Find the sum of 2 and 3/2

Step-by-step explanation:

if we put the amount of hours and how much Justin has been paid into a ratio we will get this:

$318.75 : 25 hours

in order to find out how much he has been paid for just one hour of work we must divide both sides by 25.

this is because 25 hours / 25 = 1 hour. let's try that:

$318.75 / 25 = $12.75

and 25 hours / 25 = 1 hour

let's put these values back into our ratio:

$12.75 : 1 hour

as you can see we have worked out the total amount Justin made in 1 hour of work, aka how much he earned in an hour.

if you need any more help, just ask :D

The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.

The probability of getting 2 socks of the same color is given by P(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks).Given, There are 8 blue socks. There are 8 white socks. There are 2 gray socks. Now, we will find the probability of getting 2 blue socks: Probability of selecting one blue sock from 8 blue socks is 8/18.

Probability of selecting another blue sock from 7 blue socks is 7/17.Probability of getting 2 blue socks is P(2 blue socks) = 8/18 * 7/17 = 28/153. Now, we will find the probability of getting 2 white socks: Probability of selecting one white sock from 8 white socks is 8/18.Probability of selecting another white sock from 7 white socks is 7/17.Probability of getting 2 white socks is P(2 white socks) = 8/18 * 7/17 = 28/153.

Now, we will find the probability of getting 2 gray socks: Probability of selecting one gray sock from 2 gray socks is 2/18.Probability of selecting another gray sock from 1 gray sock is 1/17.Probability of getting 2 gray socks is P(2 gray socks) = 2/18 * 1/17 = 1/153.

Therefore,The probability of getting 2 socks of the same color isP(two socks of same color) = P(2 blue socks) + P(2 white socks) + P(2 gray socks)= 28/153 + 28/153 + 1/153= 57/153 = 19/51. Hence, the required probability is 19/51.

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Answer: Option 3 = 4

Step-by-step explanation: f(x) = 6 - 2x

f(0) = 6 - 2(0) Range = 6

f(2) = 6 - 2(2) Range = 2

f(4) = 6 - 2(4) Range = -2

f(6) = 6 - 2(6) Range = -6

f(8) = 6 - 2(8) Range = -10

The only one that doesn't belong is 4 option 3.

You're welcome!!

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Answer:

10%

Step-by-step explanation:

1/10 = 0.10 = 10%

Answer:

slope - intercept form: y=2/9x+31/9

point slope form: y-5=2/9 • (x-7)

Answer:

$3

Step-by-step explanation:

All you have to do is divide 6 by 2  because 50%  is also equal to 1/2

Answer:

number 19 is letter B.hence express P(x) as the product of it's linear factors

Answer for this:

5.64

The mode for the given sample data is 58 years. (option A)

Mode: The mode of a data set is the value that occurs most frequently in the data set. The given data set is 51, 61, 62, 57, 50, 67, 68, 58, 53. The number that appears the most in the given data set is 58. Hence, the mode for the given sample data is 58 years.

Below are the ages at retirement of the nine employees:

51, 61, 62, 57, 50, 67, 68, 58, 53.

The mode of this sample data can be obtained by finding the value which appears most frequently. Here, 58 appears twice, which is the maximum frequency of any number in the data set. Therefore, the mode of the given sample data is 58 years. So, the correct option is A) 58 yr.

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Answer:

f(n) = 1

Step-by-step explanation:

Another answer for -3. FxN= -3

To obtain the weighting sequence of the system described by the given difference equation, we can use the Z-transform.

The difference equation can be written in the Z-domain as follows:

Z^2X(Z) - Z^2X(Z)z^(-1) + 0.25X(Z) = Z^2U(Z)

Where X(Z) and U(Z) are the Z-transforms of the sequences x(k) and u(k), respectively.

Simplifying the equation, we get:

X(Z)(Z^2 - Z + 0.25) = Z^2U(Z)

Now, we can solve for X(Z) by dividing both sides by (Z^2 - Z + 0.25):

X(Z) = Z^2U(Z) / (Z^2 - Z + 0.25)

Next, we need to find the inverse Z-transform of X(Z) to obtain the weighting sequence x(k).

Since the initial conditions are given as x(0) = 1 and x(1) = 2, we can use these initial conditions to find the inverse Z-transform.

Using partial fraction decomposition, we can express X(Z) as:

X(Z) = A/(Z - 0.5) + B/(Z - 0.5)^2

Where A and B are constants.

Now, we can find the values of A and B by equating the coefficients on both sides of the equation. Multiplying both sides by (Z^2 - Z + 0.25) and substituting Z = 0.5, we get:

A = 0.5^2U(0.5)

Similarly, differentiating both sides of the equation and substituting Z = 0.5, we get:

A = 2B

Solving these equations, we find A = U(0.5) and B = U(0.5) / 4.

Finally, applying the inverse Z-transform to X(Z), we obtain the weighting sequence x(k) as:

x(k) = U(0.5) (0.5^k + (k/4)(0.5^k-1))

Therefore, the weighting sequence of the system described by the given difference equation is x(k) = U(0.5) (0.5^k + (k/4)(0.5^k-1)), where U(0.5) is the unit step function evaluated at Z = 0.5.

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50%

The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.

Answer:

13) x = 62

14) x = 2.5

    y = 5.88888889

Step-by-step explanation:

x = 62 because x is the alternate interior angle of 62.

37x - 19 = 29x + 1 (subtract 29x on both sides)

8x - 19 = 1 (add 19 on both sides)

8x = 20 (divide by 8)

x = 2.5

Plug 2.5 into 29x + 1 to find 9y + 25

29(2.5) + 1 = 73.5

9y + 25 = 73.5 (subtract 25 on both sides)

9y = 48.5 (divide by 9 on both sides)

y = 5.388888889

It all checks out!

HOPE THIS HELPS!

Answer:

23 cm, 25 cm

Step-by-step explanation:

Let the Width be W cm.

Since the Length and Width are consecutive odd integers we know that the length:

Length = (W + 2) cm

Perimeter of Rectangle = Sum of all sides = 2 x Length + 2 x Width

So rewriting the perimeter , we have:

2W + 2(W+2) = 96 cm

Now lets solve for W to get the width.

2W + 2W + 4 = 96 cm

4W + 4 - 4 = 96 - 4

4W = 92 cm

W = 23 cm

Next, we know that the length = (W + 2) cm

Therefore the length = 23 + 2 = 25 cm

The smallest possible value of nullity(a) is 0, and the largest possible value of nullity(a) is 4. To determine the minimum and maximum possible values of nullity(a) for a 7 × 4 matrix, we need to consider the properties of a matrix and nullity.

Nullity(a) is defined as the dimension of the null space of the matrix 'a'. It is also equal to the number of linearly independent columns in the matrix that are not part of its column space.
Since the matrix is a 7 × 4 matrix, it has 4 columns. The rank-nullity theorem states that:
rank(a) + nullity(a) = number of columns in matrix 'a'
The minimum possible value of nullity(a) occurs when all columns are linearly independent, which would mean the rank of the matrix is at its maximum value. In this case, the maximum rank of a 7 × 4 matrix is 4. So, the smallest possible value of nullity(a) is: nullity(a) = number of columns - rank(a)
nullity(a) = 4 - 4 = 0
The maximum possible value of nullity(a) occurs when the rank of the matrix is at its minimum value. In this case, the minimum rank of a 7 × 4 matrix is 0. So, the largest possible value of nullity(a) is: nullity(a) = number of columns - rank(a)
nullity(a) = 4 - 0 = 4
To summarize, the smallest possible value of nullity(a) is 0, and the largest possible value of nullity(a) is 4.

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Answer:

hffhbvcghbvcf given ndi

Answer:

a = 20m

b = 8ft

Step-by-step explanation:

a² = 25² - 15²

a² = 625 - 225

a² = 400

a = 20m

b² = 10² - 6²

b² = 100 - 36

b² = 64

b = 8ft

It would be ideal to utilise a piece of software or an internet calculator created especially for calculating the Moody friction factor. This will produce a result that is more precise and effective.

How to find?

To find the approximate Moody friction factor, you can use the Colebrook equation, which relates the friction factor (f) to the Reynolds number (Re), pipe roughness (ε), and pipe diameter (D).

The equation is:

\(1 / sqrt(f) = -2 * log10((ε / (3.7 * D)) + (2.51 / (Re * sqrt(f))))\)

First, convert the pipe diameter from cm to meters by dividing by 100:

D = 10 cm / 100

= 0.1 m

Next, plug in the given values into the Colebrook equation and solve for the friction factor:

\(1 / sqrt(f) = -2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f))))\)

Rearrange the equation to solve for sqrt(f):

\(sqrt(f) = 1 / (-2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f)))))\)

Square both sides to solve for f:

\(f = (1 / (-2 * log10((0.06 mm / (3.7 * 0.1 m)) + (2.51 / (250,000 * sqrt(f))))))^2\)

Using an iterative method or a calculator, you can approximate the value of f.

However, since the calculation involves an iterative process, it can be quite complex to solve manually.

Therefore, it would be best to use a software or online calculator specifically designed to solve for the Moody friction factor. This will give you a more accurate and efficient result.

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After performing the iterations, we find that the approximate Moody friction factor (f) is approximately 0.022.

The Moody friction factor is a dimensionless parameter used to describe the flow characteristics of fluid in a pipe. To determine the approximate Moody friction factor, you can use the Colebrook equation:
1/√f = -2log10((ε/D)/3.7 + 2.51/(Re√f))
Where:
f is the Moody friction factor,
ε is the pipe roughness,
D is the pipe diameter,
Re is the Reynolds number.
Given:
Pipe diameter (D) = 10 cm = 0.1 m,
Reynolds number (Re) = 250,000,
Pipe roughness (ε) = 0.06 mm = 0.00006 m.

Let's substitute these values into the Colebrook equation and solve for f:
1/√f = -2log10((0.00006/0.1)/3.7 + 2.51/(250,000√f))
Now, we need to solve this equation iteratively because the friction factor appears on both sides of the equation. We can use a numerical method called the Newton-Raphson method to solve for f.
Let's start by assuming an initial value for f, let's say f = 0.02. We'll use this initial value to calculate the left side of the equation:
1/√0.02
By substituting this into the right side of the equation, we can solve for the new value of f:
-2log10((0.00006/0.1)/3.7 + 2.51/(250,000√0.02))
We continue this iteration until we reach a convergence point, where the new value of f is very close to the previous value.

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Answer: 3.65, 3.7, 323

Step-by-step explanation:

The numbers from least to greatest are as follows:

3.65, 3.7, 323

Hope this helps

Step-by-step explanation:

Let the total number of students in the choir be x

24℅ of x = 12

24/100 of x = 12

6x/25 = 12

6x = 12× 25

6x = 300

x = 50

If the sample size is larger than 30 and the population standard deviation is known, a z-test should be used.

If the sample size is smaller than 30 or the population standard deviation is unknown, a t-test should be used.

There are four hypothesis tests in this assignment, with two being z-tests and two being t-tests. The appropriate test to use, depends on the sample size.

In hypothesis testing, the choice between a z-test and a t-test depends on the sample size and whether the population standard deviation is known or unknown. A z-test is used when the sample size is large (typically greater than 30) and the population standard deviation is known. On the other hand, a t-test is used when the sample size is small (typically less than 30) or when the population standard deviation is unknown.

In the given assignment, there are four hypothesis tests. To determine whether to use a z-test or a t-test, we need to consider the sample size for each test. If the sample size is larger than 30 and the population standard deviation is known, a z-test should be used. If the sample size is smaller than 30 or the population standard deviation is unknown, a t-test should be used.

It is important to check the specific details of each hypothesis test in the assignment to determine the appropriate test to use. By considering the sample size and the information provided for each test, it can be determined whether a z-test or a t-test should be applied.

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Answer:

3

Step-by-step explanation:

7-4 = 3

4 = 1 + 1 + 1 + 1

So...

Substitute 4 with 1+1...

7 - 1 - 1 - 1 -1

Get rid of the ones one at a time:

6 - 1 - 1 - 1

5 - 1 - 1

4 - 1

3

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Answer:

8 posters

Explanation:

first you need to find how many he posted the first week. You do this by multiplying 72 by 1/3, or 72/3. That is 24. Then, you need to subtract that amount, 72-24 is 48. Then, you need to figure out how many he posted the second week. To do that, you need to figure out what 1/6 of 48 is first. So you would need to divide 48 by 6, which equals 8. So if John posted 5/6 of 48, you then need to multiply 8 by 5, equaling 40. If john posted 40 of his 48, then 48-40 is 8, meaning he has 8 posters to post.

Trica's survey of students in her computer class about their computer usage may not support a valid inference regarding the time spent on computers by students in her entire school.

The survey results may lack validity due to several reasons. First, the sample size may be limited to only Trica's computer class, which could introduce selection bias and make it unrepresentative of the entire school population. Representativeness is crucial for generalizing the findings to the broader student body accurately.

Second, the self-reported nature of the survey introduces the potential for self-reporting bias, where students may provide inaccurate or exaggerated information about their computer usage.

This could lead to unreliable results and inaccurate inferences. Additionally, the survey design and measurement techniques might not be rigorous enough to capture a comprehensive understanding of computer usage, lacking standardization and reliable measurement tools.

To obtain valid inferences, it would be necessary to employ random sampling techniques to ensure representativeness, include students from various classes or grades, verify the accuracy of reported data through cross-referencing or observation, and utilize validated measurement instruments.

By addressing these limitations, Trica can enhance the validity of the survey results and make more robust inferences about the time spent on computers by students in her school.

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The given series is convergent, and its sum is approximately 0.1524.

To determine whether the series ∑n=1∞ 1/(9+\(e^{(-n)}\)) is convergent or divergent, we can use the comparison test with the series 1/n.

Since for all n, \(e^{(-n)}\) > 0, we have \(9 + e^{(-n)}\) > 9, and so \(1/(9+e^{(-n)})\) < 1/9.

Now, we can compare the given series with the series ∑n=1∞ 1/9, which is a convergent p-series with p=1.

By the comparison test, since the terms of the given series are smaller than those of the convergent series 1/9, the given series must also converge.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a/(1-r)

where a is the first term and r is the common ratio. In this case, the first term is 1/10 (since \(e^{(-1)}\) is very small compared to 9.

We can approximate \(9+e^{(-n)}\) as 9 for large n), and the common ratio is \(e^{(-1)} < 1\). Therefore, the sum of the series is:

S = (1/10)/(1 - \(e^{(-1)}\)) = (1/10)/(1 - 0.3679) ≈ 0.1524

Therefore, the given series is convergent, and its sum is approximately 0.1524.

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Answer:

The first answer = t ≥-7

Step-by-step explanation:

If one side of an inequality is multiplied by a negative number, to find an equivalent inequality the “direction” of the inequality has to change (for example, ≥ has to change to ≤ ). Find a so that y > x is equivalent to − 3 y < a x.

If 15 people are randomly chosen, the chances that fewer than 6 have brown eyes is 26.75%.

This problem can be solved using the binomial distribution. Let X be the number of people out of the 15 who have brown eyes. Then X follows a binomial distribution with n=15 and p=0.4.

We want to find the probability that fewer than 6 people have brown eyes, i.e., P(X<6). We can use the cumulative distribution function (CDF) of the binomial distribution to calculate this probability:

P(X<6) = ΣP(X=k), where the sum is taken over all k<6.

Using a calculator or software, we can find that:

P(X<6) = 0.02675

Therefore, the answer is C.

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The magnitude of the upward force on the table due to the leg at (lx, 0) is Fx=W.

To find the upward force (Fx) on the table due to the leg at position (Lx, 0), you will need to consider the forces acting on the table. In this scenario, the force Fx is the force exerted by the leg to support the weight of the table and maintain equilibrium.  

To calculate Fx, you'll need to take into account the weight of the table (W) and any additional forces acting on it, such as objects placed on the table. Since the table is in equilibrium, the sum of all forces in the vertical direction should be equal to zero.

Using the principle of equilibrium:

ΣFy = 0

Where ΣFy represents the sum of all vertical forces acting on the table.

In this case, the upward force exerted by the leg (Fx) should be equal to the total downward force acting on the table:

Fx = W

Once you have determined the weight of the table and any additional forces, you can calculate the magnitude of the upward force Fx exerted by the leg at position (Lx, 0).

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Answer:

yes

Step-by-step explanation: