per minute. The original volume of water in the can was 7 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water
Answers
The set of ordered pairs depicts the volume of water in the can in gallons (y) as a function of time in minutes (x), beginning with the first minute after the can begins distributing water and ending with {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
What is ordered pairs?An ordered pair is a pair of objects in mathematics. The order of the objects in the pair is important: the ordered pair differs from the ordered pair unless a = b. Ordered pairs are also known as 2-tuples or 2-length sequences. An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.
Here,
A watering can dispenses water at the rate of 0.3 gallon per minute.
The original volume of water in the can was 7 gallons.
If you plot a graph of volume of water in the can (gallons) against time (minutes),
The set of points on the graph will be:
After 1 minute: (1, 7 - 0.3) = (1, 6,7)
After 2 minutes: (2, 7 - 0.6) = (2, 6.4)
After 3 minutes: (3, 7 - 0.9) = (3, 6.1)
i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}
The set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water is {(1, 6.7) , (2, 6.4) , (3, 6.1)}.
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How would you describe the following events, of randomly drawing a King OR a card
with an even number?
a) Mutually Exclusive
b)Conditional
c)Independent
d)Overlapping
Answers
Events, of randomly drawing a King OR a card with an even number describe by a) Mutually Exclusive.
The events of randomly drawing a King and drawing a card with an even number are mutually exclusive. This means that the two events cannot occur at the same time.
In a standard deck of 52 playing cards, there are no Kings that have an even number.
Therefore, if you draw a King, you cannot draw a card with an even number, and vice versa.
The occurrence of one event excludes the possibility of the other event happening.
It is important to note that mutually exclusive events cannot be both independent and conditional. If two events are mutually exclusive, they cannot occur together, making them dependent on each other in terms of their outcomes.
The correct option is (a) Mutually Exclusive.
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If f(x) = 2 + 1, then f(3) =
Answers
Can you pls help me
Will mark brainliest
Answers
The early pay will always be $60 no matter the number of days, the deposit plus will be $35, $50, $65, $80, and the daily pay would be $0, $30, $60 $90, $120.
How much will you pay with the "Early pay" option?Based on the information, if you choose the option early pay, you will pay only $60 and you can swim as many days as you want, due to this, the total paid will always be $60.
How much will you pay with the "Deposit plus" option?Day 0: $20 (deposit)
Day 5: $20 (deposit) + $15 = $35
Day 10: $20 (deposit) + $30 = $50
Day 15: $20 (deposit) + $45 = $65
Day 20: $20 (deposit) + $60 =$80
How much will you pay with the "Daily pay" option?Day 0: $0
Day 5: $30 (6x5)
Day 10: $60 (6x10)
Day 15: $90 (6x15)
Day 20: $120 (6x20)
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solve the equation
7h-5(3h-8) = 72
Answers
Answer:
h = -4
Step-by-step explanation:
7h-5(3h-8) = 72
Distribute
7h - 15h +40 = 72
Combine like terms
-8h +40 = 72
Subtract 40 from each side
-8h+40-40 = 72-40
-8h = 32
Divide each side by -8
-8h/-8 = -32/-8
h = -4
Steps:
Step 1: Simplify both sides of the equation.
7h−5(3h−8)=72
7h+(−5)(3h)+(−5)(−8)=72(Distribute)
7h+−15h+40=72
(7h+−15h)+(40)=72(Combine Like Terms)
−8h+40=72 −8h+40=72
Step 2: Subtract 40 from both sides.
−8h+40−40=72−40
−8h=32
Step 3: Divide both sides by -8
Answer: h=−4
The answer for this question is h=-4
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Hope this helps.