Question 1
The degree of recurrence relation an = 2an-2 + 5an-11 is
Question 2
In how many ways can an organization containing 47 members elect a president, treasurer and secretary (assuming no person is elected to more than one position)?
Question 3
The sum of the first 96 positive odd integers is
Question 4
The Greatest Common Divisor (GCD) of 28 × 37 × 59 and 22 × 32 × 54 is
Please I need the solution with steps.

The print you specifically described is entitled "No se puede saber por qué" (translated as "One cannot know why") in Spanish.

Goya mocks the many superstitions and illogical ideas that were pervasive in Spanish culture at the time in this print. A crowd is gathered around a fortune teller who is looking into a crystal ball in the picture. The people are portrayed in a variety of excited and anxious states, indicating their readiness to accept the fortune teller's predictions in the face of a lack of proof or logic.

Even in modern times, the topic of irrational beliefs and superstitions persists, albeit it may take many forms depending on the culture or civilization. For instance, despite the fact that there is little scientific proof to back up their claims, some people continue to turn to astrology, psychics, or alternative medicine. Similar to this, false information and conspiracy theories are still proliferating quickly in the social media age, feeding irrational views and mistrust of authorities and organizations.

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* A stratified sampling design should be used, with plants stratified by size, location, and union representation.

* Within each stratum, a random sample of employees should be selected.

* The sample size should be large enough to ensure that the results are statistically significant.

* Stratified sampling is a type of sampling in which the population is divided into groups, or strata, and then a random sample is selected from each stratum. This ensures that the sample is representative of the population as a whole.

* In this case, the population is the 10 plants of the company. The strata could be defined by plant size, location, and union representation. For example, one stratum could be plants with 500 or fewer employees, another stratum could be plants located in the United States, and another stratum could be plants that are unionized.

* Within each stratum, a random sample of employees should be selected. The sample size should be large enough to ensure that the results are statistically significant. This means that the results are likely to be accurate and representative of the population as a whole.

This sampling design will allow the company to collect data from a representative sample of employees and supervisors from all of its plants. This data can then be used to assess the feasibility of using robotics as a solution to the manufacturing worker shortage.

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Answer:

boy would be 12 brother would be 6

Step-by-step explanation:

8+4 = 12

         ----  brother = 6

          2

The function f(x) = (3x + 2)⁴ when expanded is f(x) = 81x + 216x³ + 216x² + 96x + 16

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

f(x) = (3x + 2)⁴

Using the pascal triangle at n = 4, we have the coefficients to be

Coefficient = 1     4     6     4     1

So, when the function f(x) = (3x + 2)⁴ is expanded, we have

f(x) = 1 * (3x)⁴ + 4 * (3x)³ * 2 + 6 * (3x)² * 2² + 4 * (3x) * 2³ + 1 * 2⁴

Evaluate

f(x) = 81x + 216x³ + 216x² + 96x + 16

Hence, the solution is f(x) = 81x + 216x³ + 216x² + 96x + 16

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Complete question

What is the value of f(x) = (3x + 2)⁴ when expanded?

The length of the curve described by the function is approximately 21.14 units.

The length of the curve described by the function y = f (x) can be found using the formula below:$$\int_{a}^{b} \sqrt{1+\left[\frac{d y}{d x}\right]^{2}} d x$$

Where, a and b are the limits of the function.The function is y = 3x² + 4, which is a quadratic function.

Therefore, the derivative of y can be obtained as follows:$$\frac{d y}{d x} = 6x$$

Substitute the derivative of y into the formula to obtain:$$\int_{a}^{b} \sqrt{1+(6 x)^{2}} d x$$Integrating,

we have:$$\int_{a}^{b} \sqrt{1+36 x^{2}} d x$$Let u = 1 + 36x², then du/dx = 72x

which implies dx = 1/72 du/u^(1/2).

Hence, the integral is transformed to:

$$\frac{1}{72} \int_{1}^{37} u^{1 / 2} d u$$

Therefore, the integral is equal to:

$$\frac{1}{72}\left[\frac{2}{3} u^{3 / 2}\right]_{1}^{37}

= \frac{1}{72}\left[\frac{2}{3}\left(37^{3 / 2}-1\right)\right] \approx \boxed{21.14}$$T

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The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.

So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:

A'(-3, 3 - 4) = A'(-3, -1)

B'(0, 4 - 4) = B'(0, 0)

C'(-3, 0 - 4) = C'(-3, -4)

Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).

So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).

To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

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The 11 people that were going to Canada with Harriet Tubman put an ashcake and salt herring in an old bandanna to keep themselves from getting hungry during their long journey.

The ash cake was made of cornmeal and water, which was cooked over an open fire. It was one of the cheapest and most convenient foods for the slaves to carry during their journey.

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Answer:

(2, 5 )

Step-by-step explanation:

To find the point of intersection, solve the equations simultaneously.

y = 4x - 3 → (1)

y = 9x - 13 → (2)

Substitute y = 9x - 13 into (1)

9x - 13 = 4x - 3 ( subtract 4x from both sides )

5x - 13 = - 3 ( add 13 to both sides )

5x = 10 ( divide both sides by 5 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (1)

y = 4(2) - 3 = 8 - 3 = 5

point of intersection = (2, 5 )

Answer:

The value of x = 1

Step-by-step explanation:

2x+3 = 5

=> 2x = 5-3

=> 2x = 2

=> x = 2/2

=> x = 1

Answer:

Step-by-step explanation:

In this question we are given with an equation that is 2x + 3 = 5 . And we are asked to find the value of x .

Solution : -

\( \longmapsto \qquad \: 2x + 3 = 5\)

Step 1 : Subtracting with 3 on both sides :

\( \longrightarrow \qquad \:2x + \cancel{ 3} - \cancel{3} = 5 - 3\)

On further calculations, We get :

\( \longrightarrow \qquad \:2x = 2\)

Step 2 : Dividing with 2 on both sides :

\( \longrightarrow \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2}} = \cancel{\dfrac{2}{2} }\)

On calculating further, We get :

\( \longrightarrow \qquad \: \blue{\underline{\boxed{ \sf{x = 1}}}} \quad \bigstar\)

Verifying : -

Now we are checking our answer by substituting value of x in the given equation . So ,

Therefore , our answer is correct .

Answer:

Explanations (4) Similarity is a quality of scaling: two shapes are similar if you can scale one to be like the other, like these triangles ABC and DEF. Since all circles are of the same shape (they only vary by size), any circle can be scaled to form any other circle. Thus, all circles are similar!

Step-by-step explanation:

Welcome

The percentage is 75%, the amount is 45 and the base is 60 so option (D) will be correct.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.

Given that 45 is some percentage of 60

So, 60 will be the base because we are calculating the percentage of it and the amount will be 45.

Let's say 45 is x percentage of 60

Then,

60 × x/100 = 45

x = 4500/60

x = 75%

Percentage will be 75

Hence "The percentage is 75%, the amount is 45 and the base is 60".

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The probability that a randomly chosen Ameri- can adult is a member of one of the two major political parties (Republicans and Democrats) is - (b) 0.59

12.24 This probability model is:
(a) continuous
(b) finite
(c) equally likely

Your answer: (b) finite.
Explanation: The model has a finite number of outcomes (Republican, Independent, Democrat, and Other) with assigned probabilities.

12.25 The probability that a randomly chosen American adult's political affiliation is "Other" must be:
(a) any number between 0 and 1
(b) 0.02
(c) 0.2

Your answer: (b) 0.02
Explanation: The probabilities for Republican, Independent, and Democrat affiliations are 0.28, 0.39, and 0.31, respectively. The sum of these probabilities is 0.98, so the probability of "Other" must be 1 - 0.98 = 0.02.

12.26 What is the probability that a randomly chosen American adult is a member of one of the two major political parties (Republicans and Democrats)?
(a) 0.39
(b) 0.59
(c) 0.98

Your answer: (b) 0.59
Explanation: To find the probability, add the probabilities of the Republican and Democrat affiliations: 0.28 + 0.31 = 0.59.

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An equation with the steepest graph has the largest absolute value of slope.

The equation with the steepest graph is the equation with the largest absolute value of slope.

A slope is a measure of how steep a line is.

If a line has a positive slope, it is rising to the right.

If a line has a negative slope, it is falling to the right.

If the slope of a line is zero, the line is horizontal.

To multiply the square root of 2 + i and its conjugate, you can use the complex multiplication formula.

(a + bi)(a - bi) = \(a^2 - abi + abi - b^2i^2\)

where the number is √2 + i. Let's do a multiplication with this:

(√2 + i)(√2 - i)

Using the above formula we get:

\((\sqrt{2})^2 - (\sqrt{2})(i ) + (\sqrt{2} )(i) - (i)^2\)

Further simplification:

2 - (√2)(i) + (√2)(i) - (- 1)

Combining similar terms:

2 + 1

results in 3. So (√2 + i)(√2 - i) is 3.

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a) To make the given function a legitimate probability mass function (pmf), the sum of probabilities for all possible values of x must be equal to 1.

We have the probability mass function f(x) = k(52​)x for x = 1, 2, ...

Summing the probabilities: ∑f(x) = f(1) + f(2) + f(3) + ...

       = k(52​)1 + k(52​)2 + k(52​)3 + ...

We want this sum to equal 1, so: ∑f(x) = k(52​)1 + k(52​)2 + k(52​)3 + ... = 1

Since this is an infinite geometric series with a common ratio of k(52​), we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Here, a = k(52​)1 and r = k(52​). Plugging in the values:

∑f(x) = k(52​)1 / (1 - k(52​)) = 1

Solving this equation for k:

k(52​) / (1 - k(52​)) = 1

k(52​) = 1 - k(52​)

2k(52​) = 1

k = 1 / (2(52​))

So, the value of k that makes this a legitimate pmf is k = 1 / (2(52​)).

b) To find P(X > 2), we need to sum the probabilities of all values greater than 2.  P(X > 2) = f(3) + f(4) + f(5) + ...

Using the probability mass function f(x) = k(52​)x, we substitute the values of x: P(X > 2) = k(52​)3 + k(52​)4 + k(52​)5 + ...

Since k = 1 / (2(52​)), we substitute this value:

P(X > 2) = (1 / (2(52​)))(52​)3 + (1 / (2(52​)))(52​)4 + (1 / (2(52​)))(52​)5 + ...

Simplifying, we have: P(X > 2) = (52​)2 + (52​)3 + (52​)4 + ...

This is another infinite geometric series with a common ratio of 52​. Using the sum formula: Sum = a / (1 - r)

Here, a = (52​)2 and r = 52​:

P(X > 2) = (52​)2 / (1 - 52​) = (52​)2 / (1 - 1/52​) = (52​)2 / (52​ - 1)

c)To find P(X < 5 | X > 2), we need to calculate the conditional probability of X being less than 5 given that X is greater than 2.

P(X < 5 | X > 2) = P(X < 5 and X > 2) / P(X > 2)

Using the probability mass function, we can calculate the probabilities:

P(X < 5 and X > 2) = f(3) + f(4) = k(52​)3 + k(52​)4

P(X > 2) = (52​)2 + (52​)3 + (52​)4 + ...

Since we have already derived the expression for P(X > 2) in part (b), we can use that result:

P(X > 2) = (52​)2 / (52​ - 1)

Substituting these values into the conditional probability formula:

P(X < 5 | X > 2) = (k(52​)3 + k(52​)4) / [(52​)2 / (52​ - 1)]

Remember that k = 1 / (2(52​)), so we can substitute this value:

P(X < 5 | X > 2) = [(1 / (2(52​)))(52​)3 + (1 / (2(52​)))(52​)4] / [(52​)2 / (52​ - 1)]

Simplifying further, we have

P(X < 5 | X > 2) = [52​ + (52​)2] / [(52​)2 / (52​ - 1)] = (52​ + (52​)2) * (52​ - 1) / (52​)2

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Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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The Production Possibility Frontier (PPF) is often called the "Opportunity Cost Curve" because it illustrates the concept of opportunity cost.

Opportunity cost is the cost of one alternative in terms of the benefits forgone of the best alternative. In other words, it's the cost of one choice in terms of the best alternative choice.

As we move along the PPF, we can see that as we produce more of one good, we must give up some production of the other good. This trade-off is represented by the slope of the PPF, which is the opportunity cost of producing one good in terms of the other good. The PPF illustrates the relationship between production and opportunity cost by showing the trade-offs that must be made and the opportunity costs associated with different production choices.

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The numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

A way of writing numbers is known as a number system.

There are the following number systems:

Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses 10 symbols to represent all possible numbers.

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Answer:

y = 5x + 19

Step-by-step explanation:

y = 5x + b

4 = 5(-3) + b

4 = -15 + b

19 = b

Answer:

just take the 96 and 66 and middle it then take y multiply that=answer

Step-by-step explanation:

Answer: 48

Step-by-step explanation: 96/2

Yes, the equation y = 5x represents a proportional relationship

Two or more expressions with an Equal sign is called as Equation.

The given equation is y=5x.

In a proportional relationship, the ratio of y to x is constant.

In the given equation the variable x and y has a proportional relationship.

The equation is in the form of y=mx+b

the ratio of y to x is 5, meaning that for every unit increase in x, y increases by 5 units.

Hence,  Yes, the equation y = 5x represents a proportional relationship

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\(x + 55 = 180 \\ x = 180 - 55 \\ x = 125°\)

Th given number " six hundred thousand eight" can be written in the standard form as 600,008.

To write "six hundred thousand eight" in standard form, we need to write the number using digits in the appropriate place value positions.

The digit "8" is in the "ones" position, the digit "0" is in the "tens" position, the digit "0" is in the "hundreds" position, the digit "0" is in the "thousands" position, the digit "0" is in the "ten thousands" position, and the digit "6" is in the "hundred thousands" position.

Therefore, it can be concluded that we can write the given number in standard form as 600,008.

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The domain and range of the given function are 0 ≤ x ≤ 6 and 0 ≤ y ≤ 6 respectively.

The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.

Here,
The domain is the set of the value of the independent variable in the function which is given in the graph,
From x = 0 to x = 6
or
0 ≤ x ≤ 6

The range is the set of the value of the dependent variable in the function which is given in the graph,
From y = 6 to = 0
or
0 ≤ y ≤ 6

Thus, the supplied function domain and range are 0 ≤ x ≤ 6 and 0 ≤  y ≤ 6 correspondingly.

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Since the denominator approaches 0 and the numerator is constant, the limit goes to -infinity: -∞

To evaluate the limit lim_(x->infinity) x tan(3/x), we can use the fact that as x approaches infinity, 3/x approaches zero. Therefore, we can rewrite the limit as lim_(y->0) (3/tan(y))/y, where y=3/x.

Using the limit identity lim_(y->0) (tan(y))/y = 1, we can simplify the expression as:

lim_(y->0) (3/tan(y))/y = lim_(y->0) 3/(tan(y)*y) = 3 lim_(y->0) 1/(tan(y)*y)

Now, we can use another limit identity lim_(y->0) (1-cos(y))/\(y^2\) = 1/2, which implies lim_(y->0) cos(y)/\(y^2\) = 1/2.

Multiplying and dividing by cos(y) in the denominator of the expression, we get:

lim_(y->0) 1/(tan(y)*y) = lim_(y->0) cos(y)/(sin(y)*y*cos(y)) = lim_(y->0) cos(y)/\(y^2\) * 1/sin(y)

Using the limit identity above, we can rewrite this as:

lim_(y->0) cos(y)/\(y^2\) * 1/sin(y) = 1/2 * lim_(y->0) 1/sin(y) = infinity

Therefore, the limit lim_(x->infinity) x tan(3/x) equals infinity.
To evaluate the limit lim_(x->infinity) x*tan(3/x), we can apply L'Hopital's Rule since this is an indeterminate form of the type ∞*0.

First, let y = 3/x. Then, as x -> infinity, y -> 0, and we rewrite the limit as:
lim_(y->0) (3/y) * tan(y)

Now, take the derivatives of both the numerator and the denominator with respect to y:
d(3/y)/dy = -3/\(y^2\)
d(tan(y))/dy = \(sec^2\)(y)

Using L'Hopital's Rule, the limit becomes:
lim_(y->0) (-3/\(y^2\)) / \(sec^2(y)\)

As y approaches 0,\)sec^2(y)\) approaches 1, so the limit simplifies to:
lim_(y->0) (-3/\(y^2)\)

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Answer:

it’s f(x)=135cos(34 pi t)+262

Step-by-step explanation:

got it right on edge

The function represents the height, in feet, of the tip of this blade after t minutes is h = 135sin(π3.5t)+262. Then the correct option is A.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

The height of the blade as a function f time can be written in the following way:

h = Asin(xt) + B, where:

B- The initial height of the blade above the ground.

A- The amplitude of the length of the blade.

x - period.

The initial height is 262 ft, therefore, B = 262ft. The amplitude of the length of the blade is 135ft. Therefore, A = 135.

The period is two rotations every minute, therefore the period should be:-

x =60/17

x = 3.5π

Finally, the equation that can be used to model h is:

h = 135sin(π3.5t)+262

Hence, the correct option is A.

The complete options are given below:-

A. h = 135sin(π3.5t)+262

B. h = 262sin(π3.5t)+135

C. h = 3.5sin(π262t)+135

D. h = 135sin(π262t)+ 3.5

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A calculator or statistical software, we can calculate the value of P(X = 5) to get the final answer.

To calculate the probability of getting a 4 exactly five times when rolling a six-sided die 12 times, we can use the concept of binomial probability.

The probability of getting a 4 on a single roll of a six-sided die is 1/6, since there is one favorable outcome (rolling a 4) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

Now, let's denote "success" as rolling a 4, and "failure" as rolling anything other than a 4. We need to calculate the probability of getting 5 successes (rolling a 4) in 12 trials (rolling the die 12 times), assuming each trial is independent.

Using the binomial probability formula:

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

where:

P(X = k) is the probability of getting exactly k successes

C(n, k) is the number of combinations of n items taken k at a time

p is the probability of success on a single trial

n is the number of trials

Plugging in the values for our problem:

k = 5 (number of successes)

n = 12 (number of trials)

p = 1/6 (probability of getting a 4 on a single trial)

P(X = 5) = C(12, 5) * (1/6)^5 * (1 - 1/6)^(12 - 5)

Using a calculator or statistical software, we can calculate the value of P(X = 5) to get the final answer.

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The polar coordinates of the rectangular coordinates are  (4,5π/3)Option D is correct.

A two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane is as the polar coordinate.

The polar coordinate standard form is;

\(\rm x = rcos \theta \\\\\ y= rsin \theta\)

The value of the r is the resultant of the coordinate;

\(\rm r= \sqrt{2^2+(-2\sqrt{3})^2 } \\\\r= 4\)

The angle is found as ;

\(\theta = tan^{-1}(\frac{y}{x}) \\\\ \theta = tan^{-1} \frac{-2\sqrt{3} }{2} \\\\ \theta = -60^0\)

\(x= rcos \theta \\\\ x= 4 cos(-60) \\\\ x= rcos \theta \\\\ x= 4 cos [-\frac{\pi}{3} ]\\\\ \rm y = r sin \theta \\\\ y= 4 sin [-\frac{-\pi}{6}]\)

Hence the polar coordinates of the rectangular coordinates are  (4,5π/3)Option D is correct.

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