The maximum total profit is $21,150. To find the maximum total profit, we need to determine the optimal values for price (P) and quantity (Q) that maximize profit. Profit is calculated by subtracting the total cost (TC) from the total revenue (TR).
The total revenue (TR) is given by the product of price and quantity: TR = P * Q.
The total cost (TC) is given by the equation: TC = 400 + 90Q + 2000.
We can substitute the demand function into the total revenue equation to express profit (π) as a function of Q:
π = TR - TC = (P * Q) - (400 + 90Q + 2000)
π = 20PQ - 90Q - 2400.
To find the maximum total profit, we differentiate the profit function with respect to Q and set it equal to zero:
dπ/dQ = 20P - 90 = 0.
Solving this equation, we find that P = 90/20 = 4.5.
Substituting P = 4.5 back into the demand function, we can find the optimal value of Q:
20P + Q = 5000,
20(4.5) + Q = 5000,
90 + Q = 5000,
Q = 5000 - 90,
Q = 4910.
Therefore, the optimal values for price and quantity are P = 4.5 and Q = 4910, respectively. To find the maximum total profit, we substitute these values back into the profit function:
π = 20PQ - 90Q - 2400
π = 20(4.5)(4910) - 90(4910) - 2400 = $ 21,150.
Hence, the maximum total profit is $21,150.
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20 points question: Please Help!!!! Need Explanations as well. No Links!
Answer: C
Because if you put then in order(1,3,3,4,9) you will see that once you cross them off the last one will be 3 which would be the median and the answer.
if joan reads 96 pages in 4 hours how long will it take her to read 240
Answer:
10 hours to readm240
Step-by-step explanation:
Answer:
10 hours.
Step-by-step explanation:
If you divide 96 by 4, you get 24. Then divide 240 by 24, and you get 10.
how would you rewrite f(x)f(x)f, (, x, )so it can be differentiated using the product rule?
Answer:
d/dx f(x)f(x) = d/dx f(x) + d/dx f(x)
Step-by-step explanation:
An example of the product rule is the following:
d/dx u*v = du/dx u + dv/dx v
Another way of interpreting this is that the product rule states that the derivative of a product is the derivative of the sum of the products with respect to their terms.
Solve inequality for x. 2x(2x-1)-5x<4x^2-x
The inequality of (2x1)2x5x4x can be solved by determining that x>0.
How does inequality work?In mathematics, a statement of the order connection between two integers equivalent algebraic expressions that is greater than, equal to or greater to, less than, or lower than or equal to is referred to as an inequality.
According to the given data:(2x−1)2x−5x<4x +2−x
To multiply 2x-1 by 2, use the distributive property.
(4x−2)x−5x<4x + 2 −x
multiplying 4x-2 to x using the distributive property.
4x + 2 −2x−5x<4x + 2 −x
-2x and -5x together provide 7x.
4x + 2 −7x<4x + 2 −x
Subtract 4x + 2 by both sides.
4x + 2 −7x−4x + 2 <−x
Combine 4x + 2 and −4x + 2 to obtain 0.
−7x<−x To both sides, add x.
−7x+x<0
7x and x together yield 6x.
−6x<0
The product is 0 if any of the two numbers in it is greater than 0 and the other is 0 as well. 6 > 0, indicating that x would have to be greater than 0.
x>0
The Inequality of (2x−1)2x−5x<4x is x>0
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Which measure would you use to describe central tendency for qualitative data?.
When describing the central tendency for qualitative data, the measure that is commonly used is the mode.
Unlike quantitative data, where measures such as the mean or median can be used to describe central tendency, qualitative data consists of categories or labels rather than numerical values.
Therefore, the mode is the most appropriate measure for central tendency in this context.
The mode can be useful in summarizing qualitative data by identifying the most common category or response. It provides insight into the most prevalent characteristic or attribute among the data, allowing for a better understanding of the distribution and patterns within the dataset.
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what is the square root of 6
Answer:
2.449
Step-by-step explanation:
the square root of 6 is about 2.449
Important When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: • Provide full solution, showing all of your steps. • Make sure that there is one step or idea per line.
• Use one equal sign per line.
• Make sure that equal signs line up vertically.
• Don't use self-developed short form notations. • Sketch (by hand, or with technology) a Distance - Time graph for each of the following scenarios:
1. A remote control car travels along a straight track at a constant speed of 2.0 m every second for 4 seconds and the suddenly stops for 3 seconds. It then travels 3 seconds backwards at 1.5 m per second. 2. An elevator travels from the lobby to the 36th floor in 45 seconds and stops for 15 seconds to let people off. It then descends (at the same rate) to the 28th floor, stops to let more people off (15 seconds), and returns to the lobby (at the same rate). How long does it take the elevator do complete this trip?
The total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds i.e., it takes the elevator 135 seconds to complete the entire trip.
The remote control car travels forward for 4 seconds at a speed of 2.0 m/s, then stops for 3 seconds, and finally travels backward for 3 seconds at a speed of 1.5 m/s.
The elevator travels from the lobby to the 36th floor in 45 seconds, stops for 15 seconds, descends to the 28th floor, stops for 15 seconds again, and returns to the lobby.
The total time taken by the elevator to complete this trip is calculated by adding up the times for each segment.
For the remote control car, it travels forward at 2.0 m/s for 4 seconds, covering a distance of 2.0 m/s * 4 s = 8 meters.
It then stops for 3 seconds, and finally travels backward at 1.5 m/s for 3 seconds, covering a distance of 1.5 m/s * 3 s = 4.5 meters.
Therefore, the total distance covered by the car is 8 m + 4.5 m = 12.5 meters.
For the elevator, it takes 45 seconds to go from the lobby to the 36th floor, and it stops for 15 seconds to let people off.
Similarly, it takes 15 seconds to go from the 36th floor to the 28th floor, and another 15 seconds to let people off.
Finally, it takes 45 seconds to return from the 28th floor to the lobby.
Therefore, the total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds.
In conclusion, it takes the elevator 135 seconds to complete the entire trip, including stops at different floors, based on the given information.
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What is a power of 3 equation called?
A power of 3 equation is called as cubic equation.
The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here we need to find the term that has been used for power of 3 equation.
Here we have to know that the power of 3 equation is known as cubic equation.
in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.
As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.
The general form of the power of 3 equation is written as
=> ax³ + bx² + cx + d = 0
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Please help me ASAP. Need to hand in by today
Answer:
Heyyy. Glad to see someone from malaysia taking add maths hete. Hope this helps
he expected to have 15 customers each day. to answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha
To determine whether the number of customers, which is expected to be 15 each day, follows a uniform distribution, a chi-square test for goodness of fit should be performed with a specified significance level (alpha).
The chi-square test for goodness of fit is used to determine if observed data follows an expected distribution. In this case, we want to test whether the number of customers each day, which is expected to be 15, follows a uniform distribution.
To perform the test, we need to collect data on the number of customers over a period of time and compare it to the expected uniform distribution. The observed frequencies for each category (e.g., the number of days with 0 customers, 1 customer, 2 customers, etc.) would be obtained.
Then, the chi-square test statistic can be calculated based on the observed and expected frequencies. The test statistic measures the discrepancy between the observed and expected distributions.
To interpret the test results, we compare the calculated chi-square value to the critical chi-square value at the chosen significance level (alpha). If the calculated chi-square value exceeds the critical value, we reject the null hypothesis and conclude that the number of customers does not follow a uniform distribution. Conversely, if the calculated chi-square value does not exceed the critical value, we fail to reject the null hypothesis, indicating that the number of customers can be considered to follow a uniform distribution.
Please note that the specific calculations and decision-making process require additional data and the use of statistical software or tables to obtain the critical chi-square value.
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If a || b and e | f, what is the value of x?
a
b
(x - 3)
X=
Find the largest six digits number which is divisible by 120 exactly.
Answer:
999,960
Step-by-step explanation:
let x be a multiple of 120
120x ≤ 999,999
999,999 / 120 = 8333.325
8333 ≤ x ≤ 8334
8333(120) = 999,960
8334(1200) = 1,000,080 this is a 7-digit number
Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960
help help help PLEASEEEEE
Answer:
m=4b and b=4m
Step-by-step explanation:
this is the right answer
A recent report indicates that physically attractive people are also perceived as being more intelligent (Eagly, Ashmore, Makhijani, & Longo, 1991). As a demonstration of this phenomenon, a researcher obtained a set of 10 photographs, 5 showing men who were judged to be attractive and 5 showing men who were judged as unattractive. The photographs were shown to a sample of n = 25 college students and the students were asked to rate the intelligence of the person in the photo on a scale from 1 to 10. For each student, the researcher determined the average rating for the 5 attractive photos and the average for the 5 unattractive photos, and then computed the difference between the two scores. For the entire sample, the average difference was MD = 2.7 (attractive photos rated higher) with s = 2.00. Are the data sufficient to conclude that there was a significant difference in perceived intelligence for the two sets of photos? Use a two-tailed test at the .05 level of significance.
To determine if there was a significant difference in perceived intelligence between attractive photos and unattractive photos, we will conduct a two-tailed t-test at the .05 level of significance. Here's a step-by-step explanation:
1. State the null hypothesis (H0) and alternative hypothesis (H1):
H0: There is no significant difference in perceived intelligence between attractive and unattractive photos (MD = 0).
H1: There is a significant difference in perceived intelligence between attractive and unattractive photos (MD ≠ 0).
2. Determine the level of significance (α):
α = 0.05 for a two-tailed test.
3. Calculate the t-value:
For this test, we have the sample size (n = 25), the average difference between the two scores (MD = 2.7), and the standard deviation (s = 2.00). The formula for the t-value is:
t = (MD - 0) / (s / √n)
t = (2.7 - 0) / (2.00 / √25)
t = 2.7 / (2.00 / 5)
t = 2.7 / 0.4
t = 6.75
4. Determine the critical t-value:
Using a t-distribution table or calculator for a two-tailed test with α = 0.05 and 24 degrees of freedom (n - 1 = 25 - 1 = 24), the critical t-value is approximately ±2.064.
5. Compare the calculated t-value with the critical t-value:
Since our calculated t-value (6.75) is greater than the critical t-value (2.064), we reject the null hypothesis (H0).
In conclusion, the data are sufficient to conclude that there is a significant difference in perceived intelligence between attractive and unattractive photos, supporting the alternative hypothesis (H1). The attractive photos were rated higher in perceived intelligence compared to the unattractive photos at the .05 level of significance.
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Help rn please!!! Urgent
Answer:
try 3 i need 20 more letters
Answer:
f(x) = 2x^2 + 12x +10
Step by step solution:
x = 1 x = 5 y = 10
f(x) = a(x+1)(x+5)
f(0) = a(1)(5) = 10
5a = 10
Divide by 5
a = 2
f(x)= 2(x+1)(x+5)
f(x) = 2(x^2 +6x +5)
f(x) = 2x^2 + 12x +10
brainliest much appreciated!
The formula for the volume of a cylinder is V = r²h. What is the radius for a
cylinder that has a volume of 1607 m³ and a height of 8 m? Express your answer as a
decimal rounded to the nearest tenth.
The radius is
m.
The calculated radius of the cylidner when approximated is 8.0 meters
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, h is the height, and π is a constant approximately equal to 3.14.
To find the radius of a cylinder with volume 1607 m³ and height 8 m, we can rearrange the formula as:
r^2 = V / (πh)
Substituting the given values, we get:
r^2 = 1607 / (3.14 x 8)
r^2 ≈ 63.973
Taking the square root of both sides, we get:
r ≈ 8.0
Therefore, the radius of the cylinder is approximately 8.0meters.
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a firefighter must cut a 2,700 foot rope into 75 equal pieces how long will each be?
Answer:
36
Step-by-step explanation:
75/2700=36
5. Which of these sets contains all equivalent numbers?
Which value is the solution for this equation
2/3(6h-9)=6
A) -1
B) 1
C) 3
D) 5
Answer:
h = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
2/3(6h - 9) = 6
Step 2: Solve for h
[Division Property of Equality] Divide 2/3 on both sides: 6h - 9 = 9[Addition Property of Equality] Add 9 on both sides: 6h = 18[Division Property of Equality] Divide 6 on both sides: h = 3a university found that 30% of its students withdraw without completing the introductory statistics course. assume that students registered for the course. a. compute the probability that or fewer will withdraw (to 4 decimals). b. compute the probability that exactly will withdraw (to 4 decimals). c. compute the probability that more than will withdraw (to 4 decimals). d. compute the expected number of withdrawals.
The 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
Given that, a university set up that 30 of its scholars withdraw without completing the introductory statistics course.
Assume that 20 scholars registered for the course. cipher the probability that 2 or smaller will withdraw ( to 4 numbers).
cipher the probability that exactly 4 will withdraw( to 4 numbers).
cipher the probability that further than 3 will withdraw( to 4 numbers).
We've to cipher the anticipated number of recessions.
cipher the probability that 2 or smaller will withdraw,
a) To determine, given 2 scholars from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by
0.3) ²(0.7) ¹⁸
also, multiply this volume, we get
Which is the number of ways to choose 2 scholars from the aggregate of 20. thus, the probability that exactly 2 scholars withdraw is = 190(0.3)²(0.7)¹⁹
Following an process determine that
The probability that exactly 1 pupil withdraw is(0.3) ²(0.7) ¹⁹
The probability that exactly none scholars withdraw is 20 c0(0.7) = (0.7)²⁰
Eventually, the probability that 2 or smaller scholars will withdraw is0.355
b) cipher the probability that exactly 4 will withdraw.
Following the process explained in a), the probability that 4 pupil withdraw is given by0.1304
c) cipher the probability that further than 3 will withdraw,
First cipher the probability that exactly 3 scholars withdraw, which is given by0.07
also, using a) the probability that 3 or smaller scholars withdraw is0.03550.0716 = 0.1071.
thus the probability that further than 3 will withdraw is 1-0.1071 = 0.8929.
d) cipher the anticipated number of recessions.
Hence, The 30 of the scholars withdraw, also, the anticipated number of recessions is the 30 of 20 which is 6.
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In rhombus RSTU diagonals RT and US intersect at point V, m
The length of US in the rhombus is 16 units
How to determine the length of USThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
RT = 6x + 4
SO = 7x - 6
By the properties of rhombus, we have
RT = 2 * SO
So, we have
6x + 4 = 14x - 12
Evaluate the like terms
8x = 16
So, we have
x = 2
This means that
US = 6 * 2 + 4
US = 16
Hence, the length is 16 units
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Evaluate the expression. 7⋅4+6−12÷4
Answer:
31
Step-by-step explanation:
Answer: 31
Step-by-step explanation:
1. Multiply 28+6-12/4
2. Divide 28+6-3
3. Add 34-3
4. Subtract 31
which types of geometrical symmetry does a sphere have?
Ax^2+bx+c=(x+p)(x+q) What you know about p and q if c is less than 0. WILL MAKE BRAINLIEST!! If u provide EXPLANATION :)
Answer:
From what I know there is no q.
p=0 I put a slight explanation below.Hope it helps
Step-by-step explanation:
Ax^2+bx+c-p=x
Ax^2+bx+c-p-x=x-x
Ax^2+(b-1)x+c-p=0
Find all EXACT solutions of the equation given below in the interval \( [0,2 \pi) \). \[ \sec (x)=\frac{2}{\sqrt{3}} \] Note: If there is more than one answer, enter them in a list separated by commas
The exact solutions of the equation sec(x)= \(\frac{2}{\sqrt{3} }\) in the interval [0,2π) are \(x=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}\).
To find the solutions of the equation sec(x)= \(\frac{2}{\sqrt{3} }\) in the interval [0,2π), we need to determine the values of x that satisfy this equation.
The secant function is the reciprocal of the cosine function, so we can rewrite the equation as cos(x)= \(\frac{\sqrt{3} }{2}\) .
In the interval [0,2π), the cosine function is positive in the first and fourth quadrants, where its value is \(\frac{\sqrt{3} }{2}\).
In the first quadrant (where 0≤x<π/2), the solution is x=π/6.
In the fourth quadrant (where 3π/2≤x<2π), the solution is x=11π/6.
Since the cosine function has a period of 2π, we can add multiples of 2π to the solutions to find all the solutions in the interval [0,2π).
Adding 2π to each solution, we get x=5π/6 and x= 7π/6.
Therefore, the exact solutions of the equation sec(x)= \(\frac{2}{\sqrt{3} }\) in the interval [0,2π) are \(x=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}\).
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how many odd 4-digit integers (1,000—9,999) have distinct digits?
To determine the number of odd 4-digit integers with distinct digits, we can consider the following:
1. The thousands digit: It cannot be zero since the number should be a 4-digit integer.
2. The units digit: It must be an odd number (1, 3, 5, 7, or 9) to make the entire number odd.
3. The hundreds and tens digits: They can be any digit from 0 to 9, excluding the digits used for the thousands and units digits.
Let's break down the cases:
Case 1: Thousands digit
There are 9 options for the thousands digit (1 to 9) since it cannot be zero.
Case 2: Units digit
There are 5 options for the units digit (1, 3, 5, 7, or 9) since it must be an odd number.
Case 3: Hundreds digit
There are 8 options for the hundreds digit (0 to 9 excluding the digits used for thousands and units).
Case 4: Tens digit
There are 7 options for the tens digit (0 to 9 excluding the digits used for thousands, units, and hundreds).
Now, we can calculate the total number of possibilities by multiplying the number of options for each digit:
Total number of possibilities = 9 × 5 × 8 × 7 = 2520
Therefore, there are 2520 odd 4-digit integers with distinct digits in the range of 1,000 to 9,999.
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SOMEONE HELP ME PLZZZZZZZ
Femi and Hina are both travelling by train.
Femi's train travels 120 km in 90 minutes.
Hina's train travels 495 km.
It leaves at 12:05 and arrives at 17:35.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
59400
Step-by-step explanation:
charlie's teacher claims that he does not study and just guesses on exams. on an exam with 201 true-falsequestions, charlie answered 53.7% of the questions correctly. calculations using these results show that if hewere really just guessing, there would be roughly 1 chance in 7 that he would do this well. is there statisticallysignificant evidence against the teacher's claim that charlie is just guessing? why or why not?4
There is No statisti-cally signi-ficant evidence against the teacher's-claim that Charlie is just guessing because the probability is very low.
The total number of True-false questions are = n = 201.
The probability of getting a correct answer by guessing is = p = 0.5,
Charlie answered 53.7% = 0.537 of the questions correctly,
So, P(p' ≥ 0.537)
⇒ P(z ≥ (0.537 - 0.5)/√(0.5×0.5)/201,
⇒ P(z ≥ 1.05) = 1 - P(z < 1.05)
⇒ 0.1469
Since, the probability is very low,
Therefore, there is not any significant evidence against the teachers claim.
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The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of change between the points (–3, 0) and (–2, –5)?
x
y
–5
10
–4
5
–3
0
–2
–5
–5
Negative StartFraction 1 Over 5 EndFraction
One-fifth
5
Answer:
use the slope formula y2-y1/x2-x1 and you should get -5-0/-2+3= -5 which means the rate of change should be 5
Answer:
5
Step-by-step explanation:
An analyst for an online shopping site discarded an upper outlier and calculated that the mean number of minutes customers spent on the site was 23 and the median was 26. What effects are likely if the analyst decides to include the upper outlier in the calculations? Check all that apply.
The median will stay about the same.
The mean will stay about the same.
The median will decrease.
The mean will increase.
The median will increase.
Answer:
The median will stay about the same.
The mean will increase.
Step-by-step explanation:
yeh
If the analyst decides to include the upper outlier in the calculations then the effects are likely;
1. The median will stay about the same.
4. The mean will increase.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
It is given that an analyst for an online shopping site discarded an upper outlier and calculated that the mean number of minutes customers spent on the site was 23 and the median was 26.
If the analyst decides to include the upper outlier in the calculations then the effects are likely;
1. The median will stay about the same.
4. The mean will increase.
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