A company's profit is described by the equation P(x)=-5x^2+300x+15,000
Where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?
A)$20
B)$30
C$50
D$60
The company charge for the product to generate a maximum profit is $30. Then the correct option is B.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A company's profit is described by the equation
[tex]\rm P(x)=-5x^2+300x+15000[/tex]
Where x is the price in dollars that the company charges for its product.
Differentiate the equation with respect to x.
[tex]\rm \dfrac{dP(x)}{dx}=-10x+300[/tex]
For the maximum price
[tex]\rm \dfrac{dP(x)}{dx} = 0\\[/tex]
Then we have
[tex]\begin{aligned} \rm -10x+300 &= 0\\\\\rm 10x &= 300\\\\\rm x &= 30 \end{aligned}[/tex]
Then the company charge for the product to generate the maximum profit is 30 dollars for each.
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The center circle of a soccer field prohibits a defender from being near the ball at the start or restart of a soccer game. On a professional soccer field this circle is 20 yards in diameter. Find the area of this circle. Show work or explain how you found your answer.
The area of the center circle on a professional soccer field, which has a diameter of 20 yards, is calculated using the formula for the area of a circle. The calculated area is approximately 314.16 square yards.
Explanation:To find the area of the center circle on a soccer field, we use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius of the circle. Given that the diameter of the circle is 20 yards, the radius (which is half of the diameter) would be 10 yards. Therefore, substituting 10 for r in the formula gives A = π(10)^2.
Performing the calculations, we find that A = π(100), which equals 314.16 square yards, using 3.1416 as the approximation for σ. Hence, the area of the center circle on a professional soccer field is approximately 314.16 square yards.
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Jamie was surveying students about their use of the new computer lab in a school. Which question in the survey is a STATISTICAL QUESTION?
A.) How qualified is the trainer at the computer lab?
B.) Where is the computer lab located in the school?
C.) What is the number of learning stations at the computer lab?
D.) How many class projects did you complete using the computer lab?
Answer with explanation:
To know the use of Computer Lab in the School
A Survey has been done.Out of the four Question asked,
The education of the trainer in the computer Lab does not come into consideration,to know the use of computer lab in the school, the use of computer lab can be known only by whether students are getting well versed with Computer and it's applications or not.
Number of Learning Stations in the computer lab, also can't tell the use of computer Lab in the school, because we have to check knowledge of the students about computers to know the better use of the Lab.
So, number of Class projects, or in my own words A test on computer awareness and It's software tools will be a better survey Question.
Option D is the question in the survey is a STATISTICAL QUESTION.
(D) How many class projects did you complete using the computer lab?
A ladder is leaning against a building and makes 42° angle with the ground. The top of the ladder reaches 30 feet up on the building. What is the length of the ladder?
The length of the ladder will be 44.8 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
A ladder is leaning against a building and makes a 42° angle with the ground.
The top of the ladder reaches 30 feet up on the building.
Let the length of the ladder be L.
Then the length of the ladder is given by the sine of angle 42°.
sin 42° = 30 / L
L = 30 / sin 42°
L = 30 / 0.699
L = 44.8 feet
The length of the ladder will be 44.8 feet.
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Help I don’t know the answer to this question
Solve 120000/1+48e^0.015t=24e^0.055t
From 9:00 AM to 12:00 PM, Linda's stock portfolio increased in value from $2,500 to $6,400. If Linda's portfolio continues to grow at this rate, how much will it be worth at 2:30 PM?
What is the volume of a cube with an edge length of 3.2 meters?
Enter your answer as a decimal
___ cm^3
Nora created a flag that was shaped by the triangle below.
'\
' \
5in. ' \
' \
'-----------
12in
What is the measure of the third side of the triangle?
A.13in
B.14in
C.17in
D.16in
how many 1 cup servings can be poured from 1 gallon of milk?
Eric goes for a walk every night after work. A map of the route has a scale of 1:20,000, in cm.
If Eric walked 1.2 kilometers on Monday night, how many cm is the route on the map?
susan surveys 20 people in her math class to find out the most popular movie. 5 students say star wars if the are 200 students in the total 7th grade using a proportion find out how many students susan would expect to like Star Wars
Answer:
50 people
Step-by-step explanation:
please rate and thank
What is the probability that her keys have landed within the forest?
Answer:
0.8
Step-by-step explanation:
egde
Name the algebraic property that is being shown in the example: 4(x+3) = 4x + 12
I need help trying to find the vertex y=2x^2 + 12x +26
Find the greatest common factor of 8a 3 b 2 and 12ab 4.
Answer:
4ab²
Step-by-step explanation:
The two expressions are given as 8a³b² and 12ab⁴
Now factors of 8a³b² = 2 × 2 × 2 × a × a × a × b × b
and factors of 12ab⁴ = 2 × 2 × 3 × a × b × b × b × b
Now greatest common factor will be 2 × 2 × a × b × b
= 4ab²
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The track-and-field coach wants to know whether the students in the entire school prefer track races or field events. The coach draws a random sample from the following groups:
All students in each grade
All teachers in the school
All boys in each grade in the school
All students on the track-and-field team
Which group best represents the population she should take a random sample from to get the best results for her survey? (5 points)
{A} All students in each grade
{B} All teachers in the school
{C} All boys in each grade in the school
{D} All students on the track-and-field team
The track-and-field coach should select the group which contains all students in each grade to take a random sample to get the best results for her survey.
We have a situation in which track-and-field coach wants to know whether the students in the entire school prefer track races or field events. In order to do so she draws a random sample from the following groups:
• All teachers in the school
• All boys in each grade
• All students in the track-and-field team
• All students in each grade
We have to find the best group from which she should take a random sample of the above mentioned to get the best results for her survey.
What is the condition for Set A to be a Superset of Set B?Set A is superset of Set B if Set A contains all the elements of Set B.
In our question, we have four groups in the form of four sets as -
• Set of all teachers in school (say Set T)
• Set of all boys in each grade (say Set B)
• Set of All students in track-and-field team (Say Set C)
• Set of all students in each grade (Say Set S)
Since the art teacher wants to know the opinion of students, therefore Set T is not correct. Set B contains all boys in each grade, but it would exclude the girls in each grade, therefore it is also not correct. Set C consists of all students in track-and-field team, but it would exclude students who are not in track and field team, therefore incorrect. Set S consist of all Students in each grade, this means that Set S is the superset of Set B and Set C and contains all the students of the school.
Hence, the group that contains all students in each grade should be selected to take a random sample to get the best results for her survey.
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Over the last 4 years, Michael has earned $240 interest on an initial investment of $2,000. What simple annual interest rate is the bank paying on this account?
Answer:
3%
Step-by-step explanation:
Find two square roots of 36.
Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus? 24 square units 28 square units 32 square units 48 square units
Rhombus WXYZ is graphed on a coordinate plane.
What is the area of the rhombus?
24 square units
28 square units
32 square units
48 square units
Answer:
24 square units
Step-by-step explanation:
A simulated game of chess is programmed between two computers. The game is supposed to be biased in favor of player B winning 4 out of 5 times. Which is the most suspicious set of outcomes of 30 games played between the two computers?
AABABBBABBBBBBBBABBBABBBBBBBBA
ABBABBAABBBBBABBBBBBBBBBBBBABB
ABBABABABABBABABABABABABABABAA
ABBABBBABBBBBBBBABBBABBBBBBBBB
Answer:
ABBABABABABBABABABABABABABABAA
Step-by-step explanation:
Player B is supposed to be winning 4 out of 5 times. This means that Player A is supposed to win 1 out of 5 times.
This means out of 30 games, player A should win roughly 1/5(30) = 6 times.
In the first list, player A wins 7.
In the second list, player A wins 6.
In the third list, player A wins 15. This is much different.
In the fourth list, player A wins 5.
How to solve these kind of questions.
if d=2, what is the value of 8/(4-d)
The value of the expression 8/(4-d) when d = 2 is 4.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
We have the expression,
8/(4-d)
And here, d = 2.
Substituting the value of d to the expression,
8/(4-d),
= 8/(4-2)
= 8/(2) {using simple division}
= 4
Therefore, 4 is the value of the expression.
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Cereal companies often advertise with statements like "collect all 8 dinosaurs" or "one in each specially marked box." Assume that the company sells an equal number of boxes with each type of dinosaur. If you wanted to collect all eight dinosaurs, does this mean that you will only have to purchase eight boxes of cereal? This investigation will help you better understand how theoretical probability compares to experimental probability.
Here are your goals: Use a simulation to determine the experimental probability of a problem. Compare and contrast the theoretical probability with the experimental probability.
What is the true solution on 2 in e ^in 5x=2 in 15
Can you find the measure of angle PVQ for 30 points?
A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question.
Confidence Level
90%
95%
99%
z*-score
1.645
1.96
2.58
Remember, the margin of error, ME, can be determined using the formula mc021-1.jpg.
128.75 to 147.25
130.98 to 145.02
132.10 to 143.90
137.38 to 138.62
Using the z-distribution, it is found that the 90% confidence interval for the population mean is: 132.10 to 143.90.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The other parameters are given as follows:
[tex]\mu = 138, \sigma = 34, n = 90[/tex]
Hence, the bounds of the interval are given by:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 138 - 1.645\frac{34}{\sqrt{90}} = 132.1[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 138 + 1.645\frac{34}{\sqrt{90}} = 143.9[/tex]
The 90% confidence interval for the population mean is: 132.10 to 143.90.
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A small refrigerator is a cube with a side length of 14 inches. Use the formula S = 6s2 to find the surface area of the cube.
On a map with a scale of 2 cm = 1km, the distance from Beau's house to the beach is 4.6 centimeters. What is the actual distance?
2.3
since 2 cm=1k you divide by 2
Over the period of one month 159 dogs visited the dog park. Suppose the same number of dogs visited each month for 1 year. How is this total different from the year before 95 dogs visited the dog park every 3 months for the year? Show your work and explain how you got your answer. WILL MARK BRAINLEST!!!!!!
Final answer:
The total number of dogs visiting the park in the current year, assuming 159 dogs visit each month, is 1,908 dogs/year. The previous year, with 95 dogs visiting every 3 months, saw 380 dogs/year. Hence, there are 1,528 more dogs visiting the park in the current year.
Explanation:
Calculating the Total Annual Number of Dogs Visiting the Dog Park
To calculate the total number of dogs visiting the dog park over the course of a year for the current period, we simply multiply the number of dogs that visit each month by the total number of months in a year. For the previous year, we will add up the number of dogs visiting every three months and then determine the difference between the two annual totals.
Current Period Calculation:
Number of dogs visiting each month: 159 dogsNumber of months in a year: 12 monthsTotal dogs visiting in the current year = 159 dogs/month * 12 months/year = 1,908 dogs/yearPrevious Year Calculation:
Number of dogs visiting every 3 months: 95 dogsNumber of 3-month periods in a year: 4Total dogs visiting in the previous year = 95 dogs/3 months * 4 (3-month periods) = 380 dogs/yearNow, we find the difference between the two annual totals:
Difference = Current year total - Previous year totalDifference = 1,908 dogs/year - 380 dogs/yearDifference = 1,528 dogs/yearThe total number of dogs visiting the park in the current year is 1,528 dogs more than the previous year.