Answer:
Step-by-step explanation:
Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:
4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)
To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:
179.72467632 in rounded to the nearest inch is 180 in.
Therefore, 4559.886 rounded to the nearest inch is 180.
The point (7,8) in the coordinates plane represents a ratio. Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point. Is Adela correct?
Answer:
It depends on the context of the problem and the interpretation of the ratio represented by the point (7, 8).
If we interpret the point (7, 8) as representing the ratio 7:8, then Adela's claim is incorrect. Adding the same number to both coordinates of the point would change the value of the ratio. For example, adding 1 to both coordinates would give the point (8, 9), which represents the ratio 8:9, which is not equivalent to 7:8.
However, if we interpret the point (7, 8) as representing a different type of ratio, such as the ratio of the distances from the point to two fixed points or the ratio of the areas of two shapes, then it may be possible to find an equivalent ratio by adding the same number to both coordinates of the point. In this case, Adela's claim could be correct.
Without more information about the context and interpretation of the ratio represented by the point (7, 8), it is difficult to determine the correctness of Adela's claim.
Tiffany's mom is renting a car for their upcoming vacation. She wants to spend no more than $17 per day for the car. Which of the following car rental companies will fit into her budget? Select ALL that apply.
Car Rental Company Amount Charged
A $33 for 2 days
B $50 for 3 days
C $72 for 4 days
D $89 for 5 days
A
Car Rental Company A
B
Car Rental Company B
C
Car Rental Company C
D
Car Rental Company D
Answer: i think its A and B
Step-by-step explanation: 33 divided by 2 is 16.5
50 divided by 3 is 16.6667
72 divided by 4 is 18 so that would be to much
89 divided by 5 is 17.8 which is also to much
Can a triangle with angle measures of 45-45-90 have the side lengths 30, 30 and 60?
(Geometry/Trig)
Step-by-step explanation:
No, the ratio in a 30-60-90 triangle is
::
[tex]1:1:\sqrt{2} [/tex]
not
1:1:2
A box contains four apples, six oranges, and a pear. Preston reaches into the box and selects two of the 11 fruits uniformly at random without replacement. Let m/n be the probability that he selects an apple and an orange, where m and n are relatively prime positive integers. Find m+n.
the answer is m + n = 24 + 55 = 79.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.
First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.
This can be simplified by dividing the numerator and denominator by 2:
48/110 = 24/55
So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.
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QUESTIONS 1. Lizzy a level 300 students at UEW calls her father to send her money to buy Milo which cost $4 each and books which cost $8 each. The father sent her 20 pairs of shoes and 20 pairs of new jeans trousers which she can freely see on the market for $ 20 each and $ 40 each respectively. a. Write down the equation of Lizzy's budget line and interpret the results.
b. Carefully sketch the budget line
c. If Lizzy discovers that substituting two (2) tins of milo for three (3) will not change her level of satisfaction, what must be the lowest price of books before she will substitute milo for books given that the price of milo remains $4.
a.The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I.
b.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.
c.The lowest price of books that Lizzy will substitute for Milo is $6.
What is budget line?A budget line is a graphical representation of all possible combinations of two goods that can be purchased with a limited amount of income or resources. It shows the various combinations of two goods that a consumer can afford to buy with a given income and the prices of the two goods.
In the given question,
a. The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I
where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.
Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.
b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:
4M + 8B = I - 20(20)S - 20(40)J
B = (1/2)I - 40S - 40J - 2M
This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:
4M + P(2/3)B + 20(20)S + 20(40)J = I
To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:
4 = (2/3)P
P = (3/2) * 4
P = 6
Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.
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A.The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I.
B.To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph.
C.The lowest price of books that Lizzy will substitute for Milo is $6.
What is budget line?
A budget line is a graphical representation of the limits of a consumer's purchasing power, given their income and the prices of goods and services. It shows all the possible combinations of two goods that a consumer can purchase with a given income, while spending all of their available resources.
According to given information:a. The equation of Lizzy's budget line can be written as:
4M + 8B + 20(20)S + 20(40)J = I
where M is the number of tins of Milo, B is the number of books, S is the number of pairs of shoes, J is the number of pairs of jeans, and I is the total income or budget.
Interpretation: This equation represents all the possible combinations of Milo, books, shoes, and jeans that Lizzy can buy with her given income. It shows that she has to choose between buying more of one good and less of the other goods depending on their prices and her budget.
b. To sketch the budget line, we need to solve the equation for one of the variables. Let's solve for B:
4M + 8B = I - 20(20)S - 20(40)J
B = (1/2)I - 40S - 40J - 2M
This equation shows that the maximum number of books that Lizzy can buy depends on her income (I), the prices of shoes (S) and jeans (J), and the number of tins of Milo (M) she buys. The slope of the budget line is -4, which means that for every 1 unit increase in the number of books, Lizzy has to give up 4 units of Milo.
To sketch the budget line, we can plot the points (0, I/8), (I/4, 0), and (5I/16, 3I/16) on a graph, where the x-axis represents the number of tins of Milo (M) and the y-axis represents the number of books (B). Then, we can draw a straight line connecting these points to represent Lizzy's budget line.
c. Let's assume that the lowest price of books that Lizzy will substitute for Milo is P dollars. Then, the new budget line can be written as:
4M + P(2/3)B + 20(20)S + 20(40)J = I
To find the lowest price of books that Lizzy will substitute for Milo, we need to solve for P. We can do this by setting the coefficients of M and B in the new budget line equal to those in the original budget line:
4 = (2/3)P
P = (3/2) * 4
P = 6
Therefore, the lowest price of books that Lizzy will substitute for Milo is $6.
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Rewrite the following equations in the form (x−p)2=q 0=x^2-18x+1 and the equation x^2+26x+167.5=0
For the first equation, we can complete the square to find its vertex form. Here's how we do it:
0 = x^2 - 18x + 1
0 = (x - 9)^2 - 80
So we have (x - 9)^2 = 80. This is in the form (x - p)^2 = q, where p = 9 and q = 80.
For the second equation, we can complete the square in a similar way:
x^2 + 26x + 167.5 = 0
x^2 + 26x = -167.5
x^2 + 26x + (26/2)^2 = -167.5 + (26/2)^2
(x + 13)^2 = 9.25
So we have (x + 13)^2 = 9.25. This is in the form (x - p)^2 = q, where p = -13 and q = 9.25.
I hope that helps!
The perimeter of a movie screen is 70 meters it is 23 meters wide how tall is it
Answer:
height = 12 m
Step-by-step explanation:
We can assume from the problem that the movie screen is rectangular and the formula for perimeter (P) of a rectangle is
P = 2h + 2w, where l is the length and w is the width.
Thus, we can plug in 70 for P and 23 for w and solve for h:
[tex]70=2h+(2*23)\\70=2h+46\\24=2h\\12=h[/tex]
3/10=
19/50=
5/10=
1/5=
14/25=
3/25=
Answer:
3/10 = 0.3
19/50 = 0.38
5/10 = 0.5
1/5 = 0.2
14/25 = 0.56
3/25 = 0.12
compare 9\10 and 3\2 on number line
Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
What is common denominator?A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.
The two values are 9/10 and 3/2.
Taking the LCM we have:
9/ 10 and 15/10
Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.
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On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.
What is number line?
A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.
To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:
9/10 = 0.9
3/2 = 15/10 = 1.5
Now, we can plot these two numbers on a number line:
We can see that 9/10 is to the left of 3/2 on the number line.
Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.
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How to convert 23.01 into a fraction?
Answer:
2301 / 100
Step-by-step explanation:
We take
23.01 time 100 which makes 2301/100 fraction.
Please I need help
The area of the shaded region is
The area of the shaded region under normal distribution is: 3.51
What is the area under the normal distribution?The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.
The z-table or the standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.
To the right of -2.25 and to the left of -0.35
From standard normal table, we have the p-values as:
Area to the left of -0.35 = 0.3632
Area to the left of -2.25 = 0.0122
Area of the shaded region = 0.3632 - 0.0122 = 0.351
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which is more 7,000 milliliters or 7 liters?
Answer:
It’s the same
Step-by-step explanation:
There equal
7 liters = 7000 milliliters
Find the perimeter of a rectangle with w=5 and l=9
Answer:
28 units
Step-by-step explanation:
The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.
Substituting l = 9 and w = 5, we get:
P = 2(9 + 5) = 2(14) = 28
Therefore, the perimeter of the rectangle is 28 units.
5. Andrew needs to choose a captain creature and a partner creature for his
expedition to a mysterious dungeon. Each creature belongs to the grass,
fire, or water group, and each group has 6 creatures. If the captain and
partner creatures cannot be from the same group, how many ways can
Andrew choose a captain creature and a partner creature?
Andrew needs to choose a captain creature and a partner creature for his expedition to a mysterious dungeon. Each creature belongs to the grass, fire, or water group, and each group has 6 creatures, hence there are 216 ways
If the captain and partner creatures cannot be from the same group, how many ways can Andrew choose a captain creature and a partner creature?" by using combinatorial techniques.
Since Andrew cannot choose a captain and partner creature from the same group, there are 3 choices for the captain creature and 2 choices for the partner creature.
Therefore, the number of ways that Andrew can choose a captain and partner creature is: 3 * 2 * 6 * 6 = 216
Therefore, there are 216 ways that Andrew can choose a captain creature and a partner creature for his expedition to the mysterious dungeon
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a rocket is launched from the top of a 30 foot cliff with an initial velocity of 170 feet per second. the height, h, of the rocket after t seconds is given by the equation h=-16t^2+170t+30. How long after the rocket is launched will it be 20 feet from the ground?
However, we need to choose the positive value for t, since time cannot equation be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
So we have:
[tex]-16t^2 + 170t + 30 = 20\\-16t^2 + 170t + 10 = 0\\8t^2 - 85t - 5 = 0\\t = (-b + \sqrt(b^2 - 4ac)) / 2a\\t = (-(-85) + \sqrt((-85)^2 - 4(8)(-5))) / 2(8)\\t = (85 + \sqrt(7225 + 160)) / 16\\t = (85 + \sqrt(7385)) / 16[/tex]
However, we need to choose the positive value for t, since time cannot be negative in this case. Therefore, the rocket will be 20 feet from the ground approximately 1.411 seconds after it is launched.
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What are the first three terms of the sequence defined by the following equation? a_n= 7 + (n - 1) 5
7, 2, -3
7, 12, 17
7, 35, 175
12, 17, 22
Answer:
7, 12, 17 which is the second choice
Step-by-step explanation:
The given sequence is expressed by the equation
[tex]a_n = 7 + (n - 1)5\\\\(n - 1)5 = 5n - 5\\\\a_n = 7 + (n - 1)5= 7 + 5n - 5\\\\= 2 + 5n\\\\a_n = 5 + 2n\\\\a_1 = 2 + 5(1) = 2 + 5 = 7\\\\a_2 = 2 + 5(2) = 2 + 10 = 12\\\\a_3 = 2 + 5(3) = 2 + 15 = 17\\\\[/tex]
So the first three terms are
7, 12, 17 which is the second choice
Simplify:
X- 10 > 3
please help me on this
Answer:
To simplify the inequality x - 10 > 3, we can isolate x by adding 10 to both sides:
x - 10 + 10 > 3 + 10
Simplifying, we get:
x > 13
Therefore, the simplified inequality is x > 13.
Graphical Misrepresentations of Data – Warning!
Graph can be misleading! Distorting the truth unfortunately does happen within the field of Statistics through distorting data. Some graphs are misleading and other deceive! The misrepresentation may be intentional or purely innocent on the behalf of the researcher/statistician.
When reviewing graphs, it is important to have an eye for characteristics that may manipulate the facts and in turn the data. For example, incorrect depiction of size of graphics.
Please review a few graphs from a local newspaper, magazine or professional journal. Please describe the graph, provide the source and why you chose this particular one.
Please provide 3 to 4 characteristics of a good graph.
Your statements should be:
Substantive and clearly articulated
Professionally written
Demonstrate knowledge of the content
Contribute to the discussion (possibly with a question) to further increase and deepen the understanding of the topics being discussed
You may use supporting articles, textbook references, and even personal experience (as long as it relevant and empirical in nature).
On the graph we have to ensure that the data points are seen, the text and design on the graph are meaningful along with keeping the alignment on a common scale.
What is a graph?The graph only presents the facts in an organised manner. It facilitates our understanding of the facts. The numerical information gleaned via observation is referred to as data.
For the given question,
In a graph the data should be shown clearly.
Now, displaying the data clearly entails making sure the data points are visible while also including relevant language on the graph itself.
Designing of the graph should be in a simple manner.
The alignment to be used has to be on a common scale.
The visual encoding has to be transparent.
Use of standard-forms are welcomed.
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Write 4/8 in lowest terms
Answer:
4/8 in lowest terms is 1/2.
Step-by-step explanation:
Answer: 1/2
4/8 is equivalent to 1/2
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, B' would be located at B' (3, -4).
What is a translation?In Mathematics, a translation is a type of rigid transformation which is used in moving every point of an object in the same direction, as well as for the same distance.
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (3, 1) → Coordinate B' = (1, (-3)) = (1, -3)
Lastly, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, -3) → (1 + 2, -3 - 1) = B' (3, -4).
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Express the given fraction as percent 3/4?
Answer:
75%
Step-by-step explanation:
3/4 =75%
If you divide 3 by 4 you get 0.75
1=100%
0.75=75%
Answer:
.75
Step-by-step explanation:
think of 3 quarters
PLS HELP!!! DUE TOMORROW!! 50 POINTS!! show work pls!!
The right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
How to evaluate for the solutions of the right triangle BCD.Considering the angle D for right triangle BCD, the side opposite the angle D is BD which is also equal to 11 cm, and the side adjacent to the angle D is DC.
sin D = 11/20 {opposite/hypotenuse}
sin D = 0.55 to the nearest tenth
D = sin⁻¹(0.55)
D = 33.3670
D = 33 to the nearest degree
angle B = 180 - (90 + 33) {sum of interior angles of a triangle}
angle B = 57°.
Therefore, the right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
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find the areas of the sectors formed by angleDFE. Round your answers to the nearest hundredth
The area of the sector formed by angle DFE is approximately 3.29 square feet.
What is area of the sector?
To find the area of a sector of a circle, we need to know the central angle that defines the sector and the radius of the circle. We can then use the formula:
Area of sector = (central angle / 360 degrees) x π x (radius)²
In this case, we are given that the radius of the circle is 4 feet and the central angle that defines the sector is 75 degrees. Therefore, the area of the sector can be calculated as:
Area of sector = (75 / 360) x π x (4)²
= (0.2083) x π x 16
= 3.29 square feet (rounded to the nearest hundredth)
Therefore, the area of the sector formed by angle DFE is approximately 3.29 square feet.
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To the nearest foot, what is the height of the pole?
The height of the pole to the nearest foot, given the angle of elevation and the surveyor distance, is C. 135 ft
How to find the height of the pole ?To find the height of the pole, we can use the tangent function from trigonometry. The tangent of the angle of elevation (44°) is equal to the ratio of the height of the pole (h) minus the transit height (4 feet) to the distance between the transit and the pole (140 feet).
So, we have:
tan(44°) = (h - 4) / 140
h - 4 = 140 × tan(44°)
h = 140 × tan(44°) + 4
h = 140 × 0.965 + 4
h = 135.1
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If x^2-x-6=0 then x is
, then x is
Question 1 options:
-2 or 3
-1 or 6
1 or 6
2 or -3
Answer:
-2 and 3 is the required answer
Answer: The answer is: -2 or 3
Step-by-step explanation:
x^2 -x -6 = 0
x^2 -3x +2x -6 = 0
x(x-3) + 2(x-3) = 0
(x-3)(x+2) = 0
So x-3 = 0 :: x = 3
or x+2 = 0 :: x=-2
During the candy sale, nick sold 100 bars,Olivia sold 94,Brandon sold 53, and Grace sold 75. (Rank from greatest to least
The ranking from greatest to least goes on Nick, Olivia, Grace, and Brandon.
So in this, we have to rank the person who got most of the candy bars first and that is Nick.
After Nick Olivia has 94 candy bars so she is second in order.
Then on the third Grace had 75 candy bars.
And at the least Brandon is there with 53 candy bars.
Nick sold 100 candy bars
Olivia sold 94 candy bars
Grace sold 75 candy bars
Brandon sold 53 candy bars
Therefore, the ranking from greatest to least is Nick, Olivia, Grace, and Brandon.
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An appliance store decreases the price of a 19-in. television set 28% to a sale price of $435.60.What was the original price?
Answer:
Step-by-step explanation:
Let x be the original price of the television set.
The sale price is 28% off the original price, which means that the sale price is equal to 100% - 28% = 72% of the original price.
So we can write an equation based on this information:
0.72x = 435.60
Solving for x, we get:
x = 435.60 / 0.72
x ≈ $605
Therefore, the original price of the television set was approximately $605.
Diana has watched 13 out of 25 episodes of a television series. What decimal represents the part of the series she has NOT watched yet?
Answer:
Step-by-step explanation:
Provide a trigonometric equation. Considering only the space between = 0 and 2π the equation must only have solutions at x = 1 and x = 2. Explain your thought process and the work you did to create the equation. You may round decimal values to 3 places.
Therefore , the solution of the given problem of equation comes out to be f(x) = sin(/2 x) (when x = 1 or 2).
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.
Here,
The goal is to construct a trigonometric equation with only answers at
x = 1 and x = 2.
f(x) = A sin(Bx+C+D)
=> B + C + D + A = 0 (equation 1)
=> Equation 2: A sin(2B + C + D) = 0
=> B + C sin A = 0 (equation 3)
=> Sin(2B+C) = A = 0 (equation 4)
Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:
=> B + C = nπ (equation 5)
=> 2B + C = mπ (equation 6)
with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:
=> B = (m - n)π/2 (equation 7)
=> C = nπ - B (equation 8)
=> When x = 1, C = /2 - /2 = 0.
=> When x = 2, C = − /2 = 3/2.
Thus, the result is as follows:
when f(x) = sin(/2 x) (when x = 1 or 2)
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Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
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the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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