Suppose are running a study/poll about the probability of catching the flu this year. You randomly sample 113 people and find that 83 of them match the condition you are testing.

Suppose you are have the following null and alternative hypotheses for a test you are running:

H0:p=0.69H0:p=0.69

Ha:p<0.69Ha:p<0.69

Calculate the test statistic, rounded to 3 decimal places.

To prove that X(=0), we need to show that when X is a scalar function, its derivative with respect to time is zero.

Let's consider a scalar function X(t). The derivative of X(t) with respect to time is denoted as dX/dt. To prove that X(=0), we need to show that dX/dt = 0.

The derivative of a scalar function X(t) is computed as dX/dt = AX(t), where A is a constant matrix and X(t) is a vector function.

Since X(=0), the derivative becomes dX/dt = A(0) = 0. Thus, the derivative of X(t) is zero, which proves that X(=0).

Now, let's consider the second part of the question. We are given that X1, X2, and X3 are linearly independent solutions of the differential equation X'=AX. We need to prove that 2X1-X2+3X3 is also a solution of the same differential equation.

We can verify this by substituting 2X1-X2+3X3 into the differential equation and checking if it satisfies the equation.

Taking the derivative of 2X1-X2+3X3 with respect to time, we get:

d/dt (2X1-X2+3X3) = 2(dX1/dt) - (dX2/dt) + 3(dX3/dt)

Since X1, X2, and X3 are linearly independent solutions, we know that dX1/dt = AX1, dX2/dt = AX2, and dX3/dt = AX3.

Substituting these expressions, we get:

2(dX1/dt) - (dX2/dt) + 3(dX3/dt) = 2(AX1) - (AX2) + 3(AX3)

Using the properties of matrix multiplication, this simplifies to:

A(2X1-X2+3X3)

Thus, we can conclude that 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

The proof shows that for a scalar function X(=0), the derivative is zero. Additionally, for the given linearly independent solutions X1, X2, and X3, the expression 2X1-X2+3X3 is also a solution of the differential equation X'=AX.

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The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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the area of Matthew's rectangle is 60 square units.

What is a rectangle?

Rectangles are quadrilaterals in the Euclidean plane of geometry that have four right angles. A closed, four-sided rectangle is a two-dimensional shape, according to a number of definitions, as is an equiangular quadrilateral. All of a rectangle's angles are exactly 90 degrees, and its opposite sides are equal and parallel to one another. Rectangle area is equal to A = a*b.

let's say Melodie's rectangle has a length of 7 grid squares and a width of 4 grid squares. To find the area, you would multiply 7 by 4 to get 28 square grid units. Therefore, the area of Melodie's rectangle is 28 square units.

Similarly, let's say Matthew's rectangle has a length of 10 grid squares and a width of 6 grid squares. To find the area, you would multiply 10 by 6 to get 60 square grid units.

Therefore, the area of Matthew's rectangle is 60 square units.

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Answer:

Step-by-step explanation:

circumference is 2πr

r=d/2

r=4.46m

C=2π(4.46)=28.02

It is sampled at a rate 25% higher than the Nyquist rate and quantized into L levels. The maximum acceptable error in sample amplitudes is limited to 0.1% of the peak signal amplitude.

To sketch the amplitude spectrum of g(t), we observe that sinc functions centered at 16 kHz and 10 kHz contribute amplitudes of 16x10³ and 10x10³, respectively, while the cosine component centered at 30 kHz has an amplitude of 20x10³. The horizontal axis represents the frequency (f).

The amplitude spectrum of the sampled signal, within the range -50 kHz to 30 kHz, will exhibit replicas of the original spectrum centered at multiples of the sampling frequency. The amplitudes and frequencies should be labeled according to the replicated components.

The minimum required bandwidth for binary transmission can be determined by considering the highest frequency component in g(t), which is 30 kHz. Therefore, the minimum required bandwidth will be 30 kHz.

For M-ary multi-amplitude signaling within a channel bandwidth of 50 kHz, we need to find the minimum value of M. It can be determined by comparing the available bandwidth with the required bandwidth for each amplitude component of g(t). The minimum M will be the smallest number of levels needed to represent all the significant amplitude components without violating the bandwidth constraint.

To minimize M, we need to select a pulse shape that achieves the narrowest bandwidth while maintaining an acceptable level of distortion. Different pulse shapes can be considered, such as rectangular, triangular, or raised cosine pulses.    

If a raised cosine pulse is used, the roll-off factor determines the pulse shape's bandwidth efficiency. The roll-off factor is defined as the excess bandwidth beyond the Nyquist bandwidth. The required M can be calculated based on the available channel bandwidth, the roll-off factor, and the distortion tolerance.

When using delta modulation with a sampling rate of five times the Nyquist rate, the number of levels (L) and corresponding bit rate can be determined by considering the quantization error and the maximum acceptable error in sample amplitudes. The bit rate will be determined based on the number of bits required to represent each level and the sampling rate.  

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Answer:

D. \(2^{18}\)

Step-by-step explanation:

The expression is: \((2^{6}) ^{3}\) * \(2^{0}\)

For the first term: When a term with an exponent is inside parentheses with another exponent on the outside, the two exponents are multiplied by each other:

6 * 3 =  18

Now the expression looks like this: \(2^{18}\) *   \(2^{0}\)

Any number to the power of zero is 1.

So the equation now looks like this:  \(2^{18}\) * 1

After you multiply the two terms, you end up with  \(2^{18}\).

Answer:

The answer is D 2^18

Step-by-step explanation:

Step-by-step explanation:

I assume you need the equation in slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is defined as ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

let's use the 2 points, where the line intersects the x- and the y- coordinate axis : (0, 9) and (9, 0)

that gives us "b" already : the y-value when x = 0 is 9.

about the slope "a" :

x changes by +9 (from 0 to 9).

y changes by -9 (from 9 to 0).

the slope is then -9/+9 = -1/1 = -1

and the equation is

y = -x + 9

Answer:

∠ FGH = 125°

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, then

∠ FGH + ∠ GHJ = 180° , that is

∠ FGH  + 55° = 180° ( subtract 55° from both sides )

∠ FGH = 125°

Answer: m∠FGH = 125°

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary (add up to 180°).

From the diagram, we can see that m∠GHJ and m∠FGH are adjacent.

This means that:

m∠GHJ + ∠FGH = 180° where ∠FGH is ∠x and ∠GHJ = 55°

55° + m∠x = 180° (subtract 55 from both sides)

m∠x = 125°

Each side of a square office is 5 meters long. It will cost $65.00 per square meter to replace the carpet in the office. The total cost of a square carpet is $1625.

Area of square = s × s = s²

Each side of the square office given is,

s = 5 m

Area = 5m ×5m

Area = 25 m²

Cost of per square meter = $65.00

Therefore, the total cost of a carpet = area × cost

Total cost = 25 m² × $65.00 = $1625

The total cost of a square carpet is $1625.

What is a square?

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Answer:

the 3 one

Step-by-step explanation:

Answer:

YES

Step-by-step explanation:

1:4 can be written as: \(\frac{1}{4} \\ \), and we know to make and equivalent fraction you multiply by a constant. so,

\(\frac{1}{4} \\\)×\(\frac{5}{5} \)=\(\frac{5}{20} \) (5:20)

Hope this helps!

Given :

R'S'T' is the image of RST

we will find the rule of translation using the coordinates of :

So, the rule will have the form :

So, the answer is :

T(7,-3)

7 units right ; 3 units down

Answer:

Step-by-step explanation:

=_=

Answer:

b and e I think. would be helpful to have more info

Step-by-step explanation:

Answer:

$86.83

Step-by-step explanation:

75.50 x 15% = 11.33

75.50+11.33 = $86.83

Answer:

$86.83

Step-by-step explanation:

$75.50x15%=11.33

75.50+11.33= $86.83

The Probability that there are exactly 2 books that they both select is 25/63

Describe probability.

The estimation of the probability that experiments will take place is one use of probability theory. We can compute anything using a probability, such as the possibility of making a research error or the probability of receiving heads or tails while flipping a coin. This branch of mathematics requires a thorough understanding of the formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two events joining together.

We don’t care about which books Harold selects. We just care that Betty picks 2 books from Harold’s list and 3 that aren’t on Harold’s list. The total amount of combinations of books that Betty can select is( \(\(10} \atop {5}\right.\)) = 252
There are (\(\(5} \atop {2}\right.\))= 10 there are two books on Harold's list that Betty can choose from. There are from the remaining 5 books that aren't on Harold's list(\(\(5} \atop {3}\right.\)) = 10 ways to choose 3 of them. \(\frac{10 * 10}{250} = \frac{25}{63}\)

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Answer:

20

Step-by-step explanation:

(72-60):60*100 =

(72:60-1)*100 =

120-100 = 20

Hope this helps :)

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

Clark Property Management should expect to experience some consecutive years with higher compressor failure rates.

Let X represent the number of AC compressor failures. Thus, the probability distribution of X is as follows :

Number of Compressor Failures Probability (Relative Frequency)

0 0.061 0.132 0.253 0.284 0.205 0.076 0.01.

We will select two-digit random numbers from a table of random numbers. We will simulate 20 years of compressor failure.

As a result, there will be a total of 20 values of X, each representing a year's worth of data.

We may now determine whether it is typical to have three or more consecutive years with two or fewer compressor failures per year.

The Monte Carlo simulation is used to complete this task. We may use an online random number generator if a table of random numbers is not available.

Monte Carlo simulation is a statistical modeling method that employs random sampling techniques to simulate the output of a complicated system.

It is a stochastic modeling technique that allows for uncertainty and risk evaluation in complex systems where deterministic methods are insufficient.

Monte Carlo simulation generates random input values for a system with a mathematical model, allowing it to calculate possible outcomes.

These results are then used to generate probability distributions of potential results.

In essence, the Monte Carlo simulation is an experiment conducted on a computer that provides insight into the degree of risk related to decision-making.

1. Set up a model: Determine the system and create a mathematical model that will be utilized in the Monte Carlo simulation.

2. Define input values: Identify the variables that will affect the model's output and define input probability distributions for each.

3. Generate random numbers: Using the input probability distributions, generate random numbers for each variable

4. Run simulations: Run a large number of simulations using the random numbers generated in step 3.

5. Analyze the results: Using the outputs of the Monte Carlo simulation, estimate potential outcomes and the likelihood of different results.

6. Make decisions: Use the data and insights obtained from the Monte Carlo simulation to inform your decision-making.

After conducting the Monte Carlo simulation, it was determined that it is unusual to have three or more consecutive years with two or fewer compressor failures per year.

The probability of having three or more consecutive years with two or fewer compressor failures per year is about 6.16%.

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Answer:

tu aimes les hommes

Step-by-step explanation:

Answer: hola soy nuevo

Step-by-step explanation:

Answer:

30 1/2 x 9 1/3 = 284 7/10

Step-by-step explanation:

i just used a calculator.

hope this helps <3

Answer:

line 1 to line 2 is c line 2 to line 3 is a

Step-by-step explanation:

\((10x + 3) + 4x \\ (3 + 10x) + 4x \\ 3 + 10x + 4x \\ 3 + 14x \\ \\ option \: (a) \\ thank \: you\)

Answer:

thats the answer ^^

Step-by-step explanation:

plz give me brainlyest i need it

Answer:

Option 1

Step-by-step explanation:

\(3 {x}^{2} - 18x + 5 = 47\)

\( = > 3 {x}^{2} - 18x + 5 - 47 = 0\)

\( = > 3 {x}^{2} - 18x - 42 = 0\)

\( = > 3( {x}^{2} - 6x - 14) = 0\)

\( = > {x}^{2} - 6x - 14 = 0\)

We know that

\(x = \frac{ - b + \sqrt{d} }{2a} \: or \: \frac{ - b - \sqrt{d} }{2a} \)

Where D = Discriminant of the eqn.

Discriminant of the above eqn.=

\( {b}^{2} - 4ac = {( - 6)}^{2} - 4 \times ( - 14) \times 1 = 92\)

So,

\(x = \frac{ - ( - 6) + \sqrt{92} }{2 \times 1} \: or \: \frac{ - ( - 6) - \sqrt{92} }{2 \times 1} \)

\( = > x = \frac{6 + 2 \sqrt{23} }{2} \: or \: \frac{6 - 2 \sqrt{23} }{2} \)

\( = > x = (3 + \sqrt{23} ) \: or \: (3 - \sqrt{23} )\)

Answer:

In pic below

Step-by-step explanation:

The probability that the train will be there when Alex arrives is 5/18

If Alex arrives at any time after 1.20pm the chances that train will  be there is 1/3.

However  if alex arrives at 1.00pm exactly there is no chance the train will be arrive there.

The probability that the train will be there increase linearly to 1/3 as alex's arrival time moves from 1.00pm to 1.20pm.

By arranging the probabilities over the first 20 minutes to get a 1/6 chance the train will be there if alex arrives between 1.00pm to 1.20pm

we get the final answer by

=1/3( 1/6 + 1/3 + 1/3)

=5/18

So, the probability that the train will be there when Alex arrives is 5/18

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Answer:

C.120

Step-by-step explanation:

5×4×3×2×1=120 hope its right

Answer: hi

Step-by-step explanation:

The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

\((x-a)^2+(y-b)^2=r^2\)

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)\)

where, \((x_{1},y_{1})\) and \((x_{2},y_{2})\) are two points.

Now putting the values

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)\)

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = \(\sqrt{(-2-1)^2+(3-1)^2}\)

r =\(\sqrt{(-3)^2+(2)^2}\)

r = \(\sqrt{9+4}\)

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

Answer:

Step-by-step explanation:

Use the distributive property:

\(2x^3 - 3x^2 - 7x + 2x^2 - 3x -7\)

Combine like terms:\(2x^3 -x^2 -10x-7\)