The profit of a business is described by the function P(x)=-3x^2+12x+75, where x is the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit?

The horizontal asymptote of the function f(x) = 2ˣ is y = 0.

In Mathematics and Geometry, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).

In this context, the line passing through the ordered pair (0, 1) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 0, as shown in the image attached above.

Read more on horizontal asymptote here: brainly.com/question/14492751

#SPJ1

The probability of exactly three successes in five trials of a binomial experiment with a 90% probability of success is 0.0729 or about 7.29%.

To find the probability of exactly three successes in five trials of a binomial experiment with a 90% probability of success, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Plugging in the values, we get:

P(X = 3) = (5 choose 3) * (0.9)^3 * (1 - 0.9)^(5 - 3)

= 10 * (0.9)^3 * (0.1)^2

= 0.0729

Read more about probability

brainly.com/question/24756209

#SPJ1

Answer:

P(heads) = 1/2

There are 4 prime numbers less than 10: 2, 3, 5, 7.

P(prime number) = 4/10 = 2/5

1/2 × 2/5 = 1/5

Answer:

There are 20 R100 notes and 80 R50 notes.

Step-by-step explanation:

Let's call the number of R100 notes "x" and the number of R50 notes "4x" (since there are 4 times as many R50 notes as R100 notes).

We can set up an equation to represent the total value of the notes:

100x + 50(4x) = 6000

Simplifying:

100x + 200x = 6000

300x = 6000

x = 20

So there are 20 R100 notes and 4 times as many R50 notes:

4x = 4(20) = 80

Therefore, there are 20 R100 notes and 80 R50 notes.

There is a volume of  14,000 gallons of water in the tank after 4 minutes.

To answer your question, let's consider the given terms: the rate at which water is poured into the tank (2000t + 1000 gallons per minute) and the initial volume of water in the tank (5000 gallons).

Since the rate is given in terms of time t, we can find the volume of water poured in after 4 minutes by plugging t = 4 into the rate equation:

Volume poured in 4 minutes = 2000(4) + 1000
Volume poured = 8000 + 1000
Volume poured = 9000 gallons

Now, add this to the initial volume of water in the tank:

Total water in tank after 4 minutes = Initial volume + Volume poured
Total water = 5000 + 9000
Total water = 14,000 gallons

So, after 4 minutes, there are 14,000 gallons of water in the tank.

More on volume: https://brainly.com/question/9111437

#SPJ11

If each row behind the "row-A" has 6 more seats than row immediately in front of it, then there are (b) 46 seats in "Row-G".

The number of seats in "Row A" is = 10 seats,

We know that, each row behind the "row-A" has 6-more seats than the row immediately in front of it.

So, Number of seats in "Row-B" are =  10 + 6 = 16 seats,

Number-of-seats in "Row-C" are = 16 + 6 = 22 seats,

Number of seats in "Row-D" are = 22 + 6 = 28 seats,

Number of seats in "Row-E" are = 28 + 6 = 34 seats,

Number of seats in "Row-F" are = 34 + 6 = 40 seats,

So, According to the pattern,

Number of seats in "Row-G" will be = 40 + 6 = 46 seats.

Therefore, there are 46 seats in "Row-G", Option (b) is correct.

Learn more about Seats here

https://brainly.com/question/16966977

#SPJ4

The radius of the lid would be 3. 5 cm.

To estimate the radius of the lid, we must first determine the circumference of the jar, which is equal to the jar's perimeter. The specified circumference is 21.98 cm.

The circumference is:

C = 2πr

We can solve for circumference as:

21. 98 = 2 πr

r = 21. 98 / ( 2 π )

r = 21. 98 / (2 x 3. 1416 )

r = 21. 98 / 6. 2832

r = 3. 5 cm

In conclusion, the radius of the lid is approximately 3.5 cm.

Find out more on radius at https://brainly.com/question/20489969

#SPJ1

For the food preparation time data with or without slicer, the null hypothesis for this sample data should not be rejected. So, option (b) is right answer.

We have a food preparation time data of a company. The time of preparation is significantly reduced with the handy dandy slicer. Sample size, n = 12

We have a table present in above figure which has the preparation times data consists people, with slicer and without slicer. First we calculate difference between with slicer and without slicer data, that d: -2, -6, 2, -8 , 0, -1, 1, 3, 4, -6, -5, 3.

We do all work on the difference, d.

Mean value of difference d, [tex]\bar d = \frac{\sum_{i = 1}^{n} {d_i }}{n}[/tex] = -1.25

Standard deviations, [tex] \sigma = \sqrt{\frac{ \sum {d_i^2 - (\sum d_i)²}}{n - 1}}

[/tex] = 4.115

degree of freedom= 12 - 1 = 11

Let level of significance = 0.05

The null and alternative hypothesis are defined as [tex]H_0 : \mu_d = 0 [/tex]

[tex]H_a: \mu_d < 0[/tex]

Using t-test, [tex]t = \frac{ \bar d} {\frac{ \sigma}{ \sqrt{n}}}[/tex]

[tex]= \frac{ -1.25} {\frac{ 4.115}{ √12}}[/tex]

= - 1.05

Now, using t-distribution table, value of p for t = -1.05 for 11 degree of freedom is -1.796. So, p-value = -1.796 < 0.005, Hence, we should not reject the null hypothesis.

For more information about null hypothesis, visit :

https://brainly.com/question/30535681

#SPJ4

f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.

What is the exponential function?

An exponential function is a mathematical function of the form f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

To determine if the function f(x) = x² - 2x + 3 is increasing, decreasing, even, odd, and/or invertible in its natural domain, we need to analyze its derivative and second derivative:

f'(x) = 2x - 2

f''(x) = 2

Increasing/decreasing: Since f''(x) is always positive (i.e., 2 is positive), the function is always concave up and has a minimum at x = 1. Thus, f(x) is increasing on (-∞, 1) and decreasing on (1, ∞).

Even/odd: To determine if f(x) is even or odd, we need to check if it satisfies the properties of even and odd functions.

Even function: A function f(x) is even if f(-x) = f(x) for all x in the domain. Let's check if f(x) satisfies this property:

f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3

f(x) = x² - 2x + 3

f(-x) ≠ f(x), so the function is not even.

Odd function: A function f(x) is odd if f(-x) = -f(x) for all x in the domain. Let's check if f(x) satisfies this property:

f(-x) = (-x)² - 2(-x) + 3 = x² + 2x + 3

-f(x) = -(x² - 2x + 3) = -x² + 2x - 3

f(-x) ≠ -f(x), so the function is not odd.

Invertible: To determine if f(x) is invertible, we need to check if it has an inverse function.

A function has an inverse function if it is one-to-one, which means that it passes the horizontal line test.

To check if f(x) is one-to-one, we can analyze its derivative.

Hence,  f'(x) = 2x - 2 is always positive on (-∞, 1) and always negative on (1, ∞), the function is increasing and decreasing, respectively, and therefore one-to-one. Therefore, f(x) is invertible in its natural domain.

To learn more about the exponential function visit:

https://brainly.com/question/30241796

#SPJ4

Complete question:

For the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain: f(x) = x² - 2x + 3.

Answer:

The possible radius and height for the inside of the cylinder that meets the constraints are r = 4 cm and h = 9.4 cm.

Step-by-step explanation:

The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height. We want to find a radius and height that will give us a volume between 475 and 480 cubic centimeters, with a diameter between 8 and 10 centimeters. First, we’ll use the lower limits of the constraints: a volume of 475 cubic centimeters and a diameter of 8 centimeters. The diameter is 8 centimeters, so the radius is 4 centimeters. We can plug in these values to the formula for volume and solve for h: 475 = 3.14 x 4^2 x h 475 = 50.24h h = 9.44 So a possible radius and height for the inside of the cylinder that meets the constraints are: r = 4 cm and h = 9.4 cm.

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

To know more about volume visit:

https://brainly.com/question/463363

#SPJ1

Percentiles provide information about the placement of data points in a quantitative dataset, histograms display the distribution of data, categorical data is grouped into categories, and ordinal data has an inherent order but no meaningful numerical differences.

Based on the terms you provided, we are looking for information about percentiles, histograms, categorical data, and ordinal data.
A percentile is a measure of placement in a sorted quantitative dataset.

It indicates the relative standing of a data point within the dataset.

For example, a score in the 80th percentile means that it is higher than 80% of the scores in the dataset.
A histogram is a graphical representation of the distribution of a dataset, typically used for continuous data.

The vertical axis of a histogram displays frequency or density, while the horizontal axis represents the data values divided into bins or intervals.
Categorical data is a type of data that can be divided into groups or categories, such as gender, ethnicity, or favorite color.

A numerical summary for categorical data usually involves counts or percentages for each category.
Ordinal data is a type of data where the order matters, but the difference between values is not meaningful, such as rankings or ratings.

A numerical summary for ordinal data can include measures of central tendency, such as the median or mode.

For similar question on histograms.

https://brainly.com/question/28164315

#SPJ11

The value of x in the right triangle below by using Pythagorean Theorem (H² = P² + B²) is 19.53

According to question; Perpendicular (P) = 16, Base (B) = 11.2 and Hypoteneus (H) = X

According to Pythagorean Theorem

H² = P² + B²

X² = 16² + 11.2²

X² = 256 + 125.44

X² = 381.44

X = 19.53

The Pythagorean Theorem, or, in standard algebraic notation, a² + b² = c², states that the total of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).

To know more about Pythagorean Theorem visit:

https://brainly.com/question/14930619

#SPJ1

If ethan threw away 16 Paris of solid-coloured socks and 16 Paris of patterned socks, Ethan had 140 pairs of patterned socks at first.

Let's start by assuming that Ethan had x pairs of patterned socks. According to the problem statement, Ethan had 3/4 as many solid-coloured socks as patterned socks. Therefore, the number of solid-coloured socks he had can be represented as 3/4*x.

Ethan threw away 16 pairs of solid-coloured socks and 16 pairs of patterned socks. So, after the clean-up, he had (3/4*x)-16 pairs of solid-coloured socks and (x-16) pairs of patterned socks.

The problem states that 1/5 of his socks were now solid-coloured socks. So, we can set up an equation:

(3/4x-16) = (1/5)(3/4*x + x - 32)

Simplifying and solving for x, we get:

x = 140

To learn more about pairs click on,

https://brainly.com/question/27239464

#SPJ4

The sequences that appear to be converging are:

2/7, 11/16, 26/37, 47/65, 74/101, 107/144, 146/197...

8/7, 64/49, 512/343, 4096/2401, 37768/16807, 262144/117649...

32.45, 31.80, 31.655, 31.654, 31.653, 31.652,...

converging refers to a sequence or series of numbers approaching a limit as more terms are added. It indicates that the values of the sequence or series are getting closer and closer to a specific value or point without ever reaching it.

a sequence is a list of numbers or objects arranged in a specific order. Each element in the sequence is called a term, and the position of the term in the sequence is called its index.

According to the given information:

The first two sequences are examples of converging sequences. In the first sequence, the numerators and denominators increase by a fixed amount for each term, but the ratio of the terms approaches a limit as the sequence progresses. Similarly, in the second sequence, each term is the previous term multiplied by a fixed factor, and the terms approach a limit as the sequence progresses.

The fifth sequence is also an example of a converging sequence, where the terms are decreasing and getting closer to a specific value as the sequence progresses.

The third sequence is not converging since the terms are increasing without bound, and the fourth sequence is oscillating between two values and not getting closer to any specific value.

The sixth sequence starts with a fixed value and increases by a fixed percentage for each term, so the terms are also increasing without bound and not converging to a specific value.

In summary, converging sequences have terms that approach a specific value as the sequence progresses, while non-converging sequences either increase or oscillate without getting closer to any specific value.

To know more about converging, sequence visit:

https://brainly.com/question/21961097

#SPJ1

Answer:

Okay, let's solve this step-by-step:

   There is a spinner with 14 equal areas, numbered 1 through 14

   We want to find the probability that the result is a multiple of 3 or a multiple of 4

   There are 14 possible outcomes (numbers 1 through 14) when the spinner is spun.

   Of these 14 numbers:

   4 are multiples of 3: 3, 6, 9, 12

   4 are multiples of 4: 4, 8, 12, 16

   However, 12 is also a multiple of both 3 and 4, so we have counted it twice.

   We need to subtract 1 from each to account for this:

   Multiples of 3: 3

   Multiples of 4: 4

   So there are 3 possible multiples of 3 and 3 possible multiples of 4.

   In total, there are 3 + 3 = 6 possible multiples of 3 or 4.

   To calculate probability:

   Probability = (Number of favorable outcomes) / (Total possible outcomes)

   = 6 / 14

   = 3/7

   Converting to a percent: 3/7 = 42.9%

   Rounded to the nearest whole percent: 43%

Therefore, the probability that the result is a multiple of 3 or a multiple of 4 is 43%.

Step-by-step explanation:

Thus, the obtained area of sector for the given circle is found as 43.96 in².

Two radii that meet at the centre to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle assessment and radius measurement are both crucial for solving circle-related difficulties.

The curved portion that runs along the circle's perimeter and joins the ends of a two radii that make up a sector is known as the sector arc.

given data:

Formula for the area of sector:

area of sector = Ф /360 * (πr²)

area of sector = 140/360 * (3.14 *6²)

area of sector = 7/18 * 3.14 *36

area of sector = 43.96 in²

Thus, the obtained area of sector for the given circle is found as 43.96 in².

Know more about the circle's sector:

https://brainly.com/question/30885943

#SPJ1

The solution of the system of equations in this problem is given as follows:

(4,0).

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the graph given by the image presented at the end of the answer, the solution to the system is given as follows:

(4,0).

More can be learned about a system of equations at brainly.com/question/30347294

#SPJ1

Answer: 80

Step-by-step explanation:

The algebraic expression representing her employee's contribution to Social Security Tax is given as follows:

p > 516.67.

The algebraic expression representing her employee's contribution to Social Security Tax is obtained applying the proportions in the context of the problem.

An year is composed by 12 months, hence the monthly salary is represented as follows:

p > 100000/12

p > 8,333.33.

The Social Security tax is of 6.20%, hence the expression is given as follows:

p > 8,333.33 x 0.062

p > 516.67.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The slope of the cathedral ceiling is 0.83.

To calculate the slope of the cathedral ceiling, we need to find the rise over the run. The rise is the difference in ceiling heights between the two points. The run is the horizontal distance between the two points.

From the problem statement, we know that the ceiling is 8 feet high at the west wall and 10.5 feet high three feet from the west wall. So the rise is:

rise = 10.5 - 8 = 2.5 feet

The run is the horizontal distance between the two points, which is:

run = 3 feet

Now we can calculate the slope:

slope = rise/run = 2.5/3 = 0.83

Therefore, the slope of the cathedral ceiling is 0.83.

Learn more about slope

https://brainly.com/question/3605446

#SPJ4

The correlation between the number of wins and each of the four baseball statistics would be an example of bivariate correlation analysis, which measures the strength and direction of the relationship between two variables.

The correlation between number of wins and each of the four baseball statistics would be an example of a bivariate correlation, which measures the strength and direction of the linear relationship between two variables. In this case, the two variables would be the number of wins and each of the four baseball statistics. The correlation coefficient would provide a numerical value that represents the degree of association between the two variables

A positive correlation coefficient would indicate that as one variable increases, so does the other, while a negative correlation coefficient would indicate that as one variable increases, the other decreases.

Learn more about correlation

https://brainly.com/question/30116167

#SPJ4

If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of

the four baseball statistics would be an example of bivariate analysis.

Bivariate analysis involves analyzing the relationship between two variables to determine if there is any correlation or

association between them.

In this case, the two variables are the number of wins and each of the four baseball statistics.

By conducting a bivariate analysis, you can identify if there is any significant relationship between these variables and

potentially draw conclusions about their impact on team performance.

If all these statistics were analyzed at the end of the season, the correlation between the number of wins and each of

the four baseball statistics would be an example of bivariate analysis.

for such more question on bivariate analysis.

https://brainly.com/question/29525585

#SPJ11

Answer:

A., D.

Step-by-step explanation:

A. 0.5x

B. 2

C. 12

D. x

Answer: A., D.

If for an arithmetic-sequence, the terms are t₅ = -154 and t₉ = -274, then the first-three terms are t₁ = -274, t₂ = -244 and t₃ = -214.

An "Arithmetic-Sequence" is defined as a sequence of numbers in which the difference between any two consecutive terms is always the same, which is called the "common-difference".

To find first 3 terms of an "arithmetic-sequence" given the values of t₅ and t₉, we use formulas for "nth-term" of an arithmetic sequence, which is

⇒ tₙ = t₁ + (n - 1)d,

where tₙ = nth term, t₁ = first term, n = position of term in sequence, and d = common-difference,

Given that t₅ = -154 and t₉ = -274,

So,

⇒ t₅ = t₁ + (5 - 1)d = -154,

⇒ t₉ = t₁ + (9 - 1)d = -274,

We first find the "common-difference" by subtracting "t₁" from both sides of first equation and "t₉" from both sides of second-equation,

We get,

⇒ 4d = -154 - t₁,

⇒ 8d = -274 - t₁,

Simplifying further,

We get,

⇒ 4d = 120,

⇒ d = 30,

Now, we substitute it in "4d = -154 - t₁",

We get,

⇒ 4(30) = -154 - t₁,

⇒ 120 = -154 - t₁,

⇒ t₁ = -154 - 120,

⇒ t₁ = -274

So, the first term is = -274;

Now we use "d = 30" to find second and third terms of sequence,

We get,

⇒ t₂ = t₁ + (2 - 1)d = -274 + 30 = -244,

⇒ t₃ = t₁ + (3 - 1)d = -274 + 60 = -214,

Therefore, first three-terms of arithmetic sequence are -274, -244, and -214.

Learn more about Arithmetic Sequence here

https://brainly.com/question/29137657

#SPJ4

The given question is incomplete, the complete question is

Find the first 3 terms of arithmetic sequence if t₅ = -154 and t₉ = -274. Find t₁, t₂, t₃.

The greatest distance, in feet, a person could be from the parking lot light and be detected is 4 ft. So, correct option is B.

The equation (x + 10)^2 + (y−8)^2=16 describes a circle with center (-10,8) and radius 4. The distance from the center of a circle to any point on its circumference is equal to the radius. Therefore, the greatest distance a person could be from the parking lot light and still be detected is equal to the radius of the circle, which is 4 feet.

This means that any point on the circumference of the circle with a distance of 4 feet or less from the center (-10,8) would be within the range of the motion detector.

Option (a) 2 feet is too small and would fall inside the circle, meaning the person would not be detected. Option (c) 9 feet and option (d) 256 feet are too large and fall outside the circle, meaning the person would also not be detected.

Therefore, the correct answer is option (b) 4 feet.

To learn more about equation click on,

https://brainly.com/question/3960228

#SPJ4

Answer: (-15, 20)

Step-by-step explanation:

we can see that the equation is the standard form of a circle:

(X-h)

^2 + (y-k)r^2

Where (h,k) is the center of the circle and r is the radius

H= -15

K= 20

R^2= 100

the direction angle of w=8j is 90.0 degrees. The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

what is direction angle ?

The direction angle, also known as the argument or phase angle, of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In the given question,

The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.

In this case, the complex number is w=8j, which has an imaginary part of 8 and a real part of 0. Therefore, the vector representing w points directly upwards in the complex plane, and the angle between this vector and the positive real axis is 90 degrees.

Rounding this to the nearest tenth of a degree gives 90.0 degrees.

So the direction angle of w=8j is 90.0 degrees.

To know more about direction angle, visit:

https://brainly.com/question/28522105

#SPJ1

The parallel line cannot have a y-intercept of c because then the lines would be :- The same line.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Two parallel lines have the same slope but different y-intercepts. If one of the parallel lines has a y-intercept of c, its equation is y = mx + c, where m is the slope. The other parallel line's equation would be y = mx + b, where b is a separate y-intercept.

If two lines have the same slope m and y-intercept c, their equations are the same: y = mx + c. As a result, they would be the same line rather than parallel lines.

Learn more about parallel lines here:

https://brainly.com/question/16701300

#SPJ1

Answer: 22

Step-by-step explanation:

So since Margo missed 24.6% of 90 free throws, you have to find 24.6% of 90. The easiest way to do this is to do 90 multiplied by 0.246.

To multiply by percentages in general, move the decimal point to the left by two places. For example, if it said 82.6, the decimal point would go to the left two places and be 0.826.

Back to the original question...

so 90 multiplied by 0.246 is 22.14. If you can use a calculator, this is easy, if not just do the usual multiplication.

Then, this rounds to 22, and the problem is complete!