Simplify the expressions.showing express your answers with positive exponents

Answer:

50,000

Step-by-step explanation:

5000*10

The Mean absolute deviation and the mean are not same.

Given,

The mean;-

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Mean absolute deviation;-

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset contains.

Therefore,

The Mean absolute deviation and the mean are not same.

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Answer:

\(m\angle 2=53^{\circ}\)

\(m\angle 7=74^{\circ}\)

Step-by-step explanation:

It is given that quadrilateral GHJK is a rectangle and \(n\angle 3=37^{\circ}\).

All interior angles of a rectangle are right angles. Diagonals are equal and bisect each other.

Now,

\(m\angle HKJ+m\angle HKG=90^{\circ}\)    (Interior angles of a rectangle are right angles)

\(m\angle 3+m\angle HKG=90^{\circ}\)

\(37^{\circ}+m\angle HKG=90^{\circ}\)

\(m\angle HKG=90^{\circ}-37^{\circ}\)

\(m\angle HKG=53^{\circ}\)

In an isosceles triangle, angle with equal sides are equal.

\(m\angle JGK=m\angle HKG\)

\(m\angle 2=53^{\circ}\)

Therefore, measure of angle 2 is 53 degrees.

Let the diagonals intersect each other at point O.

In triangle OGK,

\(m\angle OGK+m\angle OKG+m\angle GOK=180^{\circ}\)    (Angle su property)

\(53^{\circ}+53^{\circ}+m\angle GOK=180^{\circ}\)

\(106^{\circ}+m\angle GOK=180^{\circ}\)

\(m\angle GOK=180^{\circ}-106^{\circ}=74^{\circ}\)

Vertical opposite angles are equal. So,

\(m\angle 7=74^{\circ}\)

Therefore, measure of angle 7 is 74 degrees.

The spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

To determine how much further the spring will stretch when a 0.60 kg block is added to the 1.2 kg block, we need to consider Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.

Let's assume that the spring is initially stretched by a certain amount x when only the 1.2 kg block is attached. The force exerted by the spring is given by F = kx, where k is the spring constant.

When the 0.60 kg block is added, the total mass becomes 1.2 kg + 0.60 kg = 1.8 kg. The force exerted by the spring remains the same, but the total mass affects the acceleration of the system according to Newton's second law, F = ma.

Using F = ma, we can find the acceleration of the system: F = (1.8 kg)(9.8 m/s^2) = 17.64 N.

Since F = kx, we can rearrange the equation to find x: x = F/k.

Now, if we assume the spring constant k remains constant, the displacement x will increase by a factor of 1.8 kg/1.2 kg = 1.5.

Therefore, the spring will stretch 1.5 times further when the 0.60 kg block is added to the 1.2 kg block.

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Answer: D

Step-by-step explanation:

just got it correct.

The objective function formula that is nonlinear is - 2xy/2xy + z

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

- 2xy/2xy + z

- x + y + z

- 3x - 2y + z

A linear function is a function that has a degree of 1

Other functions with other degrees are nonlinear

Using the above as a guide, we have the following functions with a degree of 1

- x + y + z

- 3x - 2y + z

Hence, the objective function formulas that is nonlinear is - 2xy/2xy + z

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Answer:

555.1 ft

Step-by-step explanation:

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

78 ounces of dough was bought. 52 ounces of sauce was bought.

There were 13 guests .

Step-by-step explanation:

Let x = Number of guests

As per given, For each person 6 ounces of dough and 4 ounces of sauce is required.

i.e. Total ounces of dough and sauce together required = 6+4=10

The dough and sauce is 130 ounces all together.

i.e.

Divide both sides by 10 , we get

x= 13

i.e. there were 13 guests .

Total ounces of dough = 6 x ( Number of guests) = 6 x 13= 78 ounces

hence, 78 ounces of dough was bought.

Total ounces of sauce = 4 x ( Number of guests) = 4 x 13= 52 ounces

hence, 52 ounces of sauce was bought.

The standard deviation of the data set will increase by a factor of 10. This is because standard deviation measures how much variation or dispersion exists from the mean of a data set. Adding 10 to every value of the data set will increase the overall spread of the data and thus increase the standard deviation.  

To prove this mathematically, let's consider a data set A with mean M and standard deviation SD. Let's add 10 to every value of the data set to get a new data set B. The mean of set B is M+10 and the standard deviation of set B is SD'.   The formula for SD' is:  

SD':\(\sqrt{(x_{1} -(M+10))^{2} +(x_{2} -(M+10))^2+ (x_{3}-(M+10))^2 +...+ (x_{n}-(M+10))^2)/n }\) We can simplify this by substituting the values for the xi:

 SD' =\(\sqrt{(((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n) }\)  Now let's consider the original data set A and its standard deviation SD:

 SD =\(\sqrt{(((x_{1}-M)^2 + (x_{2}-M)^2 + (x_{3}-M)^2 +...+ (x_{n}-M)^2)/n) }\) ,We can substitute the values for xi in this formula as well:  

SD= \(\sqrt{ (((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n)}\)  If we compare SD and SD', we can see that they are identical, except that the value of M has been replaced with M+10. This means that when we add 10 to every value of the data set, the standard deviation increases by a factor of 10.

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The value of x is given as follows:

\(x = 2.5\sqrt{2}{/tex]

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For a right triangle with an angle of 45º, we have that:

This is because the angle of 45º has an equal value of the sine and of the cosine.

Hence the side length of the top triangle is given as follows:

s = 5.

For the bottom triangle, the side length is of x, while the hypotenuse is of 5, hence:

x² + x² = 5²

2x² = 25

\(x = \sqrt{\frac{25}{2}}\)

\(x = \frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}\)

\(x = 2.5\sqrt{2}{/tex]

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To determine the convergence or divergence of an alternating series, you can use the Alternating Series Test. This test states that if the terms of an alternating series decrease in absolute value and approach zero, then the series converges.

Additionally, if the terms do not approach zero, the series diverges.

To apply the Alternating Series Test, you need to check two conditions:

1. The terms of the series must alternate in sign.

2. The absolute value of the terms must decrease or approach zero.

If both conditions are satisfied, you can conclude that the alternating series converges. However, if either condition fails, the series diverges.

If you want to determine the convergence or divergence more precisely, you can use the Integral Test or the Comparison Test. The Integral Test allows you to compare the convergence or divergence of a series to the convergence or divergence of an improper integral. If the integral converges, the series converges, and if the integral diverges, the series diverges.

The Comparison Test is another method to determine the convergence or divergence of a series. It involves comparing the given series with a known series whose convergence or divergence is already known. If the known series converges and the terms of the given series are less than or equal to the corresponding terms of the known series, then the given series also converges. Conversely, if the known series diverges and the terms of the given series are greater than or equal to the corresponding terms of the known series, then the given series also diverges.

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Answer:

Suppose N is the size of a population of radioactive atoms at a given time t, and dN is the amount by which the population decreases in time dt; then the rate of change is given by the equation dN/dt = −λN, where λ is the decay constant.

Significant correlations are useful statistical tools for identifying relationships between variables, but they are not able to indicate causality.

While they can demonstrate the strength of the effect through the correlation coefficient, the size of the effect by examining the magnitude of the relationship, and the probability level by evaluating the likelihood that the observed relationship occurred by chance, they cannot prove that one variable directly causes changes in another variable.

Correlations can only show that two variables are related, but they do not provide information about the nature of that relationship. It is important to remember that correlation does not imply causation. There might be other factors, known as confounding variables, that affect both variables and create the appearance of a relationship where none truly exists.

To determine causality, researchers must conduct controlled experiments where they manipulate the independent variable and observe the effect on the dependent variable, while holding all other factors constant. This allows them to isolate the cause-and-effect relationship between the two variables and draw more accurate conclusions.

In summary, while significant correlations can provide valuable information about the strength, size, and probability level of the relationship between variables, they cannot establish causality. To determine if one variable truly causes changes in another, controlled experiments must be conducted.

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Answer:

There will be 9 couples, and 3 lonely girls

Hope this helps

plz like and brainly :D

\(2 - 3csc(x) > 8 \\ 2 - \frac{3}{sin(x)} > 8 \\ - 6 > \frac{3}{sin(x)} \\ - 2 > \frac{1}{sin(x)} \\ \frac{ - 1}{2} < sin(x) \: \: or \: \: \: sin(x) > \frac{ - 1}{2} \\ \\ \)

\(sin( \frac{ - \pi}{6} ) = \frac{ - 1}{2} \)

\(x \: in \: \: [0, \frac{7\pi}{6}[U] \frac{11 \pi }{6} ,2\pi] + 2k\pi\)

Answer:

D. pi<x<7pi/6 and 11pi/6<x<2

Step-by-step explanation:

Took the test and this is the correct answer

Answer:

c. y + 3 = (1/2)(x - 1)

Step-by-step explanation:

Answer:

A. \(y + 1 = (-\frac{1}{2})(x + 3)\)

Step-by-step explanation:

I used a graphing calculator. I prefer Desmos, but you can use whatever you like. I recommend Desmos or GeoGebra.

1. The equation of the perpendicular line is: y = -x + 4

2. The equation of the parallel line is: y = -x + 4

The equations of two lines that are parallel to each other will have the slope (m), while the equations of two lines that are perpendicular to each other will have slope values that are negative reciprocals of each other.

The slope-intercept form for the equation of a line is, y = mx + b, where b is the y-intercept and m is the slope of the line.

1. The slope (m) of y = x - 4 is 1. The line that is perpendicular to y = x - 4 would have a slope (m) of -1.

Substitute (a, b) = (1, 3) and m = -1 into y - b = m(x - a):

y - 3 = -1(x - 1)

Rewrite in slope-intercept form:

y - 3 = -x + 1

y = -x + 1 + 3

y = -x + 4

2. The slope (m) of y = -x - 4 is -1. The line that is parallel to y = -x - 4 would have a slope (m) of -1.

Substitute (a, b) = (3, 1) and m = -1 into y - b = m(x - a):

y - 1 = -1(x - 3)

Rewrite in slope-intercept form:

y - 1 = -x + 3

y = -x + 3 + 1

y = -x + 4

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The average rate of change of g(x) from x = 1 to x = 6 is 7

The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.

In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.

The value of g(x) at x = 1 is:

g(1) = 2(1)² - 7(1) = -5

The value of g(x) at x = 6 is:

g(6) = 2(6)² - 7(6) = 30

So the difference in the values of g(x) is:

g(6) - g(1) = 30 - (-5) = 35

The length of the interval is:

6 - 1 = 5

Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:

Rate = 35/5

Evaluate

Rate = 7

So, the rate is 7

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The average rate of change is 7.

We know that,

The average rate of change = (final value - initial value)/change in the value of x.

Now,

The given function is,

g(x)=2x²-7x

The initial value of x is 1 (given)

∴ The initial value of the function g(x), at x=1,

g(1)=2(1)²-7(1)=2-7

or, g(1)= -5

Now, the final value of x is 6,

∴ Finding the final value of the function g(x) at x=6,

i.e, g(6)=2(6)²-7(6)

or,  g(6)=72-42 = 30

∴ The change in the value of function g(x), from x= to x=6,

= g(6)-g(1)

= 30-(-5)

= 35

Now, change in the value of x = 6-1=5

∴ The average rate of change = 35/5 = 7

Hence the average rate of change is 7.

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Answer:

Step-by-step explanation:

You want the approximate value of f'(0.50) if f(x) = 5ln(3x) +6cos(3 -7x) and the approximate value of f'(4.645) if f(x) = ln(3x) +sin(5x -4) -3 using centered differencing and h = 0.001 and 0.002, respectively.

The approximate derivative using centered differencing is computed as ...

  f'(x) ≈ ((f(x +h) -f(x -h))/(2h)

The calculations using the above formula for (x, h) = (0.50, 0.001) are shown in the first half of the attachment. The approximate value is ...

  f'(0.50) ≈ -10.13569485

The calculations using the above formula for (x, h) = (4.645, 0.002) are shown in the second half of the attachment. The approximate value is ...

  f'(4.645) ≈ 4.86693212

__

Additional comment

The calculator must be in radians mode for these functions.

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I believe that its easier to understand the multiplication of a radical than that of a polynomial.

In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.

When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:

= 3✓2 × 4✓2

= 12✓4

= 12 × 2

= 24

The multiplication of a radical is easier.

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The value of the "7" in 432.0769 is 7/1000 or option A.

In the number 432.0769, the digit "7" is in the thousandths place, which means that it represents seven parts of one thousandth. The digit to the left of the thousandths place is the hundredths place, which represents one hundredth of a number. Therefore, the difference between the thousandths and hundredths place is a factor of ten, which means that the value of the digit "7" is ten times greater than the value of the digit to its right.

To put it in another way, the number 432.0769 can be broken down into its decimal representation:

4 hundreds + 3 tens + 2 ones + 0 tenths + 7 hundredths + 6 thousandths + 9 ten-thousandths

Hence the correct option is (a).

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a. The domain of the given function is (-∞, 4) U (14, ∞). b. The left-hand limit of the function f(x) at x = 4 does not exist. c. The right-hand limit of the function f(x) at x = 14 does not exist.

At what points does only the left-hand limit exist?

At what points does only the right-hand limit exist?

Graph:

To draw the graph of the given function, use the following steps:

First, solve the equation 64 - x² + 5x = 8. Simplify it and get x² - 5x + 56 = 0.

Solve for the value of x by using the quadratic formula.

Here, a = 1,

b = -5,

and c = 56.x

= (5 ± √161) / 2

= 0.9, 4.1.

On the x-axis, plot these two points (0.9, 8) and (4.1, 8)

The vertex point of the parabola is at the center, x = 2.5.

And we also know that the vertex is the maximum or minimum of the function.

In this case, it's maximum, so plot the vertex (2.5, 10).

Join all the points with the help of the curve.

This is how the graph of the given function looks like.

Domain:

The domain of a function refers to the set of all possible values of independent variable x for which the function is defined.

Here, the function is a square root function.

The radicand inside the square root cannot be negative.

Therefore, the domain of the given function f(x) is as follows:

64 - x² + 5x < 8 (because f(x) < 8)56 - x² + 5x < 0x² - 5x + 56 > 0

Factorize the quadratic function to get(x - 4) (x - 14) > 0

Solve the inequality to getx < 4 or x > 14

Thus, the domain of the given function is (-∞, 4) U (14, ∞).

Range:

The range of a function is defined as the set of all possible values of the dependent variable y for which the function is defined.

Here, we know that the lowest value of the function is 8.

And, the maximum value of the function is at the vertex (2.5, 10).

Therefore, the range of the function is (8, 10].

We have found the domain and range of f.

Now, we need to find the points at which only the left-hand or only the right-hand limit exists.

The left-hand limit exists when x approaches a certain value from the left side of that point.

That is, x → c⁻

Here, the function approaches -∞ when x → 4⁻.

Thus, the left-hand limit of the function f(x) at x = 4 does not exist.

Right-hand limit:

The right-hand limit exists when x approaches a certain value from the right side of that point.

That is, x → c⁺

Here, the function approaches -∞ when x → 14⁺.

Thus, the right-hand limit of the function f(x) at x = 14 does not exist.

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Answer:

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

Given function:

Find f(-7) by plugging in the value of x:

Answer:

\(x^{2} +9x-22=0\\(x-2)(x+11)=0\\x-2=0 ; x+11=0\\x=2, x=-11\)

All possible values for x is 2 or -11.

Answer:

-11 and 2.

Step-by-step explanation:

I am assuming that this question is \(x^{2}\)+9x-22 = 0

A few ways to answer:

You can graph and look at the x intercepts. They are at (-11,0) and (2,0).

You can also rewrite the equation like this:

(x+11)(x-2) = 0

So that means that for this equation to equal zero, either:

X+11 = 0

OR

x-2 = 0

Again, the same answers as graphing: x is -11 or x is 2.

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

A

I think it's a I'm not pretty sure.. but I calculated it and i get "A" as an Answer.

Answer:

Non-linear: red graph, table 3, table 1

Linear: blue graph, green graph, table 2

Step-by-step explanation:

The blue and green lines are straight lines, so they are linear. The red line is curved, so that is nonlinear.

I plotted out the data from each table on a graph. Tables 1 and 3 both curve when the points are connected, and table 2’s points form a straight line when connected. I am sure there is a mathematical formula to use on these tables, so the drawing wouldn’t have been required. But I knew this would at least get the answers.

Hope it helped.

Answer:

201.06

Step-by-step explanation: