To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.
Explanation:The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.
In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.
This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.
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My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz
giving brainliest please help, and give steps if possible. Im trying to learn this.
Answer:
[tex]f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
Step-by-step explanation:
[tex](fg)(x) \\ (fx) = 6 - 5x \\ g(x) = {6x}^{2} + x \\ substitute \: and \: calculate: \\ f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]
What is the simplified form of sqrt 400x100? 200x50 200x10 20x50 20x50
Answer: The required simplified form is 20 × 10.
Step-by-step explanation: We are given to find the simplified form of the following radical expression :
[tex]E=\sqrt{400\times 100}.[/tex]
We will be using the following property of radicals :
[tex](i)~\sqrt{x}=x^\frac{1}{2}\\\\(ii)~\sqrt{a\times b}=\sqrt a\times\sqrt b.[/tex]
Therefore, we have
[tex]E\\\\=\sqrt{400\times 100}\\\\=\sqrt{400}\times\sqrt{100}\\\\=\sqrt{20^2}\times\sqrt{10^2}\\\\=((20)^2)^\frac{1}{2}\times(10^2)^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times(10)^{2\times\frac{1}{2}}\\\\=20\times10.[/tex]
Thus, the required simplified form is 20 × 10.
HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!
12x2 = 18x
i need someone to explain this
Help me solve this please!
What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]
Answer:
The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.
Step-by-step explanation:
In order to find the point-slope form of any equation, start with the base form of the equation.
y - y1 = m(x - x1)
Now input the slope given as m, and the point in for x1 and y1.
y - y1 = m(x - x1)
y - 6 = 4/3(x - -4)
y - 6 = 4/3(x + 4)
A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0
Answer:
The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]
Step-by-step explanation:
The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.
We have:
[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]
Now we solve the other equation for t.
[tex]y= \sqrt{t}[/tex]
[tex]y ^ 2 = t[/tex] because [tex]t> 0[/tex]
As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]
Then:
[tex]y ^ 2 = \frac{x + 1}{2}[/tex]
The correct answer is:
D. [tex]x=2y^{2} -1, y\geq 0[/tex]
how do I solve (x-5)(x-1)=0
A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children.
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency
Which of these is equal to 50 + 21? 20 + 21 60 - 30 20 + 11 60 - 61
50 + 21 is equal to d. 11+ 60.
What is simplificarion?Simplification or simplifying fractions means simplifying a complicated mathematical expression to get a single or direct solution.
the value of 50 + 21 = 71 is option C.
a. 20 + 21
b. 60 - 30
c. 20 - 61
d. 11+ 60
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Final answer:
None of the provided options (20 + 21, 60 - 30, 20 + 11, 60 - 61) are equal to the sum of 50 + 21, which is 71. Each option computes to a different number, all of which are not equal to 71.
Explanation:
The question asks which of the given options is equal to the sum of 50 + 21. To solve this, we can compute each of the options to see which one equals 71, since 50 + 21 equals 71. Let's calculate:
20 + 21 = 41, which is not equal to 71.60 - 30 = 30, which is also not equal to 71.20 + 11 = 31, again not equal to 71.60 - 61 equals -1, which is not equal to 71.None of the provided options are equal to the sum of 50 + 21. The correct answer should be a number that when calculated results in 71, but none of these options do.
Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?
a) 48
b) 156
c) 78
d) 132
The difference of a number and 8 is the same as 34 less the number. find the number.
The angle of elevation to the top of a building in chicago is found to be 11◦ from the ground at a distance of 1000 feet from the base of the building. find the height of the building.
Express answer in exact form.
A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"
A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? write your answer is simplified radical form and rounded to the nearest tenth of an inch.
Select one:
a. About 4.9 inches
b. About 4.1 inches
c. About 5.3 inches
The correct answer is option(a) about 4.9 inches.
To find the width of a golden rectangle with a given length, we will use the golden ratio formula that is
l / w = (1 + √5) / 2
Where, l = length of rectangle & w = width of rectangle
By applying the above formula we get the golden ratio, which is ≈ 1.618.
The formula for a golden rectangle is length(l) = 1.618 × width.
Given that length is 8 inches, we set up the equation:
8 = 1.618 × width
Solving for width:
width = 8 / 1.618 = 4.948...
The simplified radical form of 4.948... is ≈ 4.9 inches.
Thus, the correct answer is about 4.9 inches or option (a).
Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1
A recipe for fruit punch calls for cranberry juice and sparkling water. The ratio of cups of cranberry juice to cups of sparkling water is 6:24. According to the recipe, how many cups of cranberry juice are needed for every 1.5 cup of sparkling water? Write your answer as a fraction in simplest form.
PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .
1/125
6/500
8/500
2/10
peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?
Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)
Answer: 21.8 inches
Given:
A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.
To get the diameter of each car wheel
Get first the length of revolution (circumference of the wheel) in inches.
Speed=50 miles/hr
=50miles/60 minutes
= 0.833333 miles/minute
=.833/5280=4400ft= 52,800 inches/minute
Since there are 770 revolutions per minute, per revolution (circumference of the wheel) =
=52,800/770
=68.57 inches
Formula of diameter given the circumference is:
D=C/π
D=68.57/3.14
D= 21.8 inches
Answer:
21.8
Step-by-step explanation:
just took test
When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.
Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.
on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed
A gym has an inclined treadmill for joggers, as shown in the figure.
What is θ, the treadmill's angle of elevation?
Round your answer to the nearest degree.
Before simplifying, how many terms are there in the expression -2x + 8 - 6y + 8x + 11?
Final answer:
The expression contains five terms before simplifying. We simplify by combining like terms to get a simplified result of 6x - 6y + 19 and then confirm the simplification by checking if the answer is reasonable.
Explanation:
The student has asked how many terms are in the expression -2x + 8 - 6y + 8x + 11 before simplifying. A term is a single mathematical expression that may consist of constants and/or variables, sometimes multiplied together but not added or subtracted to another term. In the given expression, there are a total of five terms: -2x, +8, -6y, +8x, and +11.
To simplify the algebra, we can combine like terms. Like terms are terms that contain the same variables to the same power. Here, -2x and +8x are like terms. When we combine them, we get 6x. The constants +8 and +11 are also like terms and can be added together to get +19. So, the simplified expression is 6x - 6y + 19.
Finally, we check our answer to ensure it is reasonable. Combining like terms -2x and +8x should result in +6x, and adding constants +8 and +11 should give us +19, which is our simplified result, confirming the reasonableness of our simplification.
write an equation of an ellipse in standard form with the center at the origin and a height of 3 units and width of 1 unit
The equation of an ellipse with the specified attributes, using the center as the origin, is x2/0.25 + y2/2.25 = 1.
Explanation:The question asks for the equation of an ellipse with the center at the origin and a height of 3 units and width of 1 unit. In an ellipse, the center is the midpoint of both the major and minor axes. The major axis can be the horizontal (width) or vertical (height) axis, and the minor axis is the other one.
Given that the height of the ellipse is 3 units, this determines the major axis and its length of 2a=3, which means a=1.5. The width of the ellipse is 1 unit, this determines the minor axis and its length of 2b=1, which means b=0.5.
Using these values, the equation of such an ellipse, centered at the origin, in standard form is x2/0.25 + y2/2.25 = 1
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The equation of an ellipse in standard form with the center at the origin, a height of 3 units and width of 1 unit is [tex]\(4x^2 + (y^2/2.25) = 1\).[/tex]
Explanation:The equation of an ellipse in standard form with the center at the origin can be given by [tex]\(rac{{x^2}}{{a^2}} + rac{{y^2}}{{b^2}} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Based on the information given in yourquestion, the height of the ellipse is 3 units which means the semi-major axis b is 1.5 units (since it's half the height). Similarly, the width of the ellipse is 1 unit which means the semi-minor axis a is 0.5 units (since its half the width). Substituting these values into the standard form of the ellipse we get: [tex]\(4x^2 + (y^2/2.25) = 1\)[/tex]
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