if f(1) =2 and f(n)= f(n-1)-3 find the value of f(5)

Answer:

Given the value of x varies directly with the value of y means that x and y are proportional to each other, so y = kx.

We can easily solve for k by substituting in the given x and y values into y = kx:

y = 102

x = 17

y = kx

102 = k(17)

102/17 = k

k = 6

The statement that describes the translation is given as follows:

The graph of (x,y) on the graph of y = x³ has been translated to the point (x + 3, y + 4).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

y = x³.

The translated function is given as follows:

y = (x - 3)³ + 4.

Hence:

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Sí, es posible calcular los cuartiles para un número par de datos. Los cuartiles son medidas estadísticas que dividen un conjunto de datos ordenados en cuatro partes iguales. Los cuartiles más comúnmente utilizados son el primer cuartil (Q1), que divide los datos en el 25% más bajo y el 75% más alto, y el tercer cuartil (Q3), que divide los datos en el 75% más bajo y el 25% más alto.

Para calcular los cuartiles en un número par de datos, puedes seguir estos pasos:

Ordena los datos de manera ascendente.

Calcula el valor del segundo cuartil (Q2), que es simplemente la mediana de los datos. Si tienes un número par de datos, Q2 será el promedio de los dos valores del medio.

Calcula el primer cuartil (Q1), que es la mediana de la mitad inferior de los datos (los datos que están por debajo de Q2).

Calcula el tercer cuartil (Q3), que es la mediana de la mitad superior de los datos (los datos que están por encima de Q2).

Recuerda que los cuartiles pueden ser útiles para comprender la distribución de los datos y analizar la dispersión de los mismos.

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Answer:

Step-by-step explanation:

I hope I have chosen the correct area as the shaded section...lol!

A linear equation which shows a proportional relationship include the following: B. y = -1/4(x).

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

In this context, we can reasonably infer and logically deduce that the only linear equation that represents a proportional relationship is represented by the following;

y = kx

y = -1/4(x)

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Complete Question:

Which linear equation shows a proportional relationship?

y = 1/4(x) - 5

y = -1/4(x)

y = −4x+ 1

y = 4

The point being in the shaded region of the top inequality and not in the shaded region of the bottom Inequality is the condition for a point to be a solution to the system of two inequalities.

Graphically, a point is a solution to a system of two inequalities if and only if the point lies in the shaded region of the top inequality but not in the shaded region of the bottom inequality.

To understand this concept, let's consider a system of two inequalities represented graphically on a coordinate plane.

The shaded regions represent the solutions to each inequality. In a system of two inequalities, the solution consists of the overlapping region where both inequalities are satisfied.

When we say that a point lies in the shaded region of the top inequality, it means that the point satisfies the inequality represented by the top region. Similarly, when we say that a point does not lie in the shaded region of the bottom inequality, it means that the point does not satisfy the inequality represented by the bottom region.

Therefore, a point that lies in the shaded region of the top inequality but not in the shaded region of the bottom inequality is a solution to the system of two inequalities. It satisfies the top inequality but does not satisfy the bottom inequality.

On the other hand, if a point lies in the shaded region of the bottom inequality but not in the shaded region of the top inequality, it is not a solution to the system. It does not satisfy the top inequality but satisfies the bottom inequality.

If a point lies in the shaded regions of both the top and bottom inequalities, it is a solution to the system. It satisfies both inequalities simultaneously.

Finally, if a point does not lie in the shaded region of either the top or bottom inequality, it is not a solution to the system. It does not satisfy either inequality.

the point being in the shaded region of the top inequality and not in the shaded region of the bottom inequality is the condition for a point to be a solution to the system of two inequalities.

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The value of the probability P(W) is (d) .0.1878

From the question, we have the following parameters that can be used in our computation:

P(W|¬L) = 0.18, P(¬W|L) = 0.24, P(L) = 0.13

Using the complement probability, we have

P(¬L) = 1 - 0.13

Evaluate

P(¬L) = 0.87

Using the conditional probability formula, we have

P(W|¬L) = P(W and ¬L)/P(¬L)

P(¬W|L) = P(¬W and L)/P(L)

So, we have

P(W and ¬L)/0.87 = 0.18

P(¬W and L)/0.87 = 0.24

So, we have

P(W and ¬L) = 0.1566

P(¬W and L) = 0.2088

Using P(W and ¬L) = 0.1566, we have

P(W) * P(¬L) = 0.1566

So, we have

P(W) * 0.87 = 0.1566

Evaluate

P(W) = 0.18

The closest to this is 0.1878

Hence, the value of P(W) is  0.1878

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The area of the Sector of the circle is approximately 49.06 cm².

The area of the sector of a circle:

Area = (θ/360) * π * r^2

Where θ is the central angle in degrees, π is the mathematical constant pi, and r is the radius of the circle.

Given that the central angle is 225° and the radius is 5 cm, we can plug these values into the formula:

Area = (225/360) * 3.14 * (5)^2

Simplifying the equation, we have:

Area = (0.625) * 3.14 * 25

Area = 49.0625 cm²

Rounding to the nearest hundredth, the area of the sector of the circle is approximately 49.06 cm².

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The value of x for each item is given as follows:

a) x = 3.9.

b) x = 32.6º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For item a, we have that x is opposite to the angle of 63º, while 2 is the adjacent side, hence:

tan(63º) = x/2

x = 2 x tangent of 63 degrees

x = 3.9.

For item b, we have that x is the angle, while 7 is the opposite side and 13 is the hypotenuse, hence:

sin(x) = 7/13

x = arcsin(7/13)

x = 32.6º.

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The second garden would have a Horizontal measurement of 7.5 feet and a vertical measurement of 12 feet.

The dimensions of Camilia 's second garden, we'll use the given scale factors of 75% (horizontal) and 150% (vertical). Let's assume the original dimensions of the garden are x feet (horizontal) and y feet (vertical).

the horizontal measurement of the second garden, we multiply the original horizontal dimension (x) by the horizontal scale factor (75% or 0.75):

Horizontal measurement of the second garden = x * 0.75.

the vertical measurement of the second garden, we multiply the original vertical dimension (y) by the vertical scale factor (150% or 1.5):

Vertical measurement of the second garden = y * 1.5.

Therefore, the horizontal measurement of the second garden is x * 0.75 feet, and the vertical measurement of the second garden is y * 1.5 feet.

values for x and y, so we cannot provide exact measurements for the second garden. The given scale factors only allow us to determine the proportional changes in dimensions. If you have specific values for x and y, you can substitute them into the formulas above to find the corresponding measurements for the second garden.

if the original garden has a horizontal dimension of 10 feet (x = 10) and a vertical dimension of 8 feet (y = 8)

Horizontal measurement of the second garden = 10 * 0.75 = 7.5 feet.

Vertical measurement of the second garden = 8 * 1.5 = 12 feet.

the second garden would have a horizontal measurement of 7.5 feet and a vertical measurement of 12 feet.

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The rate of change of the line that contains the given points is 0.75 or 3/4.

To determine the rate of change of the line that contains the given points, we can calculate the slope of the line.

The slope represents the rate of change between any two points on a line.

Using the formula for slope (m) between two points (x₁, y₁) and (x₂, y₂):

m = (y₂ - y₁) / (x₂ - x₁)

Let's calculate the slope using the given points (-4, -7), (0, -4), and (8, 2):

For the points (-4, -7) and (0, -4):

m₁ = (-4 - (-7)) / (0 - (-4))

= (-4 + 7) / (0 + 4)

= 3 / 4

= 0.75

For the points (0, -4) and (8, 2):

m₂ = (2 - (-4)) / (8 - 0)

= (2 + 4) / 8

= 6 / 8

= 0.75

The slope is the same for both pairs of points, which means the line is a straight line and has a constant rate of change.

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Answer: [tex]\frac{1}{4}\;tsp\;[/tex]

Step-by-step explanation:

       To find the number of teaspoons of ground nutmeg and ground clover that are used altogether, we will add these individual amounts together.

[tex]\displaystyle \frac{1}{8}\;tsp\;+\frac{1}{8}\;tsp\;=\frac{2}{8}\;tsp\;=\frac{1}{4}\;tsp\;[/tex]

Answer:

All of the above, except for 'What is the name of the doctor at Healthy Kids Pediatrics?'

Step-by-step explanation:

What is your favorite television show that you watched this week? - If we define your favourite show as that which you watched most, you could gather data here on time spent watching each show to determine the answer

What store in the mall are you most likely to purchase apparel from? - Similar to before, data on your previous trips to the mall could be gathered to determine which stores you have been to the most often, and using this make a prediction of the most likely you are to purchase apparel from

How many students at your school have a skateboard? - Here data could be gathered by asking which students have a skateboard and which do not

What is the name of the doctor at Healthy Kids Pediatrics? - This question only has an answer, and it would be the name of the doctor

Answer:

How many students at your school have a skateboard?

Step-by-step explanation:

Since it is asking multiple people it can result in data. It can't result in data if it asks just one question to someone

Answer:

what we have to find or to prove.

Answer:

D

Step-by-step explanation:

579/1124 * 578/1123

= 0.2651

Answer:

From least likely to most likely

Step-by-step explanation:

Event 1 : Choosing either a  yellow or black marble from bag A
P(Event 1 ) = 1 because when you choose a marble from bag A, it must be one of the two colors

Event 2: yellow marble from Bag A
There are 9 yellow marbles and a total of 15 marbles
So P(Event 2 ) = 9/15 = 3/5 = 0.6

Event 3: black marble from bag B
There are 10 black marbles and a total of 20 marbles
P(Event 3 + 10/20 = 1/2 = 0.5

Event 4: green marble from bag B
There are no green marbles in bag B
P(Event 4) = 0

0 < 0.5 < 0.6 < 1
So the order of events from least likely to most likely is

Event 4    
Event 3
Event 2
Event 1

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

There are 48 different possible outcomes when combining the results of the two spinners and the pyramid die.

For each event, multiply the number of outcomes:

Spinner 1 has 3 outcomes (Walk, Run, Stop).

Spinner 2 has 4 outcomes (Red, Green, Blue, Orange).

The pyramid die has 4 outcomes (1, 2, 3, 4).

The total possible outcomes are the product of these, since each event is independent.

This results in 3 outcomes * 4 outcomes * 4 outcomes = 48 total outcomes.

Therefore, there are 48 different possible outcomes when combining the results of the two spinners and the pyramid die.

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The logarithm equation is solved and the equivalent value of c = 17

Given data ,

To solve the equation log₂ 4 + log₂ (c-9) = 5, we can combine the logarithms using logarithmic properties.

Using the property log a + log b = log (a x b), the equation becomes:

log₂ (4(c-9)) = 5

To eliminate the logarithm, we can rewrite the equation in exponential form. In exponential form, the equation becomes:

2⁵ = 4(c-9)

Simplifying the left side:

32 = 4(c-9)

Dividing both sides by 4:

8 = c - 9

Adding 9 to both sides:

8 + 9 = c

c = 17

Hence , the solution to the equation log₂ 4 + log₂ (c-9) = 5 is c = 17

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The Total cost for 24 cents (pencils) + 8N cents (notebooks) + 12P cents (colored paper) = 170 cents.

The total for everything cannot be $1.70,  the individual costs and calculate the total cost separately.

the price of each notebook is N cents and the price of each sheet of colored paper is P cents.

The cost of the pencils can be calculated as follows:

For the 2 pencils at 2 cents each: 2 pencils * 2 cents/pencil = 4 cents

For the 5 pencils at 4 cents each: 5 pencils * 4 cents/pencil = 20 cents

So, the total cost of the pencils is 4 cents + 20 cents = 24 cents.

the cost of the notebooks and colored paper:

The cost of 8 notebooks is 8 notebooks * N cents/notebook = 8N cents.

The cost of 12 sheets of colored paper is 12 sheets * P cents/sheet = 12P cents.

the total cost of the notebooks and colored paper, we add these two amounts together: 8N cents + 12P cents.

the total cost for everything is $1.70, we can express it in cents as 170 cents.

Therefore, the total cost for everything can be written as:

24 cents (pencils) + 8N cents (notebooks) + 12P cents (colored paper) = 170 cents.

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Answer:

To prove that (a4 +b4 + a2b2+ a2+b2-ab)/a2+b2+ab =1 we can follow the following steps.

Step-by-step explanation:

Factoring the numerator, we get

(a^4 + 2a^2b^2 + b^4 - ab + a^2 + b^2)/(a^2 + b^2 + ab).

we can also write it as

[(a^2 + b^2)^2 - ab + a^2 + b^2]/(a^2 + b^2 + ab).

Expanding  (a^2 + b^2)^2,

we get,

(a^4 + 2a^2b^2 + b^4 - ab + a^2 + b^2)/(a^2 + b^2 + ab).

After cancellation we get

[(a^4 + 2a^2b^2 + b^4) - ab + a^2 + b^2]/(a^2 + b^2 + ab).

By simplifying we get

(a^4 + a^2 + 2a^2b^2 + b^4 - ab + b^2).

At this point, we can see that the numerator is the same as the denominator, resulting in (a^2 + b^2 + ab)/(a^2 + b^2 + ab), which simplifies to 1.

Therefore, we have proved that (a4 +b4 + a2b2+ a2+b2-ab)/a2+b2+ab =1

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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The value of the arc length of Circle is,

S = 444

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

In a circle,

Radius = 2

Central angle = 222 degree

Since, We know that;

Arc length = Radius x central angle

Substitute given values, we get;

Arc length = 2 x 222

Arc length = 444

Thus, The value of the arc length of Circle is,

Arc length = 444

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Answer:

Edison, Hilary, and Kevin

Step-by-step explanation:

To determine which of the potential buyers will purchase one of the three mountain resort plots, we need to compare their willingness and ability to purchase with the minimum selling price of $445,000. Let's analyze each buyer:

Edison: Willingness to purchase - $600,000. Since this exceeds the minimum selling price, Edison can purchase a plot.

Hilary: Willingness to purchase - $510,000. Since this exceeds the minimum selling price, Hilary can purchase a plot.

Kevin: Willingness to purchase - $470,000. Since this exceeds the minimum selling price, Kevin can purchase a plot.

Maria: Willingness to purchase - $420,000. Since this does not exceed the minimum selling price, Maria cannot purchase a plot.

Rajiv: Willingness to purchase - $390,000. Since this does not exceed the minimum selling price, Rajiv cannot purchase a plot.

Simone: Willingness to purchase - $380,000. Since this does not exceed the minimum selling price, Simone cannot purchase a plot.

Based on the given information, the potential buyers who can purchase one of the three mountain resort plots are:

Edison

Hilary

Kevin

Therefore, the correct answers are Edison, Hilary, and Kevin.

Hope this helps!

(i) Data is presented below.

(ii)The optimal solution for the LPP is

⇒ x = 7600, y = 0, and z = 2800.

Type A fixtures, 0 dozens of Type B fixtures, and 2800 dozens of Type C fixtures to maximize their profit while staying within the time constraints for each process.

According to the given information,

(I) The Linear Programming Problem can be formulated as follows:

Maximize 11x + 16y + 15z

Subject to: x + 2y + 3/2z ≤ 12000 (Molding time)

               2/3x + 2/3y + z ≤ 4600 (Trimming time)

            1/2x + 1/3y + 1/2z ≤ 2400 (Packaging time)

Where,  x, y, z >= 0

where x, y, z represent the number of dozens of each type of fixture produced.

(ii) To convert the problem to standard form,

Introduce slack variables and express all constraints as equations.

The problem in standard form can be written as,

Maximize 11x + 16y + 15z + 0s1 + 0s2 + 0s3

Subject to: x + 2y + 3/2z + s1 = 12000 (Molding time)

              2/3x + 2/3y + z + s2 = 4600 (Trimming time)

            1/2x + 1/3y + 1/2z + s3 = 2400 (Packaging time)

Where x, y, z, s1, s2, s3 >= 0

(iii) Using the simplex tableau method, we can find the optimal solution to the LPP.

The initial tableau is,

Basis x y z s1 s2 s3 RHS

Basis x     y         z   s1 s2 s3 RHS

s1         1     2        3/2   1 0 0 12000

s2        2/3     2/3 1   0 1 0 4600

s3        1/2     1/3 1/2   0 0 1 2400

-------        --- --- --- ---- ---- ---- -----

z         11     16 15    0 0 0 0

We choose s1, s2, and s3 as the initial basis since they have a non-zero coefficient in the objective function.

The pivot element is 2/3 in row 2 and column x. We perform row operations to make the pivot element 1 and eliminate the other x-coefficients in column 1:

Basis x y z s1 s2 s3 RHS

s1           0 4/3 1/3 1 -2/3 0 9400

x          1 1 3/2 3/2 0 0 18000

s3          0 -1/3 1/3 -1/6 2/9 1 600

------- --- --------- --- ----------- ----------- ---- -------

z          0 5/3 7/6 -11/3 16 0 35200

The new pivot element is 5/3 in row 2 and column y. We perform row operations to make the pivot element 1 and eliminate the other y-coefficients in column 2,

Basis x y z s1             s2 s3    RHS

s1          0 0 1/5 13/15 -2/15 0 11600

x          1 0 2/15 -7/15          1/15 0 7600

s3          0 0 2/5 1/15          2/15 1 2000

------- --- --- --------- ----------- ----------- ---- -------

z           0 1 7/15 -11/9   16/9        0 21100

Hence,

The optimal solution for the Linear Programming Problem is

⇒ x = 7600, y = 0, and z = 2800.

This means that the manufacturer should produce 7600 dozens of Type A fixtures, 0 dozens of Type B fixtures, and 2800 dozens of Type C fixtures to maximize their profit while staying within the time constraints for each process.

The maximum profit achievable with this optimal solution is,

⇒ (11 x 7600) + (16 x 0) + (15 x 2800) = R 295,600.

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Answer:

45%

Step-by-step explanation:

Based on Valeria’s sample of 40 students, where 18 of them speak Spanish at home, the percentage of students at the school who speak Spanish at home can be estimated as (18/40) * 100% = 45%. This means that, according to her sample, approximately 45% of the students at the school speak Spanish at home.

Received message. Based on Valeria's sample of 40 students, where 18 of them speak Spanish at home, the percentage of students at the school who speak Spanish at home can be estimated as (18/40) * 100% = 45%. This means that, according to her sample, approximately 45% of the students at the school speak Spanish at home.

Answer:

The Correct answer is diameter

The solution to the equation x² - 6x + 4 = 0 by graph is x = 0.76 and x = 5.24

From the question, we have the following parameters that can be used in our computation:

x² - 6x + 4 = 0

The above function is a quadratic function that has the following features

a = 1

b = -6

c = 4

This is so because a quadratic equation is represented as

ax² + bx + c = 0

Next, we plot the graph using a graphing tool by taking note of the above features

The graph of the function is added as an attachment

From the graph, the equation intersect the x-axis at:

x = 0.76 and x = 5.24

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The  polynomial function graph tat has an end behavior that is different from the rest is option D.

The difference between Option D and the rest is the the starting and ending quadrants  in which they are defined.

Note that Polynomials A to C  start from the 4th quadrant and end in the second  while Option D starts from the 1st and ends in the 3rd.

This means that Set A-C polynomials have beginning points in the fourth quadrant and final points in the second quadrant. The polynomials in set D, on the other hand, have their beginning points in the first quadrant and their ultimate points in the third quadrant.

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