Answer: $6,600
Step-by-step explanation:
Given: The profit function is given by the equation:
[tex]y=-x^2+120x+3000[/tex],where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day.
To find the maximum profit, first we need to find critical point of the function.
For that, first differentiate the above function w.r.t. x, we get
[tex]y'=-2x+120[/tex]
Now, Put [tex]y'=0[/tex], we get
[tex]-2x+120=0\\\\\Rightarrow\ x=60[/tex]
Again differentiate the above function w.r.t. x, we get
[tex]y"=-2<0[/tex]
By second derivative test, at x=60 , attains its maximum value.
Now, the Maximum profit will be :
[tex]y=-(60)^2+120(60)+3,000=6,600[/tex]
Hence, the maximum profit that the company can make = $6,600
Tina can paint a room 1.5 times faster than Joey can. If they work together, they can paint a room in 6 hours. How long would it take the slower person working alone to paint the room?
match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.
B.
C.
D.
The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.
The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.
To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.
Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.
The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.
Considering these conditions, the correct answer is: D. x + 3y \<= 38, x + y \<= 12.
trignometry help what's the answer?
Which additional information is needed to solve this problem?
John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?
A.
total amount John can save in 1 week
B.
the cost of the game
C.
amount John earns per hour babysitting
Calculate the total cost of the order: Veggiburger with cola and soup, sales tax 4%, tip 15.
Veggiburger: $3.25
Cola: $1.50
Soup: $2.25
A $8.33
B $7.28
C $7.00
D $5.50
The cost of the order, including the sales tax of 4%, comes out to be $7.28. However, the tip is unclear in the question. If it's 15%, the cost rises to $8.37, but none of the provided options match this result.
Explanation:The first step is to calculate the total cost of the Veggiburger, cola, and soup by adding them together. So, $3.25 (Veggiburger) + $1.50 (cola) + $2.25 (soup) = $7.00. Next, apply the 4% sales tax on this amount which is $7.00 * 4/100 = $0.28. So the subtotal now is $7.28 ($7.00 + $0.28). Finally, the tip mentioned in the problem is not clear whether it is a percentage or a fixed amount. If it is a 15% tip, then calculate 15% of the subtotal, i.e $7.28 * 15/100 = $1.09 (Approx). Adding this to the subtotal we get $8.37 which is not an option in the given answers. If $15 is a fixed tip amount, the total cost would be substantially larger. Please ensure the tip amount is correct.
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QS is the perpendicular bisector of PR solve for x
2x - 20 = 70 - x
3x - 20 = 70
3x = 90
x = 30
Compute the stock turnover in dollars for a product that has sales of $6,000 and an average value of inventory investment of $1,500.
Answer: 4
Step-by-step explanation:
Given: Cost of product sold = $6,000
Average value of inventory= $1,500
We know that the inventory turnover formula is given by :-
[tex]\text{Inventory turnover}=\frac{\text{ Cost of product sold}}{\text{Average value of inventory}}[/tex]
[tex]\\\Rightarrow\ \text{Inventory turnover}=\frac{\$6,000 }{\$1500}\\\\\Rightarrow\ \text{Inventory turnover}=4[/tex]
Therefore, the stock turnover for a product that has sales of $6,000 and an average value of inventory investment of $1,500 = 4
HELP!!!!!!What is the equation of the graph below?
Find the surface area of the cylinder in terms of π.
See picture
a) 1008π in.2
b) 522π in.2
c) 360π in.2
d) 396π in.2
PLS HELP! Tanisha is planning a party. She will serve hamburgers, potato salad, strawberry shortcake, and lemonade. Including Tanisha, 28 people will be at the party. Tanisha expects that each person will drink two 8−ounce glasses of lemonade at the party, and makes 448 ounces of lemonade. Tanisha's mother buys 38 lemons. They know it takes 8 lemons to make 80 ounces of lemonade. Does Tanisha need more lemons?
Answer: 7 more lemons
Step-by-step explanation:
Since she needs 448 ounces of lemonade you have to divide which is 5.6 . As a result there are 5.6 80 ounces of lemonade. 80 ounces needs 8 lemons. 448 ounces of lemonade are needed 8 x 5.6 = 44.8 lemons. Tanisha only has 38 lemons, which isn't enough. 44.8 - 38 = is about 7 more lemons.
what is the value of the expression?
Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?
Answer:
its $7.20 on APEX
Step-by-step explanation:
someone please help asap! Which statement is most likely true for this distribution?
Answer:
C) The mean is greater than the median.
Step-by-step explanation:
This distribution is right skewed; that means it has a longer tail to the right and the data is "bunched up" at the left.
In a right skewed distribution, the majority of data points are at the smaller end; for this reason, the median will be towards the left side of the graph.
The higher numbers in the "tail" will bring the mean up, making it larger than the median.
The correct statement for the distribution is the mean is greater than the median.
What is mean and median?
The mean is the average of a data set. The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle term of a distribution.
It measure determines the middle value of a dataset listed in ascending order.
Therefore, from the distribution the data are rightly skewed. The higher numbers in the "tail" will bring the mean up, thereby making it larger than the median.
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Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
What is the volume of the cylinder rounded to the nearest cubic centimeter?
What is the total volume of the four balls rounded to the nearest cubic centimeter?
What percent of the volume of the container is occupied by the four balls?
The unt informs club has 16 members. they need to elect a president, a vice president, a secretary and a treasurer. how many different ways can this group of 4 officers be formed? (order is important)
Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?
Henry's annual retirement benefit will be $2,375.
We have,
To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.
First, let's calculate 2.5% of $95,000:
2.5% = 2.5/100 = 0.025
Annual benefit = 0.025 * $95,000
Annual benefit = $2,375
Therefore,
Henry's annual retirement benefit will be $2,375.
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Tom has been given 35 chores to complete today this morning he finished seven of them how many chores does he now have left to do
Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6
The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.
Explanation:The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.
We start by simplifying the square root of each component:
Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.Now, divide and simplify:
(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)
Therefore, we get:
(4/9) * x^2 * y
HEEEELLLPP!!!!!!!!!!!!!!!WILL GIVE THE BRAIN!!!!!POINTS!!!!!!!
plz
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?
D) a = 24, c = 48, e = 22, i = 80
what is the sum of the geometric series E (-2)(-3)^n-1
Answer:
The sum is 40.
Step-by-step explanation:
Given,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}[/tex]
We know that,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=(-2)(-3)^{1-1}+(-2)(-3)^{2-1}+(-2)(-3)^{3-1}+(-2)(-3)^{4-1}[/tex]
[tex]=(-2)(-3)^{0}+(-2)(-3)^1+(-2)(-3)^2+(-2)(-3)^3[/tex]
[tex]=-2\times 1 - 2\times - 3 - 2\times 9-2\times -27[/tex]
[tex]=-2+6-18+54[/tex]
[tex]=40[/tex]
Hence,
[tex]\sum_{n=1}^{4} (-2)(-3)^{n-1}=40[/tex]
a triangle with a base of 6cm and a height of 8cm is similar to a triangle with base 21cm. What is the height of the second triangle
Suppose that a small town has seven burger shops whose respective shares of the local hamburger market are (as percent- ages of all hamburgers sold): 23 percent, 22 percent, 18 percent, 12 percent, 11 percent, 8 percent, and 6 percent. what is the four-firm concentration ratio of the hamburger industry in this town
|-x-2y| for x =-3 and y=3
What is the slip of the line given by the equation y=-1/3 x
During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?
Multiply: (2x2 − 5x)(4x2 − 12x + 10)
Answer:
[tex]8x^4-44x^3+80x^2-50x[/tex]
Step-by-step explanation:
The given expression is
[tex](2x^2-5x)(4x^2-12x+10)[/tex]
Using distributive property we get
[tex]2x^2(4x^2-12x+10)-5x(4x^2-12x+10)[/tex]
[tex]2x^2(4x^2)+2x^2(-12x)+2x^2(10)-5x(4x^2)-5x(-12x)-5x(10)[/tex]
On simplification we get
[tex]8x^4-24x^3+20x^2-20x^3+60x^2-50x[/tex]
On combine like terms.
[tex]8x^4+(-24x^3-20x^3)+(20x^2+60x^2)-50x[/tex]
[tex]8x^4-44x^3+80x^2-50x[/tex]
Therefore the product of two polynomials is [tex]8x^4-44x^3+80x^2-50x[/tex].
How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?
When each letter "z" is distinctly different, there are 60 possible arrangements.
When the letter "z" is interchangeable with the others, there are 24 possible arrangements.
1. When each letter "z" is distinctly different from the others:
- The word "fuzzy" has 5 letters in total, including 2 "z" letters.
- To calculate the number of arrangements, we use the formula for permutations with repeated elements:
- The formula is: n! / (n1! n2! ... * nk!)
- n is the total number of letters in the word (5 in this case).
- n1, n2, ... are the number of repetitions of each distinct letter.
- Calculating: 5! / (1! 2! 1! * 1!) = 120 / 2 = 60 arrangements.
2. When the letter "z" is interchangeable with the other letters:
- In this case, there are 4 distinct letters in the word "fuzzy" (f, u, z, y).
- The total number of arrangements can be calculated using the formula for permutations of distinct items.
- Calculating: 4! = 24 arrangements.
In summary:
- When each letter "z" is distinctly different, there are 60 possible arrangements.
- When the letter "z" is interchangeable with the others, there are 24 possible arrangements.
This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.
Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?