3. A square wave with a \( 10 \% \) duty cycle with period \( T=1 \) and amplitude \( A=1 \) (i.e. from \( -1 \) to 1 ), using the trigonometric method. Give your answer in the compact form and show y

Answer:

L = A/W

L = 10k^2 + 10k + 1 −  3      

                        5k−4

Answer:

15 p - 3 is the answer....

Answer:

1,331in^3

Step-by-step explanation:

\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 5200\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &10 \end{cases}\)

\(5200 = 2000e^{\frac{r}{100}\cdot 10} \implies \cfrac{5200}{2000}=e^{\frac{r}{10}}\implies \cfrac{13}{5}=e^{\frac{r}{10}} \\\\\\ \log_e\left( \cfrac{13}{5} \right)=\log_e\left( e^{\frac{r}{10}} \right)\implies \log_e\left( \cfrac{13}{5} \right)=\cfrac{r}{10} \\\\\\ \ln\left( \cfrac{13}{5} \right)=\cfrac{r}{10}\implies 10\ln\left( \cfrac{13}{5} \right)=r\implies \stackrel{ \% }{9.56}\approx r\)

The greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

From the information given, we have that;

The area of the square piece is 320 square centimeters.

It is important to note that the formula for area of a square is expressed as;

Area = a ²

Where a is the length of it's side

Let's substitute the value of the area in the formula

320 = a²

Take the square root of both sides

a = √320

a = 17. 89 centimeters

Thus, the greatest number of medium squares that Talia can cut from this​ piece is 17. 89 centimeters

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Therefore , the solution of the given problem of function comes out to be Option A  is correct.

There will be questions on design, arithmetic, each subject, and both real and imagined locations on the midterm exam. An overview of the relationships between different variable that combine to create the same result. A service is composed of numerous distinctive components which operate together to give distinctive results for each input.

Here,

All potential input values for a function are represented by the scope of the function.

We can see from the provided graph that the function is defined for all values of x (from 0 to 3) for which the graph is present.

Consequently, the following is the scope of the function this graph represents:

=> {0, 1, 2, 3}

Option A thus provides the response.

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The standard deviation measures the spread of data points around the mean. It considers all data points, not just the farthest or nearest ones. A higher standard deviation indicates a greater spread.

The standard deviation is a statistical measure that tells us how much the data points in a set vary from the mean. It provides information about the spread or dispersion of the data. To calculate the standard deviation, we take the square root of the variance, which is the average of the squared differences between each data point and the mean.

By considering all data points, the standard deviation provides a comprehensive measure of how spread out the data is. Therefore, the statement "The difference between the mean and the data point farthest from the mean" is incorrect, as the standard deviation does not focus on just one data point.

The statement "The difference between the mean and the data point nearest to the mean" is also incorrect because the standard deviation takes into account the entire data set. The statement "The difference between the mean and the median" is incorrect as well, as the standard deviation is not specifically related to the median.

Hence, the correct answer is "None of the above."

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The critical points of f(x, y) = 5xy - 4y - x²y - xy² + y² are (1,0), (4,0), (1,3) (saddle points), and (2,1) (local maximum point).

The function f(x, y) = 5xy - 4y - x²y - xy² + y² has critical points at (1,0), (4,0), (1,3), and (2,1). Among these critical points, (1,0), (4,0), and (1,3) are saddle points, and (2,1) is a local maximum point.

To find the critical points of the function f(x, y) = 5xy - 4y - x²y - xy² + y², we need to find the points where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we get:

∂f/∂x = 5y - 2xy - y²

Taking the partial derivative with respect to y, we get:

∂f/∂y = 5x - 4 - x² - 2xy + 2y

Setting both partial derivatives to zero and solving the resulting system of equations, we find the critical points:

From ∂f/∂x = 0 and ∂f/∂y = 0, we have the critical points:

(1,0), (4,0), (1,3), and (2,1).

To classify these critical points, we can use the second partial derivative test or analyze the behavior of the function near these points. By evaluating the second partial derivatives at each critical point and analyzing the behavior of f(x, y) in the vicinity of each point, we can determine their nature.

Upon classification, we find that (1,0), (4,0), and (1,3) are saddle points, indicating that they have both positive and negative curvatures. On the other hand, (2,1) is a local maximum point, suggesting that it has a concave downward shape.

Therefore, the critical points of f(x, y) = 5xy - 4y - x²y - xy² + y² are (1,0), (4,0), (1,3) (saddle points), and (2,1) (local maximum point).


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The probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to .  The odds that it will not rain tomorrow are to 0.8.

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability that it will rain tomorrow is 0.2

i.e.

P(it will rain tomorrow )=0.2

Now probability that it won't rain tomorrow is,

P(it won't rain tomorrow )=1- P(it will rain tomorrow)=1-0.2=0.8

Thus

P(it won't rain tomorrow)=0.8.

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A: 43.

B: youngest; 23. oldest; 61.

C: Quartiles:Q1 --> 39. Q2 --> 43. Q3 --> 51.

The correct answer is D.

The ratios of sin x° and cos y° share a reciprocal relationship.

In a right triangle, the sine and cosine of the angles are defined as the ratio of the side lengths of the triangle.

The sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse of the right triangle.

sin x° = opposite/hypotenuse

The cosine of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse of the right triangle.

cos y° = adjacent/hypotenuse

Therefore, the ratios of sin x° and cos y° share a reciprocal relationship since

sin x° = opposite/hypotenuse

and

cos y° = adjacent/hypotenuse.

In other words, sin x° and cos y° are reciprocals of each other:

sin x° = 1/cos y° and cos y° = 1/sin x°.

The ratios are reciprocals (4 over 5 and 5 over 4).

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The problem states that "three increased by a quotient", this implies that the three is separated from the quotient, therefore, we need to create the equation in the following manner:

The correct answer is "b".

Answer:

empezando multiplicar todos los números seria un total de 1785  que lo pondremos con m3  que un metro cubico seria 1000L entonces con los 1785 los ponemos por 1 000  

Step-by-step explanation:

respuesta 1 785 000

Answer:

x = -2

y = -4

Step-by-step explanation:

The way systems of equations  work is that you have to substitute to solve for a variable *(only one of the 2 ways to figure this out)*

so, we will use addition property of equality in a form to add the two equations together, since +5y and -5y added together will cancel out.

that would leave

5x = -10

divide both sides by 5

x = -2

Now that we know x = -2, we can plug in -2 into one of the equations to find y.

2 ( -2)  + 5y = -24

-4 + 5y = -24

-4 + 4 + 5y = -24 + 4

5y = -20

y = -4

x = -2

y = -4

Answer:

7

Step-by-step explanation:

As you can see, each time (let's say n) increases by 1, it divides by 1/2. So from a1 to a2, you get 28/2 or 14, then from a2 to a3, 14/2 or 7.

7 being your answer.

Answer:

Step-by-step explanation:

Given the recursive formula.

Use it to determine the value of te third term.

Answer:

21

Step-by-step explanation:

Answer:

The correct answer is 21 out of 140 students

Step-by-step explanation:

Hope this helped :3

Let L1 be the language of all strings over the alphabet {a}, and let L2 be the language of all strings over the alphabet {b}.

Neither L1 nor L2 is a subset of the other, but L1∗ ∪ L2∗ = (L1 ∪ L2)∗.

To find an example of languages L1 and L2 such that neither of them is a subset of the other, but their Kleene closures have the same language, we can consider the following languages:

1. Let L1 be the language of all strings over the alphabet {a}. In other words, L1 contains all strings consisting only of the letter 'a'. For example, L1 = {a, aa, aaa, aaaa, ...}.

2. Let L2 be the language of all strings over the alphabet {b}. Similarly, L2 contains all strings consisting only of the letter 'b'. For example, L2 = {b, bb, bbb, bbbb, ...}.

In this case, neither L1 is a subset of L2 nor L2 is a subset of L1 because their languages consist of different symbols.

Now, let's consider their Kleene closures:

- L1∗ includes all possible combinations of the letter 'a', including the empty string ε. So, L1∗ = {ε, a, aa, aaa, aaaa, ...}.

- L2∗ includes all possible combinations of the letter 'b', including the empty string ε. So, L2∗ = {ε, b, bb, bbb, bbbb, ...}.

On the other hand, the union of L1 and L2, denoted as L1 ∪ L2, is the set of strings that belong to either L1 or L2.

In this case, L1 ∪ L2 includes all strings consisting of 'a' or 'b'. So, L1 ∪ L2 = {a, aa, aaa, ..., b, bb, bbb, ...}.

Finally, we can observe that the Kleene closure of L1 ∪ L2, denoted as (L1 ∪ L2)∗, is the set of all possible combinations of strings from L1 ∪ L2, including the empty string ε.

Since L1 ∪ L2 includes all possible strings of 'a' and 'b', (L1 ∪ L2)∗ would include all possible combinations of 'a' and 'b', which is the same as L1∗ ∪ L2∗.

Therefore, in this example, neither L1 nor L2 is a subset of the other, but their Kleene closures satisfy the property that L1∗ ∪ L2∗ = (L1 ∪ L2)∗.

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Answer:

13

Step-by-step explanation:

4 + 2 = 6

6 + 2 = 8

8 + 2 = 10

10 + 3 = 13

Answer:

$126

Step-by-step explanation:

The plot of land is worth $18,000 and the tax on the land is $0.70 per $100. You would divide 18000 by 100 which is 180. Then you would multiply 180*0.70 which is $126.

Step-by-step explanation:

Here, given that;

The total value of land us $18000.00

tax per $100.00 is $0.70

now,

$100.00 taxes $0.70

$18000.00 taxes ($18000.00÷100)/$0.70 (as in question given that the tax is charged in each $100)

= $126.

is the required tax amount.

Hope it helps..

Answer:

90

Step-by-step explanation:

To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.

However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.

1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]

2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]

3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]

4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

c + 2 = 16

Step-by-step explanation:

Answer:

c+2=16

Step-by-step explanation: d

Answer:

2) 14 y 2 m

Step-by-step explanation:

Year 9 students: total age= 100* 14 10/12= 1400 +100*5/6= 1483 y 8 m

Year 8 students: total age= 100* 13 6/12= 1350 y

Total age of 200 students: 1483 y 8 m + 1350 y= 2833 y 8 m

Average age= 2833  8/12  ÷ 200= (12*2833+8)/12 ÷ 200 = 34004/(12*200)= 34004/2400= 14  404/2400 ≈ 14 1/6 y= 14 y 2 m

Three sons inherited 2,179 ducats from their father. The number of ways the father can bequeath the resources is

Information from the problem helped in generating the following equations

The father bequeathed the older brother 2 times more money than the younger one

let the youngest receive an amount equivalent to y

then the eldest will receive 2y

let the middle receive x

Using the sharing formula described we have

y + 2y + x = 2179

3y + x = 2179

the middle brother should receive more than the younger one, but less than the older one

x > y

x < 2y

plotting the equations on a graphing calculator and getting the solutions we have

(544.75, 544.75) and (871.6, 435.8)

y ranges from 435.8 to 544.75 using whole numbers

436 to 544

The number of ways

= 544 - 436

= 108 ways

the number of ways of sharing according to fathers will is 108

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Answer:

2280

Step-by-step explanation:

As in understandable steps,

1512x12 = 18144

18144 / 7

= 2592

2592 - 312

= 2280

An equation is formed of two equal expressions. John's salary before the pay raise is $2280.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the pay of John before the raise be x.

As it is stated that John's pay was increased by $312. And he saves 7/12 of his pay which is equal to $1512. Therefore, the equation that can represent the current saving John has,

\(\dfrac{7}{12}(x+312)=1512\\\\(x+312) = \dfrac{1512 \times 12}{7}\\\\x+312= 2592\\\\x =2592-312\\\\x = 2280\)

Hence, John's salary before the pay raise is $2280.

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Answer:

A ≈ 160 cm²

Step-by-step explanation:

the area (A) of a parallelogram given adjacent sides a and b and angle Θ between them is

A = absinΘ

here a = 12 , b = 15 and Θ = 117° , then

A = 12 × 15 × sin117° ≈ 160 cm²( to the nearest cm² )

in∆BDC

use sine rule for area

\(\\ \rm\rightarrowtail \dfrac{1}{2}absinC\)

\(\\ \rm\rightarrowtail \dfrac{1}{2}(12)(15)sin117\)

\(\\ \rm\rightarrowtail 90(0.89)\)

\(\\ \rm\rightarrowtail 80.1m^2\)

(A) the smallest upper bound for P(X > 20) is 1/4. (B) x can be a binomial random variable with n = 20 and p = 0.5. b) Yes, x could be a binomial random variable

A random variable x has expectation 10 and standard deviation 5.

a) To find the smallest upper bound for P(x > 20), we can use Chebyshev's inequality. Chebyshev's inequality states that:

P(|X - μ| ≥ kσ) ≤ 1/k²

In this case, μ = 10, σ = 5, and we want to find the smallest upper bound for P(X > 20), which is equivalent to P(X - 10 > 10). So, we can set k = 10/5 = 2 and plug in the values into the inequality:

P(|X - 10| ≥ 2(5)) ≤ 1/2²

P(|X - 10| ≥ 10) ≤ 1/4

Therefore, the smallest upper bound for P(X > 20) is 1/4.

b) It is possible for x to be a binomial random variable. A binomial random variable is characterized by a fixed number of trials (n), a fixed probability of success (p), and each trial is independent. The expectation of a binomial random variable is np and the standard deviation is √(np(1-p)).

So, if x is a binomial random variable, we can set np = 10 and √(np(1-p)) = 5. Solving for n and p, we can find that n = 20 and p = 0.5. Therefore, x can be a binomial random variable with n = 20 and p = 0.5.

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Answer:

1/9

Step-by-step explanation:

Probability  =  Expected outcome/Total outcome

From the given pi chart,

Total outcome = 360degrees (since the total angle in a circle is 360 degrees)

Since we to find the probability of scoring a 5, we can see that the angle when he scores a 5 is 40degrees, hence;

Expected outcome = 40degrees

Pr(scoring a 5) = 40/360

Pr(scoring a 5) = 1/9

Hence the probability of scoring a 5 is 1/9

Answer:

1/9

Step-by-step explanation:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Divide the number of events by the number of possible outcomes.