Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the number among four randomly selected households
that have cable TV. Then x is a binomial random variable with n = 4 and p = 0.90. (Round your answers to four decimal places.)

(a) Calculate p(3)=P(x = 3).

Interpret this probability.
a) the probability that more than three of the four randomly selected households have cable TV
b) the probability that at most three of the four randomly selected households have cable TV
c) the probability that at least three of the four randomly selected households have cable TV
d) the probability that less than three of the foor randomly selected households have cable TV
e) the probability that exactly three of the four randomly selected households have cable TV


(b) Calculate p(4), the probability that all four selected households have cable TV.

(c) Calculate P(x ≤ 3).

The coordinates of D on the given line segment is  (8/3, 0).

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

We are given that;

y = 3x – 8

Now,

When a line cuts the x-axis, its y-coordinate is always 0. Therefore, we can substitute y = 0 into the equation y = 3x - 8 and solve for x:

0 = 3x - 8

3x = 8

x = 8/3

Therefore, the point D has coordinates (8/3, 0).

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Answer: Function A is greater.

Step-by-step explanation:

just find the slope...

Slope for Function C = [tex]\frac{1}{3}[/tex] = [tex]0.33333[/tex] repeat...

and for Function A = [tex]\frac{5}{2}[/tex] = [tex]2.5[/tex]

to find the slope we use; [tex]s=[/tex] [tex]\frac{y}{x}[/tex].

After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is

⇒ (-9∠30 ) ÷ (-3∠-30) = 3

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (-9∠30 ) ÷ (-3∠-30)

Now, We can divide the expression as;

⇒ (-9∠30 ) ÷ (-3∠-30)

⇒ (-9∠30 ) / (-3∠-30)

⇒ - 9/- 3

⇒ 3

Thus, After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is

⇒ (-9∠30 ) ÷ (-3∠-30) = 3

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The scale factor of figure A to figure B is 5/3.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

A and B are similar triangles.

We need to find the scale factor.

The ratio between the scale of a given original object and a new object

Scale factor is 15/9=35/21=40/24

5/3=5/3=5/3

Hence, 5/3 is the scale factor of figure A to figure B.

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Answer:

Step-by-step explanation:

133 ft

Answer:

To find the fourth derivative of f(x), we can use the fact that f(x) can be expressed as:

f(x) = 5x^4 (1 - x)^-1

Then, using the product rule repeatedly, we can find the derivatives of f(x) up to the fourth order:

f'(x) = 20x^3 (1 - x)^-1 - 5x^4 (1 - x)^-2

f''(x) = 60x^2 (1 - x)^-1 + 40x^3 (1 - x)^-2 + 10x^4 (1 - x)^-3

f'''(x) = 120x (1 - x)^-1 + 180x^2 (1 - x)^-2 + 120x^3 (1 - x)^-3 + 20x^4 (1 - x)^-4

f^4(x) = 120 (1 - x)^-1 + 720x (1 - x)^-2 + 1080x^2 (1 - x)^-3 + 480x^3 (1 - x)^-4 + 60x^4 (1 - x)^-5

So, we have found the fourth derivative of f(x) without using the quotient rule four times.

The fourth derivative of the function f(x) = 5x⁴/(1 - x)⁻¹ is,

f''''(x) = 120/(1 - x)⁻¹ + 720x/(1 - x)⁻² + 1080x²/(1 - x)⁻³ + 480x³/(1 - x)⁻⁴

+ 60x⁴/(1 - x)⁻⁵.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

We have to find the fourth derivative of f(x), f(x) = 5x⁴/(1 - x)⁻¹

The derivatives of f(x) up to the fourth order can then be discovered by continually applying the product rule,

f'(x) = 20x³/(1 - x)⁻¹ - 5x⁴/(1 - x)⁻²

f''(x) = 60x²/(1 - x)⁻¹ + 40x³/(1 - x)⁻² + 10x⁴/(1 - x)⁻³

f'''(x) = 120x/(1 - x)⁻¹ + 180x²/(1 - x)⁻² + 120x³/(1 - x)⁻³ + 20x⁴/(1 - x)⁻⁴

f''''(x) = 120/(1 - x)⁻¹ + 720x/(1 - x)⁻² + 1080x²/(1 - x)⁻³ + 480x³/(1 - x)⁻⁴ +

60x⁴/(1 - x)⁻⁵.

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If  −2 ≤ x ≤ 5 and a ≤ 4x + 1 ≤ b, then the inequality can be written as:

−7 ≤ 4x + 1 ≤ 21

What is expression ?

An expression in mathematics is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a value or a quantity. Expressions can be simple or complex, and they can be written in various forms, such as using variables, exponents, radicals, logarithms, trigonometric functions, and more.

For example, 2x + 5 is an expression that contains a variable x and represents a value that depends on the value of x. Another example is √(a^2 + b^2), which is an expression that contains two variables a and b and represents the square root of the sum of their squares.

According to given condition :

We know that −2 ≤ x ≤ 5. Therefore, the smallest possible value of 4x is −8 (when x = −2) and the largest possible value of 4x is 20 (when x = 5). Adding 1 to both sides of the inequality, we get:

−8 + 1 ≤ 4x + 1 ≤ 20 + 1

−7 ≤ 4x + 1 ≤ 21

So, a = −7 and b = 21.

Therefore, if  −2 ≤ x ≤ 5 and a ≤ 4x + 1 ≤ b, then the inequality can be written as:

−7 ≤ 4x + 1 ≤ 21

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The missing side length is 7 yd.

The object given is made up of two rectangles. The width of the upright rectangle is to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.

Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.

Width of the upright rectangle = 15 - 8 = 7 yd

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Estimate of the total distance traveled in the first 6 hours of travel for a particle v(t)=−t^2 +4t+6 is 36m.

We have v(t)=−t² +4t+6

For finding the distance we have to find the integration of the given equation:

s = ∫ -t² +4t+6

= -t³/3 + 4t²/2 + 6t

= -t³/3 + 2t²/ + 6t

For the value of t = 6 hours

= -6³/3 + 2(6)² + 6(6)

= -72 + 72 + 36

= 36

Estimate of the total distance traveled in the first 6 hours is 36 m.

When a moving object has a positive velocity, its position is constantly rising. (We focus on the case when velocity is always positive; we will soon explore cases where velocity is negative.) We have shown that the area under the velocity curve represents the precise distance travelled whenever is constant on an interval. Finding the areas of rectangles that closely resemble the area under the velocity curve allows us to calculate the total distance travelled when is not constant.

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The median did not change because the 5th and 6th term of data is same.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

Given that;

The median of data set with nine numbers= 36

After the addition of tenth value median= 36

Now,

Median is the middle term of data

Here, the middle value and 6th term must be same.

So, 5th term= 6th term= 36

Therefore, the median of the given data set is same.

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Answer:

Least common denominator is 3.

Step-by-step explanation:

2/3 = 2/3 x 1/1 = 2/3

1/3 = 1/3 x 1/1 = 1/3

The most  important reason to avoid using a volunteer sample is Your conclusions could not be reliably generalized to a larger population.

Then, we want to determine the most important reason to avoid using a volunteering sample.

A levy sample is a slice system where people can choose whether or not they share in the check. While easier, this system can beget issues statistically.

The primary issue that this slice fashion faces is that the sample won't be arbitrary. You'll probably get people who are more opinioned about the subject the sample enterprises. This means that the sample won't truly be arbitrary, which in turn means it'll not be representative of the population. However, also the conclusions from the sample can not be generalized to the population, If the sample isn't representative of the population.

Thus, the answer is B. Your conclusions couldn't be reliably generalized to a larger population.

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The effective rate for a nominal rate of 5% compounded continuously over a time period of 1 year is 5.13%.

To find the effective rate corresponding to a nominal rate compounded continuously, we use the formula:

r_effective = [tex]e^{(r\_nominal * t)} - 1[/tex]

where r_nominal is the nominal rate, and t is the time period.

For a nominal rate of 5% compounded continuously, the effective rate can be calculated as follows:

r_effective = [tex]e^{(0.05*t)}-1[/tex]

Note that the time period t is usually expressed in years. For example, if we want to find the effective rate for a time period of 1 year, we have:

r_effective = [tex]e^{(0.05*t)}-1[/tex]

= 1.051296 - 1

= 0.051296 or 5.13%

So, the effective rate for a nominal rate of 5% compounded continuously over a time period of 1 year is 5.13%.

It's important to understand the difference between nominal and effective rates. The nominal rate is the rate that is advertised or quoted, while the effective rate takes into account the frequency of compounding. The effective rate is a more accurate representation of the true interest rate because it shows the actual amount of interest earned over a given time period.

Continuous compounding means that interest is calculated and added to the principal continuously, rather than at regular intervals. This results in a higher effective rate compared to the same nominal rate compounded at regular intervals.

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Given two lines with slopes m<1 and m<2, the slope of a third line that is perpendicular to these lines would be the negative reciprocal of either slope. The negative reciprocal of m<1 is -1/m<1 and the negative reciprocal of m<2 is -1/m<2.

Since m<1 = 38 degrees, the negative reciprocal of m<1 would be -1/38.

And since m<2 = 78 degrees, the negative reciprocal of m<2 would be -1/78.

So, if m<3 is the slope of a line perpendicular to the lines with slopes m<1 and m<2, then m<3 could be either -1/38 or -1/78, depending on which slope is chosen.

Answer:

Rachels age = 3 years

Greg's age = 9 years

Step-by-step explanation:

Present age:

                         Let Rachels age = x years

              5 time of Rachel's age = 5*x = 5x

                          6 less than 5x  = 5x - 6

                                Greg's age = (5x - 6) years

Age after four years:

                    Rachel's age = (x + 4) years

                      Greg's age =  5x - 6 + 4

                                          = ( 5x - 2) years

          Sum of their ages = 20

           x + 4 + 5x - 2        = 20

                  x + 5x + 4 - 2 = 20

   Combine like terms,

                            6x  + 2 = 20

Subtract 2 from both sides,

                                    6x = 20 - 2

                                    6x = 18

Divide both sides by 6,

                                      x = 18 ÷ 6

                                       x = 3

Rachel's age = 3 years

Greg's age = 5*3 - 6

                   = 15 - 6

                   = 9 years

We can use the Law of Sines to find the measure of angle W:

sin(W)/w = sin(V)/v

sin(W) = w*sin(V)/v

sin(W) = 7.2*sin(8°)/6.2

sin(W) ≈ 0.1001

Taking the inverse sine of both sides, we get:

W ≈ 5.78° or W ≈ 174.22°

Since W is an angle in a triangle, it must be between 0° and 180°. Therefore, the only possible value for ∠W is:

W ≈ 5.78° (to the nearest tenth of a degree).

Answer:

Step-by-step explanation:

The inequality to determine the number of gigabytes Paisley can use while staying within her budget can be written as:

60 + 3g < 75

Solving for g:

60 + 3g < 75

-60 -60

0 + 3g < 15

/3 /3

g < 5

So Paisley can use up to 5 gigabytes while staying within her budget.

Answer:

a. Never

b. Never

c. Sometimes

Step-by-step explanation:

a. The difference of a binomial and a binomial is never a binomial, as the result will always be another type of expression.

b. When a 6th-degree polynomial with 5 terms is written in standard form, the second term will always have a degree that is less than the 6th degree, since there are only 5 terms and the degree of each term decreases as its position increases.

c. The sum of a 4th-degree polynomial and a 2nd-degree polynomial is sometimes a 2nd-degree polynomial, depending on the coefficients of the terms. It is possible for the degree of the sum to be lower than the degree of both individual polynomials if the coefficients of the higher degree terms cancel out.

The difference of a binomial and a binomial always yields a binomial. A 6th-degree polynomial with 5 terms in standard form always has a degree of 5 for the second term. The sum of a 4th-degree polynomial and a 2nd-degree polynomial never results in a 2nd-degree polynomial.

1. For the operation a. The difference of a binomial and a binomial is a binomial.

Answer: Always

Reason: This is true because when you subtract a binomial from another, the result is always a binomial as well. For instance, (x+y)-(x-y) would result in 2y, a binomial.

2. For the operation b. When a 6th-degree polynomial with 5 terms is written in standard form, the second term has a degree of 5.

Answer: Always

Reason: This is always the case because in ordered or standard form, the terms decrease by degree in sequence

3. For the operation c. The sum of a 4th-degree polynomial and a 2nd-degree polynomial is a 2nd-degree polynomial.

Answer: Never

Reason: The highest degree of the sum of two polynomials is the higher degree of the individual polynomials, in this case, it would be a 4th degree polynomial.

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Using standard deviation, the probability that the service technician will have to work overtime to fix the machine today is 0.5.

The degree of variance or dispersion in a set of data values is measured by standard deviation. It gauges how far the data values depart from the data set's mean (average).

The mean of the data set is first determined, then the standard deviation. The difference between each data point and the mean is then squared for each data point. After dividing the total number of data points by the sum of these squared differences, minus one, the standard deviation is calculated by taking the square root of this result.

a. The expected number of emails that are tracked can be found by multiplying the total number of emails by the probability that an email is tracked:

Expected number of tracked emails = 50 x 0.4 = 20

Therefore, we can expect that 20 out of 50 received emails will be tracked.

b. To find the variance and standard deviation for the number of tracked emails, we can use the formula:

Variance = np(1-p)

Standard deviation = sqrt(np(1-p))

where n is the number of trials (in this case, 50) and p is the probability of success (0.4).

Variance = 50 x 0.4 x (1 - 0.4) = 12

Standard deviation = sqrt(50 x 0.4 x (1 - 0.4)) ≈ 3.46

Therefore, the variance for the number of tracked emails is 12 and the standard deviation is approximately 3.46.

c. The probability distribution for the duration of a service call is:

Duration (hours) Probability

1                               0.25

2                               0.25

3                               0.25

4                               0.25

d. The probability that a service call will take three hours is 0.25, as shown in the probability distribution table.

e. To find the probability that the service technician will have to work overtime, we need to calculate the probability that a service call will take longer than two hours, since the technicians usually get off at 5:00 P.M. and it is currently 3:00 P.M.

The probability that a service call will take longer than two hours is:

P(call takes 3 hours or 4 hours) = P(call takes 3 hours) + P(call takes 4 hours) = 0.25 + 0.25 = 0.5

Therefore, the probability that the service technician will have to work overtime to fix the machine today is 0.5.

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The graph of the equation y = -0.5x + 12 will be a straight line

The equation y = -0.5x + 12 represents a linear function

Based on the slope -0.5 this means that as the value of x increases, the value of y will decrease.

Additionally, since the y-intercept is 12, the line will cross the y-axis at the point (0, 12).

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The function that models the data is y = 42 ([tex]\frac{1}{2}[/tex])ˣ.

Exponential functions are functions where the independent variable, x is in the exponent.

From the graph, it is clear that it is an exponential function.

Exponential functions will be of the form y = k bˣ.

We have the point (0, 42).

Substituting the point,

k b⁰ = 42

k = 42, since any number raised to 0 is 1, b⁰ = 1.

So the function is y = 42 bˣ.

Substituting the point (1, 21),

42 b¹ = 21

b = 21 / 42

b = 1/2

So the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.

Hence the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.

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The magnitude of the acceleration due to gravity would decrease with increasing height.

If the two shells were fired simultaneously with the same speed, their initial velocity would be the same. However, the shell that hits ship A, which is closer, would take less time to reach its target compared to the shell that hits ship B.

Since the magnitude of the acceleration due to gravity is constant, the vertical motion of the shells would be described by the following equation:

h = vi * t + (1/2) * g * [tex]t^2[/tex]

where h is the height of the shell, vi is the initial velocity, t is the time, and g is the acceleration due to gravity.

The horizontal motion of the shells would be described by the following equation:

d = vi * t

where d is the horizontal distance travelled by the shell.

By solving the above equations, we can determine the time taken by each shell to reach its target and therefore, the time difference between the two shells.

Note that this analysis assumes that air resistance is negligible and that the magnitude of the acceleration due to gravity is constant. In reality, air resistance would play a role in the motion of the shells, and the magnitude of the acceleration due to gravity would decrease with increasing height.

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Answer:

C

Step-by-step explanation:

in the triangle with respect to the 50° angle, the side opposite is c and the adjacent side is 14.

thus using the tangent ratio in the right triangle

tan50° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{c}{14}[/tex] ( multiply both sides by 14 )

14 × tan50° = c , then

c ≈ 16.7  ( to 1 decimal place )

In this problem, the cosine function is used to solve for the length of side C in a right-angled triangle, because the angle and the adjacent side are known. According to trigonometry, the cosine for an angle is the length of the adjacent side divided by the hypotenuse.

In the given right-angled triangle, since the length of side C (hypotenuse) is unknown and one of the acute angles (50 degrees) is known, you should use the cosine function to solve for the length of side C. According to Trigonometry, cosine of an angle (in a right-angled triangle) is equal to the adjacent side divided by the hypotenuse. Hence, cos(50) = 14 / C. You could solve this equation for C.

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Answer:

The recursive formula for this sequence is y(n) = 2 * y(n-1). Starting with y(1) = -3, this formula produces the sequence of -3, -6, -12, -24, -48, and -96.

The youngest age for which the average income of a lawyer is $275,000 is 27.91 year.

Quadratic Equation helps solve quadratic equations. First, put the equation into the form ax²+bx+c=0. where a, b, and c are the coefficients. Then plug these coefficients into the equation.

(-b±√(b²-4ac))/(2a) . See examples of solving various equations using formulas

The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with with the following function:

I = - 425x² + 45500x - 650000 .......... (1)

If the average annual income of the lawyer at the age of x years is $275000, then from the equation (1) we can write

- 425x² + 45500x - 650000 = 250000

I=-425x^(2) + 45,500x-650,000

275000 = -425x^(2) + 45,500x-650,000

-425x^(2) + 45,500x -650000-275000=0

425x^(2) -45,500x +925000=0

x = 900/17 ± 10√(1810)/17

= 77.96 and 27.91

here we are not accepting the ans 77.96 because we have already less value which is 27.91 so final ans will be 27.91

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Answer: 85 miles left

Step-by-step explanation:

65 miles x 7 hours = 455 miles

540 miles - 455 miles = 85 miles

The constraint 3X₁²  + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.

The correct answer is an option (e)

We know that a linear constraint in linear programming occurs when linear components are added or subtracted. Also the resulting expression must either increase, decrease, or be exactly equal to a right-hand side value.

Any constraint of a linear programming problem is referred to as linear if all of its terms are of the first order.

We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.

Here we can observe that the constraint 3X₁²  + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.

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The complete question is:

Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?

a. 2X₁ + X₂ − 3X₃ ≥ 50

b. 2X₁ + √X₂ ≥ 60

c. 4X₁ - 1/3 X₂ = 75

d. 3X₁ + 2X₂ - 3x₃ / X₁ + X₂ + X₃ ≤ 0.9

e. 3X₁²  + 7X₂ ≤ 45

The proof is completed as follows

       Statement                             Reason

NL/AB =  MN/BC = LM/CA          ratios of side of similar triangles are equal

Δ ABC is similar to Δ LNM         Definition of similar triangles

Similar triangles are triangles that have the same shape but may differ in size. That is to say, they have the same angles but their sides may be scaled differently.

When two triangles are similar, their corresponding angles are congruent and the corresponding sides are in proportion to each other.

This means that if you know the lengths of any two sides of a similar triangle, you can use those ratios to find the lengths of the other sides.

In the proof, the equation NL/AB =  MN/BC = LM/CA means that proportions are equal

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