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The frequency range of UHF is band between 470 MHz and 608 MHz.

Given is to find the frequency range of the UHF broadcast station

Therefore, the frequency range of UHF is band between 470 MHz and 608 MHz.

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{Complete question -

What is the frequency range of the UHF broadcast station?}

The value of k for the given differential equation is exact is,

⇒ k = 12

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

Given that;

The given differential equation is,

⇒ (y³ + kxy⁴ - 2x) dx + (3xy² + 24x²y³) dy = 0

And, The given differential equation is exact.

Now, We know that;

For the differential equation M dx + N dy = 0;

The condition of exactness is,

⇒ dM / dy = dN / dx  .. (i)

Here, We have;

M = y³ + kxy⁴ - 2x

N = 3xy² + 24x²y³

Hence, We get;

M = y³ + kxy⁴ - 2x

dM / dy = 3y² + 4kxy³

N = 3xy² + 24x²y³

dN / dx = 3y² + 48xy³

From (i);

⇒ dM / dy = dN / dx

⇒ 3y² + 4kxy³ = 3y² + 48xy³

⇒ 4kxy³ = 48xy³

⇒ 4k = 48

⇒ k = 48/4

⇒ k = 12

Thus, The value of k = 12

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The amount of two plane tickets are a scarce resource, meaning there are not enough to provide for all three people.

A scarce resource is something that is in limited supply. In this case, the two plane tickets are the scarce resource because there are not enough to provide for all three people. This means that if Andy wants to travel to Philadelphia with his two nephews, only two of them can go. This is because while they may have three tickets to the show, they still need to find a way to get there. The two plane tickets are a scarce resource, as they are not enough for all three of them. This means that Andy must make a difficult decision about who can go and who has to stay home. The two plane tickets are the only way for two of them to get to Philadelphia, so they are a scarce resource in this situation.

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The relative change in tuition tells us the tuition in 2016/17 decreased by 9.99 %.

The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage. Additionally, indicators that are expressed as percentages, such as the unemployment rate, are subject to the concepts of absolute and relative change.

Given:

The tuition in University if Washington in 2015-16 = 10,203

and, The tuition in University if Washington in 2016-17 = 9,183

so, the relative change is

= (10203 - 9183)/ 10203

= 1020/ 10203

= 0.0999

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The area of the polygon is 42 metres squared.

The figure is a composite figure. The area of the figure is the sum of the area of the individual shapes.

Therefore,

area of the figure = area of the rectangle + area of trapezium

Hence,

area of the rectangle = lw

where

Therefore,

area of the rectangle = 6 × 4

area of the rectangle = 24 m²

area of trapezium = 1  /2 (a + b)h

area of trapezium = 1 / 2 (4 + 8)3

area of trapezium = 1 / 2 (36)

area of trapezium = 18 m²

Therefore,

area of the figure = 18 + 24

area of the figure = 42 m²

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Let G be the number of general seats sold.

Let R be the number of reserved seats sold.

The total number of seats sold is G + R = 1139

Since general seats costs $2 each, 2G is the total receipts from general tickets sales.

Since reserve seats costs $3.50 each, 3.5R is the total receipts from reserved ticket sales.

The total receipts is 2G + 3.5R = 2716

We now have two equations in two unknowns and can solve for G and R.

If we consider between mean and median in case of better measure of the center, median is likely to be the better measurement.

The list of values given here is 25, 29, 23, 26, 25, 27, 10, 26, 23, 23, 26.

First we are making or rearranging it in ascending/ descending order.

10, 23, 23, 23, 25, 25, 26, 26, 26, 27, 29.

Mean will be  the average of the given set.

Median will be the exact middle number or the average of the two middle entries.

Mean = 23.9

Median = 25

If we consider the range of data and how it is distributed, you can see it ranges from 10 to 29.

But the problem is that, after 10, the second least value is 23 and rest of the values are nearer also.

There is a clear gap between the values of other data points and the first data entry 10.

As mean is the average of every data, this 10 can directly influence the value of mean and cannot gave us an approximation of center.

Imagine that if the last entry is somewhat very big number, then the mean will surely slant to the higher number as it is the sum average of the given set of data.

But median is then also the exact middle number and not influenced by the range of the given data.

Mean and median can be the same in certain cases but when we approximate the measurement of center more than mean, median will likely to give better answer.

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Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.

The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"

(1/2) x (1/2) x (1/2) = 1/8.

Similarly, the probability of getting three tails in a row is also:

(1/2) x (1/2) x (1/2) = 1/8.

Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.

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P(a purple marble then a white marble) is 6/105 ⇒ 1st answer

* Lets explain how to solve the problem

- There are 2 green marbles

- There are 7 blue marbles

- There are 3 white marbles

- There are 4 purple marbles

- Once a marble is drawn, it is NOT replaced

- We need to find P(a purple marble then a white marble)

* At first lets find the total number of marbles by adding all color

∵ There are 2 green , 4 purple , 3 white and 7 blue

∴ The total number of marbles = 2 + 4 + 3 + 7 = 16

∴ There are  16 marbles in the bag

∵ Probability = number of events/number of all outcomes

∵ There are 4 purple marbles

∴ The probability of chosen a purple marble is P(purple) = 4/15

∵ Once a marble is drawn, it is NOT replaced

∴ The total number of marbles = 15 - 1 = 14 marbles

∵ The number of white marbles is 3

∴ The probability of chosen a white marble is P(white) = 3/14

∵ P(a purple marble then a white marble) = P(purple) . P(white)

∵ P(purple) = 4/15

∵ P(white) = 3/14

∴ P(a purple marble then a white marble) = (4/15)(3/14) = 6/105

* P(a purple marble then a white marble) is 6/105

3.5 kilograms is 3500 grams

Answer: 3500

Step-by-step explanation: one kilogram is 1000 gram so multiply 3.5 x 1000

Answer:

Step-by-step explanation:

EVALUATE

n(m ^5+m−n) divided by

m(m−n)

​

EXPAND

m^2mn Divided by

mn-n^2+nm^5

The probability that a randomly chosen fitness club member signs up for a free running session is 20%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.


This is because 30 members signed up for a free session, with 10 signing up for the running session, 10 signing up for the swimming session, and 10 signing up for the weightlifting session. Since the running and swimming sessions are each twice as popular as the weightlifting session, there is a 20% chance that any given member will choose the running session.

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No, it is not possible to have a function f defined on [2,4] that is continuous and has an unbounded range. This is because of the Extreme Value Theorem, which states that a continuous function on a closed interval must have a maximum and minimum value within that interval. If the range of f is unbounded, then there is no maximum or minimum value, which contradicts the Extreme Value Theorem. Therefore, it is not possible to have such a function.

If we modify the condition to allow for an unbounded range in only one direction (either unbounded from above or unbounded from below), then it is possible to have a function that is continuous on [2,4] with an unbounded range.

For example, consider the function f(x) = 1/(x-4) defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the negative direction, as f(x) approaches negative infinity as x approaches 4 from the left.

Another example is the function g(x) = x^2 defined on the interval [2,4]. This function is continuous on [2,4] and has an unbounded range in the positive direction, as g(x) approaches infinity as x approaches 4 from the right.

So, it is possible to have a continuous function on [2,4] with an unbounded range in one direction, but not in both directions simultaneously.

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The formula for the volume of a rectangular box is V = l × w × h, where l is the length, w is the width, and h is the height. Since the density is given as 1 g/cm³, the mass of the object is equal to its volume in cubic centimeters (cc):

mass = volume × density

728 g = V × 1 g/cm³

V = 728 cm³

We are given the length and width of the box, so we can substitute these values into the formula for volume:

V = l × w × h

728 cm³ = 20.8 cm × 7 cm × h

Simplifying the right-hand side:

728 cm³ = 145.6 cm² × h

Dividing both sides by 145.6 cm²:

h = 728 cm³ ÷ 145.6 cm²

h = 5 cm

Therefore, the height of the box is 5 cm.

Answer:

1.48

1 minute and 48 seconds

Answer:

c

Step-by-step explanation:

The colonists thought of King George III as a tyrant, which is evident when looking at the founding documents of the United States and the political parties. The Constitution created separation of powers so nobody would be able to become a tyrant or dictator. There are checks and balances to keep people from gaining too much power and overtaking the government. When looking into the political parties later on, there were the Anti-federalists, who did not want a strong central government because they did not want another King George, who they just got out of a war with.

The population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It may be referred to as scientific form or standard index form.

Given that, the population of a large US city is 1,703,210. we need to show this number in Scientific Notation.

We know that, a number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

The number is written in two parts:

The digits, with the decimal point placed after the first digit, followed by × 10 to a power that puts the decimal point where it should be

Therefore,

1,703,210 = 1.70321 × 10⁶

Hence, the population of a large US city is 1.70321 × 10⁶ in Scientific Notation.

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The function's two zeros are: x = -1 and x = 6.

In mathematics, a function is a set of ordered pairs (input, output), where each input is associated with exactly one output. The input is commonly referred to as the independent variable, and the output is referred to as the dependent variable. A function can be represented algebraically, graphically, or verbally. Algebraically, a function is often represented by an equation that defines the relationship between the independent variable and the dependent variable. For example, the equation y = 2x + 1 defines a linear function, where x is the independent variable and y is the dependent variable.

Here,

The zeros of a function are the values of the independent variable for which the function equals zero. To determine all zeros for the function f(x) = (2x + 2)(x - 6), we need to find the solutions to the equation f(x) = 0.

To do this, we can set the two factors equal to zero and solve for x:

2x + 2 = 0

x = -1

x - 6 = 0

x = 6

These are the two zeros of the function: x = -1 and x = 6.

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The scales in the ratio of 1 : n are:

a) 1 : 80

c) 1 : 80000

d) 1 : 100000

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

a)

5 cm and 4 m

1 m = 100 cm

So,

4 m = 4 x 100 cm

4 m = 400 cm

Ratio.

= 5 cm : 4 m

= 5 cm : 400 cm

= 1 : 80

c)

5 cm and 4 km

1 km = 100000 cm

So,

4 km = 400000 cm

Ratio.

= 5 cm : 400000 cm

= 1 : 80000

d)

4 cm and 5 km

1 km = 100000 cm

So,

5 km = 500000 cm

Ratio.

= 5 cm : 500000 cm

= 1 : 100000

Thus,

The scales in the ratio of 1 : n are:

1 : 80

1 : 80000

1 : 100000

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Answer:

[tex]x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}[/tex]

Step-by-step explanation:

First, multiply out the set of parentheses and simplify the resulting quadratic expression.

[tex]4(x - 1)(3x - 1) = 0[/tex]

[tex]4(3x^2-x-3x+1) = 0[/tex]

[tex]4(3x^2-4x+1) = 0[/tex]

Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.

[tex]4(3(x^2-\dfrac{4}{3}x+\dfrac{1}{3})) = 0[/tex]

[tex]12(x^2-\dfrac{4}{3}x+\dfrac{1}{3}) = 0[/tex]

Finally, complete the square.

[tex]12\left(x^2-\dfrac{4}{3}x + \left(\dfrac{-\dfrac{4}{3}}{2}\right)^2\right) = 12\left(-\dfrac{1}{3}\right) + 12\left(\dfrac{-\dfrac{4}{3}}{2}\right)^2[/tex]

[tex]12\left(x^2-\dfrac{4}{3}x + \dfrac{4}{9}\right) = -4 + \dfrac{16}{3}[/tex]

[tex]12\left(x - \dfrac{2}{3}\right)^2 = \dfrac{4}{3}[/tex]

[tex]\left(x - \dfrac{2}{3}\right)^2 = \dfrac{1}{9}[/tex]

↓ take the square root of both sides

[tex]x - \dfrac{2}{3}\right = \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm \sqrt{\dfrac{1}{9}}[/tex]

[tex]x = \dfrac{2}{3} \pm\dfrac{1}{3}[/tex]

↓ split into two equations

[tex]x = \dfrac{2}{3} + \dfrac{1}{3} \ \ \ \text{OR} \ \ \ x = \dfrac{2}{3} - \dfrac{1}{3}[/tex]

[tex]\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = \dfrac{1}{3}}[/tex]

Answer: The actual roots of f(x) = 2x² + 2x - 24 are -3 and 4.

Step-by-step explanation:

The discontinuity of the function is removed and the value of the function at 1 after removing the discontinuity is 8.

What is meant by a discontinuity in a function?

In algebra, a discontinuous function is one that has a point at which the function is not defined, at which the left-hand limit and right-hand limit are equal but not equal to the value of the function at that point, or at which the limit of the function does not exist. If a function in algebra is not continuous, it is referred to as a discontinuous function. A discontinuous function has a discontinuous curve, just like a continuous function does.

Given f(x) = 2x²+4x-6 / (x-1)  

This function has a  discontinuity at 1 because when we substitute x =1, the denominator becomes 0 and the function becomes undefined.

But this discontinuity is removable and can be done as shown:

We can factorize the numerator as below:

2x²+4x-6 = 2x²+6x - 2x -6 = 2x(x+3) -2(x+3) = (2x - 2)(x+3) = 2(x-1)(x+3)

Now when we substitute the factorized form of the numerator in the function. Then,

f(x) =  2(x-1)(x+3) / (x-1)

(x-1) can be cancelled from both the numerator and denominator. So the discontinuity is removed.

f(x) = 2(x+3)

Now f(1) = 2 * (1+3) = 8

Now the function is continuous at 1.

Therefore the value of the function at 1 after removing the discontinuity is 8.

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Answer:

a. 48:16

b. 3:1

Step-by-step explanation:

Part a asks for a ratio of the two speeches. You simply separate the two numbers with a colon to show that it's a ratio.

Part b asks that the second quantity (which is the speeches made by B) be 1. To do this, divide 16 on both sides. 48 divided by 16 is 3, and 16 divided by 16 is 1. Thus, 3:1

The probability of finding gold in that land is 0.8.

Given is that a mining company buys a piece of land in Peru. The studies determined the following prior probabilities -

We can write the probability of finding gold in that land as -

P{E} = P(find good quality gold) + P(find poor quality gold)=0.30

P{E} = 0.5 + 0.3

P{E} = 0.8

Therefore, the probability of finding gold in that land is 0.8.

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{QUESTION IN ENGLISH -

A mining company buys a piece of land in

Peru. The studies determined the following

prior probabilities:

to.

P(find good quality gold)=0.50

b. P(find poor quality gold)=0.30

C. P(find no gold)=0.20

Calculate the probability of finding gold in that}

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Answer:

1.             0             10             20           30            40            50

             10             14             18            22            26            30

2. (the immage)

3. Yes this is a liner equation

Step-by-step explanation:

An equation connecting y and x.​is given as y = 15/x

What is inverse variation?

In Maths, inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases

y∞1/x

This implies that y=k/x            where k is a constant

5 = k/3

Making k the subject of the relation

therefore, k = 15

The equation connecting y and x would be y = 15/x

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Answer:

Angles 11 and 10 both make a 180-degree angle, but so do 5 and 3. I would go with 11 and 10

Answer:

D, <11 and <10

Step-by-step explanation:

Supplementary angles are angles that sum to 180°

The total distance driven by Ryan is given as follows:

20.5 miles.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

Considering that 12 minutes = 12/60 = 0.2 hours, the distance for the first customer was of:

40 = d/0.2

d = 40 x 0.2

d = 8 miles.

Considering that 15 minutes = 15/60 = 0.25 hours, the distance for the second customer was of:

50 = d/0.25

d = 0.25 x 50

d = 12.5 miles.

Hence the total distance was of:

8 + 12.5 = 20.5 miles.

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the standard matrix of T. T: R2→R2 is [ 0 1 ]

                                                               [ 1  0]

We must locate the pictures of the standard basis vectors of R2 under T and translate those images into columns of a 2x2 matrix in order to get the standard matrix of T.

Let's start by thinking about the reflection along the line x2 - x1. The point (x1, x2) is mapped to the point via this reflection (x2, x1).

We apply T to the first standard basis vector, e1 = (1,0), to determine its image:

T(e1) = (0,1) (0,1)

We also use T: to determine the image of the second standard basis vector, e2 = (0,1).

T(e2) = (1,0) (1,0)

Hence, (0,1) and (1,0) are the images of the standard basis vectors,  These photos can now be expressed as columns in a matrix:

[0 1]

[1 0]

This is the standard matrix of T.

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