5 1/6 x 2 2/7 as a mixed number

Given

Find

NQ

Explanation

As we see ,

NQ = NP + PQ

NP = 1 1/4 in

PQ = 1 in

so ,

NQ =

Final Answer

Hence , the length of NQ is 2 1/4 in

Answer:5

Step-by-step explanation:

1x2 2 times 1x1 once

if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28. So correct option is A.

In mathematics, an equation is a statement that shows that two expressions are equal to each other. An equation typically consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equals sign (=).

Equations are used to represent mathematical relationships and to solve problems in a variety of fields, including physics, engineering, economics, and finance. They can be linear or non-linear, and they may involve one or more variables.

If the equation is y = 5x, and the value of x doubles, then the new value of x would be 2x. To find the corresponding value of y, we can substitute 2x for x in the equation:

y = 5(2x)

y = 10x

So if the value of x doubles, the value of y will also double, since y is directly proportional to x with a constant of 5. Therefore, the answer is 28.

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A pair of vertical angles is; Angle 1 and Angle 4

A pair of supplementary angles are; Angle 2 and angle 1

Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.

Two angles are defined as adjacent angles when they share the common vertex and side.

Two angles are defined as supplementary angles if they sum up to 180 degrees.

By those definitions above, we can say that;

Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.

We can also say that;

Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

Step-by-step explanation:

It is an arithmetic sequence with common difference d = -7

a₂₉ = a₄ + (29-4)d = -61 + 25(-7) = -236

Answer:

67,914

Step-by-step explanation:

Let x = total employees.

18.7% of x = 12,700

0.187x = 12,700

x = \(\frac{12700}{0.187}\) = 67914.438 → 67,914

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

AUBUC= { a,b,c,d,e,f,g,h,i,o,u}

A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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Answer:

x=40

y=− 17 /6

Step-by-step explanation:

True -  the statement says that a basic variable corresponds to a pivot column in the coefficient matrix. From the definition of basic variables, basic variables correspond to the columns that have a leading 1's (pivot columns).

A mathematical system model based on the use of a linear operator is known as a "linear system" in systems theory. In contrast to nonlinear cases, linear systems often display considerably simpler traits and attributes.

In linear systems, the variables are really only multiplied with constants and then added together; they are never multiplied by each other. In order to express both static and dynamic relationships between variables, linear systems are used.

Something relating to a line is linear. To build a line, all of the linear equations are used. Any equation that doesn't result in a straight line is considered as non. It has a variable slope value and appears as a curve on a graph.

A linear system is one in which both the superposition and homogeneity principles hold true.

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Random data padding can be effective when the cryptographic algorithm is strong and resistant to known-plaintext attacks. The length of block plays a role, with longer block lengths providing better security.

Now, let's delve into the explanation:

When padding the message with random data instead of using a session key, the effectiveness relies on the cryptographic algorithm's strength. The algorithm should be designed in such a way that it remains secure even when a portion of the plaintext is known. This ensures that an attacker cannot exploit the random data padding to gain information about the original message.

Additionally, the length of the block used by the cryptographic algorithm impacts the effectiveness of random data padding. In general, longer block lengths provide stronger security. With longer blocks, the random data padding becomes more significant, making it more difficult for an attacker to distinguish between the actual message and the random padding. Shorter block lengths may make it easier for an attacker to identify patterns or guess the original message.

Therefore, the effectiveness of using random data padding without a session key depends on the strength of the cryptographic algorithm and the length of the block used. A strong algorithm with a longer block length increases the security of the approach.

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Answer:

f(3) = -9

Step-by-step explanation:

Given that,

→ f(x) = -7x + 12

Then the value of f(3) will be,

→ f(3) = -7(3) + 12

→ f(3) = -21 + 12

→ [ f(3) = -9 ]

Hence, the value is -9.

1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters

2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters

Since we know that the wavelength = speed of light / frequency

The speed of light is 3.00 × \(10^8\) meters per second.

For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;

wavelength of A = (3.00 ×  \(10^8\)  m/s) / (4.30 × 10^15 Hz)

wavelength of A = 6.98 ×  \(10^{-8}\) meters

For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;

wavelength of B = (3.00 ×  \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)

wavelength of B = 3.45 ×  \(10^{-11}\)  meters

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a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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The data used consists Standing/Walking time (minutes per day) spent by two types of people (Lean and Obese).

The claim is that lean people spend more time walking and standing than obese people. We will be using right-tailed test.

The steps include:

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Answer:

If the temp is higher so is the amount of people on the beach

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

In the confidence interval, the population parameter is unknown and the interval is a random variable.

The Columbia Power Company experiences power failures with a mean of µ=210 per day. To find the probability that there are exactly two power failures in a particular day, we can use the Poisson probability formula:

P(x) = (e^(-µ) * (µ^x)) / x!

In this case, x = 2 (since we want to find the probability of exactly two power failures) and µ = 210. Plugging in the values, we get:

P(2) = (e^(-210) * (210^2)) / 2!

Calculating this expression, we get P(2) ≈ 0.018. So, the probability that there are exactly two power failures in a particular day is approximately 0.018.

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22! / 20! × 2!

\(21 \times 11 = 231 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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The first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

Given function is f(x) = x³ - 3x + 1. We have to compute the first derivative of the function at the point x0 = 2 using a five-point formula with h = 5.

Here, we use the five-point formula for differentiation. The five-point formula is given by

\(f′(x) = (-f(x+2h) + 8f(x+h) − 8f(x−h) + f(x−2h))/(12h)\)

Using h = 5 and x0 = 2, we have, h = 5, x = 2

Therefore, x−2h = −8, x−h = −3, x+h = 7, x+2h = 12

Now substitute these values in the above formula:

\(f′(2) = (-f(12) + 8f(7) − 8f(−3) + f(−8))/(12×5)f′(2) = [-1993 - 8(359) + 8(13) + 1349]/60f′(2) = −31.17\) (approx)

Now, we need to find the differentiation error. To find differentiation errors, we use the error formula

|E| = K * h⁴,

where K is a constant, h is the step size and |E| is the maximum error|E| = K * h⁴. Since h = 5, we get|E| = K * 5⁴. To find K, we need to find the maximum value of

\(|f⁽⁵⁾(x)|.f(x) = x³ - 3x + 1\)

∴ \(f′(x) = 3x² - 3\)

∴ \(f′′(x) = 6x\)

∴ \(f′′′(x) = 6\)

∴ \(f⁽⁴⁾(x) = 0\)

∴ \(f⁽⁵⁾(x) = 0\)

So, the maximum value of \(|f⁽⁵⁾(x)| = 0\).

∴ K = 0|E| = K * h⁴ = 0.

f′(2) = -31.17 (approx). The differentiation error is 0.

We are given a function f(x) = x³ - 3x + 1 and we have to find the first derivative of the function at the point x0 = 2 using the five-point formula with h = 5.

The five-point formula is

\(f′(x) = (-f(x+2h) + 8f(x+h) − 8f(x−h) + f(x−2h))/(12h)\)

Using h = 5 and x0 = 2, we have h = 5 and x = 2.

Substituting these values in the formula for the five-point formula for differentiation, we get

\(f′(2) = (-f(12) + 8f(7) − 8f(−3) + f(−8))/(12×5)\)

Substituting the values of f(12), f(7), f(-3) and f(-8) from the given function, we get

\(f′(2) = [-1993 - 8(359) + 8(13) + 1349]/60= −31.17\)(approx)

Now, we need to find the differentiation error. To find the differentiation error, we use the error formula

|E| = K * h⁴,

where K is a constant, h is the step size and |E| is the maximum error.

|E| = K * h⁴

Since h = 5, we get|E| = K * 5⁴. To find K, we need to find the maximum value of |f⁽⁵⁾(x)|.

Differentiating f(x) five times, we get

\(f′(x) = 3x² - 3f′′(x) = 6xf′′′(x) = 6f⁽⁴⁾(x) = 0f⁽⁵⁾(x) = 0\)

The maximum value of |f⁽⁵⁾(x)| = 0. Therefore, K = 0|E| = K * h⁴ = 0. Therefore, the differentiation error is 0. Hence, the first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

The first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

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Answer:

99

Step-by-step explanation:

5x^2 -4x -9

5(-2)^2 -4(-2) -9

-10^2 +8 -9

100-1

99

Answer:

don´t ge it sorry

Step-by-step explanation:

The graph of each function in the piecewise function is added as an attachment

The equation of the piecewise function is given as

f(n) = n/2 if n is even

        3n + 1 if n is odd

In the above definition of the piecewise function, we have the following functions and the domains

Note that:

The domain of the function is the set of input values of the graph

This in other words mean the domain of a function is the set of x values of the graph.

Next, we plot the graph of each function in the piecewise function in their respective domain

See attachment for the graph of each function in the piecewise function,

On the graph, the blue line represents f(n) = n/2 while the other line represents f(n) = 3n + 1

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Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

Answer: 21

Step-by-step explanation:

70x30/100

= 21

Hope this helps! :)

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The coordinates of the location where the facility should be built are (7, 0).

We are given the coordinates of three cities J(5, 2), K(-7, 2) and L(-5, -8).

A television station wants to build a new broadcast facility that is equidistant from the three cities.

We need to find out the coordinates of the location where the facility should be built.

We can use the distance formula to find the distance between two points (x1, y1) and (x2, y2):d

= √[(x₂ - x₁)² + (y₂ - y₁)²]

Let (x, y) be the coordinates of the broadcast facility.

We know that the distance from the facility to city J is equal to the distance from the facility to city K, and also equal to the distance from the facility to city L.

Using the distance formula, we can write these three equations:√[(x - 5)² + (y - 2)²]

= √[(x + 7)² + (y - 2)²]  [Distance from facility to city J = distance from facility to city K]

√[(x - 5)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city J = distance from facility to city L]√[(x + 7)² + (y - 2)²]

= √[(x + 5)² + (y + 8)²]

[Distance from facility to city K = distance from facility to city L]

Squaring both sides of these equations, we get: (x - 5)² + (y - 2)² = (x + 7)² + (y - 2)²  ...

(1)Simplifying this equation, we get: x = -1

Similarly, (x - 5)² + (y - 2)² = (x + 5)² + (y + 8)²  ...

(2)Simplifying this equation, we get: x² + y² - 10x - 4y + 90 = 0

Similarly, (x + 7)² + (y - 2)² = (x + 5)² + (y + 8)²  ..

.(3)Simplifying this equation, we get: x² + y² - 4x - 10y - 6 = 0

Now, we need to solve equations (2) and (3) for y and x respectively.x² + y² - 10x - 4y + 90 = 0

[Equation (2)]x² + y² - 4x - 10y - 6 = 0 [Equation (3)]

Multiplying equation (2) by 10, and equation (3) by 4,

we get:10x² + 10y² - 100x - 40y + 900 = 0  ...(4)

4x² + 4y² - 16x - 40y - 24 = 0  ...

(5)Subtracting equation (5) from equation (4),

we get:6x² + 6y² - 84x + 924 = 0

Simplifying this equation by dividing both sides by 6,

we get:x² + y² - 14x + 154 = 0

Completing the square, we get:(x - 7)² + y² = 95

This is the equation of a circle with center at (7, 0) and radius √95 units.

Therefore, the coordinates of the broadcast facility are (7, 0).

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