a) The number of units that produces maximum profit is q = 12.
b) The price per unit that produces maximum profit is p = $39.
c) The maximum profit is P = $386.
What is profit?
a) To find the number of units that produces maximum profit, we need to find the point where revenue equals cost. The revenue function is given by:
R(q) = pq = (63-2q)q = 63q - 2q²
The cost function is given by:
C(q) = 70 + 15q
The profit function is given by:
P(q) = R(q) - C(q) = (63q - 2q²) - (70 + 15q) = -2q² + 48q - 70
To find the number of units that produces maximum profit, we take the derivative of the profit function with respect to q, and set it equal to zero:
P'(q) = -4q + 48 = 0
Solving for q, we get:
q = 12
Therefore, the number of units that produces maximum profit is q = 12.
b) To find the price per unit that produces maximum profit, we substitute q = 12 into the price function:
p = 63 - 2q = 63 - 2(12) = 39
Therefore, the price per unit that produces maximum profit is p = $39.
c) To find the maximum profit, we substitute q = 12 and p = 39 into the profit function:
P = -2q² + 48q - 70 = -2(12)² + 48(12) - 70 = $386
Therefore, the maximum profit is P = $386.
To know more about profit , visit:
https://brainly.com/question/28061772
#SPJ1
A discounted amusement park ticket costs $44 dollars, which is $12.95 less
than the original price p. Write and solve an equation to find the original
price.
Answer:
p-(p*.2274)
Step-by-step explanation:
P is the original price
P multiplied by .2274 gives the discount that's taken off
So the answer is P minus the discounted sum
1) Find the minimum and maximum values for the function with the given domain interval.
c(x) = √x, given 1/121 <_x<_17
Answer:
√17 good luck
Step-by-step explanation:
The function c(x) = √x is a continuous and increasing function over the interval [0, ∞), which means that its minimum and maximum values on the given domain interval [1/121, 17] will occur at its endpoints.
At x = 1/121, we have c(1/121) = √(1/121) = 1/11.
At x = 17, we have c(17) = √17.
Therefore, the minimum value of c(x) on the given domain interval is 1/11, and the maximum value is √17.
Which lines best approximate the directrices of the
ellipse? Round to the nearest tenth.
O x= -4.6 and x = 4.6
O x = -3.5 and x = 3.5
O y=-4.6 and y = 4.6
O y = -3.5 and y = 3.5
Option A : The lines that best approximate the directrices of the ellipse are x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.
The directrices of an ellipse are lines that are equidistant from the two foci. In this case, the foci of the ellipse are located at (-5,0) and (5,0). The distance between the foci is 2c, where c is the distance from the center to a focus, and can be found using the equation [tex]c^2 = a^2 - b^2[/tex], where a and b are the lengths of the major and minor axes, respectively.
From the given diagram, we can see that the length of the major axis is 10 and the length of the minor axis is 8. Therefore, a = 5 and b = 4. The value of c can be found as follows:
[tex]c^2 = a^2 - b^2[/tex]
[tex]c^2 = 5^2 - 4^2[/tex]
[tex]c^2 = 9[/tex]
c = 3
Therefore, the directrices are the vertical lines that pass through (-5,-3) and (5,-3) and are equidistant from the foci. These lines are given by x = -5 and x = 5.
Therefore, the lines that best approximate the directrices of the ellipse are A. x= -4.6 and x = 4.6, which are the closest to x = -5 and x = 5.
To learn more about directrices please click on below link
https://brainly.com/question/16935223
#SPJ1
Which lines best approximate the directrices of the ellipse? Round to the nearest tenth.
A. x= -4.6 and x = 4.6
B. x = -3.5 and x = 3.5
C. y=-4.6 and y = 4.6
D. y = -3.5 and y = 3.5
HELP PLEASE ANYONE !!HELP!!PLEASE :(
Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
What is meant by events?
In probability theory, an event is a set of outcomes or results that can occur when performing a random experiment. An event can consist of a single outcome or multiple outcomes, and it is defined as a subset of the sample space of the random experiment.
1.Rolling a dice and flipping a coin are two independent events. The probability of rolling any particular number on a dice is 1/6, and the probability of flipping heads on a coin is 1/2. Since the outcome of rolling a dice does not affect the outcome of flipping a coin and vice versa, these events are considered independent.
2.Spinning two spinners each round are independent events. The probability of each spinner landing on a particular section is fixed, and the outcome of one spinner does not affect the outcome of the other spinner. Therefore, these events are considered independent. The probability of the first spinner landing on a specific section and the second spinner landing on another specific section at the same time is the product of their individual probabilities.
3.Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. In the beginning, there are 12 S tiles and 9 M tiles in the bag. The probability of drawing an S tile is initially 12/21 or 4/7. If an S tile is drawn first, the number of S tiles in the bag decreases to 11, and the probability of drawing an M tile on the second draw becomes 9/20. Therefore, the probability of drawing an S tile and then an M tile is (4/7) x (9/20) = 18/70 = 9/35.
4.Pulling a candy, eating it, and then pulling another out of a bag are dependent events. Initially, there are a certain number of candies in the bag. After one candy is drawn and eaten, the number of candies in the bag decreases, affecting the probability of drawing a specific candy on the second draw. Therefore, these events are considered dependent.
Therefore, Rolling a dice and flipping a coin are two independent events. Spinning two spinners each round are independent events. Grabbing an S out of the scrabble bag and then grabbing an M are two dependent events. Pulling a candy, eating it, and then pulling another out of a bag are dependent events.
To learn more about events visit:
https://brainly.com/question/29280399
#SPJ1
Find the interest on deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016
The simple interest on a deposit of 3650 from 3 January 2016 at the rate of 10% p.a up to 17 March 2016 is given as follows:
$7.4.
How to obtain the balance using simple interest?The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are listed and explained as follows:
A(t) is the final balance.P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time in years.The interest accrued is modeled as follows:
I(t) = Prt.
The parameter values for this problem are given as follows:
P = 3650.r = 0.1.t = 74/365 -> there are 74 days from Jan 3 2016 to March 17 2016.Then the interest accrued is given as follows:
I = 365 x 0.1 x 74/365
I = $7.4.
More can be learned about simple interest at https://brainly.com/question/20690803
#SPJ1
3 workers can do a job in 28 hours, how many more workers are needed to complete the job in 12 hours
Answer:
7 workers are required, so we need 7-3 or 4 more workers.
Step-by-step explanation:
can somebody please help me with these problems !
Answer:
divide figure in many parts.
Then, find volume of each divided figure :- v= l*b*h
Then add volume of all divided figure
Given the graph of y = a sin b(x + c) +d, determine the amplitude.
A -1
C 6
B
3
D 12
- 27
9 Y
2T
Answer:
Step-by-step explanation:
The general equation for a sinusoidal function of the form y = a sin b(x + c) + d is:
a is the amplitude (the maximum displacement from the midline).
b determines the period (the distance between two consecutive peaks or troughs).
c is the horizontal shift (the amount by which the graph is shifted horizontally).
d is the vertical shift (the amount by which the graph is shifted vertically).
From the given information, we can see that:
The amplitude is not given.
b = 3, which means the period is 2π/3.
c = 6, which means the graph is shifted 6 units to the left.
d = 9, which means the graph is shifted 9 units up.
Since the amplitude is not given, we need to look at the graph to determine it. However, the graph is not provided, so we cannot determine the amplitude with the given information.
GIVING BRAINLIEST look at image and please fill the blanks !
Answer:
see the attachment
Step-by-step explanation:
A convenience store sold 14 half-gallon containers of milk and 28 quars of orange juice. Write a sentence comparing the total number of gallons of milk sold to the total number of gallons of orange juice sold. Explain how you know that your comparison is correct without multiplying.
Who ever answers nicely gets 40 points
Answer:
The total number of gallons of milk sold is equal to the total number of gallons of orange juice sold. This is because there are 2 quarts in a half-gallon, so the 14 half-gallon containers of milk sold is equal to 28 quarts. Therefore, the total amount of milk sold is the same as the total amount of orange juice sold, which is 28 gallons.
Sloan Transmissions, Inc., has the following estimates for its new gear assembly project: price = $1,700 per unit; variable costs = $480 per unit; fixed costs = $4.1 million; quantity = 95,000 units. Suppose the company believes all of its estimates are accurate only to within :t15 percent. What values should the company use for the four variables given here when it performs its best- case scenario analysis? What about the worst-case scenario?
The company should use the following values: Price per unit = $1,445; Variable costs per unit = $552; Fixed costs = $4.715 million ; Quantity = 95,000 units.
what is variables ?In algebra, a symbol (typically a letter) is used to represent an undetermined quantitative score in an expression or algebraic expression. Simply put, a variable is a number that may be changed yet remains fixed. Categorical and numeric variables are the two main types of variables. Then, discrete or continuous categories are made for each category for numerical and categorical variables, respectively. An overview of various types is given in this section. a metric that has a wide range of possible values. Something that can change; a variable's sign; an element of a science experiment that could vary.
To perform a best-case and worst-case scenario analysis, we need to adjust the estimates for each variable based on the given percentage error of 15%.
Best-case scenario analysis:
Price per unit = $1,700 + (15% x $1,700) = $1,955
Variable costs per unit = $480 - (15% x $480) = $408
Fixed costs = $4.1 million - (15% x $4.1 million) = $3.485 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Worst-case scenario analysis:
Price per unit = $1,700 - (15% x $1,700) = $1,445
Variable costs per unit = $480 + (15% x $480) = $552
Fixed costs = $4.1 million + (15% x $4.1 million) = $4.715 million
Quantity = 95,000 units (no adjustment needed as it is a fixed quantity)
Therefore, for the best-case scenario, the company should use the following values:
Price per unit = $1,955
Variable costs per unit = $408
Fixed costs = $3.485 million
Quantity = 95,000 units
And for the worst-case scenario, the company should use the following values:
Price per unit = $1,445
Variable costs per unit = $552
Fixed costs = $4.715 million
Quantity = 95,000 units
To know more about variable visit :-
https://brainly.com/question/2466865
#SPJ1
Solve the arithmetic operation.
4* 3+9-8 ^ 3 %4+9*4
Answer: 57
It won't let me show the steps, since I've already edited my answer once...
Find the length of the arc. Round answer to nearest tenth show work pls no.2
Using the length of the arc formula we get the arc's length to be 57.33rad.
Define length of an arc?The following formulas can be used to determine a circle's arc length: Arc Length = r, where r is the radius of the circle and is the central angle that the arc subtends.
When is expressed in radians, this formula is employed. Arc Length is equal to (/180) r, where r is the radius of the circle and is the central angle that the arc subtends.
In the question,
Radius of the circle = 11ft.
Angle created by the arc = 300°.
We need the length of the arc.
Length of the arc = S= 2πr×(θ/360) °
S = 2 × 3.14 × 11 × 300/360
= 57.33 rad
To know more about length of arc, visit:
https://brainly.com/question/16403495
#SPJ1
please help…………………………….
The shaded area above the line y = -x + 3 and below the line -2x + y = -1 is the solution region of the system that is option A.
What is graph?A graph is a visual representation of data or mathematical concepts. It is a diagram that shows how variables or quantities relate to each other, often using points, lines, bars, or other symbols. In mathematics, a graph can be used to represent a set of points or a function, where the x-axis represents the input values and the y-axis represents the output values. A graph can show the shape of a function, its range, its domain, and other important features.
Here,
To graph the system, we can first graph the boundary lines of the two inequalities.
For the first inequality, y > -x + 3, we can draw the line y = -x + 3 and shade the area above the line. This is because the inequality is y > -x + 3, which means that all points above the line satisfy the inequality.
Next, for the second inequality, -2x + y < -1, we can draw the line -2x + y = -1 and shade the area below the line. This is because the inequality is -2x + y < -1, which means that all points below the line satisfy the inequality.
To know more about graph,
https://brainly.com/question/29070347
#SPJ1
Rearrange b=4+5g2 to make g the subject
Answer:
b-4/5×2 =g
Step-by-step explanation:
if u wrote down the equation correctly
Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches. Which statement describes the meaning of the MAD in this situation?
The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.
Mean absolute deviation:The absolute deviation is a measure that quantifies the average deviation of data points from a central point, which can be any point in the data set such as the mean, median, or mode.
Typically, the mean is used as the central point. The formula to calculate the mean absolute deviation (MAD) involves finding the average of the absolute deviation (distance) of each data point from the mean of the data set.
Here we have
Melinda planted 18 tomato seeds on the same day. She then measured each plant 7 weeks later and determined that the mean stem length was 8 inches with a mean absolute deviation (MAD) of 2.4 inches
In this situation, the MAD of 2.4 inches means that on average, the stem length of each tomato plant deviated from the mean stem length of 8 inches by 2.4 inches.
Therefore,
The mean absolute deviation gives an idea of how spread out the data is from the mean, indicating that the stem lengths of the tomato plants are varying considerably.
Learn more about Mean Absolute Deviation at
https://brainly.com/question/10528201
#SPJ9
Valeria conducted a survey at the local mall. She
sat and counted 50 people exiting the mall and
noted how many of them were carrying bags of
things they purchased. Using this information,
predict how many of the 4,800 visitors to the
mall on this day purchased something.
With Bag
37
Without Bag
13
We can use the proportion of people carrying bags from the sample of 50 people to estimate the number of visitors who purchased something out of the total 4,800 visitors to the mall.
The proportion of people carrying bags in the sample is:
37/50 = 0.74
This means that 74% of the sample of 50 people were carrying bags.
To estimate the number of visitors who purchased something out of the total 4,800 visitors, we can multiply the proportion by the total number of visitors:
0.74 x 4,800 = 3,552
Therefore, we can predict that approximately 3,552 visitors out of the total 4,800 visitors purchased something on that day.
What is the slope of the line containing (–2, 5) and (4, –4)? A. -2 B. 1 C. 1/2 D. -1/2
The slope of the line on this graph with points (2, 5) and (4, 4) is equal to: D. =1/2.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (5 - 4)/(2 - 4)
Slope (m) = -1/2
In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to -0.5 or -1/2.
Read more on slope here: brainly.com/question/3493733
#SPJ1
Question Details
To earn full credit, you must show ALL
of your steps and calculation leading to
your solution. You will be assessed on
your mathematical communication, use
of mathematics and accuracy of your
results.
A rectangular prism and a square
pyramid were joined to form a
composite figure. What is the surface
area of the figure?
Concerns about climate change and C02 reduction have initiated the commercial production of blends of biodiesel eg from renewable sources and petrodiesel from fossil fuels. Random samples of 35 blended fuels are tested in a lab to ascertain the bio total carbon ratio
URGENT ANSWER BOTH A/B and C
The answer of the given question is (a) 95% of the sample means will fall within the interval from 0.9448 to 0.9512. (b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. (c) We used the central limit theorem to answer part (b).
What is Central Limit theorem?The central limit theorem is a fundamental concept in statistics that states that for a sufficiently large sample size, the distribution of the sample mean will be approximately normal, regardless of the distribution of the population from which the sample is drawn. This means that if we take repeated random samples from a population, the distribution of the means of those samples will approach a normal distribution, even if the population itself is not normally distributed.
(a) We can use the formula for the confidence interval of a mean:
σ is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.
Substituting the given values, we get:
CI = 0.9480 ± 1.96*(0.0060/√35)
CI = (0.9448, 0.9512)
Therefore, 95% of the sample means will fall within the interval from 0.9448 to 0.9512.
(b) The sampling distribution of X is approximately normal with μ = 0.9480 and σ = 0.0060/√35. This is because the central limit theorem states that for a sufficiently large sample size (n[tex]\geq[/tex]30), the sampling distribution of the sample mean will be approximately normal, regardless of the distribution of the population.
(c) We used the central limit theorem to answer part (b).
To know more about Confidence Interval visit:
https://brainly.com/question/17588303
#SPJ1
The fraction 3 8 is a multiple of what unit fraction?
Answer: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8
Step-by-step explanation:
The cost of renting a chain saw is $3.90 per hour plus $6.50 for a can of gas. Find the cost of using the chain saw for 7.5 hours.
Equation and Answer
Answer:
$35.75----------------------------
The total cost is the cost for a can of gas plus rental cost per number of hours.
So the total cost is:
6.50 + 7.5*3.90 = 6.50 + 29.25 = 35.753. Create a graph that shows three linear relationships with different y-intercepts using
the following slopes, and write an equation for each line.
Slopes:
●
5/5 5/5 115
3
y
Setting x = 0, we get the y-intercept: y = 31/5. So, the equation of the line is y = 6/5x + 31/5.
What does line intersect?In geometry, a line intersect is a point where two or more lines cross or meet. When two lines intersect, they share a single point in common, which is called the point of intersection. This point of intersection is the solution to the system of equations formed by the two lines.
by the question.
To find different y-intercepts using the given slopes, we need to use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. To find the y-intercept, we can set x = 0 and solve for y.
For slope 1/5, let's choose the point (2, 3) on the line. Using the point-slope form, we get:
y - 3 = 1/5(x - 2)
y - 3 = 1/5x - 2/5
y = 1/5x + 13/5
Setting x = 0, we get the y-intercept: y = 13/5. So, the equation of the line is y = 1/5x + 13/5.
For slope 3/5, let's choose the point (4, 2) on the line. Using the point-slope form, we get:
y - 2 = 3/5(x - 4)
y - 2 = 3/5x - 12/5
y = 3/5x + 8/5
Setting x = 0, we get the y-intercept: y = 8/5. So, the equation of the line is y = 3/5x + 8/5.
For slope 6/5, let's choose the point (-1, 5) on the line. Using the point-slope form, we get:
y - 5 = 6/5(x + 1)
y - 5 = 6/5x + 6/5
y = 6/5x + 31/5
To learn more about point-slope:
https://brainly.com/question/837699
#SPJ1
noah is filling a tank with water at a constant rate of 0.5 gallons per minute. what is the rate of filling in minutes per gallon?
Noah is consistently adding 0.5 gallons of water every minute to a tank. 2 minutes are spent filling a gallon.
The rate of filling is the amount of water that is filled per unit of time. In this instance, Noah is consistently adding 0.5 gallons of water each minute to the tank.
To determine the rate of filling in minutes per gallon, we can simply take the reciprocal of the rate of filling in gallons per minute.
That is:
Rate of filling in minutes per gallon = 1 / Rate of filling in gallons per minute
So, the rate of filling in minutes per gallon is:
1 / 0.5 gallons per minute = 2 minutes per gallon
Therefore, Noah is filling the tank at a rate of 2 minutes per gallon.
To learn more about the rate of filling, refer:-
https://brainly.com/question/19451577
#SPJ1
What is 2/3 of a full rotation
Answer:
240°
Step-by-step explanation:
A full rotation is 360°
2/3 x 360 = 240
Helping in the name of Jesus.
someone please help me. alg 2. spam comments will be reported and deleted.
Answer:
hope this helps
Step-by-step explanation:
The equation of a line is y=1/4x-2. What is the equation of the line that is parallel to the first line and passes through (4, –2)?
A. y=-4x+14
B. y=-1/4x-1
C. y=-4x+3
D. y=1/4x-3
Two parallel lines have the same slope, so we need to find the slope of the first line y = (1/4)x - 2, and then use it to find the equation of the parallel line that passes through (4, -2).
The slope of the first line is 1/4, so the slope of the parallel line will also be 1/4.
Using the point-slope form of the equation, we can write the equation of the parallel line as:
y - (-2) = (1/4)(x - 4)
Simplifying this equation, we get:
y + 2 = (1/4)x - 1
Subtracting 2 from both sides, we get:
y = (1/4)x - 3
Therefore, the equation of the line that is parallel to y = (1/4)x - 2 and passes through (4, -2) is y = (1/4)x - 3, which is option D.
find the length of BC
The length of line BC as shown in the diagram below is 5√3.
What is length?
Length is the distance between two points.
To calculate the length of Line BC, we use the formula below.
Formula:
BC = AC×sin∅............................... Equation 1Where:
∅ = Angle facing line BCFrom the diagram,
Given:
AC = 10∅ = 60°Sin60° = √3/2Substitute these values into equation 1
BC = (10×√3/2)BC = 5√3Hence, BC is 5√3.
Learn more about length here: https://brainly.com/question/28108430
#SPJ1
Can you please help me with this problem
Answer:
X = 35°
Y = 72.5°
Step-by-step explanation:
x is vertically opposite to 35° so x = 35°
35 × 2 = 70
360 - 70 = 290
290 / 4 = 72.5
Y = 72.5°
Answer:
x = 35
y = 72.5
Step-by-step explanation:
At your level, it is assumed that those lines are straight. Keeping this in mind, we can find the answer to this problem.
First, we have to find x.
x = 35º because opposite angles are equal (xº is opposite to 35º).
Then, we have to calculate y.
You should know that angles in a straight line add up to 180º.
So: yº + yº + 35º = 180º
You know have to solve this equation (solve for y).
y + y + 35 = 180
y + y = 180 - 35
y + y = 145
2y = 145
y = 145 / 2
y = 72.5
Check: 72.5 + 72.5 + 35 = 180
A cup of water holds about 8 ounces is a recipe calls for 1/3 cup of water which is the best estimate of the number of ounces that are needed draw a bar diagram if necessary
Answer:
One-third cup of water is equivalent to approximately 2.67 ounces (8 ounces divided by 3).
Here is a bar diagram to illustrate this:
|
|
|
|
|
|
|
|______
2.67 oz
In this diagram, the vertical line represents the total amount of water in the cup (8 ounces), and the shaded portion represents the 1/3 cup of water needed for the recipe, which is approximately 2.67 ounces.
Answer:
1/3 cup is approximately equal to 2.67 ounces
Explanation:
In cooking and baking, recipes often use measurements that are different from the standard units of measurement used in daily life. One such measurement is the cup, commonly used to measure liquids like water, milk, and oil. A cup of water typically equals 8 fluid ounces in the United States.
If a recipe calls for 1/3 cup of water, we need to convert this measurement into ounces to know how much water is needed. To do this, we can use the fact that 1 cup is equal to 8 ounces.
To convert 1/3 cup to ounces, we can multiply the number of cups by the number of ounces in one cup. That is:
1/3 cup * 8 ounces/cup = 8/3 ounces
However, 8/3 ounces is not a convenient number to work with, so we need to round it to a more practical value. One reasonable approximation for 8/3 is 2.67. Therefore, we can say that 1/3 cup equals approximately 2.67 ounces.
This approximation is reasonable because it is close to the exact value of 8/3 ounces. Using 2.67 ounces as an estimate for 1/3 cup of water in a recipe should provide a good approximation of the water needed.