If p ( x ) = 8 + 6 x − 4 x 2 p(x)=8+6x-4x2 represents the profit in selling x x thousand boombotix speakers, how many speakers should be sold to maximize profit?

Answers

Answer 1

Final answer:

To maximize the profit from selling Boombotix speakers, the company should sell 0.75 thousand speakers, or 750 speakers, which is determined by finding the vertex of the profit function p(x) = 8 + 6x - 4x2.

Explanation:

The function p(x) = 8 + 6x - 4x^2 represents the profit from selling x thousand Boombotix speakers. To find the number of speakers that should be sold to maximize profit, we need to find the vertex of the parabola represented by this quadratic function, which is a downwards opening parabola because the coefficient of x^2 is negative (-4).

The vertex form of a quadratic function is p(x) = a(x-h)2 + k, where (h, k) is the vertex of the parabola. The x-coordinate of the vertex (h) can also be found using the formula h = -b/(2a) where a is the coefficient of x2 and b is the coefficient of x in the standard form of the quadratic function. In this case, a = -4 and b = 6. Applying the formula:

h = -b/(2a) = -6/(2 * -4) = -6 / -8 = 0.75

Hence, the company should sell 0.75 thousand speakers, or 750 speakers, to maximize profit.

Related Questions

if a certain type of bacteria quadruples every 15 minutes, how many bacteria will be presents after 90 minutes if the initial population was 5 bacteria?

HELP ME FOR 97 POINTS !!!!

Answers

For this case we have an equation of the form:
y = A (b) ^ (t / n)
Where,
A: initial amount
b: growth rate
t: time
n: number of time periods
Substituting values we have:
y = 5 * (4) ^ (90/15)
y = 20480
Answer:
will be presents after 90 minutes about:
y = 20480 bacteria

PLEASE HELP ME OUT ON THIS CRITICAL HARD QUESTION!!!!!!!! NEEDS THINKING!!!! MARK THE BRAINIEST

Answers

You are getting into stats and I have to warn you that the condition of my stats knowledge is almost as limited as what I know about Biology which is practically nothing. But let's see if we can do something about this.

The first thing you have to do is make sure that the sales reps face the same conditions. Geography is going to matter. Start with the simple stuff. Does it matter whether or not the sales representatives were in the city of the country? If in the country, do the people have money enough to buy what is being sold? If in the city, what is the employment situation like? Make sure that you are comparing Apples and Apples.

What about crops? Do they matter? What about livestock does it matter? What do these rural areas need? Is he selling what they need? It's going to be harder to sell something in Detroit or Flint than it is San Francisco?

Did people experience a devastating winter? Especially in the Northeast? If they did, their heating bills are going through the roof. Literally. More money on heating less on whatever he's selling.

In short he has to consider conditions. Perhaps training will make no difference. There's other things that people have to live through. Maybe this was just a bad year. (It certainly was where I live. We got nothing but snow into mid April and East winds which are strong, cold, miserable and very nasty.)

Credit scores. I'd be well aware of any credit stats that I can obtain. What are people doing with their credit cards. You may be able to sell the stuff on credit, but will you ever receive payment that you can rely on or are these people one step away from bankruptcy? Is it different in the rural areas than in the cities? I can tell you I would hate to have it known that I disregard my credit cards in the town I live in (700 people). It would be cash only for everything.

Single or married? What's the demographics of the areas he's trying to sell in. We're retired. We don't take well to door to door sales people. Retired people have very little money to throw away on things we don't need. People on 3000 a month live very differently from those on 10000 a month.

Finally what's the competition like? Sears going under is a huge warning. Where do people get the products you are selling? This is especially important in rural areas. We have made over 170 mail purchases (we won't do that any more -- postage rates are just prohibitive).

If he has a sales force of 1000 people in 2 regions, he should think about moving some of them to other regions. Don't use this point.

Many of the things I've pointed out require a study before the the training is administered. You have to separate out what mitigates the efforts of the sales force and what they have little or no control over.

Amy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax?

Answers

11.70 is what wouldve been spent without adding tax, if you add tax you wouldve spent around $12-$12.50

Here, we need to find the cost of each pen, including tax. Since, information about tax was not given, so we will not consider this.

Total money Amy had = $ 26.

She is left with $ 14.30. The money she spent will be -

Total money - Money left = Money spent

$ 26 - $ 14.30 = $ 11.70

Total money she spent on 10 pens = $ 11.70

So, money spent on = $ 11.70 ÷ 10 = $ 1.17

So, the cost of each pen will be = $ 1.17

what is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)

Answers

[tex] \frac{x+5}{x+2} - \frac{x+1}{x^{2}+2x } = \frac{x^{2}+4x-1 }{ x^{2} +2x} [/tex]

Answer:

[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]

Step-by-step explanation:

Given two expression, we have to find the difference of these two.

[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]

[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]

[tex]\text{Taking (x+2) common from the denominator }[/tex]

[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]

[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]

[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]

which is required difference.

hey can you please help me posted picture of question

Answers

From the graph we can observe that G(x) is obtained by shifting F(x) 3 units to the left and 1 unit upwards.

Thus, both horizontal and vertical translations are involved. Horizontal translation of 3 units to left can be obtained by adding 3 to x in the equation and vertical translation of 1 can be obtained by adding 1 to the entire function.

So,

G(x) = F(x+3) + 1

G(x) = (x+3)² + 1

Thus the correct answer is option C

PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE

Answers

We have the following equation:
x2 + y2 + 6y - 72 = 0
Rewriting we have:
x2 + y2 + 6y = 72
Complete squares we have:
x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
x2 + y2 + 6y + 9 = 72 + 9
x2 + (y + 3) 2 = 81
So, the center is:
(0, -3)
The radio is:
r = 9
Answer:
(0, -3)
r = 9

How to find the answers to nine and ten? Please show your work.

Answers

Nine
Comment
The figure consists of 2 figures, a rectangle and a trapezoid. You should break them up and find the area of each separately and add to get the total.

Rectangle.
Area = L * W
L = 40 yd
W = 25 yd.
Area = 40 * 25 = 1000 square yards.

Trapezoid
B1 = 40 yards
B2 = 65 yards
H = 55 - 25 yards
H = 30 yards
Area = (B1 + B2)* H / 2
Area = (40 + 65)*30 / 2 Add the 2 bases together.
Area = ( 105) * 30 / 2 You can divide either the 30 or the 105 by 2. Do the 30
Area = (105) *15
Area = 1575 square yards.

Find the total Area
Total Area = rectangle + trapezoid
Total Area = 1000 + 1575
Total Area = 2575 <<<<< Answer

Ten
Comment
Assume the other side has no windows or doors. Both sides consist of 1 triangle and 1 rectangle.

Problem A
Rectangle
Area = l * w
L = 28 feet
W = 8.5 feet
Area = 28 * 8.5
Area = 238 square feet.

Triangle
Area = 1/2 Base * Height
Base = 28 feet
Height = 12.5 - 8.5
Height = 4
Area = 1/2 * 28 * 4
Area = 56 square feet.

Total Area (1 Side)
Total Area (1 Side) = 56 + 238
Total Area (1 side) = 394

Total Area (Both sides)
Total Area (both sides) = 2 * 294
Total Area (both sides) = 588 square feet.

Problem B
Comment
You have 588 square feet. First figure out the number of bundles and then calculate the cost.

Bundles
Bundles = Total Square Feet (Rounded up) / 100
Bundles = 588 / 100 = 5.88 bundles.
But you cannot buy 0.88 bundles So you have to round up, otherwise you'll have a bit of the building uncovered.

You may not care in reality, but the question does. So your answer is that you have 6 bundles.

Cost
1 bundle costs 75 dollars.
6 bundles cost x

1/6 = 75 / x
x = 6 * 75
x = 450 dollars <<<<< Answer 10B

10q-3r=14 write a formula for g (r) in terms of r

Answers

Answer:

3/10r +7/5

Step-by-step explanation:

10q−3r=14

10q=3r-14

10q=3r/10 +14/10

q=3/10r+7/5

Final answer:

To find g(r) in terms of r, the equation 10q-3r=14 is manipulated algebraically to isolate q as g(r)=(14+3r)/10.

Explanation:

The student's question involves solving a linear equation for a variable. This is a standard algebraic task often encountered in high school mathematics. The student is given the equation 10q-3r=14 and is asked to write a formula for g(r) in terms of r, implying a need to solve for q as a function of r, which can be named g(r).

To isolate q, we perform algebraic manipulations:

First, add 3r to both sides of the equation to get 10q = 14 + 3r.Next, divide both sides of the equation by 10 to solve for q, which gives us q = (14 + 3r) / 10.Last, we rename q as g(r) which results in the final function: g(r) = (14 + 3r) / 10.

This function represents q in terms of r, and g(r) is thereby defined.

Q # 9 Find the circumference

Answers

Circumfernce: C=2*Pi*r
Pi=3.14
Radius of the circumference: r=3 m
C=2*3.14*(3 m)
C=18.84 m

Answer: First option 18.84 m

Consider a box with a square base that has a volume of 64 cubic inches and a height of 4 inches. What is the volume of a similar box whose square base has an area of 4 square inches?

Answers

We know that the square base of the new box is 4 sq. in. This means that each side has to equal 2 in., because A = l*w and 4 = 2x2; we also know that since it is a square, both sides have to be equal, so it must be a 2x2 square and not a 4x1 rectangle.

That being said, the first box had dimensions of 4x4x4 - and this is confirmed by the volume being 64 sq. in. and the height being told to us as 4 in. as well as the square base having to have equal sides.

Because of this, since the question states "similar," all of the dimensions have to be reduced by the same factor. Since the square base was reduced by 1/2, we can assume the height is also reduced by 1/2, thus giving us a height of the new box as 2 in.

So, the volume of the new box is 2x2x2, which equals 8 sq. in.

WILL MARK BRAINLEST * PLEASE HELP AND FAST :)

Answers

A stem and leaf plot is an abbreviated way of presenting data by grouping the data based on the leading number. In this plot, the minimum number is 54 (5|4), and the maximum is 96(9|6).

The range of a data set is the largest value minus the smallest value; the range for this data set would be 96-54, or 42.

The range of this stem and leaf plot is 42.

Experts/ace/geniuses helppp asapp

Answers

Point E is the correct answer! :D

[tex] \sqrt{10}=3.1622... [/tex]
therefore if you round the 3.1622... it would be closer to 3.2 so point F is actually correct

(-2q^4)(-8q^3b^6)
help I need to simplify this problem

Answers

Multiply the constants. Multiply the variables according to the rules of exponents.
[tex](-2q^{4})(-8q^{3}b^{6}) = ((-2)(-8))q^{(4+3)}b^{6}\\\\=16q^{7}b^6}[/tex]

The scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. What percent of the scores are greater than 81?

A. 50%

B. 13.5%

C. 84%

D. 16%

Answers

The difference between 81 and the mean is
81 - 74 = 7
This is exactly the value of the standard deviation. You know that the "empirical rule" tells you 68% of all scores lie within 1 standard deviation of the mean. That tells you 32% of all scores lie beyond 1 standard deviation from the mean.

The normal distribution is symmetrical, so half of those (16%) lie above 1 standard deviation above the mean; the other half (16%) lie below 1 standard deviation below the mean. We're only concerned with the first group—those scores above 1 standard deviation above the mean.

The appropriate choice is
D. 16%

What is the sum of the first 51 consecutive odd positive integers?

Answers

We call:

[tex] a_{n} [/tex] as the set of the first 51 consecutive odd positive integers, so:

[tex]a_{n} = \{1, 3, 5, 7, 9...\} [/tex]

Where:
[tex]a_{1} = 1[/tex]
[tex]a_{2} = 3 [/tex]
[tex]a_{3} = 5 [/tex]
[tex]a_{4} = 7 [/tex]
[tex]a_{5} = 9 [/tex]
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

[tex]a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\} [/tex]

Then:

[tex]a_{n} = a_{1} + (n-1)d[/tex]

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

[tex] S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k[/tex]

Therefore, we need to find:
[tex] a_{k} = a_{51} [/tex]

Given that [tex]a_{1} = 1[/tex], then:

[tex]a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1 [/tex]

Thus:
[tex]a_{k} = a_{51} = 2(51)-1 = 101[/tex]

Lastly:

[tex] S_{51} = ( \frac{1 + 101}{2} ).51 = 2601[/tex]

The number pi goes on forever with no repeating pattern; therefore, it is rational. A) True or B) False

Answers

false, it's irrational.

False, Because it is an Irrational number.

What is Rational number?

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

We have to given that;

The number π goes on forever with no repeating pattern.

Therefore, it is rational.

Since, We know that;

Number π cannot be expressed as the ratio of one number to another

Hence, in other words, Number π is an 'irrational' number that goes on forever, never repeating itself.

Hence, Statements in false, Because it is an Irrational number.

Learn more about the rational numbers visit:

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Find the value of x. If necessary, found your answer to the nearest tenth. The figure is not drawn to scale

Answers

sqrt(6^2 + 8^2) = 10

HOW CAN YOU WRITE THE EQUATION OF A LINE THAT IS PARALLEL AND/OR PERPENDICULAR TO ANOTHER LINE USING A POINT ON THAT LINE.?

Answers

The point-slope equation of a line is useful for this purpose. It is often seen in the form
y -k = m(x -h)
for a line of slope m through the point (h, k).

You can add k to this equation to put it in a form more like slope-intercept form:
y = m(x -h) +k

Either of these can be used to write the equation of a parallel or perpendicular line through the point (h, k). The slope "m" of a parallel line will match that of the given line.

The slope "m" of a perpendicular line will be the negative reciprocal of the slope of the given line. That is, if you are given a line with slope "s", the slope of the perpendicular line will be m = -1/s.

what if the value of x? show all work

Answers

For this case we can make use of the Pythagorean theorem.
We have then:
(root (117)) ^ 2 = x ^ 2 + 6 ^ 2
Clearing x we have:
x ^ 2 = (root (117)) ^ 2 - 6 ^ 2
Rewriting:
x = root (117-36)
x = root (81)
x = 9
Answer:
The value of x is given by:
x = 9 cm

Evaluate the expression
4^2+6⋅5^2−3^3÷3^2.

Answers

[tex]4^2 + 6 \times 5^2- 3^3 \div 3^2.[/tex]

Evaluate exponents:
[tex]=16 + 6 \times 25- 27 \div 9[/tex]

Evaluate multiplication and division:
[tex]= 16 + 150- 3[/tex]

Evaluate addition and subtraction:
[tex]= 163[/tex]

There are five green marbles numbered 1-5 and there are 4 yellow marbles numbered 1-4. what is the probability of picking a green or odd numbered marble

Answers

{g,g,g,g,g,y,y,y,y}

5+4=9

P(odd/green)=3/9 = 1/3 = .33 or 33% approximately

Mission Control sends a signal to a Mars robot to travel to a mysterious rock 52.8 meters away. A return signal 59.0 minutes later tells scientists that the robot is at the rock. It took the signal 9.5 minutes to get from Earth to Mars, and the same time to get back. What was the robot’s average speed in meters per minute?

Answers

The response time includes the round-trip signal time plus the robot's travel time.
59 min = 2*(9.5 min) +travel time
59 min -2*(9.5 min) = travel time = 40 min

The speed is distance / travel time
speed = (52.8 m)/(40 min) = 1.32 m/min

The robot's average speed was 1.32 meters per minute.

The length of the shorter base in an isosceles trapezoid is 4 in, its altitude is 5 in, and the measure of one of its obtuse angles is 135°. Find the area of the trapezoid.

Answers

The answer is 45.

Ask me if you still don't understand it because I didn't write any explanation.

Answer:

Step-by-step explanation:

a soccer ball has the same diameter as a lenght of a cube shaped box. if the diameter of the soccer ball is 12 inches what volume inside that is not filled by a soccer ball

Answers

diameter is the length, width, and height of the box, therefore, volume of box is length x width x height= 12 x 12x 12= 1728
volume of ball is (4/3) x pi x radius cubed =288 pi
then answer is 1728 - 288 pi

Please rate me don't just say thanks

The volume of box which is not used is (1728 - 288π) inch³.

What is Volume?

Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.

If the diameter of the soccer ball is 12 inches.

So, Volume of box

= length x width x height

= 12 x 12 x 12

= 1728 inch³

and, Volume of ball

= 4/3 πr³

= 4/3π (6)³

= 864/3 π

= 288 π inch³

So, the volume of box which is not used

= 1728 - 288π

Learn more about Volume here:

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What are the relationships among radii, chords, tangents, and inscribed angles?

Answers

The relationship between these four sectors are:

The plural of radius is what we call radii. For any line that joins the center or is joining the center to any point in the circumference of a circle is what we call radii.
Note:
If there is an infinite line from the center to circumference then is it called infinite radii.

For any line that joins or is joining two points on the circumference of a circle is known as chord and any line touching the circle is what we call as tangent to the circle.

Lastly, the intersection of bisector angles is known as in-center or inscribed.

Below are attached pictures of figures

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
a. significance level
b. critical value
c. test statistic
d. parameter

Answers

The answer for the completion exercise shown above is the second option (option b), which is:

b. critical value.

Therefore, you have that the text is: "A critical value is a numerical quantity computed from the data of a sample..."

This numeral quantity is used in statitics. Then, if the absolute value is greater that the quantity defined before, the null hypothesis must be rejected.

On a blueprint with a scale of 1cm = 2ft, the length of a wall is 12cm. If the scale of the blueprint were 1cm = 3ft, what will be the length of the wall?

(Please show work, I will mark brainliest)

Answers

I will assume that this question asks for the length of the wall on the new blueprint. It is not worded nicely.
The actual length of the wall is
12 cm * (2 ft / 1 cm) = 24 ft
On the new blueprint of 1 cm = 3 ft, the length on blueprint becomes
24 ft * (1 cm / 3 ft) = 8 cm
The length of the wall on the new blueprint is 8 cm.

Find the general form of the complete partial fraction decomposition of the integrand. use it to determine whether or not a term of each type listed below occurs in the complete partial fraction decomposition. select true if it does occur and false if it does not.

Answers

The answer is int(x^2-4x / X = 3).

A statistician observes the number of heads that occur when a coin is tossed 1000 times

Answers

A coin wouldn't be a coin without two sides

Identify the problem with the following study.

It was found that a third of all people in the United States live in urban centers. This finding is based on a study involving 3 randomly selected individuals.

reported results

small sample

missing data

loaded question

Answers

If the question is, why is this study faulty? Then you can answer it.
We know nothing about what was asked. (How could it be much more than "Where do you live?" The last one is wrong.

Is there missing data? We don't know. So the second last one is not the best answer.

The sample is too small. So far that's your best answer.

The results cannot be at fault. How can saying 2/3 of the people answered that they lived in the country.

B <<<<<< second one down <<<<< Answer

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Dissolved oxygen (DO) levels of 6 ppm were recorded in a lake the day before a sewage spill. Three days later, the DO levels in the same location were measured to be 0.5 ppm. What is the probable cause of this change in DO?A. Decreased water temperature caused a decrease in gas solubility.B. Decreased turbidity due to the sewage caused an increase in photosynthetic algae.C. Decreased oxygen is available due to bacterial decomposition of organic waste.D. Decreased carbon dioxide is produced by photosynthetic algae.E. Decreased nitrate levels eliminated a source of dissolved oxygen. Tina's mother and father pay her car insurance as long as she makes good grades. This is an example of which economic concept? A) scarcity B) law of demand C) positive incentive D) negative incentive A pet store has 26 rabbits and hamsters. The number of rabbits is 2 more than double the number of hamsters. How many hamsters does the pet store have? Without (blank) control, a business may fail what tissue is responsible for holding together the intestines Karina bought a camera with the regular price of $99. It was on sale at a 20% discount. There was a 7% tax on the sale price. How much did Karina spend to buy the camera? PLEASE SHOW YOUR WORK Descartes introduces the thesis on the "evil genius" for the purpose of casting doubt on Answer fast PLEASE my semester depends on literally this last question!!!!!!!A person has developed a condition where his heart valves are damaged. Use complete sentences to explain the effects of such a condition on the circulatory system. (2 sentences will be good :) The hypotenuse of a right triangle is 5 m long. The longer leg is 1 m longer than the shorter leg. Find the side lengths of the triangle. Mr. carlucci brought 8 3/4 pounds pepperoni for large sandwiches. He cut the pepperoni into 1/12 pound slices. A skateboarder bumped into his table and 2 7/12 pound of the pepperoni fell on the ground and was eaten by 3 dogs. Does mr. carlucci have enough pepperoni left to make 74 sandwiches if he puts one slice on each sandwich? By how much is he over or under the amount of pepperoni he needs? A group of students stood in a circle to play a game. The circle had a diameter of 22 meters. Which measurement is closest to the circumference of the circle in meters? The exceptionally strong warming of the eastern pacific is referred to as ________. eastern pacific deep water warming eastern pacific shallow water warming the coriolis effect la nia el nio What is the equivalent fraction?Drag the answer into the box to match the decimal.0.7 In terms of in-house custom engines versus third-party engines (like Unity), what has changed today from decades ago, and why? a pool is in shape of a rectangular prism. on monday water was pumped out of the pool at a constant rate starting at 12:00 pm to 12:15 pm the water in pool was 45 inches deep. at 12:35 pm the water in the pool was 41 inches deep by how many inches does the depth of the water decrease each minute ? simplify the expression 11x-(2x^2+8x). Escoge el mandato que est escrito correctamente. -Ten cuidado. -Digas la verdad. -Veas a la biblioteca. A forklift lifts 5 boxes from the ground to a height of 2 meters (m). The boxes push down with a force of 1000 newtons (N). How much work was done by the forklift to lift the boxes? Find the sum or difference: 2.8 - -5.1 Why the small Mexican untied army was able to win the battle against a large army