Factorise completely

28x²y² - 21x²y³

Answer: x= 4 and y= 540

You should read the corresponding values inorder to figure out the other value

The sum of the first 7 terms of the series is,

⇒ S = 14.91

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

The series is,

8, 6, 9/2, …

Now, We can find the common ratio as;

Common ratio = 6 / 8 = 3 / 4

And, 9/2 ÷ 6 = 3/4

Hence, The series is geometric series.

So, The sum of nth term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

Where, 'a₁' is first term and 'r' is common ratio.

Here, a = 8, r = 3/4

Hence, The sum of 7th term of geometric series is,

S = a₁ (1 - rⁿ) / (1 - r)

S = 8 (1 - (3/4)⁷) / (1 - 3/4)

S = (8 (4096 - 2187) / 4096 ) / (1/4)

S = 8 × 1909 × 4 / 4096

S = 14.91

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Answer:

See the attached worksheet

Step-by-step explanation:

The function is transformed by subtracting 3 from both the x and y values. I'm uncertain how this is expressed in a functional form.

One common unit of measure that serves as a conversion factor between linear and angular measurements is the radian (rad).

A radian is defined as the angle subtended at the center of a circle by an arc of the circle equal in length to the radius of the circle.

Since the circumference of a circle is 2π times the radius, there are 2π radians in a full circle. Therefore, one can use the following conversion factors

1 radian = 180/π degrees (approx. 57.3 degrees)

1 degree = π/180 radians (approx. 0.01745 radians)

These conversion factors allow you to convert between linear measurements (such as arc length or circumference) and angular measurements (such as angles in degrees or radians) when dealing with circular motion or rotational systems.

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Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

The relations in a right triangle are given as follows:

In this problem, we have that:

Hence:

\(\sin{\alpha} = \frac{10}{12}\)

\(\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}\)

\(\alpha = 56.4^\circ\).

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The mass of the radioactive sample at the beginning of the 8th day of the experiment a_13=310.7.

In a lab experiment, the decay of a radioactive isotope is being observed.

At the beginning of the first day of the experiment, the mass of the substance was 1300 grams and the mass decreased by 6% per day.

\(a_n=a_1r^{n-1}\)

Use the given value in the formula so we get,

\(a_{13}=1100(0.9)^{13-1}\)

Simplify the given term

\(a_{13}=310.7\)

Therefore, The mass of the radioactive sample at the beginning of the 8th day of the experiment a_13=310.7.

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Answer:

389

Step-by-step explanation:

Answer:

It can go 250 m deep

Step-by-step explanation:

Answer: We have to solve the provided inequality:

The detailed steps for the solution to inequality (1) are as follows:

Therefore the answer is that x is less than -42.

The 95 percent confidence interval is wider than the 90 percent confidence interval.

A confidence interval (CI) is a statistical measurement used to estimate the unknown parameter's true value. When calculating the CI, the researcher must determine the confidence level, which is frequently 90 percent or 95 percent. This implies that if the research were repeated several times, the true parameter would be found within the specified limits of the CI at least 90 percent or 95 percent of the time.

When constructing a confidence interval for a population parameter, the interval must account for both the level of confidence and the sample size. Wider intervals provide more assurance that the actual population parameter falls within the limits of the interval.

On the other hand, a narrower interval provides a more precise estimate of the population parameter but with a lower degree of assurance. A confidence level of 90 percent is more stringent than a confidence level of 95 percent. As a result, to achieve the same degree of assurance, a 90 percent confidence interval must be wider than a 95 percent confidence interval.

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Notice that the blue object seems to have no beginning nor end; therefore, it is a line.

Furthermore, we can define a line by identifying two points on it. Thus, the blue line can be named as EA, AE, AD, DA, ED, or DE.

Hence, the answer is option c. line, AE

Answer: -6y= -3x-9

Since the slope is -6

y will be -6y

and the rest is -9, -3x

The projection of vector u in the direction of vector v is equal to P = - 6.354 i - 5.718 j.

In this problem we need to determine the expression of the projection of vector u in the direction of vector v, whose formula is now introduced:

P = [(u • v) / ||v||²] · v

Where:

If we know that u = - 7 i - 5 j and v = - 10 i - 9 j, then the projection of the vector is:

u • v = 70 + 45

u • v = 115

||v||² = 100 + 81

||v||² = 181

P = (115 / 181) · (- 10 i - 9 j)

P = - (1150 / 181) i - (1035 / 181) j

P = - 6.354 i - 5.718 j

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Answer:

x and y

Step-by-step explanation:

Answer:

7^12

Step-by-step explanation:

when dividing subtract the power . when multiplying add of the power.

hope this helps :]

p.s sorry if wrong

Answer:

7¹², I did all the math its right

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

jcxk

Step-by-step explanation:

The measure of the arc TQ is 180°.

Given that a circle with an angle subtended outside is 38° and a small arc of 104°, we need to determine the measure of arc TQ.

So, according to the property of a circle, we have,

m ∠R = 1/2 [m arc TQ - m arc SQ]

38° × 2 = m arc TQ - 104°

76° = m arc TQ - 104°

m arc TQ = 76° + 104°

m arc TQ = 180°

Hence the measure of the arc TQ is 180°.

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Answer:

The practice of using brass rings to stretch the neck, also known as neck elongation or neck stretching, is traditionally associated with the Padaung ethnic group from Myanmar (formerly known as Burma).

From a sociological perspective, the use of brass rings to stretch the neck can be seen as an example of deviance, which refers to behavior that violates social norms and expectations. Deviance can be either criminal or non-criminal, depending on the specific behavior in question and the cultural context in which it occurs.

In the case of Padaung women, the use of brass rings to elongate the neck is a form of non-criminal deviance, as it does not violate any laws. However, it does violate cultural norms and expectations in many other societies, where elongated necks are not seen as desirable or attractive.

Therefore, the practice of neck elongation among Padaung women can be seen as a form of cultural deviance, in which members of a particular group engage in behavior that is not considered acceptable or desirable by the larger society in which they live. At the same time, it can also be seen as an expression of cultural identity and tradition, as the practice has been passed down through generations and is an important part of Padaung culture and heritage.

I'm not sure but I think it's 5

The influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A hypothesis known as the null hypothesis states that sample observations are the result of chance.

The correct statement regarding the influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A small alpha level (typically denoted as α) is the significance level used in hypothesis testing to determine the threshold for rejecting the null hypothesis. By setting a small alpha level, such as 0.01 or 0.05, we are reducing the probability of making a Type I error, which is the incorrect rejection of a true null hypothesis.

In other words, a small alpha level provides a stricter criterion for rejecting the null hypothesis, making it less likely to reject the null hypothesis when it is true. This reduces the likelihood of claiming a significant result when there is no true effect or relationship in the population.

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The building is 5.88 units tall.

It is given that the ball is dropped from a tall building.

The formula in the box relates the distance in meters "d" fallen to the time in seconds "t".

The formula is given below :

d = 4.9*t

The ball falls for a total of 1.2 seconds before hitting the ground.

The ball will travel a distance in the time interval from when the ball is dropped until it hits the ground.

The time for which the ball travels the distance is 1.2 seconds.

The distance travelled by the ball is :

d = 4.9*t

d = 4.9*1.2

d = 5.88

Hence, the ball travels a distance of 5.88 after it is dropped from the top of the building and before hitting the ground.

The height of the building is equal to the distance calculated.

The height of the building is 5.88.

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a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

none of these

Step-by-step explanation:

ans : 514 496+18 = 514

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

The correct statement is The image segment is longer than the original segment.

To determine the image of the line segment after dilation, we can use the formula for dilation in the coordinate plane. The formula states that the coordinates of the image point (x', y') are related to the coordinates of the original point (x, y) by the following equation:

(x', y') = (h + k(x - h), v + k(y - v))

Where:

(h, v) represents the center of dilation.

k represents the scale factor.

In this case, the center of dilation is (0, 6), and the scale factor is 3. The endpoints of the line segment are P(2, 3) and Q(4, 6). Let's find the image points P' and Q' after dilation.

For point P(2, 3):

x' = 0 + 3(2 - 0) = 0 + 3(2) = 6

y' = 6 + 3(3 - 6) = 6 + 3(-3) = 6 - 9 = -3

Therefore, the image point P' after dilation is P'(6, -3).

For point Q(4, 6):

x' = 0 + 3(4 - 0) = 0 + 3(4) = 0 + 12 = 12

y' = 6 + 3(6 - 6) = 6 + 3(0) = 6 + 0 = 6

Therefore, the image point Q' after dilation is Q'(12, 6).

Now, let's analyze the coordinates of the image points P' and Q' to determine which statement is true.

The image segment is longer than the original segment.

The image segment is shorter than the original segment.

The image segment has the same length as the original segment.

To compare the lengths of the line segments, we can use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For the original segment PQ:

Distance(PQ) = √((4 - 2)² + (6 - 3)²) = √(2² + 3²) = √(4 + 9) = √13

For the image segment P'Q':

Distance(P'Q') = √((12 - 6)² + (6 - (-3))²) = √(6² + 9²) = √(36 + 81) = √117

Since √13 is approximately 3.6056 and √117 is approximately 10.8167, we can conclude that the image segment P'Q' is longer than the original segment PQ.

Therefore, the correct statement is:

The image segment is longer than the original segment.

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The Cpk value measures the capability of a process to stay within the specified limits. Without knowing the lower specification limit, we cannot determine if the process is capable or not.

To calculate the Cpk of this process, we need to use the formula: Cpk = min((USL - μ) / (3 * σ), (μ - LSL) / (3 * σ)) Where: - USL is the upper specification limit, which in this case is 6 minutes - LSL is the lower specification limit, which is not mentioned in the question - μ is the mean waiting time, which is 4 minutes - σ is the standard deviation, which is 0.5 minutes

Since the LSL is not given, we cannot calculate the exact Cpk value.

The Cpk value measures the capability of a process to stay within the specified limits. Without knowing the lower specification limit, we cannot determine if the process is capable or not.

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The angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\),\) which is approximately 1.107 radians or 63.43 degrees.

To determine the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\),\) we can follow these steps:

1. Express \(\(z_0\)\) in polar form: To find the polar form of \(\(z_0\)\), we need to calculate its magnitude \((\(r_0\))\) and argument \((\(\theta_0\))\). The magnitude can be obtained using the formula \(\(r_0 = |z_0| = \sqrt{\text{Re}(z_0)^2 + \text{Im}(z_0)^2}\)\):

\(\[r_0 = |2i + 1| = \sqrt{0^2 + 2^2 + 1^2} = \sqrt{5}\]\)

  The argument \(\(\theta_0\)\) can be found using the formula \(\(\theta_0 = \text{arg}(z_0) = \arctan\left(\frac{\text{Im}(z_0)}{\text{Re}(z_0)}\right)\)\):

\(\[\theta_0 = \text{arg}(2i + 1) = \arctan\left(\frac{2}{1}\right) = \arctan(2)\]\)

2. Find the polar form of \(\(w\)\): The polar form of \(w\) can be expressed as \(\(w = |w|e^{i\theta}\)\), where \(\(|w|\)\) is the magnitude of \(\(|w|\)\) and \(\(\theta\)\) is its argument. Since \((w = z^2\)\), we can substitute z with \(\(z_0\)\) and calculate the polar form of \(\(w_0\)\)using the values we obtained earlier for \(\(z_0\)\):

 \(\[w_0 = |z_0|^2e^{2i\theta_0} = \sqrt{5}^2e^{2i\arctan(2)} = 5e^{2i\arctan(2)}\]\)

3. Determine the argument of \(\(w_0\):\) To find the argument \(\(\theta_w\)\) of \(\(w_0\)\), we can simply multiply the exponent of \(e\) by 2:

  \(\[\theta_w = 2\theta_0 = 2\arctan(2)\]\)= 1.107 radians

Therefore, the angle of rotation at the point \(\(z_0 = 2i + 1\)\) when \(\(w = z^2\)\) is \(\(2\arctan(2)\).\)

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The complete question is:

"Determine the angle of rotation, in radians and degrees, at the point z0 = 2i + 1 when w = z^2."