let sn be the number of successes in n independent bernoulli trials, where the probability of success for each trial is 1/2. evaluate the following limits.
(a) n→[infinity]lim P( 2n− 3n ≤S n ≤ 2n​ + 3n)
(b)n→[infinity] lim P( 2n− 4n ≤S n ≤ 2n+ 4n)
(c) n→[infinity]lim P(2n−20≤Sn ≤ 2n+20)

Demographic segmentation is considered for identifying subgroups of the overall marketplace based on factors such as age or income level.

A precise method of identifying an audience is known as demographic segmentation. It is based on information such as age, gender, marital status, family size, income, education, race, occupation, nationality, and/or religion. It is one of the four primary categories of marketing segmentation and is possibly the most used approach.

By concentrating on specific qualities that may represent relevant markets for a firm, demographic segmentation joins consumers and potential customers together. The five primary demographic subgroups are :

Demographic segmentation is the process of dividing a market into subgroups based on factors such as age, gender, income level, education level, and geographic location. This is a common way for businesses to identify and target specific groups of consumers who are likely to be interested in their products or services. By understanding the characteristics of different demographic segments, businesses can tailor their marketing efforts and products to better meet the needs and preferences of these groups. This can help businesses to effectively reach and engage their target audience, and ultimately increase sales and profits.

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Answer:

22years old

Step-by-step explanation:

Let Fiona's age = x

Darwin age

2x+6 = 50

2x = 50 -6

2x = 44

x= 44/2

x = 22years old

Answer:

1/2x

Step-by-step explanation:

Answer:

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

Let the numbers be x and y, where x is greater and y is lesser.

Given that x = 2y.

Find y:

The function f such that F = ∇f does not exist, and the answer is DNE (does not exist).

Generally, To determine whether or not the vector field is conservative, we need to check if its curl is zero. The curl of the given vector field is:

curl(F) = ∇ x F

          = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k

Substituting in the values of the components of F, we get:

curl(F) = (-cos(z))i + (0)j + (-y sin(z))k

Since the curl of the vector field is nonzero, the vector field is not conservative.

Therefore, the solution is DNE, and the function f such that F = f does not exist (does not exist).

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H(x) is a decreasing function too.  fog will be decreasing function.

An easy definition of a function?

As a set of inputs with one output for each, a function is defined as a relationship between them.

                     In plain English, a function is an association between inputs in which each input is connected to precisely one output.

Let  h(x) = f(g(x))

 Hence,

        h'(x) = f'(g(x) ) . g(x)

  h'(x) = f'g(x)) . g(x)

 Now g(x) is a strictly decreasing function.

Then

  g'(x) < 0 for all real x.

Hence

     h'(x) < 0

since h'(X) = f'(g(X)) . g'(X) and g'(x) < 0

 Therefor h(x) is a decreasing function too.

 Hence fog will be decreasing function.

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The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).

The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.

If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :

G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).

We have , two triangles with vertices,

a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).

b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).

Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).

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Complete question:

Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)

b) (1,5),(3,8),(0,2)

The inequality statement that same as x ≥ -3 or x > 2 is option (A) x ≥ -3

The inequality statement is

x ≥ -3 or x > 2

The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal to, greater than, greater than or equal to etc.

The compound inequality is

x ≥ -3 or x > 2

The value of x is greater than or equal to -3 also value of x is greater than 2

Here x ≥ -3 express then values of the compound inequality

Therefore, the same inequality statement is option (A) x ≥ -3

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Answer:

To solve the equation |2x - 5| = 7, you can set up two equations, one for the positive solution and one for the negative solution.

For the positive solution, you can start by isolating the absolute value expression on the left-hand side of the equation: |2x - 5| = 7 can be rewritten as 2x - 5 = 7. Then, you can solve this equation by adding 5 to both sides to get 2x = 12, and then dividing both sides by 2 to get x = 6.

For the negative solution, you can start by noting that the absolute value of a number is equal to its opposite if it is negative, so |2x - 5| = 7 can be rewritten as -(2x - 5) = 7. This equation can be solved by multiplying both sides by -1 to get 2x - 5 = -7, and then adding 5 to both sides to get 2x = -2. Then, dividing both sides by 2 to get x = -1.

Therefore, the two equations to solve the equation |2x - 5| = 7 are 2x - 5 = 7 and 2x - 5 = -7.

Answer:

C

Step-by-step explanation:

To solve the equation |2x - 5| = 7, we need to set up two equations, one for the case where the absolute value is equal to the positive value of the expression inside the absolute value bars, and one for the case where the absolute value is equal to the negative value of the expression inside the absolute value bars.

The first equation we need to set up is 2x - 5 = 7. In this case, the absolute value is equal to the positive value of 2x - 5, so we can simply set the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

2x - 5 = 7

The second equation we need to set up is -(2x - 5) = 7. In this case, the absolute value is equal to the negative value of 2x - 5, so we need to set the negative of the expression inside the absolute value bars equal to the given value of 7. This equation can be written as follows:

-2x+5 = 7

We can use these two equations to solve for the value of x. To solve the first equation, we can simply add 5 to both sides to get 2x = 12, and then divide both sides by 2 to get x = 6. To solve the second equation, we can first distribute the negative sign to get -2x + 5 = 7, and then add 5 to both sides to get -2x = 2. Finally, we can divide both sides by -2 to get x = -1.

Therefore, the two solutions to the equation |2x - 5| = 7 are x = 6 and x = -1.

Alternative:

2x-5 = 7

2x-5 = -7

The graph of the equation y=-3/5+3 will be a straight line

The graph of a straight line is always straight.  The equation is written in slope intercept for where -3/5 is the

The form of an equation in slope intercept form is y=mx+c

Here, m=-3/5

c=3

To draw the line, from the point 3 on the x-axis, rise negative 3 and run 5

The draw the line for form a straight line

Note that the formula for slope is

S=rise/run

In conclusion, the equation forms a straight line.

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Answer: C

Step-by-step explanation:

It's easy! Don't worry!

f(x) = 1/2(3x+7)

f(9) = 1/2(3(9)+7)

f(9) = 1/2(27+7)

f(9) = 1/2(34)

f(9) = 17

Trust me when you finish algebra this stuff is cake not going to lie. I did it under a minute. ;)

Also, gl passing algebra!

Answer: I think that y =18

Step-by-step explanation: I thought this bc the one across from it is also 18 and they look equal. I hope I helped

Answer: C. 2x+3y=7.20  4x+2y=8.80

Step-by-step explanation: 2x and 4x = grapefruit,  3y and 2y = oranges

We have to make sure that we are taking square roots of non-negative values to stay within the real number system.

You have to make sure x^2-16 ≥ 0 for the inner square root to stay in the real numbers.

You also have to make sure sqrt(x^2-16)-3 ≥ 0 for the outer square root to stay in the real numbers.

Solving x^2-16 ≥ 0 we have that x^2 ≥ 16, so either x≥4 or x≤-4.

Solving sqrt(x^2-16)-3 ≥ 0, we have

     sqrt(x^2-16) ≥ 3

              x^2-16 ≥ 9

                   x^2 ≥ 25

    either x ≥ 5 or x ≤ -5.

Since that second condition is more restrictive that x ≥ 4 or x ≤ -4, we can default to just using

   { x | x ≥ 5 or x ≤ -5 }

   (-infty, -5) U (5, infty)

The continuous function f is defined on the closed interval −6 ≤ x ≤ 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It is known that the point (3, 3 −√5 ) is on the graph of f. 4.

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.

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Answer:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Step-by-step explanation:

The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term (in this case, 11) and q is a factor of the leading coefficient (in this case, 5).

Using this information, we can determine that the potential rational roots of the polynomial f(x) = 5x³-7x+11 are all of the following:

1/5

-1/5

11/5

-11/5

1

-1

11

-11

Note that this list includes all possible rational roots of the polynomial, but not all of these roots will necessarily be actual roots. To determine which of these potential rational roots are actual roots, we would need to test them by plugging them into the polynomial and solving for x.

The total time taken by Amy to complete her assignments is 19/20 hours.

Addition is one of the four basic operations of arithmetic, Addition in maths is a process of combining two or more numbers.

Given that, Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.

Total time taken by Amy = Time taken for chemistry assignment + Time taken for history assignment

= 1/5+3/4 = (15+4)/20

= 19/20

Hence, The total time taken by Amy to complete her assignments is 19/20 hours.

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Answer:

Your Polynomial: [tex]x^3-13x^2+36x=0[/tex]

Step-by-step explanation:

Given information: 0 , 4 , 9

0 -> x = 0 -> (x - 0) = 0

4 -> x = 4 -> (x - 4) = 0

9 -> x = 9 -> (x - 9) = 0

(x - 0)(x - 4)(x - 9) = 0

x * (x - 4) * (x - 9) = 0

(x^2 - 4x) * (x - 9) = 0

x^3 - 9x^2 - 4x^2 + 36x = 0

The solution set of the compound inequality is written as:

(-∞, -4] U (6,  ∞)

First, we need to simplify the two given inequalities, the first one is:

7x + 6 > 4x + 24

Grouping like terms we will get:

7x - 4x > 24 - 6

3x > 18

x > 18/3

x > 6

The other inequality gives:

2*(-13x - 1) - 8 ≥ -10x + 54

-26x - 2 - 8 ≥ -10x + 54

-26x - 10  ≥ -10x + 54

-10 - 54 ≥ -10x + 26x

-64 ≥ 16x

-64/16 ≥ x

-4 ≥ x

So the compound inequality is:

-4 ≥ x

x > 6

Then the solution set written as an interval is:

(-∞, -4] U (6,  ∞)

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Is Shaylee able to invest in all of these projects simultaneously is no. Since the company has limited excess of money i.e. 2 Million to invest.

What is probability index?

The present value of benefits for each dollar of investment is calculated using the profitability index approach. In other words, it involves the ratio that is produced by comparing the ratio of the initial investment to the present value of future cash flows from a project.

A solid investment is one with a profitability index of greater than 1.0, with higher values indicating more alluring enterprises.

The ratio between the initial investment and the present value of future cash flows is measured by the profitability index (PI). The index can be used to rate investment projects and display the value produced per investment dollar.

Profitability Index = Present Value of Cash INflows / Present Value of Cash Outflows

Project : Profitability Index

A : 1.8434 (765,000 / 415,000)

B : 1.8043 (415,000 / 230,000)

C : 1.6667 (1200,000 / 720,000)

D : 1.6508 (1560,000 / 945,000)

Order of Preference

Project - Order of Preference

A - First Preference

B - Second Preference

C - Third Preference

D - Fourth Preference

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The AR(1) model was used to create an updated forecast for Amazon sales that account for trend, seasonality, and serial correlation is 97.6510

Accounting and revenue

Given that:

Equation of regression

Revenue = 22.67 + 2.538*t - 10.44*Q1 + 11.156*Q2- 8.77*Q3

t = 1 for the third quarter of 2013.

t = 33 for the third quarter of 2021

Revenue = 22.67 + 2.538*33 - 8.77 = 97.6510 billion dollars.

Therefore, Revenue = 97.6510 billion dollars

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8/3X = 1 + 5/3X

8/3X - 5/3 = 1 + 5/3X - 5/3X

3/3X = 1

X = 1

first box = 8

second box = 8

third box = 5/3x

fourth box = 3

fifth box = 1

sixth box = 1

Answer: To make 7 servings of the recipe, you will need:

Sauce: 7 servings * 15 cups/5 servings = <<7*15/5=21>>21 cups

Oregano: 7 servings * (2.5 tsp/5 servings) = <<7*(2.5/5)=1.75>>1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

Step-by-step explanation:

They will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, To make 7 servings of the recipe, you will need:

Sauce:

⇒ 7 × 15 /5

⇒ 21 cups

Oregano: \

⇒ 7 × (2.5 /5 )

⇒ 1.75 tsp

So, you will need 21 cups of sauce and 1.75 tsp of oregano to make 7 servings of the recipe.

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We are 95% confident that the interval 29.7215 to 30.5029 includes the population mean age of all respondents.

What does a 95% confidence interval indicate?

With a 95 percent confidence interval, you have a 5 percent chance of being wrong. With a 90 percent confidence interval, you have a 10 percent chance of being wrong. A 99 percent confidence interval would be wider than a 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).

According to the given question:

Conclusions about statistical significance are possible with the help of the confidence interval. If the confidence interval does not include the value of zero effect, it can be assumed that there is a statistically significant result.

±2828.6, ±3370.3, and ±4429.6

a. A larger sample size would cause the interval to narrow.

b. Near certainty; 50.1% (a majority) is far below the 95% confidence interval for the population proportion.

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a.) 0.5367 feet

b.) 0.5223 feet'

Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).

The amount of growth can be gotten by integrating the given rate equation as shown:

[tex]\int\limits {0.5} \, + \frac{6}{(t+4)^{3} } dt[/tex]

[tex]=\int\limits {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx[/tex]

[tex]=0.5t+\int\limits6u^{-3} du \, \,where \,u=t +4 \, and \, du=dt[/tex]

[tex]=0.5t+6*\frac{u^{-3} }{-2} + C[/tex]

[tex]=0.5t-3u^{-2}+C[/tex]

[tex]=0.5t-3(t+4)^{-2} +C[/tex]

a)  The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from  t =1 to t = 2

[tex]\int\limits^2_1 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \, =[0.5t-3(t+4)^{-2} ][/tex]

[tex]=[0.5(2)-3(2+4)^{-2} ]-[0.5-3(5)^{-2} ][/tex]

[tex]=\frac{11}{12}-\frac{1}{2}-\frac{3}{25}[/tex]

[tex]=0.9167-0.5+0.12[/tex]

[tex]=0.5367[/tex]

b)  The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from  t =2 to t = 3

[tex]\int\limits^3_2 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \,[/tex]

[tex]=[0.5t-3(t+4)^{-2} ][/tex]

[tex]=[1.5-\frac{3}{49} ]-[1-\frac{1}{12} ][/tex]

=1.439-0.9167

=0.5223 feet

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The probability that the student lived in the Gold dorm and was an underclassmen is of:

0.035 = 3.5%.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

The parameters for this problem are given as follows:

Hence the probability that the student lived in the Gold dorm and was an underclassmen is calculated as follows:

p = 0.7 x 0.05 = 0.035 = 3.5%.

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No , the carpeted rooms does not have more bacteria than uncarpeted rooms .

Given ,

α=0.05

n1=8

n2 = 8

mean = ∑x / n

x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2

and

x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78

Variance ,

s1  =2.6

s2 = 3.2

HYPOTHESES

H0 : μ 1 =μ 2

H1 : μ 1  ≠μ 2

​Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.

On calculating we get the test statistic t as,

t = 1.771

The null hypothesis is rejected if the test statistic's value falls within the rejection zone.

0.956<1.771,

therefore , fail to reject H .

Therefore , there is no support for the null hypothesis , so we accept the alternate hypothesis as true.

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​

Answer:

6.5 cm < x < 14.5 cm

Step-by-step explanation:

The length of the side of a triangle must be greater than the difference of the lengths of the other two sides and less than the sum of the other two sides.

Difference: 10.5 cm - 4 cm = 6.5 cm

Sum: 10.5 cm + 4 cm = 14.5 cm

Answer: 6.5 cm < x < 14.5 cm

When one adds a one digit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added.

It's important to bite that a decade number simply means the numbers that are counted when counting numbers by tens to 100.

In this situation, when one adds a one diigit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added. Any example will be:

= 10 + 2

= 12

In this case, the 2 is in the units value of the number

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The standard deviation of the income that the insurer will receive can be determined which is 9708 using the distribution and mean.

Given in the question that the high probability would gain  in premiums. If die, would lose almost . Selling insurance is not risky for an insurance company that insures many thousands of -year-old men.

According to the information, the gain around is 1250

Amount would lost in case of death is 100000.The expected value with its probability is:

E(X) = ∑x ×P(x)

=(-99750) × 0.00183 + ...+ (1250) × 0.99058

= 303.35

The standard deviation of the investment return is used to determine the risk of an investment. The riskier the investment is, the more varied the return is

The standard deviation of Y can be determined as

α = under root {∑x2 × P(x) - (∑x × P(x) }

= 9708

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The linear function is y = 5x + 12 and the number of customers after 3 and 4 hours are 27 and 41 respectively.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.

Using the data in the table, we can write can a linear function to represent it.

Taking two points;

The slope of the line is calculated as;

m = y₂ - y₁ / x₂ - x₁

m = 17 - 12 / 1 - 0

m = 5 / 1

m = 5

Using the value of the slope to calculate the y - intercept.

y = mx + b

17 = 5(1) + b

17 = 5 + b

b = 17 - 5

b = 12

The linear function is written as y = 5x + 12

a) The number of customers in the store after 3 hours is

y = 5x + 12

y = 5(3) + 12

y = 15 + 12

y = 27

b) The number of customers in store after 4 hours is

y = 5x + 12

y = 5(4) + 12

y = 20 + 12

y = 41

The linear function to model the table is y = 5x + 12

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