The equation y = - 3/4x + 1 represents a given line. Write the equation for the line that passes through (6, 6) and is perpendicular to the given line. pls show me how u got it, thx​

Answer:   The height is 3  units.

Step-by-step explanation:

By using the give figure we can form right angle out of the whole figure  with a base of  4  and an hypotenuse of 5.

By using this information we can use the Pythagorean Formula to find the height

a^2 + b^2 =c^2     a= base, b = height and c will be the hypotenuse.

4^2 + b^2 = 5^2     Solve for B

16  + B^2 = 25  

-16               -16

    b^2 = 9    

    b = \(\sqrt{9}\)  

  b  = 3

The height, h, of the triangular prism is 3 units.

Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.

Given that, vertical cross-section of the triangular prism shown in the given figure is an isosceles triangle.

Here, equal sides of an isosceles triangle is 5 units and base of the isosceles triangle is 8 units.

By using Pythagoras theorem,

5²=h²+4²

25=h²+16

h²=9

h=3

Therefore, the height, h, of the triangular prism is 3 units.

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To avoid bias in the survey, the human resources director creates a list of all the employees and randomly selects 150 of them to complete the survey.

In this scenario, we have a company that employs 650 people and wishes to survey a sample of its employees about the company culture.  Let's match each term with its corresponding description:

1. Population: The population refers to the entire group of individuals that the survey aims to represent. In this case, the population is the total number of employees in the company, which is 650.

2. Sample: A sample is a subset of the population that is selected for data collection and analysis. It represents a smaller portion of the population. In this scenario, the sample consists of the 150 employees randomly selected by the human resources director.

3. Random Selection: Random selection is the process of choosing individuals from the population in a way that ensures each member has an equal chance of being included in the sample. By randomly selecting the 150 employees, the human resources director avoids bias and increases the likelihood that the sample represents the entire population.

4. Survey: A survey is a data collection method used to gather information from individuals within the sample. In this case, the selected employees will be asked to complete a survey about the company culture.

By randomly selecting 150 employees from the total population of 650, the company aims to create a sample that is representative of the entire workforce. This helps to avoid bias and increase the generalizability of the survey findings. The survey responses from the selected employees will provide insights into the company culture, which can then be used to make informed decisions or improvements. It's important to note that the quality of the survey and the representativeness of the sample can impact the validity and reliability of the survey results. Therefore, careful consideration should be given to the sampling method and survey design to ensure accurate and meaningful findings.

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The measure of the minor arc BE is 104⁰.

Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.

This implies that;

∠APE = ∠ EPD = x

2x + 55 + 41 + 166 = 360 ( sum of angles in a circle)

2x + 262 = 360

2x = 98

x = 98 / 2

x = 49⁰

The measure of the minor arc BE is calculated as;

BE = 55⁰ + 49⁰

BE = 104⁰

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Answer:

a) The amplitud of the plain wave is 25, b) The wave length of the plain wave is \(\frac{\pi}{2}\), c) The frequency of the plain wave is \(\frac{\pi}{60}\), d) The speed of propagation of the plain wave is 0.082.

Step-by-step explanation:

A plain wave is modelled after the following mathematical model as a function of time and horizontal position. That is:

\(y(t, x) = A \cdot \sin (\omega\cdot t - \frac{2\pi}{\lambda}\cdot x)\)

Where:

\(y(t, x)\) - Vertical position wave with respect to position of equilibrium, dimensionless.

\(A\) - Amplitude, dimensionless.

\(\omega\) - Angular frequency, dimensionless.

\(\lambda\) - Wave length, dimensionless.

After comparing this expression with the equation described on statement, the following information is obtained:

\(A = 25\), \(\omega = 120\) and \(\frac{2\pi}{\lambda} = 4\)

a) The amplitude of the plain wave is 25.

b) The wave length associated with the plain wave is found after some algebraic handling:

\(\frac{2\pi}{\lambda} = 4\)

\(\lambda = \frac{\pi}{2}\)

The wave length of the plain wave is \(\frac{\pi}{2}\).

c) The frequency can be calculated in term of angular frequency, that is:

\(f = \frac{2\pi}{\omega}\)

Where \(f\) is the frequency of the plain wave.

If \(\omega = 120\), then:

\(f = \frac{2\pi}{120}\)

\(f = \frac{\pi}{60}\)

The frequency of the plain wave is \(\frac{\pi}{60}\).

d) The speed of propagation is equal to the product of wave length and frequency:

\(v = \lambda \cdot f\)

Given that \(\lambda = \frac{\pi}{2}\) and \(f = \frac{\pi}{60}\), the speed of propagation is:

\(v = \left(\frac{\pi}{2} \right)\cdot \left(\frac{\pi}{60} \right)\)

\(v \approx 0.082\)

The speed of propagation of the plain wave is 0.082.

Range = 12

■ Maximum value = 10.

■ Minimum value = -2

■ Count of numbers within the set = 13

B and D are perfect squares.

Simply plug \(\sqrt{81}\) and \(\sqrt{144}\) into a calculator.

B explanation:

9 x 9 = 81

D explanation:

12 x 12 = 144

A graph of four points with integer coordinates that are each 3 units away from (2, 3) is shown in the image attached below.

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).

Where:

In order to write an equation that models the four points with integer coordinates that are each 3 units away from (2, 3), we would have to apply a set of translation to f(x) by 3 units:

A (5, 3)

B (-1, 3)

C (2, 6)

D (2, 0)

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Answer:

81 & 100

Step-by-step explanation:

97 lies between 81 and 100, so its square root lies between 9 and 10.

Answer:

97 lies between 81 and 100, so its square root lies between 9 and 10.

Step-by-step explanation:

Domain

\(-\infty \: < x < \infty\)

Range

\(f\left(x\right)\ge \:-7\:\)

Answer:

plot between 1/3 and 2/3 or 1/2.

Answer:

let the first term of an A.P. is 'a' and common difference 'd'

∴ 8th term = sum of the first 8 terms

a8 = S

a + 7d = 8/2(2a + (8 - 1)d)

a + 7d = 8/2(2a + 7d)

2a + 14d = 16a + 56d

16a + 56d - (2a + 14d) = 0

14a + 52d = 0

divide eq. by 14 we get  ,

a + 3d = 0

and a + 3d = a4  = 0

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises is a "false" statement.

A circuit workout consists of six or more exercises that are alternated with brief rest intervals and performed for either a predetermined number of reps or a certain duration of time.

Some features of circuit training exercise are-

Benefits of doing circuit training exercise-

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The complete question is -

In circuit training, exercises are usually set up so that the same muscle group is worked in back to back exercises.(True/False)

Answer:

n - 11 = 18n

Step-by-step explanation:

n−11=18n

Step 1: Subtract 18n from both sides.

n−11−18n=18n−18n

−17n−11=0

Step 2: Add 11 to both sides.

−17n−11+11=0+11

−17n=11

Step 3: Divide both sides by -17.

−17n−17=11−17

n=−1117

Answer:

n = −11/17

Answer:

7/8 < 1

Step-by-step explanation:

1 is larger than 7/8 so thats why it is 7/8 < 1

I hope it helps! Have a great day!

Lilac~

The correct statement is 7/8<1

An inequality is an inequation separated by <,>, ≥, ≤.  The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given here 7/8 which is equal to 0.875 thus which is less than 1 and thus we can construct the inequality 7/8<1

Hence, the  correct statement is 7/8<1

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This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

17.5 hour

Mean = (5x0.15) + (15x0.28) + (20x0.31) + (25x0.26) = 17.5 hours

The mean of the variable is calculated by multiplying the value of each individual category with its probability, and then summing the resulting values. In this case, the mean is calculated as (5x0.15) + (15x0.28) + (20x0.31) + (25x0.26) = 17.5 hours. This indicates that the average number of hours worked by the part-time employees is 17.5 hours per week.

the complete question is :

Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.Weekly hours worked Probability5 0.1515 0.2820 0.3125 0.26Find the mean of this variable.

Weekly hours   worked Probability

5                              0.15

15                            0.28

20                           0.31

25                           0.26

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The interior angle of a parallelogram is proportional to the measure of another angle with a ratio of 0.25:1.

A parallelogram is a four-sided flat shape that has opposite sides that are parallel and equal in length. The sum of the interior angles of a parallelogram is equal to 360 degrees. If the measure of one interior angle is 0.25 times the measure of another angle, this means that there is a proportionate relationship between the two angles. To find the measure of the second angle, we can use the formula:

Angle 2 = (Angle 1) / 0.25

For example, if Angle 1 is 100 degrees, then Angle 2 is 100 / 0.25 = 400 degrees. This means that if one angle measures 100 degrees, the other angle measures 400 degrees. The sum of the two angles is 500 degrees, which is still less than the total sum of interior angles in a parallelogram, which is 360 degrees.

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Answer: its E and B

Step-by-step explanation:

2/100 is .02 which is 2%

Answer:

2%= 2/100= 0.02

so correct answer is b and e

The solution to the system of inequalities y ≤ 2x + 2 and y < -2x - 3 can be represented by a graph. The inequality y ≤ 2x + 2 represents a line with a slope of 2 and y-intercept of 2. The inequality y < -2x - 3 represents a line with a slope of -2 and y-intercept of -3. ( The graph attached)

The inequality y ≤ 2x + 2 represents a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 2. To graph this inequality, we can first plot the line by using the y-intercept, which is the point (0,2) on the graph. Then, we can use the slope to find additional points that fall on the line, such as (1,4) or (-1,0). Once we have plotted several points, we can connect them to form the line.

The inequality y < -2x - 3 represents a similar line, but with a different slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. To graph this inequality, we can use the same process as before by first plotting the y-intercept (0,-3), and then using the slope to find additional points that fall on the line.

The solution to the system of inequalities is the area that lies on one side of the first line and the opposite side of the second line, which is the area between the two lines. This area can be represented by shading the region below the first line and above the second line on the graph. It is important to note that the solution region is not including the lines themselves, because the inequalities are strict inequalities.

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An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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a) The probability that exactly five men will still be alive in 20 years is approximately 0.024.

b) The probability that more than eight men will still be alive in 20 years is approximately 0.057.

c) The probability that at least two men will still be alive in 20 years is approximately 0.999.

To calculate the probabilities, we can use the binomial distribution formula, where n is the number of trials, p is the probability of success, and x is the number of successes. Therefore,

a) P(X = 5) = (10 choose 5) * (0.69)⁵ * (0.31)⁵ ≈ 0.024

b) P(X > 8) = P(X = 9) + P(X = 10) = [(10 choose 9) * (0.69)⁹ * (0.31)¹] + [(10 choose 10) * (0.69)¹⁰ * (0.31)⁰] ≈ 0.057

c) P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) = 1 - [(10 choose 0) * (0.69)⁰ * (0.31)¹⁰] - [(10 choose 1) * (0.69)¹ * (0.31)⁹] ≈ 0.999

In summary, we have used the binomial distribution formula to calculate the probability that exactly five men, more than eight men, and at least two men will still be alive in 20 years, given that the probability that a man of this particular age will be alive in 20 years is 0.69.

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Question

Seat belt use in a state was estimated at 89%,

which means 89 % of people use their seat belts. Suppose two independent drivers have been randomly selected.

a. What is the probability that both of them are using a​seatbelt?

b. What is the probability that neither of them is using a​seatbelt?

c. What is the probability that at least one is using a​seatbelt?

The probability that both of them are using a seatbelt is ?

Answer:

a

\(P(B) = 0.7921\)

b

\(P(B)' = 0.0121\)

c

\(P(K) = 0.9879\)

Step-by-step explanation:

From the question we are told that

    The proportion of seat belt use is  p =  0.89

     The  sample  size n =  2

Generally the probability that both drivers are wearing seat belt is mathematically represented as

       \(P(B) = (p)^n\)

=>     \(P(B) = (0.89 )^2\)

=>     \(P(B) = 0.7921\)

Generally the probability that neither of the two drivers are wearing seat belt is  

      \(P(B)' = (1 - p)^2\)

=>   \(P(B)' = (1 - 0.89)^2\)

=>   \(P(B)' = 0.0121\)

Generally the probability that at least one of the drivers is wearing a seat belt is  

        \(P(K) = 1 - P(B)'\)

=>     \(P(K) = 1 - 0.0121\)

=>     \(P(K) = 0.9879\)

According to the given information, (yn) is convergent.

What is the convergence and divergence of the sequence?

Convergence: A sequence approaches a fixed number as the number of terms increases.

Divergence: A sequence does not approach a fixed number as the number of terms increases.

Yes, (yn) is convergent.

Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.

Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.

Combining these two inequalities, we have:

|yn - L| = |yn - xn + xn - L|

≤ |yn - xn| + |xn - L|

< ε + ε (for all n ≥ M)

Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.

Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).

Hence, (yn) is also convergent.

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Answer:

Im not sure what type of solution you are looking for. You should be more specific. Though I will still give you some helpful solutions and you use the one you need.

Step-by-step explanation:

Factored: y=168x+67y-49

Solved for Y; -28x/11 + 49/66

Solved for X: -11y/28 + 7/24

X and Y intercepts:

X=( 7/24, 0 )

Y= ( 0, 49/66 )

I hope these answers help. Next time be more specific to what your looking for and make sure your equation is written correctly.

Answer:

12÷3=4

4inches is 2/3 of a foot.

Step-by-step explanation:

The elevator has an acceleration and deceleration of magnitude 1.0 m/s^2, so it takes (5 m/s) / (1 m/s^2) = 5 seconds to reach its maximum speed of 5 m/s.

To come to a stop from this maximum speed, it will also take 5 seconds.

The time it takes for the elevator to travel the entire distance of 200 m is given by:

t = 5 s + 5 s + d / v

where d is the distance traveled at constant speed and v is the constant speed.

We know that the total time is equal to t = 10 s + d / 5 m/s.

Thus, d = (10 s - 5 s) * 5 m/s = 25 m.

So the elevator spends 5 seconds accelerating, 5 seconds decelerating, and 10 - 5 = 5 seconds at constant speed.

As per duality theory, every original linear programming problem has an associated dual problem. The dual of the original linear programming problem is feasible and the optimal cost is infinite.

Let's consider a general linear programming problem in standard form that is infeasible. We aim to demonstrate that the dual of the original problem is feasible, and the optimal cost is infinite.

Linear programming (LP), or linear optimization, is a mathematical technique used to determine the optimal solution for a given mathematical model with linear relationships, typically involving maximizing profit or minimizing cost. LP falls under the broader category of optimization techniques.

As per duality theory, every original linear programming problem has an associated dual problem. Solving one problem provides information about the other problem, and vice versa. The dual problem is obtained by creating a new problem with one variable for each constraint in the original problem.

To show that the dual of the original problem is feasible and the optimal cost is infinite, we will follow these steps:

Derive the dual of the given linear programming problem.

Demonstrate the feasibility of the dual problem.

Establish that the optimal cost of the dual problem is infinite.

Step 1: Dual of the linear programming problem

The given problem is:

Minimize Z = c'x

subject to Ax = b, x >= 0

Here, x and c are column vectors of n variables, and A is an m x n matrix.

The dual problem for this is:

Maximize Z = b'y

subject to A'y <= c, y >= 0

In the dual problem, y is an m-dimensional column vector of dual variables.

Step 2: Feasibility of the dual problem

Since the primal problem is infeasible, it means that no feasible solution exists for it. Consequently, the primal problem has no optimal solution. By the principle of weak duality, the optimal solution of the dual problem must be less than or equal to the optimal solution of the primal problem. As the primal problem has no optimal solution, the dual problem must have an unbounded optimal solution. Therefore, the dual problem is feasible.

Step 3: The optimal cost of the dual problem is infinite

Since the primal problem has no optimal solution, the principle of weak duality states that the optimal solution of the dual problem must be less than or equal to the optimal solution of the primal problem. As the primal problem has no optimal solution, the dual problem must have an unbounded optimal solution. Consequently, the optimal cost of the dual problem is infinite.

In conclusion, we have shown that the dual of the original problem is feasible, and the optimal cost is infinite.

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Step-by-step explanation:

To multiply the negative of a fraction by the inverse of another fraction, follow these steps:

1. Convert the first fraction to its negative equivalent.

- The negative of 2/3 is -2/3.

2. Find the inverse (or reciprocal) of the second fraction.

- The inverse of 9/7 is 7/9.

3. Multiply the two fractions.

- Multiply the numerators: (-2) * (7) = -14

- Multiply the denominators: (3) * (9) = 27

The result is -14/27.