On the grid below segment AB is shown with endpoints A(-1,-1) and B(7,5). Its midpoint, M, is also
labeled and has coordinates of M (3, 2).

(a) Draw the perpendicular bisector of AB on the grid. Think about its slope compared to that of AB.
b) Write the equation of the line you drew in (a).

The measure of the missing length in the figure, found using Pythagorean Theorem is; x = 37 mm

Pythagorean Theorem states the relationship between the lengths of the sides of a right triangle. According to Pythagorean Theorem, the sum of the squares of the leg lengths of a right triangle is equivalent to the square of the length of the hypotenuse side.

Please find attached a possible figure in the question, obtained from a similar question posted on the website.

The 13 mm side hypotenuse length of the right triangle on the left  indicates a other leg length of the right triangle can be found using Pythagorean Theorem as follows;

Square of the length of the hypotenuse side = Sum of the square of the length of the other two sides

13² = 5² + (second leg length)²

The second leg length of the right triangle on the left = √(13² - 5²) = 12

The 12 mm leg length of the right triangle on the left indicates that the leg length of the right triangle on the right which correspond with the 12 mm leg length on the left is 12 mm

The length of the hypotenuse of the right triangle on the right, which is the missing length, x is therefore;

x² = 12² + 35² = 1369

The measure of the missing length x is therefore;

x = √(1369) = 37

The missing length in the figure is; x = 37 mm

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The given system is :

a) Linear

b) Time-invariant

c) Casual

d) Impulse response function is h(n) = 2δ(n-1) + δ(n-2).

a) Linear: A system is considered linear if it satisfies the superposition principle, meaning that if the inputs x1(n) and x2(n) produce outputs y1(n) and y2(n), respectively, then the output of the system to a weighted sum of inputs is equal to the weighted sum of the outputs. In this system, 2x(n-1) and x(2n) are both linear operations, and the sum of two linear operations is also a linear operation. Therefore, this system is linear.

b) Time-invariant: A system is considered time-invariant if the output is not dependent on the current time, but only on the input and its previous values. In this system, the coefficients 2 and 1 do not change with time, and the system does not depend on the current time. Therefore, this system is time-invariant.

c) Causal: A system is considered causal if the output only depends on the present and past inputs, and not on future inputs. In this system, x(2n) only depends on the past and present inputs, and x(n-1) only depends on past inputs. Therefore, this system is causal.

d) Impulse response function: The impulse response function of the system can be found by taking the unit impulse as the input, solving for the output and normalizing it.

h(n) = 2δ(n-1) + δ(n-2)

where δ(n) is the unit impulse function and h(n) is the impulse response function of the system.

Correct Question :

y(n) = 2x(n-1) + x(2n). is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system

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The initial height of the ball is the y-intercept of the function. The initial height she threw the ball from was 35.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient, and 'c' is called the absolute term of f (x).

The function is as follows:

h(x) = -16x² + 3x + 35

Substitute the value of x = 0.

So, we have:

h(0) = -16(0)² + 3(0) + 35

Evaluate the exponent

h(0) = -16(0) + 3(0) + 35

Evaluate the products

h(0) = 0 + 0 + 35

Evaluate the sum

h(0) = 35

Hence, the initial height she threw the ball from was 35.

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In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class.

Cumulative frequency is a running total of the frequencies of a data set. It is used to keep track of how many observations fall within a certain range of values. It is the sum of the frequencies of all the classes up to a certain point.

The second class is 1150-1219 which means it includes the price of refrigerators that fall within the range of $1150 and $1219. To find the cumulative frequency of the second class, you would need to count the number of prices in the data set that fall within that range and add it to the cumulative frequency of the previous class.

In this case, the cumulative frequency of the second class would be the number of prices in the data set that fall within the range of $1150 and $1219 plus the cumulative frequency of the first class. Since the cumulative frequency of the first class is not provided, we cannot calculate the cumulative frequency of the second class without more information.

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The two expressions that add to get a sum of - n + 6 are

A. (-6n) + (6 + 2n) and

B. (- 10n + 2) + (6n + 4)

Now, According to the question:

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The expression is :

-4n + 6

Now the expression as

A. (-6n) + (6 + 2n)

After adding, we have;

(-6n) + (6 + 2n) = -6n + 6 + 2n

= - 4n + 6

B. (- 10n + 2) + (6n + 4)

After adding we have;

(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4

= - 4n + 6

Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)

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There must be some reason why Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12: I bought just enough packets of each to have the same number of each therefore the number of items which were on the receipt is eleven (11).

This is referred to as an operation that represents the basic idea of repeated addition of the same number and will be used to get the same number of each in this scenario.

Since Hot Dog sausages are sold in packets of 10 and the bread rolls in packets of 12, to get the same number of each will be to look for values which when multiplied will give the same number which are 6 and 5 respectively to give equal number of 60 each. therefore the number of items on the receipt will be 6+5 = 11.

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Oliver runs a mile in 6 minutes. He runs 2 miles North and 3 miles east, so the total distance he ran is 2 + 3 = 5 miles.

Since he ran the same distance back to his house, the total distance he ran is 52 = 10 miles.

Since he runs a mile in 6 minutes, the total time of Oliver's run was 106 = 60 minutes.

Therefore, Oliver's total run time is 60 minutes.

Within his budget, he can still purchase 6 tickets. The inequality is 40 < 5x + 10.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

In light of the query

With his $40, Jamal may get tickets for himself, his friends, and a show.

If he spends $10 to join a membership,

Money remaining = $40 - $10 = $30

Now he may purchase the ticket at $5 apiece.

Now, tickets that he may purchase while staying within his budget found using utilizing the unitary technique.

Tickets= $30 / $5

Tickets = 6

As a result, he may purchase the remaining 6 tickets for his budget.

A:

Number of tickets = x

Hence, the inequality is 40 < 5x + 10.

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The entropy produced by the heat source is 2.17 J/K per hour.

In order to calculate the amount of entropy produced by a heat source, we need to use the formula for entropy change: ΔS = Q/T,

where Q is the amount of heat transferred and T is the temperature of the surroundings in kelvins.

To convert the temperature to Kelvin, we add 273.15 to the temperature in degrees Celsius.

In this case, the heat source generates 70.0 W of heat and the temperature of the surroundings is 28.5 °C.

So, to find the entropy change per hour, we need to multiply the power generated by the time:

ΔS = (70.0 W) * (3600 s/h) / (28.5+273.15)

This calculation results in approximately 2.17 J/K * h or 2.17 J/K per hour.

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The total area of the pyramid is (24√3 + 72) square units or 113.57 square units.

A hexagonal pyramid is a 3D design in which the base is hexagonal and the faces or sides are isosceles triangles, which come together to form the hexagonal pyramid at the summit of the pyramid. A hexagonal pyramid has six sides on the base and six isosceles triangles on the sides.

Given a hexagonal pyramid,

base length = 4

slant height = 6

area of pyramid = sum of the area of the base to the lateral area

area of pyramid = A(base) + A(lateral)

Area of base = 3√3/2*(a²)

a = base length = 4

Area of base = 3√3/2*(4²)

Area of base = 24√3 square units

now lateral area or area of triangular faces,

lateral area = 6*1/2*b*h

h = height of triangle = 6

b = base of triangle = 4

lateral area = 6*1/2*4*6

lateral area = 72 square units

total area =  A(base) + A(lateral)

total area = (24√3 + 72) square units

Total area = 113.57 square units.

Hence the area of the pyramid is (24√3 + 72) square units or 113.57 square units.

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Answer: -1.9d + 5.4h - 13

Step-by-step explanation:

Answer:

1/16 gallons per minute

Step-by-step explanation:

The water level drops from 8 gallons to 6 gallons in 32 minutes

The volume of water that has leaked is 8 - 6 = 2 gallons

Since this volume of water has leaked in 32 minutes, rate of leak

+ 2/32 = 1/16 gallons per minute

A graph of the solution of this inequality w ≤ 200 is shown in the image attached below.

In this exercise, we would solve the given inequality by making w the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the less than or equal to (≤) symbol.

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Answer:

Step-by-step explanation:=2/11+10/5

                                            =10/55+110/55

                                            =120/55

                                            =24/11

Answer:

The slope of the line is -2.

Step-by-step explanation:

Rise/Run

you have 2 points on the graph since this is a negative slope you start on the top point

you count straight down up to your next point and you should get 8.

then you count to the right to your next point and should get 4.

that would give you 8/4 as your slope.

8/4 simplified is 2.

The slope is 2

Answer:

x + 5 = 8

Step-by-step explanation:

x + 5 = 8

Subtract 5 from both sides.

x + 5 - 5 = 8 - 3

x = 3

Answer: x+5=8

Step-by-step explanation:

Some steps you might take after coming to a solution include all of the following:

A. Create a logical name for the variable.

E. Present your answer with units.

In Computer technology and Mathematics, a problem solving process can be defined as a systematic approach that is used typically for identifying and determining the optimal and effective solution to a particular problem.

Generally speaking, you must ensure that a logical name for the given variable is created after developing a solution to any mathematical or scientific problem.

In conclusion, the final answer (solution) must be presented with the correct and appropriate unit of measurement.

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The equation of the parabola with the given vertex and y-intercept is:

y = -(x - 3)² + 3

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a nonzero constant. To find the equation of the parabola that satisfies the given conditions, we can use the vertex and the y-intercept to find the values of a, h, and k.

The vertex of the parabola is (3, 3), so h = 3 and k = 3. The y-intercept of the parabola is (0, -6), which means that when x = 0, y = -6. Substituting these values into the equation of the parabola, we get:

y = a(x - 3)² + 3

When x = 0, y = -6. Plugging in the value of x and y, we get

-6 = a(0 - 3)² + 3

-6 = 9a + 3

-9 = 9a

a = -1

Therefore, the equation of the parabola that satisfies the given conditions is:

y = -(x - 3)² + 3

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Workers in an office of 40 staff were asked their favourite type of take- away.1/9 bit of a person is one degree.

What's Fraction?

An element of a total is a bit. The number is represented mathematically as a quotient, where the numerator and denominator are resolve. Both are integers in a simple bit. A bit appears in the numerator or denominator of a complex bit. The numerator of a proper bit is lower than the denominator.

The magnitude of an angle is measured using a unit of dimension. In magnitude, 1 degree is original to1/360 of a full gyration.

Degree 1 – direct.

Degree 2 – quadratic.

Degree 3 – boxy.

Degree 4 – quartic( or, if all terms have indeed degree, biquadratic)

Given that;

total workers = 40

Bit of a person = 1 degree

we know that 360 ° = 40 person

so for 1 degree = 40/360 = 1/9

Hence,1/9 bit of a person is one degree.

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Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.

It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.

So the equation can be modeled as:

f(x) = 4800 * 1.5^x

Where x is the number of weeks and f(x) is the number of site visits.

Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.

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If David spends $10, he may call for 50 minutes.

As per the data given in the above question are as bellow,

Let x represent the duration of David's phone calls.

The following linear equation can be used to express the call's cost:

Price = x + (x - 3) (0.10)

By setting the equation's value to 10 and finding the value of x, we can determine how long David will talk on the phone if he spends $10:

10 = 0.25x + (x-3)(0.10) (0.10)

The right side of the equation is first made simpler:

10 = 0.25x + 0.10x - 0.30

Next, we may combine related words as follows: 10 = 0.35x - 0.30

10 plus 0.30 equals 0.35x when applied to both sides.

Consequently, x = 50. David talks on the phone for 50 minutes.

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The correct statement is parameter because the value is a numerical measurement describing a characteristic of a population.

A parameter is a numeric value that describes a population feature in probability and statistics. It is a fixed value that is typically unknown and used to define or describe a probability distribution. The population's mean, variance, and standard deviation are a few examples of parameters.

Typically, these parameters are calculated using statistical techniques like maximum likelihood estimation from a sample of data. One can learn something about the entire population from a parameter. In the case of a given question, this implies that after asking everyone in that group, one will know something. All 1506 seniors at college were included in the survey and it was discovered that 65% of them own a television.

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Answer: Keith on top, Patricia below Keith, Jim below Patricia, and Sara at the bottom.

By Interception of a point f(x) = 3.75b + 25 and this we get the Value 3.75.

Examples :

f(x) = 3.75b + 25

Axis interception points of 3.75b + 25:

X intercepts:(-20 / 3,0),

Y intercepts : (0.25)

Slope of 3.75b + 25: 3.75.

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The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

According to the question,

91 pts nine percent of Americans have rh-negative o blood type.

In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?

by Using central limit theorem,

P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)

so,

P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)

= P(Z<1.4825)

= 0.9309 (from Z table)

= 0.93 (Rounded to second decimal place)

so, The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

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