A study was conducted in order to estimate the proportion of u. S. Adults that use a computer at home more than 20 hours a week. Suppose 36 out of a random sample of 81 adults use a computer at home more than 20 hours a week. Is the sample size large enough to compute a confidence interval for the proportion of u. S. Adults who spend more than 20 hours a week on a home computer?.

(a) The first order lowpass filter isHc(s) = 10/(s+1)The analog bandpass filter has a cutoff frequency of ω1 = 50 rad/sec and ω2 = 100 rad/sec.

The transfer function of the analog filter is given byH(s) = s/(s^2 + 0.1506s + 1)Let s = jω and use the given frequencies, we getH(j50) = j50/(0.1506j50 + 1)

≈ j0.3257H(j100)

= j100/(0.1506j100 + 1)

≈ j0.6522The pole-zero diagram is shown below:b) The bilinear transformation used to convert the analog filter to a digital filter is given byThe bilinear transformation is a nonlinear transformation of s-plane to z-plane.

For Td = 2, we getz = (2+s)/(2-s)Let H(z) be the transfer function of the digital filter. Substituting z from above we getH(z) = H(s)|s=(2z-2)/(z+1)Substituting the transfer function of analog filter, we getH(z) = (1 - z^-1) / (1 + 0.1506z^-1 + 0.9900z^-2)The pole-zero diagram is shown below:c) The frequency response of the filter is given byH(ω) = |H(z)|z=ejωUsing the transfer function obtained in part (b), we getH(ω) = |(1 - e-jω) / (1 + 0.1506e-jω/2 + 0.9900e-jω)|The magnitude plot of the frequency response is shown below:

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Simplified version of the given radical expression would be...

\(5x^2\sqrt{7x}\)

Hope this helps!

The correct points are (1, 2) and (0,1).

To find the points that lie in the inverse of the graph of a function g(x), we need to swap the x and y values of the original graph.

Let's start by representing the original graph of g(x):

x | g(x)

-1 | 0.5

0 | 1

1 | 2

2 | 4

3 | 8

Now, we swap the x and y values:

y | x

0.5 | -1

1 | 0

2 | 1

4 | 2

8 | 3

These are the corresponding points for the inverse function.

So, the points that lie in the inverse of the graph of g(x) are:

(-1, 0.5), (0, 1), (1, 2), (2, 4), (3, 8).

Hence the correct points are (1, 2) and (0,1).

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Answer:

1000 miles

Step-by-step explanation:

Given the following :

Number of miles driven :

First trip = 240 miles

Second day = 205 miles

Third day = 315 miles

Fourth day; miles driven before arriving at their final destination = 220 miles

Total number of miles driven after 4 days before reaching their destination :

(240 + 205 + 315 + 220) = 980 miles

However, they still haven't reached their destination ;

Using front end estimation :

We can take the total miles recorded and make an estimation based on the first digit of the recorded miles traveled:

In other to estimate 980 using front end estimation : the actual number is replaced with a number with only one nonzero digit (which is the first digit)

Hence,

980 - - - - > we round the digit after 9 either 1 or 0, since it is greater than 4, then it is rounded to and added to the first digit, all subsequent dots are rounded to zero

Hence 980 - - - - > 1000

Hence, estimated miles driven = 1000 miles

EF = 45

Step-by-step explanation:

Area if Trapezium = \(\frac{a + b}{2} h\)

Median = \(\frac{1}{2} (a + b)\)

Median = 5x

5x = 1/2 ((x + 3) + 78)

5x = (x + 81) / 2

10x = x + 81

9x = 81

x = 9

EF = 5x

EF = 5(9)

EF = 45

The length of the arc of the circle, to the nearest tenth of a centimeter, is approximately 5.0 cm.

To find the length of an arc of a circle, we use the formula:

Length of arc = radius × radian angle

In this case, the radius of the circle is 4 cm, and the radian angle is (2π)/5. Plugging these values into the formula, we have:

Length of arc = 4 cm × (2π)/5

To find the length to the nearest tenth of a centimeter, we can evaluate this expression:

Length of arc ≈ 4 cm × (2 × 3.14159)/5

≈ 5.026548 cm

Rounding this to the nearest tenth gives us:

Length of arc ≈ 5.0 cm

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Answer:

-15/4, 250%, 3.0, 5

Step-by-step explanation:

ToTo obtain the Maclaurin series for the function f(x) = 8cos(x^3), we can use the Maclaurin series expansion of the cosine function and substitute x^3 in place of x.

The Maclaurin series for cosine function is:

cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...

Substituting x^3 for x, we have:

cos(x^3) = 1 - [(x^3)^2]/2! + [(x^3)^4]/4! - [(x^3)^6]/6! + ...

Simplifying the powers of x^3, we get:

cos(x^3) = 1 - (x^6)/2! + (x^12)/4! - (x^18)/6! + ...

Now, since we want to find f(x) = 8cos(x^3), we multiply each term of the series by 8:

f(x) = 8[1 - (x^6)/2! + (x^12)/4! - (x^18)/6! + ...]

Therefore, the Maclaurin series for f(x) = 8cos(x^3) is:

f(x) = 8 - (8x^6)/2! + (8x^12)/4! - (8x^18)/6! + ...

In the table, when n = 0, the Maclaurin series term is 8.

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The original size of the bag is given by the equation A = 14 ounces

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the original size of the bag be = A

Now , the equation will be

The increased size of the bag = 16.8 ounces

The percentage increase in the size of the bag = 20 %

So , the equation for the percentage increase in the size of the bag is

Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag

Substituting the values in the equation , we get

A + ( 20/100 ) x A = 16.8

( 120 / 100 ) A = 16.8

On simplifying the equation , we get

Multiply by 100 on both sides of the equation , we get

120A = 1680

Divide by 120 on both sides of the equation , we get

A = 14 ounces

Therefore , the value of A is 14 ounces

Hence , The original size of the bag is 14 ounces

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Answer:

polynomial: x⁴ - 13x² + 36

Step-by-step explanation:

the factors are derived by equating each root to be equivalent to x and making the right hand side 0(in case u don't understand that part)

The statement If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 [f(x)]/[g(x)] does not exist, is True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = 0 0 so the limit does not exist, is True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = ∞ so the limit does not exist, is False.

1.

Consider the functions f(x) = (x - 7) and g(x) = x - 7. Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7) = 7 - 7 = 0

lim x→7 g(x) = lim x→7 (x - 7) = 7 - 7 = 0

Now, let's evaluate the limit of their quotient:

lim x→7 [f(x)]/[g(x)] = lim x→7 [(x - 7)/(x - 7)]

In this case, we have an indeterminate form of 0/0 at x = 7. The numerator and denominator both become 0 as x approaches 7, and we cannot determine the limit value directly.

To further illustrate this, let's simplify the expression:

lim x→7 [f(x)]/[g(x)] = lim x→7 [1] = 1

In this example, we can see that the limit of [f(x)]/[g(x)] exists and is equal to 1.

However, this does not contradict the statement. The statement states that the limit does not exist, but it is indeed true in general when considering all possible functions.

Therefore, the correct evaluation is: True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 [f(x)]/[g(x)] does not exist.

2.

Consider the functions f(x) = (x - 7)² and g(x) = x - 7. Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7)² = (7 - 7)² = 0

lim x→7 g(x) = lim x→7 (x - 7) = 7 - 7 = 0

Now, let's evaluate the limit of their product:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)² * (x - 7)] = lim x→7 [(x - 7)³]

In this case, we have an indeterminate form of 0 * 0 at x = 7. The product of the functions f(x) and g(x) becomes 0 as x approaches 7, but this does not determine the limit value.

To further illustrate this, let's simplify the expression:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)³] = (7 - 7)³ = 0³ = 0

In this example, we can see that the limit of f(x) g(x) exists and is equal to 0. However, this does not contradict the statement. The statement states that the limit does not exist if both f(x) and g(x) approach 0 individually, and their product does not provide a consistent limit value.

Therefore, the correct evaluation is: True. If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = 0 0, and the limit does not exist.

3.

Consider the functions f(x) = (x - 7)² and g(x) = 1/(x - 7). Both functions approach 0 as x approaches 7:

lim x→7 f(x) = lim x→7 (x - 7)² = (7 - 7)² = 0

lim x→7 g(x) = lim x→7 1/(x - 7) = 1/(7 - 7) = 1/0 (which is undefined)

Now, let's evaluate the limit of their product:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)² * 1/(x - 7)] = lim x→7 [(x - 7)]

In this case, we have an indeterminate form of 0 * ∞ at x = 7. The product of the functions f(x) and g(x) results in an indeterminate form.

To further illustrate this, let's simplify the expression:

lim x→7 f(x) g(x) = lim x→7 [(x - 7)] = 7 - 7 = 0

In this example, we can see that the limit of f(x) g(x) exists and is equal to 0, not infinity. Therefore, the statement "If lim x→7 f(x) = 0 and lim x→7 g(x) = 0, then lim x→7 f(x) g(x) = ∞ so the limit does not exist" is false.

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Answer:

I need more information.... ??

Step-by-step explanation:

The complete answers regarding flow of people and occupancy are solved as follows:

(a) The flow of people from downtown to campus is the rate at which the shuttle buses can transport passengers from the downtown bus stop to the campus bus stop.

(b) The flow of people from campus to downtown is equal to the rate at which passengers are coming to the campus bus stop.

(c) The average bus occupancy from campus to downtown is equal to the number of passengers on each bus divided by the number of seats on each bus.

Dispatching the buses from downtown to campus at equal headways would reduce the average waiting time of passengers going from campus to downtown. This is because the slower bus would have more time to pick up and drop off passengers, and the faster bus would not be slowed down by having to wait for the slower bus. The overall result would be a reduction in the average waiting time for all passengers.

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Complete Question:

Suppose that two shuttle buses operate (without coordination) between the campus and downtown. One bus can carry 20 people and has a round trip time of 8 min (including loading and unloading passengers), the other can carry 25 people but has a round trip time of 10 min. There is always a queue of people waiting at the downtown bus stop, but passengers come to the campus bus stop at a steady rate of 2/min. If neither bus is idle at any time, determine:

(a) The flow of people from downtown to campus.

(b) The flow of people from campus to downtown.

(c) The average bus occupancy from campus to downtown.

If one insisted on dispatching these buses from downtown to campus at equal headways, we would only slow down the faster bus. Would you expect this strategy to reduce the average waiting time of passengers going from campus to downtown?

Figure shows right angle, angles are 30-60-90 degrees, and side ratio 1:√3: 2.

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f(x)/g(x)

(x2-1)/(x-1)

x cannot equal 1 because this would render the denominator, also known as the divisor, as zero.

x can be greater than 1.

If you would like, we can factor the numerator...

x2-1

(x+1)(x-1)

FIRST...(x)(x)=x2

OUTER...(x)(-1)=-1x=-x

INNER...(1)(x)=1x=x

LAST...(1)(-1)=-1

x2-x+x-1

x2-1

So...

f(x)/g(x)=[(x+1)(x-1)]/(x-1)

(x-1) is in the numerator and denominator.  It cancels...

f(x)/g(x)=(x+1)

1. X(w) in cartesian form is X(w) = 2 + j(w/3 + 4w). The real part of X(w) is 2, and the imaginary part of X(w) is w/3 + 4w.

X(w) in cartesian form: The given expression for X(w) is in cartesian form, which represents a complex number in the form a + jb, where a is the real part and b is the imaginary part.

In this case, the real part of X(w) is 2, as it is a constant term in the expression. The imaginary part of X(w) is w/3 + 4w, as it is a linear function of w in the form of w times some constants (1/3 and 4).

2. X(w) in polar form is X(w) = |X(w)|ejθ. |X(w)| = √(22 + (w/3 + 4w)2) = √(4 + w2/9 + 16w2). θ = tan-1(w/3 + 4w)/2.

X(w) in polar form: The polar form of a complex number represents it in terms of its magnitude (denoted by |X(w)|) and its angle (denoted by θ). In this case, |X(w)| is given as √(22 + (w/3 + 4w)2), which is the square root of the sum of the squares of the real and imaginary parts of X(w).

This represents the magnitude or the distance of X(w) from the origin in the complex plane. θ is given as tan-1(w/3 + 4w)/2, which represents the angle formed by the complex number X(w) with the positive real axis in the complex plane.

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Because the scaling factor is a whole number, which is 3, the enlargement of the dashed triangle is a dilatation.

Recall:

Thus:

For the dashed triangle, measure the separation between the points (2, -2) and (0, -2).

Using the coordinates (6, -6) and (0, -6) for the solid triangle, calculate the equivalent distance:

Scale factor = 6/2 = 3

The dilation is an enlargement because the scale factor is a whole number.

In conclusion, the enlarged dashed triangle indicates a dilatation because the scale factor, which is 3, is a whole number.

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The estimated coefficient for Fitness Center in a regression analysis represents the expected change in the dependent variable associated with a unit increase in the independent variable.

It tells us how much having a Fitness Center affects the rent price. To determine how much the rent price for a 1-bedroom apartment would be if the complex has a Fitness Center, Parking Space, and Wireless Internet, we would need to know the specific coefficients for each of these independent variables in the regression analysis, as well as the constant term. We could then plug in the values for each variable and calculate the predicted rent price. It is important to note that the estimated coefficient for Fitness Center does not necessarily imply causation. Other factors could be influencing both the presence of a Fitness Center and the rent price, and a regression analysis only captures the relationship between the variables that are included in the model. Additionally, the size and direction of the coefficient can vary depending on the data and methodology used in the analysis.

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Answer:

x = 48

Step-by-step explanation:

log⁡〖 (2x+4)〗=2

Raise each side to the base of 10

10 ^log⁡〖 (2x+4)〗=10^2

The 10 ^log cancels

2x+4 = 100

Subtract 4 from each side

2x+4-4 = 100-4

2x = 96

Divide by 2

2x/2 = 96/2

x =48

Answer:B I’m not sure if it is correct

Step-by-step explanation:

Answer: 60 also your welcome

Answer:

the answer is c: 17/2

Step-by-step explanation:

The root of this equation is determined to be approximately 0.567143.The root is found to be approximately -0.673253.

The Newton-Raphson method is an iterative numerical technique used to find the roots of equations. In the first equation, y = f(x) = e^x - x, the initial approximation x0 is set to 0. By applying the Newton-Raphson method, successive approximations of the root are calculated until convergence is achieved. The root of this equation is determined to be approximately 0.567143.

In the second equation, x^3 + 2x^2 + 6x + 3 = 0, the root is sought within the range (-1, 0). The Newton-Raphson method is employed again, starting with an initial approximation x0 of -1. Through iterative calculations, the root is found to be approximately -0.673253.

Both equations demonstrate the effectiveness of the Newton-Raphson method in finding roots within specific ranges by iteratively refining approximations until a satisfactory solution is obtained.

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Answer:

First situation

More than 3 hours

At least 10

15

75

Step-by-step explanation:

Let x be the number of hours

The equation will be

\(5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3\)

So, she needs to work more than 3 hours in order to make more than $15.

The situation that represents \(5x>15\) is the first one.

Let x be the additional number of cans

The inequality will be

\(x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10\)

So, the additional number of cans to be bought is at least 10.

Let x be the number of comic books Clarice has.

\(x>15\)

So, Clarice needs to have more than 15 comic books.

Let x be age of Elizabeth

The equation will be

\(x=5\times 15\\\Rightarrow x=75\)

So, Elizabeth is 75 years old.

Answer:

The number is 51

Step-by-step explanation: 51+9 = 60

60/6 = 10

Hope it help you :))))

Have a good day

Answer: Your welcome!

Step-by-step explanation:

a) In 5 years' time, there are expected to be 136 beetles in the area of rainforest (20 * 1.66^5 ≈ 135.9, rounded to 136).

b) In 20 years' time, there are expected to be 8,000 beetles in the area of rainforest (20 * 1.66^20 ≈ 8,002.2, rounded to 8,000).

A graph of the solution of the inequality is: graph F.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given inequality by making x the subject of formula as follows;

x - 5 < 14

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 14 + 5

x < 19

Note: The line on a number line should be open when the inequality symbol is greater than (>) or less than (<).

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The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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