An analogue sensor has a bandwidth which extends from very low frequencies up to 8.75 kHz. Using the Sampling Theorem (Section 3.3.1), what is the minimum sampling rate (number of samples per second) required to convert the sensor output signal into a digital representation without incurring any aliasing?

If each sample is now quantised into 512 levels, what will be the resulting sensor output bitrate in kbps?

Give your answer in scientific notation to one decimal place.

Hint: you need to determine the number of bits per sample that allows for 512 quantisation levels (see Sections 2.4 (Block 1) and 3.3.2 (Block 3)).

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what's the best way to recreate the incident as it happened and to picture

The equation for the relationship between the total fee and vertical distance is: y = 100 + x/3000.

Vertical distance is the measurement of the straight line distance between two points in a vertical plane. It is the difference between the higher and lower altitudes of two points and is measured in a straight line from the highest point to the lowest point.

This equation can be explained as follows. The total fee for a trip to climb Mount Kilimanjaro is split into two parts. The first part is the initial fee of $100, which is a fixed cost independent of the distance climbed. The second part is the cost per vertical meter, which is calculated by dividing the vertical distance climbed (x) by 3000 (the constant fee for each vertical meter climbed) and then multiplying the result by the constant fee. Therefore, the equation for the relationship between the total fee and vertical distance is y = 100 + x/3000.

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Option D is correct as 16% and 26% results in a percentage of 42%, in line with percentages in the "At least one vitamin" row of the table of random sample.

In random sample:

The student is incorrect. To determine the proportion of participants taking vitamins, we need to add up the percentages in the "At least one vitamin" row of the table. Adding 23.5% and 48.2%, we get a total of 71.7%, which is not more than half. Therefore, option A is incorrect.

Option B is also incorrect, as adding 27.4% and 49.5% gives a total of 76.9%, which is more than half but does not match the percentages in the table.

Option C is incorrect, as adding 11.4% and 23.5% gives a total of 34.9%, which is lower than the percentages in the table.

Option D is correct, as adding 16% and 26% gives a total of 42%, which matches the percentages in the "At least one vitamin" row of the table. Therefore, the correct answer is D.

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the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.

Factorization, also known as factoring, is the process of expressing a mathematical object (such as a number, polynomial, or matrix) as a product of simpler objects.

To determine when the rocket hits the ground, we need to find the value of t when the height, h, is equal to 0. We can set h(t) = 0 and solve for t:

-16t²+ 76t = 0

-16t(t - 4.75) = 0

So either -16t = 0 or t - 4.75 = 0. The first equation has no solutions, so we solve the second equation:

t - 4.75 = 0

t = 4.75

Therefore, the rocket will hit the ground after 4.75 seconds.

To determine when the rocket is 70 feet above the ground, we need to find the value of t when h(t) = 70. We can set h(t) = 70 and solve for t:

-16t² + 76t = 70

-16t²+ 76t - 70 = 0

We can simplify this equation by dividing each term by -2:

8t² - 38t + 35 = 0

We can factor this equation:

(4t - 5)(2t - 7) = 0

So either 4t - 5 = 0 or 2t - 7 = 0. Solving these equations gives:

4t - 5 = 0

t = 1.25

2t - 7 = 0

t = 3.5

Therefore, the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.

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By solving the increase in percentage, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

What is an increase in percentage?

An increase in percentage is a measure of the change in a quantity expressed as a percentage of the initial value. It is calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying the quotient by 100 to express the result as a percentage. The formula for calculating the percentage increase is:

percentage increase = (final value - initial value) / initial value * 100

To find the increase in the number of students enrolled in an associate degree program from 2014-2015 to 2024-2025, we can first calculate the amount of increase as a percentage of the initial enrollment:

Increase = 21.5% * 6,500,000 = 1,397,500

Therefore, the increase in the number of students is approximately 1,397,500.

To find the projected number of students in an associate degree program in 2024-2025, we can add the increase to the initial enrollment:

Projected enrollment = 6,500,000 + 1,397,500 = 7,897,500

Therefore, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

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The set of data that Zoey should use for the linear graph is given as follows:

D the temperature of a water sample increasing 2° every hour.

The graph represents a linear function, meaning that the rate of change of the output variable relative to the input variable must be constant.

The input and output variables of the graph are given as follows:

As the rate of change must be constant, the correct option is given by option d, which has a rate of change of 2º every hour. For the other options, the rate of change is not constant.

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Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².

Another option is to plot the shape on a grid and count the squares: The rectangle's surface area is 15. Example: If each square is one meter in size, the area is 15 m2 (15 square meters).

To find the area of the polygon, we need to use the formula:

Area = (1/2) x Base x Height

We are given that the base of the polygon is 11 cm and the height is 4 cm. Therefore, we can substitute these values in the formula to get:

Area = (1/2) x 11 cm x 4 cm

Area = 22 cm²

Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².

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According to the given information, measure of angle FNL is given by 234 - 13x.

What is angle ?

In geometry, an angle is a figure formed by two rays, or line segments, that share a common endpoint, called the vertex of the angle. The two rays are called the sides or legs of the angle.

line FN || line EM || line DL,

line FD and line NL intersects line FN,line EM and line DL at pts F,E,D and N,M,L respectively

FE = ED ,NM = ML

angle FNL = (9x-40)deg

angle FDL = (4x-14)deg

Since line FN is parallel to line EM, we have:

angle FNM = angle FEL (corresponding angles)

Since line FN is parallel to line DL, we have:

angle FNL = angle FLD (alternate interior angles)

Similarly, since line FD intersects line FN and line EM at points F and E, we have:

angle FEL + angle FED = 180 degrees (linear pair)

Since FE = ED, we have:

angle FEL = angle FED (opposite angles of a parallelogram are equal)

Combining the above equations, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

Also, since NM = ML, we have:

angle NML = angle MLM

Now, applying the angle sum property in triangle FNL, we get:

angle FNL + angle FLD + angle FEL = 180 degrees

Substituting the given values, we get:

(9x-40) + (4x-14) + (180 - angle FEL) = 180

Simplifying, we get:

13x - 54 + 180 - angle FEL = 180

13x - angle FEL = 54

Solving for angle FEL, we get:

angle FEL = 13x - 54

Substituting this value in the equation we derived earlier, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

= 180 - (13x - 54)

= 234 - 13x

Therefore, measure of angle FNL is given by 234 - 13x

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Answer:

Third choice
π = 1/2 and 1 - π = 1/2

Step-by-step explanation:

Formula for binomial distribution is
[tex]P(x) = \dfrac{n!}{x!(n-x)!} \pi^x (1-\pi)^{n-x}[/tex]

where
x is the number of successes

n = number of trials

π = probability of success on a single trial

The variance of the binomial distribution is
[tex]\sigma^2 = n \cdot \pi(1-\pi)[/tex]

The maximum variance occurs when
[tex]\pi = (1- \pi) = 1/2[/tex]

Hence the correct choice is the third choice
π = 1/2 and 1- π = 1/2

Answer:

B

Step-by-step explanation:

The function that models the situation is an exponential decay function of the form:

t(m) = a(1 - r)^m

where:

t(m) is the number of trees after m months

a is the initial number of trees (5,500 in this case)

r is the monthly rate of decrease (3.2% or 0.032 as a decimal)

Substituting the values given in the options, we get:

A) t(m) = 5,500(0.032)^m

B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m

C) t(m) = 5,500(1.032)^m

D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m

Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.

Answer: The formula for exponential decay is given by:

t(m) = a(1-r)^m

where

a = initial value

r = decay rate

Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:

t(m) = 5,500(1 - 0.032)^m

t(m) = 5,500(0.968)^m

Therefore, the answer is (D) t(m) = 5,500(0.968)^m.

Your welcome (;

Answer:

C). 8/9n - 1 1/3

Step-by-step explanation:

Answer:

[tex]\frac{8}{9} n - 1\frac{1}{3}[/tex]

Step-by-step explanation:

Using the distributive property [tex]\frac{4}{9}[/tex] times 2 equals [tex]\frac{8}{9}[/tex] and [tex]\frac{4}{9}[/tex] times 3 equals [tex]\frac{4}{3}[/tex] which simplifies to [tex]1\frac{1}{3}[/tex]

In this case, the population is children from 6 to 18 years old who had nonlethal scorpion sting; on the other hand, the sample is the 245 children selected.

In a research study, the population is considered as the group of individuals being studied. However, as this number is often high, researchers often select a small random percentage that should be representative of the population, which is known as the sample.

Based on this, the population can be children  from 6 to 18 years old who had nonlethal scorpion sting, while the sample are those children selected (245) to carry out the research study.

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The function is positive on the interval (-1, 1)," is the only answer that is accurate. Due to the fact that the function accepts positive values for x between -1 and 0, accepts 0 at x = 0, and then accepts positive values.

When a function is specified at each point along an interval without any gaps, leaps, or interruptions, the interval is said to be continuous for that function.

When we examine the function's graph, we can observe that:

Because the function accepts negative values for x > 1 and positive values for x -1, it does not have a maximum value of 0.

The function does not approach as x approaches. Instead, as x rises, the function alternates between positive and negative values.

There are times when the function increases. Rather, it is rising on the interval (1, ) and falling on the intervals (-, 1). At x = -1, it has a local minimum, while at x = 1, it has a local maximum.

Due to the fact that it accepts negative values for x between -1 and 0, the function is not positive on the range (-1, 1).

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Answer: is mature enough to vote

Step-by-step explanation: the second drop box is asking about the opposing claim, which is the one that the professor gives.

Answer:

the last option, " is mature enough to vote".

Step-by-step explanation:

Professor Steinberg believes that 16 old can vote as their brains are mature enough to make informed decisions like voting.

The answer of the question based on graph function is given below, graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.

A graph  is visual representation of data or functions. It is way to display information in  visual format, usually with  use of coordinates and shapes.

The given equation is:

y = (-1/4 x)² - 4

To transform the graph of the parent function y = x², we can apply the following transformations:

Horizontal compression by a factor of 2: This will compress the graph horizontally, making it wider and shorter. The coefficient -1/4 in front of the x² indicates this compression.

Reflection across the x-axis: This will flip the graph of y = x² upside down. The negative sign after the x² in the equation indicates this reflection.

Vertical shift downward by 4 units: This will shift the entire graph downward by 4 units. The constant -4 at the end of the equation indicates this shift.

Using these transformations, we can graph the equation as follows:

Start with the graph of the parent function y = x²:

Apply the horizontal compression by a factor of 2 by multiplying the equation by -1/4:

y = (-1/4 x)²

Apply the reflection across the x-axis by negating the equation:

y = -(1/4 x)²

Apply the vertical shift downward by 4 units by subtracting 4 from the equation:

y = -(1/4 x)² - 4

The resulting graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.

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The values that complete the table would be: $140, $160, $180, $200, $220, $240, $260. This is a linear relationship because the data on the graph would show an ascending line with a constant slope.

To complete the table we must take into account the information, in this case Erick saves $20 per week, so we would have to add $20 to his initial budget of $120 and add $20 each week. Based on this information, the data that completes this table would be:

The graph with this data would be a linear expression, so the line would go up from $120 to $260 constantly, with a difference of $20 each week.

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Through the given statement we can say that the vertical distance travelled by the ball  is 84 m.

One limitation of this model is that it assumes that the ball rebounds to the same percentage of its previous maximum height after every bounce.

The formula for vertical distance from the earth is y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2, where g is the acceleration of gravity and h is an elevation.

So :

C) the required total vertical distance that the given dropped ball travels until its bouncing stops:

= (12 m) + 2*(12 m)*(3/4)*[1 + 3/4 + (3/4)^2 + (3/4)^∞] [the factor 2 is for equal distance being covered up and down after each bounce of the ball]

= (12 m) + (24 m)*(3/4)*

(sum of an infinite GP series whose 1st term is 1 and common ratio is 3/4)

= (12 m) + (24 m)*(3/4)*[1/(1 - 3/4)]

= (12 m) + (24 m)*(3/4)*4

= (12 m) + (72m) = 84 m

D) This model's assumption that the ball will always bounce back to a certain proportion of its maximum height is one of its limitations. In fact, the rebound height can differ from one bounce to the next due to factors like air resistance, the ball's elasticity, and the surface it bounces on.

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The measure of the angles is 143°

From the given diagram, the given measures are alternate exterior angles and they are equal.

Given the following parameters

∠A =7x + 24

∠B = 3x + 92

Equate

7x + 24 = 3x + 92

7x - 3x = 92 - 24

4x = 68

x = 17

Determine the measure of the angles

∠A = ∠B = 7x + 24

∠A = ∠B = 7(17) + 24

∠A = ∠B = 143 degrees

Hence the measure of the angles is 143°

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Answer:

$839.95

Step-by-step explanation:

To get the amount of tax Ella would have to pay for, multiply the price of the computer by the tax rate

785 x .07 = 54.95

Then add the computer price and tax to get how much she paid for in total

785 +54.95= $839.95

Answer:

Step-by-step explanation

I:

Answer:

Step-by-step explanation:

To determine the mean number of water tanks supplied to the construction site in March 2022 during weekdays, we need to add up the number of tanks supplied during weekdays and divide by the number of weekdays in March 2022:

March 2022 had 23 weekdays.

From the information given, we don't know the number of tanks supplied during weekdays in March 2022. Therefore, we cannot calculate the mean number of tanks supplied during weekdays in March 2022.

The numerical data recorded on the calendar in ANNEXURE A by the contractor was the number of water tankers supplied to the construction site on each day of the month.

To determine the modal number of water tankers that were supplied to the construction site in June 2022, we need to find the number that appears most frequently in the data:

From the information given, we don't have the data on the number of water tankers supplied to the construction site in June 2022. Therefore, we cannot determine the modal number of water tankers supplied in June 2022.

Given that the water tanker has a fuel capacity of 460 litres and the rate of fuel consumption of the Mercedes water tanker averages 5 km/l, we can calculate the distance traveled on a full tank of fuel:

The distance traveled on a full tank of fuel is 460 litres x 5 km/l = 2,300 km.

Finally, we are given the prices of fuel per litre in March and June 2022:

In March 2022, the price of diesel 50 ppm was R19.55 per litre.

In June 2022, the price of diesel 50 ppm was R24.14 per litre.

Answer:

1065.09 square meters

Step-by-step explanation:

The inner circle has a diameter of 21.4 cm

Its radius is half that = 21.4/2 = 10.7 m

Area of the inner circle = π (10.7)² = 114.49π  m²

The outer circle has a radius
= radius of inner circle + 10.6
= 10.7 + 10.6

= 21.3 m

Therefore the area of the outer circle
= π(21.3)² = 453.6π m²

Area of shaded region
= Area of outer circle - Area of inner circle

= 453.6π - 114.49π  
= 339.2 π

Taking π = 3.14

Area of shaded region
= 339.2  x 3.14
= 1,065.088 m²
= 1065.09 m² (rounded to nearest hundredth)

According the Question the value οf x will be 6.

The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line. Units like cm οr unit m are typically used tο measure it.

The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.

The side οf the circle JH . JG = JK . JM

JM = 7*16/8 = 14

X = 14-8 =6

Hene the value οf x will be 6.

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Answer:

4[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

Answer:

4 3/8

Step-by-step explanation:

4*8=32 35-32=3

(-2, -4)

Systems of equations are sets of two or more equations that share the same variables.

Graphing

To graph a system of equations, simply graph each line individually. Both of the equations given are linear. Attached is a graph of both equations. As you can see the graphs intersect at (-2, -4).

Solutions to Systems of Equations

The solution to a system of linear equations is the coordinate point that the lines intersect. This is the point where the x and y-values make both equations true. To check the answer, plug the values into the equations. If both remain true, the answer is correct.

First, y = 2x

This is true. Next, y = x - 2

This is also true; thus the answer is (-2, -4).

Answer: 85.5

Step-by-step explanation: divide 855 by ten or move the decimal to the left one place for every zero

Answer: 113.2 - 10.8x=70

Step-by-step explanation:

The points on line segment in  Question 1 is C (52, 3)( 5 2 , 3) and the answer to Question 2 is A (112, 3)( 11 2 , 3).

What is a line segment?

A line segment is a straight line that is bounded by two distinct endpoints. It is the shortest distance between two points and is usually represented by an arrow. Line segments are an essential part of geometry, as they form the basis for many shapes, such as triangles and rectangles.

A line segment can be divided into two parts in a given ratio if the difference of the coordinates of the end points of the line segment is divided in the same ratio.

For Question 1, the ratio of the line segment is 1:3. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 1:3. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 1:3. After dividing the difference of the coordinates into the ratio 1:3, we get the coordinates of the point on the line segment PQ as (52,3).

For Question 2, the ratio of the line segment is 3:1. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 3:1. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 3:1. After dividing the difference of the coordinates into the ratio 3:1, we get the coordinates of the point on the line segment PQ as (112,3).

In conclusion, the point on the line segment PQ that divides the line segment into the ratio of 1:3 is C (52, 3)( 5 2 , 3) and the point on the line segment PQ that divides the line segment into the ratio of 3:1 is A (112, 3)( 11 2 , 3).

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The translation of f(x) to g(x) is described by - translation of 4 units up.

As you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for such vertices of the figure will alter on the coordinate plane.

Apply the identical modification to every point in order to graph a translation.

As there is the shift of coordinates on y axis upward by 4 units units.

Thus, the translation of f(x) to g(x) is described by - translation of 4 units upward.

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