(b) Check whether the function fu.x(u, v) = { ty-tv, 0≤ 2, 121-1-2 otherwise is a valid probability density function.

Answer:

if i didnt get anything mixed up it would be A. dependent

Step-by-step explanation:

When the outcome affects the second outcome, which is what we called dependent events. Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event.

If the random variable z has a standard normal distribution, then we can use a standard normal distribution table or a calculator to find the probability of a range of values for z. In this case, we want to find the probability that z falls between 1.17 and 2.26.

Using a standard normal distribution table, we can look up the probabilities for each of these values individually:

- The probability that z is less than or equal to 1.17 is 0.8790.
- The probability that z is less than or equal to 2.26 is 0.9886.

To find the probability that z falls between these two values, we can subtract the probability of the lower value from the probability of the higher value:

- P(1.17 ≤ z ≤ 2.26) = P(z ≤ 2.26) - P(z ≤ 1.17)
- P(1.17 ≤ z ≤ 2.26) = 0.9886 - 0.8790
- P(1.17 ≤ z ≤ 2.26) = 0.1096

Therefore, the probability that z falls between 1.17 and 2.26 is 0.1096, or approximately 11%.

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For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

For a clinical trial (study) on the mean GPA of night students, the appropriate null and alternative hypotheses would be given by:

In conclusion, we can infer and logically deduce that this test would be right-tailed.

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Answer:

AC= 3.2

Step-by-step explanation:

two trianglesare similar

so AC : BC = DF : EF

AC : 4 = 3:2.4

4×3.2 = AC×4

12.8=4×AC >>>> (÷4) both sides

3.2= AC

Answer:

A basic formula, solving for x, guides us in the setting up of an equation: D/H x Q = x, or Desired dose (amount) = ordered Dose amount/amount on Hand x Quantity

Step-by-step explanation:

Medications are available in multiple concentrations, therefore orders written in "mL" rather than "mg" are not acceptable and require further clarification.

...

Example 2.

Step 1. Calculate the dose in mg: 18 kg × 100 mg/kg/day = 1800 mg/day

Step 2. Divide the dose by the frequency: 1800 mg/day ÷ 1 (daily) = 1800 mg/dose

Answer:

The answer is 10cm

Step-by-step explanation:

the ratio RQ:PQ=1:2

let the ratios be multiplied by x

1x:2x

but 2x=20

then x=10.

so the length is 10cm

The sum of the expressions 8x - 2 and - 3x² - 7 is, - 3x² + 8x - 9.

A quantity or number that is combined with a variable is known as a coefficient. The variable is often multiplied by an integer, which is then printed next to it.

Terms that have the same variables raised to the same power are referred to as like terms. The only difference is in the numerical coefficients.

Given, Two expressions, 8x - 2 and - 3x² - 7.

Now, Sum implies adding.

Therefore, The sum of 8x - 2 and - 3x² - 7 is,

(8x - 2) + (- 3x² - 7).

= - 3x² + 8x - 2 - 7.

= - 3x² + 8x - 9.

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The angle that make highway with a horizontal line is 12.95°.

Horizontal line is type of  straight line that goes from to the  left to right or right to thd left. In co-ordinate geometry, a line is said to be the horizontal if two points are  on the line have the to  same Y- coordinate points. It's comes from the terms “horizon”. It means that this  horizontal lines are always in the parallel to the horizon or to the x-axis.

Section of highway is constructed with 23% grade.

So, y= 1

And x= 4-35

For grade 23% = angle

= tan-1(y/x)

= tan-1(1/4.35)

= 12.95°

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To calculate the probability of the largest pile having four cards, we divide the number of combinations of ten elements taken four at a time by the total number of possible combinations of ten cards. This equals 210/1024, or approximately 0.20703125.

The probability of the largest pile having four cards when ten cards are chosen at random is equal to the number of ways four cards can be chosen from the ten, divided by the total number of possible combinations of ten cards. Mathematically, this probability can be expressed as C(10,4) / 210, where C(10,4) stands for the number of combinations of 10 elements taken 4 at a time, which is equal to 210. Therefore, the probability that the largest pile has 4 cards is 210/1024, or approximately 0.20703125.

To calculate this probability, we need to first determine the number of ways in which four cards can be chosen from ten. This is the number of combinations of ten elements taken four at a time, which is equal to C(10,4) = 10! / 4!(10-4)! = 210.

Then, we need to determine the total number of possible combinations of ten cards. This can be calculated by raising two to the power of ten, which is equal to 210 = 1024.

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To solve the given linear programming problem using the graphical method, we can plot the constraints and then find the feasible region.

Then we can find the optimal solution by plotting the objective function and finding the minimum value within the feasible region. So, the given LP problem is:\(Min Z = 25A + 25Bsubject to:4A + 3B ≥ 245A + 27B ≥ 24A, B ≥ 0\)Let's plot the constraints one by one:\(4A + 3B ≥ 24On plotting 4A + 3B = 24,\) we get a straight line passing through the points (0, 8) and (6, 0) as shown below:\(5A + 27B ≥ 24On plotting 5A + 27B = 24\), we get a straight line passing through the points (4.8, 0) and (0, 0.89) as shown below:

The optimal solution is the point where the objective function intersects the feasible region. This occurs at the point (4, 4) with \(Z = 25(4) + 25(4) = 200\).Hence, the optimal solution of the given LP problem is \(A = 4, B = 4 and Z = 200.\)

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Answer:

James was 35 feet from the ground

Step-by-step explanation:

17 - 7 + 25

10 + 25

= 35

Comparing the two simplified ratios, 4:3 and 10:9, we see that they are not equal, so the ratios 60:45 and 10:9 do not form a proportion.

We must examine whether the cross-products are equal in order to determine whether the ratios of 60:45 and 10:9 constitute a proportion.

60 x 9 = 540 is the cross product of 60 and 9.

45 x 10 = 450 is the cross product of 45 and 10.

The cross-products are not equal, hence the ratios of 60:45 and 10:9 do not constitute a proportion (540 is not equal to 450, for example).

Simplifying two ratios to their simplest form is another technique to determine if they constitute a proportion.

By dividing both components by their greatest common factor, which is 15, the ratio 60:45 can be reduced to 4:3.

The 10:9 ratio has already reached its lowest point.

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The possible values of k are 3 or 150.

Given a matrix A and its inverse matrix A-1. Let v be a non-zero vector. Suppose that v is an eigenvector of A-1 corresponding to the eigenvalue k. To find the possible values of k, let's begin with the equation A-1v = kv.

Given:

Matrix A=⎝⎛​211​121​112​⎠⎞​We are required to find all the possible values of k.

Using the definition of the eigenvector, we know that

A-1v = kvA-1v - kv = 0(A-1 - kI)v = 0

where I is the identity matrix.We know that a non-zero solution for the equation (A-1 - kI)v = 0 exists only when the matrix A-1 - kI is singular.

This means that det(A-1 - kI) = 0.

We have (A-1 - kI) as:⎛⎜⎝​21-k1​1- k2​1- k1​⎞⎟⎠Det(A-1 - kI) = (21-k) [(1-k)(2-k) - 1(1-k)] - (1-k)[1(2-k) - 1(1-k)] + (1-k)[1(1-k) - 1(1-k)] = (21-k) [(1-k)(1-k) - 1] = (k-3)(k-150)

Equating the determinant to zero we get,(k-3)(k-150) = 0k = 3 or k = 150

Therefore, the possible values of k are 3 or 150.

learn more about The possible values of k are 3 or 150.

Given a matrix A and its inverse matrix A-1. Let v be a non-zero vector. Suppose that v is an eigenvector of A-1 corresponding to the eigenvalue k. To find the possible values of k, let's begin with the equation A-1v = kv.

Given:

Matrix A=⎝⎛​211​121​112​⎠⎞​We are required to find all the possible values of k.

Using the definition of the eigenvector, we know that

A-1v = kvA-1v - kv = 0(A-1 - kI)v = 0

where I is the identity matrix.We know that a non-zero solution for the equation (A-1 - kI)v = 0 exists only when the matrix A-1 - kI is singular.

This means that det(A-1 - kI) = 0.

We have (A-1 - kI) as:⎛⎜⎝​21-k1​1- k2​1- k1​⎞⎟⎠Det(A-1 - kI) = (21-k) [(1-k)(2-k) - 1(1-k)] - (1-k)[1(2-k) - 1(1-k)] + (1-k)[1(1-k) - 1(1-k)] = (21-k) [(1-k)(1-k) - 1] = (k-3)(k-150)

Equating the determinant to zero we get,(k-3)(k-150) = 0k = 3 or k = 150

Therefore, the possible values of k are 3 or 150.

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The statement "If two events are mutually exclusive, then they are independent" is False, because occurrence or non-occurrence of one event provides information about other event.

Mutually exclusive events and independent events are two different concepts in probability theory.

Mutually-Exclusive events are events that do not occur at same-time. If one event happens, the other event cannot occur. For example, rolling an even number and rolling an odd number on a fair six-sided die are mutually exclusive events.

The independent events are events where the occurrence of one event does not affect the probability of the other event. In these events the outcome of one event has no influence on the outcome of the other event.

For example, flipping a fair-coin twice, where the outcome of the first flip does not impact the outcome of the second flip, represents independent events.

Therefore, mutually exclusive events cannot occur simultaneously, independent events can occur independently of each other, so the statement is False.

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The statement 'DVDs have replaced CDs as the standard optical disc' is True.

The statement 'DVDs have replaced CDs as the standard optical disc' is True.

DVDs have indeed replaced CDs as the standard optical disc. DVDs have a higher storage capacity compared to CDs, allowing them to store more data. This makes DVDs more suitable for storing and distributing larger files, such as movies, videos, and software. DVDs also offer better video and audio quality compared to CDs, making them the preferred choice for multimedia content.

However, it's important to note that CDs are still commonly used for audio recordings, such as music albums. CDs have a lower storage capacity but are sufficient for storing audio files. They are also more affordable and widely compatible with various devices.

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These are: Increasing the sample size, Decreasing the confidence level. Thus, the correct answer is (B) ll only.

Confidence interval refers to the range of values, which is probable to contain an unknown population parameter.

A confidence level shows the degree of certainty regarding an estimated range of values.

Hence, a wider interval indicates less certainty and the smaller the interval, the greater the certainty.

How to decrease the width of a confidence interval for the mean There are two methods to decrease the width of a confidence interval for the mean.

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Answer:

yes

Step-by-step explanation:

3+3=6

6+6=12

so yes, that statement is correct

Answer: yes this statement is completely correct.

Step-by-step explanation:

Answer: A, C and E.

Step-by-step explanation: They all equal to 5.

The intercept in the given linear regression model, which is -631.25, does not have a reasonable interpretation in the context of ticket sales at a water park.

The intercept in a linear regression model represents the predicted value of the dependent variable (in this case, ticket sales per hour) when the independent variable (in this case, current temperature in °F) is equal to zero. However, in the context of the given model, it is not meaningful to interpret a negative intercept of -631.25 for ticket sales at a water park.

This is because ticket sales cannot be negative, and it does not make sense to predict ticket sales when the temperature is at absolute zero (0 °F), as that is not a realistic scenario. Additionally, a negative intercept implies that the model predicts negative ticket sales at extremely low temperatures, which is not feasible.

Therefore, the intercept of -631.25 in the given linear regression model does not have a reasonable interpretation in the context of ticket sales at a water park

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A type IV hip has an alpha angle of less than 43 degrees and a beta angle that is immeasurable. The alpha angle is a measurement used to assess the shape of the femoral head-neck junction. In a type IV hip, the alpha angle is typically less than 43 degrees, indicating a relatively shallow and abnormal angle.

The beta angle, on the other hand, is used to evaluate the orientation of the acetabulum. In a type IV hip, the beta angle is often immeasurable, suggesting a severely abnormal orientation of the acetabulum. It is important to note that these angle measurements are used in the classification of developmental hip dysplasia and are indicative of specific abnormalities in hip anatomy.

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To calculate the number of MADs that the means are apart, we need to find the difference between the two means and then divide that by the MAD.

The difference between the means is 20 - 16 = 4.

Dividing that by the MAD of 2.5, we get:

4 / 2.5 = 1.6

Therefore, the means are 1.6 MADs apart.

1. Find the difference between the two mean ages: 20 years (mean age of second sample) - 16 years (mean age of first sample) = 4 years.

2. Divide the difference by the MAD: 4 years (difference between means) / 2.5 (MAD) = 1.6.

So, the means are 1.6 MADs apart.

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The solution to the fraction division problems are:

7) ¹/₄ ÷ 2 = ¹/₈

8) ¹/₃ ÷ 5 = ¹/₁₅

9) ¹/₂ ÷ 6 = ¹/₁₂

10) ¹/₉ ÷ 4 = ¹/₃₆

11) ¹/₁₂ ÷ 4 = ¹/₄₈

12) ¹/₈ ÷ 8= ¹/₆₄

7) ¹/₄ ÷ 2

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₄ * ¹/₂ = ¹/₈

8) ¹/₃ ÷ 5

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₃ * ¹/₅ = ¹/₁₅

9) ¹/₂ ÷ 6

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₂ * ¹/₆ = ¹/₁₂

10) ¹/₉ ÷ 4

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₉ * ¹/₄ = ¹/₃₆

11) ¹/₁₂ ÷ 4

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₁₂ * ¹/₄ = ¹/₄₈

12) ¹/₈ ÷ 8

When dividing like this, we will make the number on the right a reciprocal and the sign will be multiplication to get:

¹/₈ * ¹/₈ = ¹/₆₄

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The correct answer is option B) 2.4 ml. The 2.4 milliliters would be needed to be drawn up for one dose.

To calculate the amount of Dexamethasone 4 mg/5 mL needed for a 12 mg dose, we can use a simple proportion:

4 mg / 5 mL = 12 mg / x

Cross-multiplying, we get:

4 mg * x = 60 mg

x = 60 mg / 4 mg/mL

x = 15 mL

Therefore, to administer a 12 mg dose of Dexamethasone using the available drug concentration of Dexamethasone 4 mg/5 mL, we need to draw up only 2.4 mL.

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Answer:

The range is 8

Step-by-step explanation:

Recall that the range of a data set is the distance between the maximum and the minimum, therefore:

Range = Maximum - Minimum = 9 - 1 = 8

Answer:

Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is

9−1=8

Step-by-step explanation:

So therefore,the range is 8

(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = \(\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }\)

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = \(\sqrt{35^{2}(0.5611) }\) = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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Answer:

131°.

Step-by-step explanation:

its equal to that other angle i forgot how but i learned this 1 week ago

Given:

Machine A covers 5/8 square feet in 1/2 hour.

Machine B covers 2/3 square feet in 1/3 hour.

Solution:

The unit rate of the machine A will be as

The unit rate of the machine B will be as

Answer:

Hence, the unit rate of the machine B is greater.

Given:

Total number of food cans = 12

Cans of Beets = 8

Cans of corn = 3

Can of beans = 1

To find:

How many distinct orders can the cans be arranged if two cans of the same food are considered identical.

Solution:

To find the distinct ways arrangement, we have a formula:

\(\text{Number of distinct ways}=\dfrac{n!}{r_1!r_2!...r_k!}\)        ...(i)

Where, n is the number of objects and \(r_1,r_2,...,r_k\) are repeated objects.

Total number of food cans is 12. So, \(n=12\).

She has 8 cans of beets. So, \(r_1=8\)

She has 3 cans of corns. So, \(r_2=3\)

She has 1 can of beans. So, \(r_3=1\)

Substituting these values in (i), we get

\(\text{Number of distinct ways}=\dfrac{12!}{8!3!1!}\)

\(\text{Number of distinct ways}=\dfrac{12\times 11\times 10\times 9\times 8!}{8!\times 3\times 2\times 1\times 1}\)

\(\text{Number of distinct ways}=\dfrac{11880}{6}\)

\(\text{Number of distinct ways}=1980\)

Therefore, the number of distinct orders to arrange the cans is 1980.