The dotplot shows the distribution of passing rates for the bar
ex4m at 185 law schools in the United States in a certain year. The
five number summary is
27​,
77.5​,
86​,
91.5​,
100.
Draw the
Homework: Section 3.5 Homework Question 10, 3.5.72 Part 2 of 2 HW Score: 72.62%, 8.71 of 12 points O Points: 0 of 1 Save The dotplot shows the distribution of passing rates for the bar exam at 185 law

We must solve for x using the addition principle, the equation is as follows

In conclusion, the answer is x = -9

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

of means multiply

18% * 50

Change to decimal form

.18 * 50

9

There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

There are 12 elements of the group     \(U_{13}\)   , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are     \(\phi (\phi (n))\)    of them. So we must compute     \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\)   . There are 4 incongruent primitive roots.

To find them, take the powers each element in turn:

1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1  (2 has order 12, it is a primitive root)

Of course, the higher powers of 2 cannot be.

Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.

For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.

Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.

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Answer:

Step-by-step explanation:

12C4=495

10C2-5=40

40*6=240

240/495=48/79

The probability that there is exactly 1 matching pair of socks among these 4 socks is 48/79

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Give:

Dragomir has 6 pairs of socks in a drawer.

So, \(^{12}C_4\)

= 12! / 8! 4!

= 12 x 11 x 10 x 9 x 8! / 8! x 4x 3x 2

=495

again,

\(^{10}C_2\)-5

= 10! / 8! 2! - 5

=45 - 5

=40

Thus, for 6 pairs of socks

= 40*6

=240

Hence, probability that there is exactly 1 matching pair of socks among these 4 socks  = 240/495=48/79.

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The transformation x-Ax can be decomposed into a rotation and scaling if and only if A is symmetric.

If A is symmetric, then its eigenvalues will be real and its eigenvectors will be orthogonal. The scaling factor is determined by the magnitude of the eigenvalues, and the rotation angle is determined by the angle between the eigenvectors. However, without knowing the matrix A, I cannot determine the values for these.

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For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Answer:

Area of square yard is 289 square units.

Step-by-step explanation:

Problem: find the area of yard

Given

side measure of yard is equal to length of garage.

Dimension of rectangular garage : 17 by 10

we know that rectangle consist of 4 sides with opposite of equal length.

Additionally in rectangle value of length is always greater than measure than width of rectangle.

Thus, in the given dimension 17 by 10, 17 is greater than 10.

hence length of garage is 17

this length is equal to side of square yard.

Thus, measure of yard = 17

we know area of square is given by = \(side^2\)

thus, area of square yard = \(17^2\) = 289

Area of square yard is 289 square units.

Amount of pretzel each person receives is 17/16 lb.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Total weight of the bag of pretzels = 34 ounce

Elisa shares this among her two sisters equally.

Share of pretzels each sister gets = 34 / 2 = 17 ounces

We need this amount in pounds.

We know that,

16 ounce = 1 lb.

17 ounces = 17/16 lb.

Hence the amount of pretzels each get is  17/16 lb.

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The mathematical relationship that best describes the dependence of capacitance on plate separation is an inverse relationship.

This means that as the plate separation increases, the capacitance decreases and vice versa. The equation that describes this relationship is:

C = εA / d

where C is the capacitance, ε is the permittivity of the dielectric material between the plates, A is the area of the plates, and d is the plate separation. As we can see from the equation, the capacitance is inversely proportional to the plate separation, meaning that as the plate separation increases, the capacitance decreases.

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A performance appraisal based on the number of cars sold or the percentage of defects on an assembly line is an example of a quantifiable performance metric.

A quantifiable performance metric is a measure that can be expressed in numerical terms. In the case of a performance appraisal based on the number of cars sold, it provides a clear and objective measure of an employee's sales performance. The higher the number of cars sold, the better the performance. Similarly, measuring the percentage of defects on an assembly line allows for an assessment of the quality of work. A lower percentage of defects indicates better performance in ensuring product quality and customer satisfaction.

Quantifiable performance metrics have several advantages. First, they provide an objective basis for evaluating performance, as they are not influenced by subjective opinions or biases. Second, they allow for easy comparison and benchmarking across individuals or teams, providing a standardized measure of performance. Finally, quantifiable metrics enable organizations to set clear goals and targets, which can motivate employees to strive for improved performance. However, it's important to note that relying solely on quantifiable metrics may overlook other important aspects of performance, such as teamwork, customer service, or innovation. Therefore, a well-rounded performance appraisal system should consider a combination of both quantifiable and qualitative measures to provide a comprehensive evaluation.

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9514 1404 393

Answer:

  x = -7, x = 9

Step-by-step explanation:

We presume your equation is ...

  x² -2x -63 = 0

Factors of -63 that have a sum of -2 are -9 and +7. Then the factored equation is ...

  (x -9)(x +7) = 0

Solutions make the factors zero.

  x -9 = 0   ⇒   x = 9

  x +7 = 0   ⇒   x = -7

The solutions to the quadratic equation are x = -7 and x = 9.

Answer:

True

Step-by-step explanation:

it makes sense

~Plz tap the crown~

~Thank you~

Answer:

depending on what sample it is.

Answer:

2968.78

Step-by-step explanation:

took the test

Answer:

where are the equations

Step-by-step explanation:

m is how much more she needs to save

510+8+6=516+m

m=8

These measurements are not identical due to confounding;

When the effects of two or more explanatory variables on a response variable cannot be distinguished from one another, confounding occurs in an experiment.

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The half-life of this isotope (in hours) is 13.0

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

An important application of isotopes is in the determination of the isotopic signature of element samples via isotope analysis. This is generally done via the process of isotope ratio mass spectrometry.

28% decay means, 72% remains.

Now,

\(N=N_{n} (\frac{1}{2})^{t/t_{12} } \\72=100(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\(\frac{72}{100} )=(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\\)

Taking long as both sides & solving we get,

\(t_{\frac{1}{2} } = 13.0 hours\)

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Answer:

Acapulco

Step-by-step explanation:

The sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function\(f(x) = 0\) on the interval \(I = [0, \infty)\).

To examine the uniform convergence of the sequence\(f_n(x) = e^{-nx}\) on the interval\(I = [0, \infty)\), we need to check if the sequence converges uniformly to a limit function on that interval.

For uniform convergence, we need the following condition to hold:

Given any\(\(\epsilon > 0\\)), there exists an \(\(N \in \mathbb{N}\\)) such that for all \(n > N\) and for all \(x \in I\), we have\(\(\left| f_n(x) - f(x) \right| < \epsilon\)\), where \(\(f(x)\)\) is the limit function.

Let's find the limit function\(\(f(x)\\)) of the sequence \(f_n(x) = e^{-nx}\) as \(n\) approaches infinity. Taking the limit as \(\(n\)\)goes to infinity

\(\[f(x) = \lim_{n \to \infty} e^{-nx}\]\)

We can rewrite this limit using the exponential function property:

\(\[f(x) = \exp\left(\lim_{n \to \infty} -nx\right)\]\)

Since the limit inside the exponential is\(\(-\infty\)\) as \(\(n\)\) goes to infinity, we have:

\[f(x) = \exp(-\infty) = 0\]

Therefore, the limit function \(f(x)\) is the constant function\(\(f(x) = 0\\)) on the interval \(I = [0, \infty)\).

To check for uniform convergence, we need to evaluate the difference \(\left| f_n(x) - f(x) \right|\) and see if it is less than any given \(\epsilon > 0\) for all \(n > N\) and for all \(x \in I\).

\(\[\left| e^{-nx} - 0 \right| = e^{-nx}\]\)

To make this expression less than\(\(\epsilon\),\) we need to find an \(N\) such that \(e^{-nx} \(< \epsilon\)\) for all\(n > N\) and for all\(\(x \in I\).\)

However, as \(\(x\)\) approaches infinity, \(e^{-nx}\) approaches 0. But for any finite \\((x\)\) in the interval \([0, \infty)\), \(e^{-nx}\)  will always be positive and never exactly equal to 0. This means we cannot find an\(\(N\)\)that satisfies the condition for uniform convergence.

Therefore, the sequence\(f_n(x) = e^{-nx}\) does not converge uniformly to the limit function \(f(x) = 0\) on the interval \(I = [0, \infty)\).

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Step-by-step explanation:

So it's important to define what parallel is. If one line is parallel to another line, it will never intersect the other line. This means the two lines must be changing by the same amount simultaneously. In other words, they have the same slope. It's also important to remember that same slope doesn't mean they're parallel. You also have to look at the y-intercept. If they have the same y-intercept, and the same slope, then they're the same line. So two lines are only parallel, if the slopes are the same and they have different y-intercepts.

So now that you understand what's parallel let's look at some of the problems

1. So this is kind of tricky, because as I mentioned before, parallel lines have the same slope, but in this case a slope cannot be defined. For two vertical lines to be parallel, they just have to have different a different x-constant. Because x is what's constant, and if they're different, then the two lines will never intersect. This gives us the general formula for a vertical parallel line: \(x=a\text{ where a} \ne3\) (this is specific to this problem, since the constant in the graph is x=3). Since the parallel line must pass through (-5, -4) this means that the constant for x, must be -5, because the x is constant, if it equals anything else, it will never equal -5. So the parallel line in this case will be: \(x=-5\)

2. So the equation is already in slope-intercept form, so we don't have to solve for the slope. The slope in this case is 8, which can be determined by looking at the formula. This gives us the general formula for the parallel line: \(y=8x+b\text{ where b}\ne 4\). b cannot equal 4, because if it did, then we would have two lines that are the same, not parallel, otherwise b can be anything else. Since we have a point that the parallel line goes through, we can plug this in as (x, y) to solve for b: \(21=8(4)+b \implies21=32+b\implies -11=b\). So now this gives us the complete equation: \(y=8x-11\)

3. The image is a bit low quality, although from what I can see the linear equation intersects the origin (0, 0) and (4, -1). This gives us the equation for the slope -1/4 (rise/run). which gives is the slope -1/4. So this gives us the general equation: \(y=-\frac{1}{4}x+b \text{ where b} \ne0\). b cannot equal 0, since it would then have the same y-intercept, meaning the two lines would be the same. In this case we also get some coordinates which we can plug into the equation to solve for b: \(-5=-\frac{1}{4}(12)+b\implies -5=-3+b\implies-2=b\). This gives us the complete formula: \(y=-\frac{1}{4}x-2\)

4. This is similar to the vertical line, as there is a constant value, but in this case a slope can be defined, and that slope is 0; it's 0 for all horizontal lines. So we have the general equation: \(y=0x+b \text{ where b}\ne4\). This can be simplified to: \(y=b \text{ where b} \ne4\). Since the line passes through (13, -7), that means b must equal -7, because the y does not depend on x. It's a constant value. So you have the equation: \(y=-7\)

5. \(y-6=\frac{3}{5}(x+5)\). So in this case we have the point-slope form. We don't need to convert it to the slope-intercept form, since all we need to form the parallel line is the slope, sort of. You technically do need the y-intercept, so you know what b cannot equal, so that you don't have the same line, but I'm assuming, the coordinates they're giving you, do not pass through the original line, but rather a parallel line. So we have the general equation: \(y=\frac{3}{5}x+b\). Plugging the given coordinates give you the equation: \(8=\frac{3}{5}(0)+b \implies8=b\). You didn't really need to do this, since if you noticed the coordinates have x=0, which means the y-value by definition is what b is equal to, since b is the y-intercept. So this gives you the equation: \(y=\frac{3}{5}x+8\)

Answer: = 4y + 7z + 8

Answer:

7z+4y+8

Step-by-step explanation:

Collect the like terms so 12z-5z would be 7z, then since there is only 1 y term it would be 4y, and -7 + 15= 8

Answer:

Step-by-step explanation:

\(x^{2}\) + 18x +c = 25+c

\(x^{2}\) + 18x +\(9^{2}\) =25+\(9^{2}\)    (the c just cancels out and add \(9^{2}\))

\((x+9)^{2}\) -106 = 0

Answer:

population and moment ne

The volume of the resulting solid is 72π cubic units.

To find the volume of the solid generated by rotating the region bounded by the curves y² - x²= 9 and y = 4 about the x-axis, we can use the method of cylindrical shells.

First, let's sketch the curves and the region bounded by them:

The curve y² - x² = 9 represents a hyperbola with its center at the origin (0,0) and its branches opening vertically.

The curve y = 4 is a horizontal line. The region bounded by these curves lies in the first and second quadrants.

Now, we'll express y² - x² = 9 in terms of y to find the upper and lower boundaries for integration:

=> y² - x² = 9

=> x² = y² - 9

=> x = ±√(y² - 9)

Since we are rotating about the x-axis, the radius of each cylindrical shell will be the distance between the x-axis and the curve y = 4, which is 4 - y.

Now, let's set up the integral to calculate the volume using the cylindrical shell method:

V = ∫[a,b] 2πy(4 - y) dy

To find the limits of integration, we need to determine the y-values where the curves intersect. From the equation y² - x² = 9, we have x = ±√(y² - 9).

Setting x = 0, we find the y-values where the curves intersect:

=> 0 = ±√(y² - 9)

=> y² - 9 = 0

=> y² = 9

=> y = ±3

Therefore, the limits of integration are from y = -3 to y = 3.

Now we can calculate the volume using the integral:

V = ∫[-3,3] 2πy(4 - y) dy

Simplifying the integral:

V = 2π ∫[-3,3] (4y - y²) dy

= 2π [2y² - (1/3)y³] |[-3,3]

= 2π [(2(3)² - (1/3)(3)³) - (2(-3)² - (1/3)(-3)³)]

= 2π [18 - 9 - (-18 + 9)]

= 2π [36]

= 72π

Therefore,

The volume of the resulting solid is 72π cubic units.

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The magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

The value of the net electrostatic force on the 5.0-nC

charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0),

charge Q2 = −1.0 nC is at (0, 0.10 m), and

charge Q3 = 5.0 nC is at (0, 0) can be calculated as follows:

Given data,Charge Q1 = 6.0 nC is at (0.30 m, 0),

Charge Q2 = -1.0 nC is at (0, 0.10 m),

Charge Q3 = 5.0 nC is at (0, 0)

The formula to find out the force on the third charge Q3 is:

                      F = k * |Q1 * Q3| / r1^2 + k * |Q2 * Q3| / r2^2

Here, k = 8.99 × 10^9 N·m^2/C^2, Q1 = 6.0 nC, Q2 = -1.0 nC, Q3 = 5.0 nC

For the third charge Q3, the distance from Q1 is:

                                r1 = √(0.3^2 + 0^2) = 0.3 m

And the distance from Q2 is: r2 = √(0^2 + 0.1^2) = 0.1 m

Substituting all the given values in the formula:

                               F = 8.99 × 10^9 * [ (6.0 × 10^-9 * 5.0 × 10^-9) / 0.3^2 ] + 8.99 × 10^9 * [ (-1.0 × 10^-9 * 5.0 × 10^-9) / 0.1^2 ]F = 6.21 N

Therefore, the magnitude of the net electrostatic force on the 5.0−nC charge due to the other charges when the charge Q1 = 6.0 nC is at (0.30 m, 0), charge Q2 = −1.0 nC is at (0, 0.10 m), and charge Q3 = 5.0 nC is at (0, 0) is 6.21 N.

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The equation that can be solved to determine the number of days when both jobs would have the same cost is 120d + 1,500 = 110d + 2,500.

The equations that would be formed would be linear equations. A linear equation is an equation that has a single variable that is raised to the power of one. A linear equation is a straight line when it is drawn on a graph.

The equation that represents the total bonus of the first job is: fixed pay + total variable pay

1,500 +( $120 x d)

1,500 + 120d

The equation that represents the total bonus of the second job is: fixed pay + total variable pay

$2,500 + ($110 x d)

$2,500 + $110d

When the amount at both jobs are equal, the two above linear functions would be equal

$2,500 + $110d = 1,500 + 120d

Combine similar terms together:

$2,500 - $1,500 = $120d - $110d

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