What is the greatest commen factor of 338

Step-by-step explanation:

It's answer is x_> -27 by using inequality rule

Answer:

\(7 \sqrt{3} \)

Step-by-step explanation:

Simply combine like radicals:

\(3 \sqrt{3} + 4 \sqrt{3} = 7 \sqrt{3} \)

1. Factor the denominators as follow:

2. Write the expresion with the less common denominator:

Multiply the first fraction by (x+6) (both parts, numerator and denominator):

Multiply the second fraction by 4 (both parts, numerator and denominator):

Rewrite the expression with the less common denominator:

3. Remove parentheses and simplify:

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

The coordinates of point b are :

(4.25,8.25)

To find the point b, we need to use the concept of dividing a segment in a given ratio. We can use the following formula to find the coordinates of point b:

b = ( (1-r) * a + r * c ), where r is the ratio in which the segment is divided.

Here, the ratio is 3:1, which means that ab is three times smaller than bc.

So we can write :

r = 3/(3+1) = 0.75

Substituting the values in the formula, we get:

b = ( (1-0.75) * (2,6) + 0.75 * (5,9) )
b = ( 0.25 * (2,6) + 0.75 * (5,9) )
b = ( (0.5,1.5) + (3.75,6.75) )
b = (4.25,8.25)

Therefore, the coordinates of point b are (4.25,8.25).

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The point B that partitions the line segment AC with endpoints A(2,6) and C(5,9) into a 3:1 ratio is found using the formula for dividing a line segment in a specific ratio. Upon substituting the given values into the formula, we get the coordinates of point B as (3.75, 8.25).

The subject of your question is Mathematics, specifically, it involves the concept of partitioning a line segment in a certain ratio. In this case, we are given a segment with endpoints A (2,6) and C (5,9), and a point B partitions this line into a ratio of 3:1. We can use the formula for dividing a line segment in a given ratio to find point B. The formula is:

[(m*x2 + n*x1) / (m+n), (m*y2 + n*y1) / (m+n)] where x1, y1 and x2, y2 are the coordinates of the two points and m:n is the given ratio. Let's substitute the known values into the formula: B = [(3*5 + 1*2) / (3+1) , (3*9 + 1*6) / (3+1) ] =

(3.75, 8.25) .Therefore, your answer is (3.75, 8.25).

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The measure of ∠JMK =52° and ∠KML = 38°.

Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove:  is a right angle.

Proof:

Statements  Reasons

1. m∠JMK = 52°                  Given

2. m∠KML = 38°                  Given

3. m∠JMK + m∠KML = m∠JML

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52° + 38° =m∠JML            Substitution property of equality

5. 90° = m∠JML                    Simplification

6. ∠JML is a right angle.      Definition of right angle

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Answer:

Step-by-step explanation:

a. d^2 - 7d + 6 = 0

(d - 1)(d - 6) = 0

d - 1 = 0,  d - 6 = 0 therefore:

d = 1,  6.

b, x^2 + 18x + 81 = 0

(x + 9)(x + 9) = 0

x = -9  multiplicity 2.

c   u^2 + 7u - 60 = 0

(u + 12)(u - 5) = 0

u = -12, 5.

In a balanced reaction "2Al + 6HBr = 2AlBr3 + 3H2", HBr will get used up first so it's a limiting reactant and Al is in excess.

Since 2 moles aluminium are required for every 6 moles of hydrogen bromide, yet we only have 3.22 moles aluminium and 4.96 moles hydrogen bromide, it implies that HBr will get used up first and is hence the limiting reactant, while Al is in excess.

The limiting reagent is a substance that prevents a chemical reaction from occurring completely. When a limiting reagent is used in a chemical reaction, the atoms, molecules, or ions of the other reactant that it (the limiting reagent) reacts with will either remain free or unreacted.

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Answer:

24/9

Step-by-step explanation:

Answer:

7. m^21n^27

8. a^21b^28

Step-by-step explanation:

7. since m^7 raised to the 3rd power = m^( 7 * 3 ) = m^21

then  n^9 raised to the 3rd power = n^( 9 * 3 ) = n^27

your answer is m^21n^27

8. a^3 raised to the 7th power = a( 3 * 7 ) = a^21

b^4 raised to the 7th power = b( 4 * 7 ) = b^28

your answer is a^21b^28

hope this helps:)

Answer:

I think its C. but if its wrong im so sorry bc im not 100% sure but if it isnt C. then try B. idrk the answer but thats what im thiking its either C or D im not 100% sure hope this helped in some kind of way i tried :/..

Step-by-step explanation:

Here's a scenario where you would use that expression:

A rectangular playground is x foot wide, and its lenght is 3ft more than the double of is widht.

Find an expression for the lenght of the playground.

Solution: The lenght of the playground is:

The area that the dog can wander based on the information provided will be 931π.

From the information, we are told that the dog dog is attached to a 35-foot rope fastened to the outside corner of a fenced-in garden that measures 28 feet by 36 feet.

In this case, the dog is in an outside corner. The dog can trace 3/4 of a circle when it starts walking in a circle away form the wall.

The area that the dog can wander will be:

= 3/4(π35²) + 1/4(π(35 - 28)²)

= 3/4π(35)² + 1/4π(7)²

= (3/4 × 1225)π + (1/4 × 49)π

= 918.75π + 12.25π

= 931π

Therefore, the area that the dog can wander based on the information provided will be 931π.

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I don't know I don't know

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

15x6=90 90/10= 9

Step-by-step explanation:

I used a calucaltor

This is the polar equation for the curve represented by the Cartesian equation xy = 1.

To find the polar equation for the curve represented by the Cartesian equation xy = 1, we can substitute the Cartesian coordinates with their equivalent polar coordinates.

In polar coordinates, x = r * cos(θ) and y = r * sin(θ).

Substituting these into the equation xy = 1:

(r * cos(θ)) * (r * sin(θ)) = 1

Expanding and simplifying:

r² * cos(θ) * sin(θ) = 1

Since cos(θ) * sin(θ) is equal to (1/2) * sin(2θ), we can rewrite the equation as:

(r²/2) * sin(2θ) = 1

Dividing both sides by (r²/2), we get:

sin(2θ) = 2/r²

This is the polar equation for the curve represented by the Cartesian equation xy = 1.

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Answer:

The answer is -285

Step-by-step explanation:

Answer:

X=60

Step-by-step explanation:

Sum of the Quadrilateral interior angles:360

360-70-130-100=60

Given:

A graph of bell peper patch is given as below

Find:

we have to find the Maximum possible area of bell peper patch represented by the function p corresponding to the length of the tomato patch x.

Explanation:

From the given graph of function p(x), it is observed that the function has maximum value at x = 6.

Therefore, when x = 6, we get

as the function p represents the area of the bell peper patch,

Therefore, Maximum possible area of the bell peper patch is p = 18 square feet, when the length of the zomato patch is x = 6 feet.

Answer:

(3+a)

Step-by-step explanation:

3a + a^2

-------------

a

Factor out an a in the numerator

a(3+a)

-------------

a

Cancel like terms

(3+a)

Step-by-step explanation:

\( \frac{3a + {a}^{2} }{a} \\ = \frac{3a}{a} + \frac{ {a}^{2} }{a} \\ = 3 + a \\ thank \: you\)

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

The Father's birthday is on April 11.

Step-by-step explanation:

Ben: After the 10th, but before 20th, so 11, 12, 13, 14, 15, 16, 17, 18, or 19

Bob: After 5th, but before 12th, so 6, 7, 8, 9, 10, 11

Only overlapping date is the 11th

b) The Markov chain is both irreducible and aperiodic, it is ergodic.

c) The  two-step transition matrix is:

\(\left[\begin{array}{ccc}1/4&1/4&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right]\)

d) The state distribution π2 for t = 2 is \(\left[\begin{array}{ccc}0.1575, 0.1575, 0.15\end{array}\right]\).

(a) The transition diagram of the Markov chain can be represented as follows:

\(1--\frac{1}{2}-- > 1\\|\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ |\\\frac{1}{3} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\frac{1}{2}\\ |\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ |\\2--\frac{1}{2}-- > 3\\\)

(b) To determine if the Markov chain is ergodic, we need to check if it is both irreducible and aperiodic.

- Irreducibility: The Markov chain is irreducible if there is a positive probability of going from any state to any other state in a finite number of steps.

- Aperiodicity: A state is aperiodic if the greatest common divisor (GCD) of the number of steps required to return to the state is 1.

Since the Markov chain is both irreducible and aperiodic, it is ergodic.

(c) To compute the two-step transition matrix, we multiply the given transition matrix by itself:

\(\left[\begin{array}{ccc}1/2&1/2&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right] * \left[\begin{array}{ccc}1/2&1/2&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right] = \left[\begin{array}{ccc}1/4&1/4&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right]\)

So, the two-step transition matrix is:

\(\left[\begin{array}{ccc}1/4&1/4&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right]\)

(d) To find the state distribution π2 for t = 2, we multiply the initial state distribution π0 by the two-step transition matrix:

π0 = (0.3, 0.45, 0.25)T

π2 = π0  x two-step transition matrix

So, π2 = (0.3, 0.45, 0.25)T x \(\left[\begin{array}{ccc}1/4&1/4&0\\1/3&1/3&1/3\\1/2&1/2&0\end{array}\right]\)

π2 = \(\left[\begin{array}{ccc}0.3*1/4+0.45*1/3+0.25*1/2\\0.3*1/4+0.45*1/3+0.25*1/2\\0.3*0+0.45*1/3+0.25*0\end{array}\right]\)

π2 = \(\left[\begin{array}{ccc}0.1575, 0.1575, 0.15\end{array}\right]\).

Therefore, the state distribution π2 for t = 2 is \(\left[\begin{array}{ccc}0.1575, 0.1575, 0.15\end{array}\right]\).

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The sample size needed to achieve a probability of a type II error of 0.05 is approximately 1536.

To find the probability of a type II error, we need to know the significance level (alpha), the population standard deviation (sigma), the hypothesized mean (mu_0), and the alternative mean (mu_a).
Let's assume the significance level is alpha = 0.05, the population standard deviation is sigma = 100 pounds, the hypothesized mean is mu_0 = 2100 pounds, and the alternative mean is mu_a = 2100 pounds.

The type II error occurs when we fail to reject the null hypothesis (mu = mu_0) even though it is false (mu = mu_a). In this case, we want to find the probability of failing to reject the null hypothesis when the true mean weight of giraffes is actually equal to 2100 pounds.

To calculate the probability of a type II error, we need to determine the critical value or the rejection region in the sampling distribution under the alternative hypothesis. The rejection region is the range of sample means that would lead us to reject the null hypothesis.

Since the null hypothesis is mu = mu_0, the rejection region is defined by sample means that are far from the hypothesized mean. We can use the Z-test statistic to find the critical value.

Now, let's find the critical value using the Z-table or Z-distribution. Given alpha = 0.05, we can find the critical Z-value using the Z-table or calculator.

Assuming a two-tailed test, we need to find the critical Z-value that leaves a probability of 0.025 in each tail. The critical Z-value is approximately ±1.96. This means that the rejection region lies beyond ±1.96 standard deviations from the mean.

Next, we need to find the sample size needed so that the probability of a type II error is 0.05. The probability of a type II error is denoted as beta (β). In this case, we want beta = 0.05.

The power of a statistical test is equal to 1 - beta. Since the power is given as 0.95 (1 - beta = 0.95), we can use the power formula to find the required sample size.

Power = 1 - beta = 0.95

To find the required sample size, we need to know the effect size (delta), which is the difference between the hypothesized mean (mu_0) and the alternative mean (mu_a). In this case, delta = mu_a - mu_0 = 2100 - 2100 = 0.

Using the formula for power, we have:

Power = 1 - beta = 1 - P(Type II Error) = P(Reject H0 | H0 is false) = P(Z < critical value | mu = mu_a)

Since the null hypothesis is mu = mu_0, the probability of rejecting the null hypothesis when the true mean is equal to mu_a is given by:

Power = P(Z < (critical value - mu_a + mu_0) / (sigma / sqrt(n)))

Substituting the values, we have:

0.95 = P(Z < (1.96 - 0 + 0) / (100 / sqrt(n)))

Simplifying the equation, we can solve for the sample size (n):

sqrt(n) = (1.96 * 100) / 0.05

n = [(1.96 * 100) / 0.05]^2

n ≈ 1536

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To construct an 86% confidence interval with 15 data points, you would use a t-score of approximately 1.761, assuming the data follows a normal distribution.

To construct an 86% confidence interval with 15 data points, we will first need to find the appropriate t-score.

The t-score is based on the t-distribution, which is used when the sample size is small (less than 30) and the population standard deviation is unknown.

The t-score depends on the desired level of confidence and the degrees of freedom, which is equal to the sample size minus 1 (15 - 1 = 14).

To find the t-score for an 86% confidence interval, we must look at a t-distribution table or use a statistical calculator. We need to find the value corresponding to 0.930 (1 - [(1 - 0.86)/2]) in the cumulative probability column and 14 degrees of freedom in the table. The appropriate t-score is approximately 1.761.

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