BASED ON THESE NUMBERS, AND YOUR KNOWLEDGE OF FIBONACCI NUMBERS, IS THE STATEMENT THAT FOLLOWS TRUE OR FALSE? F(N+2) IS EXACTLY EQUAL TO THE SUM OF THE FIRST N TERMS OF THE FIBONACCI SEQUENCE.
A. TRUE
B. FALSE

The maximum profit the company can earn is $90,250 when 500,000 units of the product are sold. Therefore, to yield a maximum profit, 500,000 units must be sold.

The given quadratic equation:

y = -0.001(x - 600)² + 90represents the expected profit, in thousands of dollars, of the company where x represents the number of thousands of units of the product sold by the company. We are required to determine the number of units that must be sold to yield a maximum profit.It can be noted that the given equation is in the vertex form:

y = a(x - h)² + kwhere (h, k) are the coordinates of the vertex of the parabola, and the sign of the coefficient 'a' determines the shape of the parabola. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.In the given equation, the coefficient of the squared term is -0.001 which is less than zero. Therefore, the parabola opens downwards. Hence, the vertex of the parabola will give us the maximum profit that the company can earn. Thus, we need to find the value of x that corresponds to the vertex of the parabola.To find the vertex of the parabola, we can use the formula:h = -b/2a, and k = c - b²/4a

where the quadratic equation is in the standard form of ax² + bx + c = 0

On comparing the given quadratic equation with the standard form, we get:

a = -0.001, b = 1, and c = 90Substituting these values in the formula, we have:

h = -b/2a = -1/(2 × -0.001) = 500k = c - b²/4a= 90 - (1)²/4(-0.001)= 90.25

Hence, the vertex of the parabola is (500, 90.25).

This implies that the maximum profit the company can earn is $90,250 when 500,000 units of the product are sold. Therefore, to yield a maximum profit, 500,000 units must be sold.

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Answer:

(5v)²-(2)²

(5v-2)(5v+2)

Hence the factors are 2/5 and -2/5

Answer:

33

Step-by-step explanation:

Answer: 800 dollars per month

Step-by-step explanation:

12000 divided by 15 is 800

800 x 15 = 12000

Remove the brackets.

Take the like terms closer.

Now do the addition and subtraction

Let us split the middle term

Now take x as common from the first two terms and -1 from the next two terms.

Answer:

(x - 1)(7x + 12)

Hope you could understand.

If you have any query, feel free to ask.

Solve (6x² + 5x - 3) + (x² - 9)

(x-1) (7x+12)

please look at the attached picture :)

Answer:

58°

Step-by-step explanation: Nick was able to view the museum painting through the mirror due to reflection. The painting was reflected after hitting the plane mirror. According to the law of reflection, the angle of incidence is equal to the angle of reflection. The incident angle is the angle which the incident ray( the ray which strikes or hits the plane mirror) makes with the normal(line perpendicular to the tangent).

Thus, the angle which the painting makes with the mirror is equal to the angle at which the painting is being viewed = 58°.

The line given by the equations x + 3 = 3y + 4 = -4z - 8 intersects the xy-plane at the point (-7, -1, 0).

To find the point of intersection with the xy-plane, we set z = 0 and solve for x and y. From the given equations, we have:

x + 3 = 3y + 4 = -8

From the third equation, we obtain x = -11. Substituting this value into the first equation, we have -11 + 3 = 3y + 4, which simplifies to -8 = 3y. Solving for y, we get y = -8/3.

Therefore, the line intersects the xy-plane at the point (-11, -8/3, 0), which can be simplified to (-7, -1, 0) by dividing all coordinates by a common factor of 3.

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Answer:

Adult Ticket: £7

Child Ticket: £2

Step-by-step explanation:

Let the cost of 1 child ticket be c, adult ticket be a.

\(2a + 3c = 20 \\ \\ a + 4c = 15 \\ a = 15 - 4c \\ \\ 2(15 - 4c) + 3c = 2 0 \\ 5c = 10 \\ c = 2 \\ \\ a = 15 - 4(2) \\ a = 7\)

Aryabhata, also called Aryabhata I or Aryabhata the Elder, (born 476, possibly Ashmaka or Kusumapura, India), astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name. He flourished in Kusumapura—near Patalipurta (Patna), then the capital of the Gupta dynasty—where he composed at least two works, Aryabhatiya (c. 499) and the now lost Aryabhatasiddhanta.

Aryabhatasiddhanta circulated mainly in the northwest of India and, through the Sāsānian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight.

Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries. The work was written in verse couplets and deals with mathematics and astronomy. Following an introduction that contains astronomical tables and Aryabhata’s system of phonemic number notation in which numbers are represented by a consonant-vowel monosyllable, the work is divided into three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).

Answer: -75.96°

(i) To find the gradient of the normal to the curve at the point where the curve intersects the y-axis, we need to find the derivative of the curve equation and negate it. The derivative of y = -x³ + 3x² - 4x + 2 is given by:

dy/dx = -3x² + 6x - 4

At the point where the curve intersects the y-axis, x = 0. So, the gradient of the normal to the curve at this point is:

-3 * 0² + 6 * 0 - 4 = -4

(ii) To find the angle that this normal to the curve makes with the x-axis, we can use the tangent function. The tangent of an angle is equal to the gradient of a line, so we have:

tan(θ) = gradient of the normal = -4

The inverse tangent function (arctan) gives us the angle θ in radians, which we can then convert to degrees:

θ = arctan(-4) = -75.96°

So, the angle that the normal to the curve makes with the x-axis is approximately -75.96°.

Step-by-step explanation:

To answer this question, we need to know the median and upper quartile of the data set. Once we have these values, we can determine what percentage of the data falls to the right of the median and to the left of the upper quartile.
Let's say the median of the data set is 50 and the upper quartile is 75. To find the percentage of measurements to the right of the median, we need to look at the data values that are greater than 50 and divide that number by the total number of measurements. Let's say there are 40 data values greater than 50 and a total of 100 measurements.

Then, the percentage of measurements to the right of the median would be:

(40/100) x 100% = 40%

To find the percentage of measurements to the left of the upper quartile, we need to look at the data values that are less than or equal to 75 and divide that number by the total number of measurements. Let's say there are 60 data values less than or equal to 75 and a total of 100 measurements. Then, the percentage of measurements to the left of the upper quartile would be:

(60/100) x 100% = 60%


Your answer:
1. 40% of the measurements lie to the right of the median.
2. 60% of the measurements lie to the left of the upper quartile (Q3).

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Answer:

196

Step-by-step explanation:

I calculated it with my calculator

The probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018. The probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003.

To calculate the probability of winning $100 by matching exactly three of the first five and the sixth numbers, we first need to determine the total number of possible combinations for the first five numbers. Since each of the five numbers can be any number between 1 and 69, there are 69 choose 5 (written as 69C5) possible combinations, which is equal to 11,238,513. Out of these 11,238,513 possible combinations, we need to choose three numbers that will match the drawn numbers and two numbers that will not match. The probability of matching three numbers is calculated as 5C3/69C5, which is equal to 0.0018. The probability of not matching the remaining two numbers is 64C2/64C2, which is equal to 1.

Therefore, the probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018 x 1, which is equal to 0.0018. To calculate the probability of winning $100 by matching four of the first five numbers but not the sixth number, we need to determine the total number of possible combinations for four of the first five numbers. Since each of the four numbers can be any number between 1 and 69, there are 69 choose 4 (written as 69C4) possible combinations, which is equal to 4,782,487.

Out of these 4,782,487 possible combinations, we need to choose four numbers that will match with the drawn numbers and one number that will not match. The probability of matching four numbers is calculated as 5C4/69C4, which is equal to 0.0003. The probability of not matching the remaining number is 64/64, which is equal to 1. Therefore, the probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003 x 1, which is equal to 0.0003.

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Answer:

Average rate of change

=

26.5

Explanation:

Use the slope formula to find average rate of change:

m

=

y

2

−

y

1

x

2

−

x

1

To use the slope formula, you need 2 points on the curve - we only have to x values, so we need to find f(8) and f(10).

f

(

8

)

=

92

f

(

10

)

=

145

These means are points are

(

x

1

,

y

1

)

=

(

8

,

92

)

and

(

x

2

,

y

2

)

=

(

10

,

145

)

.

m

=

145

−

92

10

−

8

m

=

53

2

m

=

26.5

Step-by-step explanation:

The average rate of change on the interval from 0 to 10 is 30

The function is given as:

f(x)=3x^2-8

The interval is given as:

0 to 10

Calculate f(0) and f(10)

f(0)=3 *(0)^2 -8

f(0) = -8

f(10)=3 *(10)^2 -8

f(10) = 292

The average rate of change is then calculated as:

Rate = (f(10) - f(0))/(10 - 0)

This gives

Rate = (292 +8 )/(10 - 0)

Evaluate

Rate = 30

Hence, the average rate of change on the interval from 0 to 10 is 30

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Answer:

x=1045/13

let x be the unknown side

here 13,19 & 55,x are in proportion

13:19=55:x

13/19=55/x

13x=55×19

x=1045/13

You can use the fact that number of breads purchased cannot be negative since a customer either buys them or not and usually do not sell to the shopkeeper.(if somehow they end up selling to shop owner, then yes that will go in negative, but we'll assume it is wrong in most cases as generally shop owners are there to sell stuffs).

The third table of values matches the equation and includes only viable solutions.

It is talking about those solutions which are seen in real world. As stated above, a customer either buys the bread or not, thus number of breads sold will be either positive or 0(in case of no selling). Thus, we cannot have number of breads as negative.

Such solutions which are correct in the real world context here are called here as viable solutions.

For first table, the number of breads are in negative, thus it is not going to have viable solution.

For second table, we have:

b = 0 thus c = 3.5b = 3.5 times 0 = 0 which is correctly given in second column.

b = 0.5, thus c = 3.5b = 3.5 times 0.5 =1.75 which is correctly given.

b = 1, thus c= 3.5 times 1 = 3.5 which is correctly given

b = 2001.5 thus c = 3.5 times 2001.5  = 7005.25 which is not correctly given, thus wrong.

For third table, we have:

b = 0, thus \(c = 3.5 \times 0 = 0\), correctly given in second column.

b = 3, thus \(c = 3.5 \times 3 = 10.5\), correctly given.

b = 6, thus \(c = 3.5 \times 6 = 21\), correctly given.

b = 9, thus \(c = 3.5 \times 9 = 31.5\), correctly given.

Thus, the third table of values matches the equation and includes only viable solutions.

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Answer:

its c to be exact

Step-by-step explanation:

The binomial distribution is not applicable because likelihood of discovering a golden ticket could not be independent

Given data ,

The probability of finding a golden ticket in one box of cereal is:

p = 64,000/800,000 = 0.08

We can use the binomial probability formula to find the probability of finding exactly 3 golden tickets in 15 boxes:

P(X = 3) = (15 choose 3) * (0.08)³ * (0.92)¹²

P(X = 3) ≈ 0.233

Therefore , the probability of finding exactly 3 golden tickets in 15 boxes is approximately 0.233

The likelihood of discovering a golden ticket could not be independent for each box, which is one reason why the binomial distribution would not be a suitable model for this circumstance.

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1. (f∘g)(2): We evaluate g(2) first, which gives us 2³ + 8 = 16. Then we evaluate f(16) by taking the square root of 16, which equals 4.

2. (f∘f)(25): We evaluate f(25) first, which gives us √25 = 5. Then we evaluate f(5) by taking the square root of 5.

3. (g∘f)(x): We evaluate f(x) first, which gives us √x. Then we substitute this into g(x), which gives us (√x)³ + 8.

4. (f∘g)(x): We evaluate g(x) first, which gives us x³ + 8. Then we substitute this into f(x), which gives us √(x³ + 8).

In summary, we simplified the compositions as follows: (f∘g)(2) = 4, (f∘f)(25) = √5, (g∘f)(x) = x^(3/2) + 8, and (f∘g)(x) = √(x³ + 8).

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Answer:

-69/323

Step-by-step explanation:

6/19-9/17=6*17-19*9/19*17

=102-171/323

= -69/323

This is greater than the threshold of 0.01 coffee shops per person, so the Mom & Pop Coffee Shop cannot open a new location in the downtown area based on their criteria.

A fraction is a mathematical expression that represents a part of a whole. It consists of two numbers separated by a horizontal or slanted line, where the number on the top is called the numerator and the number on the bottom is called the denominator. The numerator represents the number of equal parts that are being considered, while the denominator represents the total number of equal parts that make up the whole.

Here,

To find the population density of coffee shops per person in the downtown area, we need to calculate the total number of people in the area and the total number of coffee shops.

The downtown area consists of 20 city blocks, with a population density of 225 people per block. Therefore, the total population of the downtown area is:

20 blocks x 225 people per block = 4,500 people

The number of coffee shops in the downtown area is given as 48.

So the population density of coffee shops per person in the downtown area is:

48 coffee shops / 4,500 people = 0.0107 coffee shops per person

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In a simple linear regression model (one independent variable),               2 parameters need to be estimated. The correct option is (c).

In a simple linear regression model with one independent variable, we are trying to model a linear relationship between the dependent variable and the independent variable. The model can be written as:

y = β0 + β1x + ε

where y is the dependent variable, x is the independent variable, β0 is the intercept, β1 is the slope coefficient, and ε is the error term.

To estimate the parameters of this model, we need to estimate β0 and β1. Therefore, the answer is (C) 2 parameters need to be estimated.

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Answer:

A (equals -320.0064 just like in the question)

Answer:

1. AB= 8.94,

2. AB= 7.28

3. AB= 16.4

4. AB= 19.21

Step-by-step explanation:

This is fun! Well you have to find the (1,4) (or point e) point and count the distance to the other points point a and point b.

4 units from a to e and 8 b to e

a² + b² = c²

8² + 4² = c²

64 +16 = c

√80 = √c²

8.94 = c

It dose not matter which units you plug in for a and b but c has to be the long side of the triangle/ hypotonuse.

Follow the same steps for the rest of the problems.

On proplems 3 and 4 plot points first you can subtract the x-x and y-y as a short cut to find the units.

Answer:

-3 <= x < 5

Step-by-step explanation:

Because x is less than 5, we put a less than sign. And x is greater than or equal to -3, so we have to put that specific sign.

Answer:

4750

Step-by-step explanation:

Take 95, move the decimal. 0.95

then multiply 5000 by 0.95

Answer:

No solutions.

Step-by-step explanation:

-10 = 7

No solutions

The height and radius of the cone-shaped cup that will use the smallest amount of paper, that is the maximum volume is  3.72 and  2.632 respectively.

Formula used in the solution is

Volume of the cone= (1/3)π(r^2)h

Area of the cone= πr√(l^2 + r^2)

Given, the volume of the cone is 27 cm^3.

(1/3)π(r^2)h =27

Simplifying the equation to get the value of r.

π(r^2)=81/h

r^2=81/hπ

\(r=\sqrt{\frac{81}{\pi h} }\)

Substituting the value of r in area, we get

\(A=\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }\)

\(\frac{dA}{dh} =\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }\)

dA/dh=√81 × (π - 162/\(h^{3}\)) × 1/√(πh + 81/\(h^{2}\))

At dA/dh=0, we will get,

√81 × (π - 162/\(h^{3}\)) × 1/√(πh + 81/\(h^{2}\))=0

√81 × (π - 162/\(h^{3}\))=0

\(\pi - \frac{162}{h^{3} }=0\)

Thus, \(\pi h^{3} -162=0\)

\(\pi h^{3} =162\)

\(h^{3} =\frac{162}{\pi}\)

h^3= 51.5662015618

h= 3.7221

Now, substitute h in radius,

\(r=\sqrt{\frac{81}{\pi \times 3.7221} }\)

r=2.632

Hence, the height of the cone shaped cup is 3.7221 and the radius is 2.632.

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