The cost in dollars of making 2 items is given by the function () = 10x + 800, a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. Fixed cost = $ Number 1 b. What is the cost of making 25 items? C (25) = $ Number c. Suppose the maximum cost allowed is $3300. What are the domain and range of the cost function, C(x)? Do not enter any commas in the numbers in your answers. Dumin C (25) = $ Number c. Suppose the maximum cost allowed is $3300. What are the domain and range of the cost function, C(x)?
Answers
The fixed cost for this item is $800.
The cost of making 25 items is $1050.
The domain of the cost function C(x) is x ≤ 250.
The range of the cost function C(x) is C(x) ≥ $800.
We have,
a.
The fixed cost is determined when zero items are produced. In this case, x = 0.
Plugging x = 0 into the cost function C(x) = 10x + 800:
C(0) = 10(0) + 800
C(0) = 0 + 800
C(0) = 800
b.
To find the cost of making 25 items, plug x = 25 into the cost function C(x) = 10x + 800:
C(25) = 10(25) + 800
C(25) = 250 + 800
C(25) = 1050
c.
Suppose the maximum cost allowed is $3300.
To determine the domain and range of the cost function C(x), we need to find the values of x for which C(x) does not exceed $3300.
Setting C(x) ≤ $3300:
10x + 800 ≤ 3300
10x ≤ 3300 - 800
10x ≤ 2500
x ≤ 2500/10
x ≤ 250
As for the range, the cost function C(x) can take on any value greater than or equal to the fixed cost, which is $800.
Thus,
The fixed cost for this item is $800.
The cost of making 25 items is $1050.
The domain of the cost function C(x) is x ≤ 250.
The range of the cost function C(x) is C(x) ≥ $800.
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Related Questions
Solve the system of equations below for x, y, and z.
4x – 2y + 3z = 9
x - 2y=-3
2x + 3y=1
What is the solution (x, y, z)?
Answers
The solution to given system of equations are x = -1, y = 1 and z = 5 which is determined by the substitution method.
The given system of equations below as
4x – 2y + 3z = 9 ....(i)
x - 2y = -3 ....(ii)
2x + 3y = 1 ....(iii)
By equation (ii) and solving for x to get
x - 2y = -3
x = 2y - 3 ....(iv)
Substitute the value of x = 2y - 3 in the equation (iii)
2(2y - 3) + 3y = 1
4y - 6 + 3y = 1
7y = 7
y = 1
Substitute the value of y = 1 in equation (iv) to get,
x = 2(1) - 3
x = -1
Substitute the values of x = -1 and y = 1 in equation (i), and solve for z
4(-1) – 2(1) + 3z = 9
-4 - 2 + 3z = 9
3z = 15
z = 5
Therefore, the solution to given system of equation are x = -1, y = 1 and z = 5.
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The sum of three consecutive numbers is eighty-four. Create the equation you would use to solve this problem using x as the variable for the first of the three consecutive numbers. (Do not use spaces)
Answers
Answer:
27,28,29
Step-by-step explanation:
x+x+1+x+2 =84
3x +3 =84
3x=84-3
3x=81
x=81 :3
x=27 (the first number
27 +1=28 (the second number
27 +2 =29 (the third number
^PLZ HELP, I NEED IT BY TODAY!!! (PART B and PART C only) PLZ THANKS
Answers
Part B (Taxi):
12 miles = 0.5 miles + (115×0.1) miles
Rate: $2.40 + (115×0.20)
= $25.40
Total cost (with tip): $25.40 + $2
= $27.40
20 miles = 0.5 miles + (195×0.1) miles
Rate: $2.40 + (195×0.20)
= $41.40
Total cost (with tip): $41.40 + $2
= $43.40
50 miles = 0.5 miles + (495×0.1) miles
Rate: $2.40 + (495×0.20)
= $101.40
Total cost (with tip): $101.40 + $2
= $103.40
Part B (Uber):
12 miles (rate) = $1 + ($1.05×12)
= $13.60
Total cost (with tip): $13.60 + $2
= $15.60
20 miles (rate) = $1 + ($1.05×20)
= $22
Total cost (with tip): $22 + $2
= $24
50 miles (rate) = $1 + ($1.05×50)
= $53.50
Total cost (with tip): $53.50 + $2
= $55.50
Part C
Uber is a better mode of transportation. This is because given the same distance travelled for both the taxi and the Uber, Uber has a lower cost compared to the taxi.
Find the 6th term of the geometric sequence whose common ratio is 2/3 and whose first term is 8.
Answers
To solve this question, we need to find the formula for the nth term of the geometric sequence. The formula is:
\(a_n=a_1r^{n-1}\)Where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
r is the common ratio
In this case:
a_1 8
r = 2/3
\(a_6=8\cdot(\frac{2}{3})^{6-1}=8\cdot(\frac{2}{3})^5=8\cdot\frac{32}{243}=\frac{256}{243}\)The answer is:
256/243
Khan Academy
layer 1
layer 2
layer 3
surface
layer 4
layer 1 and layer 4
layer 2 and layer 6
layer 3 and layer 5
layer 5
layer 6
surface
Which two layers are approximately the same age?
Answers
Layer 1 and Layer 4 are approximately the same age.
The geological structure of the earth's crust can be analyzed by studying the layers of sedimentary rocks. These layers represent various geological periods in the history of the Earth and provide information on the events that have occurred throughout time.
The Khan Academy is an online platform that offers various courses and lessons on different subjects, including geology. The different layers of the earth's crust are named and classified according to their age, composition, and position in the crust. The layers of the earth's crust are as follows:
Layer 1: The surface layer or the soil. It is the layer that contains the organic matter that supports plant growth.
Layer 2: The subsoil, which is composed of partially decomposed organic matter and clay.
Layer 3: The layer of weathered rock. It is the layer that has been altered by the action of water and wind.
Layer 4: The solid bedrock that is composed of igneous, metamorphic or sedimentary rocks. This layer is considered to be the oldest layer of the earth's crust.
Layer 5: The asthenosphere, which is a semi-solid layer of the upper mantle.
Layer 6: The mantle, which is the thickest layer of the earth's crust. The two layers that are approximately the same age are layer 1 and layer 4. Layer 1, which is the surface layer or the soil, is relatively young and is formed by the accumulation of organic matter.
On the other hand, layer 4 is the solid bedrock that is composed of igneous, metamorphic or sedimentary rocks. This layer is considered to be the oldest layer of the earth's crust.
Therefore, layer 1 and layer 4 are approximately the same age.
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Identifying values in the domain PLS HELP
Answers
Taylor spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -13.8°F. Between 9am and noon, the temperature rose 13.6°F. Between noon and 3pm, the temperature went up 11.1°F. Between 3pm and 6pm, the temperature decreased by 17.5°F. What was the temperature at 6pm?
Answers
Answer:
The temp is -47F
According to data from 2015, women's shoe sales in the us are roughly normally distributed by shoe size with a mean of size 8 and a standard deviation of 1.25 sizes.
a) if a women's shoe sold in the us is a size 7.5, what is the z-score?
b) what size of women's shoe would have a z-score of 1.3?
c) if a women's shoe sold in the us is a size 9, what is the z-score and percentile? z-score:
percentile:
d) what size of women's shoe would have a z-score of -1.5? what percentile is that? shoe size:
percentile:
e) what women's shoe size represents the 80th percentile? z-score:
shoe size:
Answers
a) The z-score for a shoe size of 7.5 is approximately -0.4.
b) The shoe size corresponding to a z-score of 1.3 is approximately 9.625.
c) The z-score for a shoe size of 9 is approximately 0.8.
d) The shoe size corresponding to a z-score of -1.5 is approximately 6.125.
e) To find the shoe size representing the 80th percentile, we need to determine the corresponding z-score using a z-score table or calculator and then use the formula x = (z * standard deviation) + mean.
a) To calculate the z-score, we use the formula: z = (x - mean) / standard deviation. For a shoe size of 7.5, the z-score would be: z = (7.5 - 8) / 1.25 = -0.5 / 1.25 = -0.4.
b) To find the shoe size with a z-score of 1.3, we rearrange the formula: x = (z * standard deviation) + mean. Plugging in the values, we get: x = (1.3 * 1.25) + 8 = 1.625 + 8 = 9.625.
c) For a shoe size of 9, the z-score is: z = (9 - 8) / 1.25 = 1 / 1.25 = 0.8. The percentile can be found using a z-score table or calculator.
d) With a z-score of -1.5, we can use the same formula as before: x = (z * standard deviation) + mean. Plugging in the values, we get: x = (-1.5 * 1.25) + 8 = -1.875 + 8 = 6.125. The percentile can be found using a z-score table or calculator.
e) To find the shoe size representing the 80th percentile, we can use the inverse of the z-score formula: x = (z * standard deviation) + mean. The z-score corresponding to the 80th percentile can be found using a z-score table or calculator.
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How can intervention development be driven by ABC data that are collected on the function of the target behavior?a. Determine how the ABC contingency can be altered to promote more positive behavior.b. The antecedent condition can be replaced with reinforcement.c. The rate of the behavior can be calculated to set a baseline for shaping.d. All of the above.
Answers
Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )
The method that intervention development will be influenced by the ABC data that are gathered on the function of the target behavior is through the determination of how the ABC contingency can be changed to encourage more positive behavior.
By identifying the functional reinforcers that sustain problem behavior, practitioners can create therapies that are more effective (i.e., from a smaller pool of potential interventions to choose from) and efficient.
Linking therapies to the outcomes of functional assessments has become accepted clinical practice and is now covered by both federal and state laws. This represents a significant and advantageous change in the method of behavioral intervention.
Therefore,
Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )
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help plzz Charli pays $18.00 for 5 t-shirts he needs your help to answer the following questions.
Answers
Answer:
What do you but in the chart? Also, part 2 is 72
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
If each t-shirt costs 3.6 dollars then you would have to multiply 3.6 by 20 shirts which will equal to 72. So Charlie has to pay 72 dollars for 20 shirts.
whats the value of n
n/80 3/30
Answers
3/30 = 8/80
N = 8
An auto mechanic earns $498.75 in 35 hours during the week. His pay is $2.50 more per hour on weekends. If he works 6 hours on the weekend in addition to 35 hours during the week, how much does he earn?
Plz show work and i will be so grateful
Answers
Answer:
35 hours during week pay: 498.75
2.50 more on weekends
Lets us find unit rate
498.75/35= 14.25
14.25 dollars on weekday add 2.50 and...
16.75 dollars is pay per hour on weekends
16.75*6= 100.5
100.5+498.75=
599.25 dollars
Step-by-step explanation:
Answer:
512.75$
Step-by-step explanation:
2.50 x 6 = 15.00$
So, add 15 to 498.75 by using standard algorithm.
Your result should be 512.75$
Therefore, your answer would be 512.75$
-kiniwih426
Al released his balloon from the 10-yard line, and it landed at the 16-yard line. If the ball reached a height of 27 yards, what equation represents the path of his toss?
Answers
The equation of the path of the parabola is y = a(x - 13)² + 27
Given data ,
To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola
Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.
The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:
h = (10 + 16) / 2 = 13
Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)
Now, let's substitute the vertex coordinates (h, k) into the general equation:
y = a(x - 13)² + k
Substituting the vertex coordinates (13, 27)
y = a(x - 13)² + 27
To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).
This means that the highest point (13, 27) lies on the parabola
Substituting the vertex coordinates (13, 27) into the equation
27 = a(13 - 13)² + 27
27 = a(0) + 27
27 = 27
Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number
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2. Which rule defines the function in the graph shown?
Answers
Answer:
Function rule is option c.
(1 point Rework probiem 8 from section 1.4 of your text, involving a product code. Assume that X=\{D, A, B, G, F \mid and Y=\{5,4,1,2,6\} . A code consists of 3 different symbol
Answers
The number of possible product codes that can be formed using three different symbols from the given set is 60.
The number of possible product codes, we need to find the number of ways we can choose three different symbols from the given set of five symbols. This can be done using the combination formula.
Number of ways to choose 3 symbols from 5 = 5C3 = (5*4*3)/(3*2*1) = 10
Now, for each choice of three symbols, we can arrange them in 3! = 6 ways.
Therefore, the total number of possible product codes = 10 * 6 = 60.
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Hi can someone thoughrly answer the question below for brainliest please
Answers
The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
12n > 135 + 4.50n
In order to make a profit and solve inequality,
12n - 4.50n > 135
7.5n > 135
n > 18
Thus, it needed to sell more than 18 to make a profit.
Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".
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Which equations represent the phrase “y is two less than half of a number “?
Answers
Answer:
C and A
Step-by-step explanation:
What is the length of the unknown
leg of the right triangle?
Answers
Answer:
2ft
Step-by-step explanation:
HELP!! (7th grade math) find the surface area of the composite figure 8in 11in 6in 3in 3in 11in 3in 6in
Answers
The surface area, SA, of the composite figure, obtained from the sums of the areas of the rectangular surfaces is 488 square inches
SA = 488 in.²
What is a composite figure?A composite figure is a figure that comprises of two or more simpler figures.
The surface area of the composite figure can be calculated as follows;
The area of the rare of the figure = 11 in × 9 in = 99 in²
The area of the four surfaces of the top cuboid = 2 × 3 × 3 + 11 × 3 + 11 × 3 = 84 in²
The area of the exposed surface of the lower cuboid = 6 × 11 + 2 × 6 × 8 + 5 × 11 + 8 × 11 = 305 in²
The surface area, A, of the composite figure is therefore;
A = 99 + 84 + 305 = 488 in²
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Chose the step below that correctly uses the distributive property to begin solving the equation:
3(x + 1) + 6 = 33
A. 3x+1+6= 33
B. 3x + 7 = 33
C. x+1+2= 11
D. 3x + 3+ 6 = 33
Answers
Answer:
D. 3x + 3 + 6 = 33
Step-by-step explanation:
3(x +1) + 6 = 3
multiply 3 by everything in the parenthesis
3(x) + 3(1) + 6 = 33
3x + 3 + 6 = 33
I hope this helps!
about 2% of the population has a particular genetic mutation. 100 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Answers
The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4
From the information given,
About 2% of the population has a particular genetic mutation, and 100 people are randomly selected.
The standard deviation for the number of people with the genetic mutation in such groups of 100 is obtained below;
The required standard deviation is,
p = 0.02 and n = 100;
1 - p = 1 - 0.02
= 0.98
σ = \(\sqrt{n*(1-p)*p}\)
σ = \(\sqrt{100*0.02*0.98}\)
σ = 1.4
The standard deviation for the number of people with the genetic mutation in such groups of 100 is 1.4
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help- this is already late-
Answers
Answer:
it's answer is 2a + 6a - 21
Step-by-step explanation:
2a + 3 ( 2a - 7)
= 2a + 6a - 21
Hope it will help :)❤
The sum of the ages of two brothers;Kofi and kwaku is 35 kofi's age is two-thirds of kwaku's age. find their ages.
Answers
Kofi's age is 20 and Kwaku's age is 15.
The sum of the ages of two brothers;Kofi and kwaku is 35 kofi's age is two-thirds of kwaku's age and to find their ages let's assume Kwaku's age to be x, then Kofi's age would be (2/3)x.
According to the problem, the sum of their ages is 35, so we can write the equation:
x + (2/3)x = 35
Multiplying both sides by 3, we get:
3x + 2x = 105
5x = 105
x = 21
Therefore, Kwaku's age is 21, and Kofi's age is (2/3) x 21 = 14.
Hence, the ages of the two brothers are 21 and 14 respectively.
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Kofi's age is 14 and Kwaku's age is 21.
Let's represent The Kofi's age as K and Kwaku's age as W.
The sum of the ages of two brothers; Kofi and kwaku is 35 kofi's age is two-thirds of kwaku's age
so,
K + W = 35
Kofi's age is two-thirds of Kwaku's age: K = (2/3)W
We can solve this system of equations to find their ages.
Substituting the second equation into the first equation:
(2/3)W + W = 35
(5/3)W = 35
W = (3/5) * 35
W = 21
Substituting the value of W back into the second equation to find Kofi's age:
K = (2/3) * 21
K = 14
Therefore, Kofi's age is 14 and Kwaku's age is 21.
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Katalin drove 180 miles on her vacation. She drove an average of 1.5 times faster on the second 90 miles of her trip than she did on the first 90 miles of her trip. Which expression represents the time she spent driving? Let x = her speed on the first half of the trip.
Answers
===================================================
Work Shown:
x = speed on 1st half of the trip
distance = rate*time
90 = x*t
t = 90/x
She spent 90/x hours driving on the 1st half of the trip
1.5x = speed on the 2nd half of the trip
d = r*t
t = d/r
t = 90/(1.5x)
t = 60/x
She spent 60/x hours driving on the 2nd half of the trip
Overall, she spent 90/x+60/x hours driving the entire 180 mile trip.
Edit:
That expression simplifies to 150/x since 90+60 = 150
5(2x+9)+2(x+11)=3(3x+4)+46
Answers
Answer:
x=-3
Step-by-step explanation:
Answer:
x = - 3
Step-by-step explanation:
10x + 45 + 2(x + 11) = 3(3x + 4) + 46
10x + 45 + 2x + 22 = 9x + 12 + 46
12x + 45 + 22 = 9x + 12 + 46
12x + 67 = 9x + 58
12x + 67 - 9x = 58
12x - 9x = 58 - 67
3x = 58 - 67
3x = - 9
Help me please don’t scam
Answers
Question 2: 3 + x = 12 x = 9
What is 2.35 rounded to the nearest hundredth.
Answers
2.35 is already rounded to the nearest hundredth.
Will give 20 points to whoever answers and brainiest if it's correct!
Answers
Answer:
3
Step-by-step explanation:
Write and solve an equation to answer the question.
The perimeter of the Puerto Rican flag is 150 inches. What are the dimensions of the flag?
Answers
Answer:
\(length = 45 \\ width = 30\)
Step-by-step explanation:
Perimeter =150 , length = 3/2y , width = y .
Perimeter of rectangle = (length + width ) × 2
\(150 = ( \frac{3}{2} y \: + y) \times 2 \\ \\ 150 = ( \frac{3}{2} y+ \frac{2}{2} y ) \times 2 \\ \\ 150 = ( \frac{5}{2} y) \times 2 \\ \\ 150 = 5y \\ \\ y = \frac{150}{5} \\ \\ y = 30\)
width = y = 30
\(length = \frac{3}{2} y = \frac{3}{2} \times 30 = 3 \times 15 = 45 \)
I hope I helped you^_^
A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let p denote the probability that the flaw is detected during any one fixation (this model is discussed in "Human Performance in Sampling
Required:
a. Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)?
b. Give an expression for the probability that a flaw will be detected by the end of the nth fixation.
c. If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection?
d. Suppose 10% of all items contain a flaw [P (randomly chosen item is flawed) = .1]. With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it s flawed)?
e. Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for p = .5.
Answers
a. The probability that a flaw is detected by the end of the second fixation is given by the formula: P(flaw is detected by the end of the second fixation) = 1 - P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation).
b. Similarly, the probability that a flaw will be detected by the end of the nth fixation is given by the formula: P(flaw is detected by the nth fixation) = 1 - P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * ... * P(flaw is not detected in n-th fixation).
c. To calculate the probability that a flawed item will pass inspection, we can use the formula: P(B'|A), where A is the event that an item has a flaw and B is the event that the item passes inspection. Thus, P(B'|A) is the probability that the item passes inspection given that it has a flaw. Since the item is passed if a flaw is not detected in the first three fixations, and the probability that a flaw is not detected in any one fixation is 1 - p, we have P(B'|A) = P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * P(flaw is not detected in third fixation) = (1 - p)³.
d. To find the probability that an item is chosen at random and passes inspection, we can use the formula: P(C) = P(item is not flawed and passes inspection) + P(item is flawed and passes inspection). We can calculate this as (1 - 0.1) * 1 + 0.1 * P(B|A'), where A' is the complement of A. Since P(B|A') = P(flaw is not detected in first fixation) * P(flaw is not detected in second fixation) * P(flaw is not detected in third fixation) = (1 - p)³, we have P(C) = 0.91 + 0.1 * (1 - p)³.
e. It's important to note that all of these formulas assume certain conditions about the inspection process, such as the number of fixations and the probability of detecting a flaw in each fixation. These assumptions may not hold in all situations, so the results obtained from these formulas should be interpreted with caution.
The given problem deals with calculating the probability that an item is flawed given that it has passed inspection. Let us define the events, where D denotes the event that an item has passed inspection, and E denotes the event that the item is flawed.
Using Bayes’ theorem, we can calculate the probability that an item is flawed given that it has passed inspection. That is, P(E|D) = P(D|E) * P(E) / P(D). Here, P(D|E) is the probability that an item has passed inspection given that it is flawed. P(E) is the probability that an item is flawed. And, P(D) is the probability that an item has passed inspection.
Since the item is passed if a flaw is not detected in the first three fixations, we can find P(D|E) = (1 - p)³. Also, given that 10% of all items contain a flaw, we have P(E) = 0.1.
Now, to find P(D), we can use the law of total probability. P(D) = P(item is not flawed and passes inspection) + P(item is flawed and passes inspection). This is further simplified to (1 - 0.1) * 1 + 0.1 * (1 - p)³.
Finally, we have P(E|D) = (1 - p)³ * 0.1 / [(1 - 0.1) * 1 + 0.1 * (1 - p)³], where p = 0.5. Therefore, we can use this formula to calculate the probability that an item is flawed given that it has passed inspection.
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