Generaly speaking, the amount of gun powder particles found around a bullet hole is ____ to the distance from which the weapon was fired:

Answer:

SOH CAH TOA

The ratios of sine, cosine and tangent.

Step-by-step explanation:

Sine: Opposite / Hypotenuse

Cosine: Adjacent / Hypotenus

Tangent: Opposite / Adjacent

The graph of the function f(x) = |x| and g(x) = −2|x| is attached below, the function f(x) = |x|  is always positive whereas the function g(x) = −2|x| is always negative.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

The given functions are,

f(x) = |x| and g(x) = −2|x|

Here, the graph of the modulus function f(x) = |x| is always on the positive y-axis as the range of the function is always positive,

Whereas, the graph of g(x) = −2|x| is always on the negative y-axis, as the range of the function is negative.

Put the values of x in the function, and calculate the value of the function mark the values of x in the x-axis and the values of the function in y and then join all the points to get the graph.

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Answer:

a. acute triangle (all the angles measure less than 90 degrees)

b. scalene triangle (none of the angles are congruent, so none of the sides are congruent)

While statistical significance indicates the reliability of the study results, clinical significance reflects its impact on clinical practice.

Can you have clinical significance without statistical significance?

Clinical researchers and practitioners should concentrate on clinically relevant improvements rather than statistical significance, which is the emphasis of most research. A research result may be clinically important but not statistically important, and vice versa.

In clinical research, statistically significant study results are frequently considered to be of clinical significance. Clinical significance emphasizes the study's influence on clinical practice, whereas statistical significance highlights the validity of the study's findings.
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The activity that would most likely result in the greatest degree of muscle soreness 12-24 hours post-exercise is  4. there would be identical degrees of soreness because it is new.

People of every age and genders will have sore muscle mass. When you attempt a brand new bodily pastime or transfer up your exercising routine, you could enjoy delayed-onset muscle soreness (DOMS). Muscle aches can also additionally come on six to twelve hours after a exercising and last as long as forty eight hours. You experience ache because the muscle mass heal and get stronger.  Sore muscle mass after exercising -It can have an effect on humans of all health levels, especially after attempting a brand new pastime or pushing your self a chunk tougher than usual. Usually your muscle mass will prevent aching in 2 to five days and also you may not want any clinical attention.

Thus, option 4 is the correct choice.

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Answer:

Step-by-step explanation:

The answer is 22 the reason why is because 5 + 5 + 8 + 4= 22 so you just add all the numbers up!

The solution to the compound inequality in interval notation is [-7, 5)

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

3x - 10 < -5x + 30 AND 3(-7x - 7) + 6 ≤ - 6x + 132

Evaluate the like terms in the above expression

So, we have the following representation

8x - 10 < 30 AND 3(-7x + 7) + 6 ≤ - 6x + 132

Open the brackets

This gives

8x - 10 < 30 AND -21x + 21 + 6 ≤ - 6x + 132

Evaluate the like terms in the above expression

So, we have the following representation

8x < 40 AND -15x ≤ 105

Divide both sides by the coefficient of x

This gives

x < 5 AND x ≥ -7

Combine the inequalities

[-7, 5)

Hence, the solution is [-7, 5)

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If X and Y are independent standard normal random variables, joint density function of u and v is 1/(π+v²).

We have X and Y are independent standard normal random variables. It is given that X and Y are two independent standard normal random variables.

That is, The probability density function of standard normal random variable X and Y as shown below:

f(x) = 1/√2π exp{ -x²/2}

f(y) = 1/√2π exp{ -y²/2}

The joint density function of X and Y is shown as

f(x,y) = 1/2π exp{ -(x² + y²)/2}

It is given that, U = X , V = x/y

=> Y = X/V = U/V

The Jacobean transformation is shown below:

J = | ∂x/∂u ∂x/∂v |

| ∂y/∂u ∂y/∂v |

= det [ 1 0 ; 1/v -u/v²]

= 1 ×(-u/v²) - 0×(1/v)

= -u/v²

The joint density function of u and v is,

f(u,v) = fₓₓ(x,y)|J| =1/2π exp{ -(u² + (u/v)²} u/v²

find the value of f(x/y)

fᵥ (V) = ∫ f(u,v) du where limits u = -∞ to u= ∞

=∫{1/2π exp{ -(u²+ (u/v)²)} u/v²du , u = -∞ to u = ∞

= 2 ∫1/2π exp{ -(u² + (u/v)²)} u/v²du, u = 0 to u = ∞

(since, integrand is even function of u)

Using the change of variable,

u²₁ = u²(1+v²) we have

fᵥ (V) = ∫ 1/(π+v²) exp( -u₁²/2) u/v² du₁, u = 0 to u = ∞

= 1/(π+v²) ∫exp( -u₁²/2) d(u₁/v²) = 1/(π+v²)(1) =1/(π+v²)

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The equation that represents the number of miles Hailey ran is [tex]$3 \cdot h=27$[/tex],  

[tex]$h=\frac{1}{3} \cdot 27$[/tex] and  [tex]$h=3 \cdot 27$[/tex].

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: The formula is (Number/Variable, Math Operator, Number/Variable).

The addition, subtraction, multiplication, and division arithmetic operators are used to write a group of numbers together to form a numerical statement in mathematics. The expression of a number can take on various forms, including verbal form and numerical form.

Let the given information be "Last week, Devan ran 27 miles, three times Hailey's distance".

Let h be the number of miles Hailey ran.

then, we get

[tex]$3 \cdot h=27$[/tex],  

[tex]$h=\frac{1}{3} \cdot 27$[/tex] and

[tex]$h=3 \cdot 27$[/tex]

Therefore, the correct answer is option

a) [tex]$3 \cdot h=27$[/tex]

b) [tex]$h=\frac{1}{3} \cdot 27$[/tex]

d) [tex]$h=3 \cdot 27$[/tex]

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Answer:

71/12 = 5 11/12

Step-by-step explanation:

To solve this equation you first have to put the whole number with fraction (mixed number) and convert it into an improper fraction. To do this you have to multiply the whole number by the denominator which is 6 x 2 and you'd get 12 but then you still have the numerator so then you add your answer with the numerator and you'd get 12+1 which is 13. So your improper fraction is 13/2.

Now you set up your equation and you'd subtract. But your denominators are not the same so you have to figure out and find the common denominator. Which is 12. So then for 13/2 you'd multiply both of them by 6 and you'd get 78/12. And the 2nd one you'd multiply it by 1 getting 7/12.

Once you get to this point now you can properly set up the equation and subtract. You'd subtract 78/12 - 7/12 getting 71/12 or if you want it as a mixed number (whole number with fraction) then it is 5 11/12.

(I tried to explain how I got the answer...hopefully you were able to understand how I did it...)

On solving the provided question, Triple product - A.(BXC) = B.(CXA)=C.(AXB) and AX(BXC) = B(A.C) - C(A.B)

A vector field is a vector association with each point in a subset of space in the field of vector mathematics and physics. For example, a vector field in the plane can be represented as a series of arrows. Each arrow is associated with a point in the plane and each has a specific size and direction.

Triple product -

A.(BXC) = B.(CXA)=C.(AXB)

AX(BXC) = B(A.C) - C(A.B)

Product Rules-

∇(fg) = f(∇g) + g()∇f

∇A.B = AX (∇XB) + BX(∇XA) + (AX∇)B + (B.∇)A

∇(fA) = f(∇.A) + A(∇.f)

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The associative property states that the way in which numbers are grouped in an arithmetic expression does not affect the result of the computation. For example, in the expression (a + b) + c, the addition of a + b can be done first, and then added to c, or the addition of b + c can be done first and then added to a. The result will be the same either way.

In the expression you provided, the associative property can be used to group the terms in the following way:

(8/9 / 7/5) x 3/16

= (8/9 x 3/16) / (7/5)

Then, the division and multiplication operations can be carried out in the order that they appear, from left to right:

= (24/144) / (7/5)

= (1/6) / (7/5)

Finally, the division operation can be carried out to obtain the final result:
= (5/42)

Answer:

[tex]\frac{5x}{42}[/tex]

Step-by-step explanation:

8/9/7/5 = 8 · 5

               9 x 7

Apply the fraction rule

8 x 5x x 3

9 x 7 x 16

cancel 8 x 5x x 3        5x

9 x 7 x 16               :     3 x 7 x 2

= 5x

3 x 7 x2

= 5x

3 x 7 x 2

Multiply the numbers 3 x 7 x 2 = 42

= 5x

  42

Answer:

{1073, 6829}

Step-by-step explanation:

There is 0.17% of the time is Judy idle.

It will take 25 minutes on average, does a student spend waiting in line.

The waiting line on average is 4.1 customers.

The probability that an arriving student will find at least one other student waiting in line is 0.68.

Given students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take on average 5 minutes to be processed.

The service counter is staffed by only one clerk, Judy gumshoes, who works eight hours per day.

Assume Poisson arrivals and exponential service times.

It was said in the question Students arrive at the Administrative Services Office at an average of one every 15 minutes which means that:

λ = 60/6 = 10customers/hr

μ = average of 5 minutes = 60/5 = 12customers/hr

1) What percentage of time is Judy idle?

The percentage when Judy was idle = 1- λ/μ = 1- 0.83= 0.17

%Service time = 0.83

%idle time = 0.17

There is 0.17% of time is Judy idle.

2) How much time, on average, does a student spend waiting in line?

A student spends waiting in line then we make use of the formula below:

λ /μ(λ-μ )

= 0.41 × 60

= 25 minutes

It will take 25 minutes on average, does a student spend waiting in line.

3) How long is the waiting line on average?

To calculate How long the waiting line is on average;

average waiting time x arrival rate = 0.41hrs x 10 customers/hr =  4.1 customers

The waiting line on average is 4.1 customers.

What is the probability that an arriving student will find at least one other student waiting in line?

P1( Probability of having a customer to attend to) = 0.17 x 0.83 = 0.141

P2( Probability of having 2 customer to attend to) = 0.17 x 0.83 x 0.83 = 0.117

The probability of finding at least one customer = 1 -[ po + p1]

= 1 - 0.17 - 0.141 = 0.68

The probability that an arriving student will find at least one other student waiting in line is 0.68.

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Answer:

1. A

2. Simplification: (not sure)

[tex] \frac{ - 3x {}^{5} + 6x { }^{2} - 4x - 15 }{9x {}^{2} - 12x + 4 } [/tex]

Answer:

5 kg of 30% nitrogen an d 15 kg of 10% nitrogen.

Step-by-step explanation:

Answer:

25a² +

Step-by-step explanation:

5a is put in the equation replacing the previous variable and then the whole square follows and hence. g(5a) =25a²+

f(x, y) = 3x + 2y + C

To know if a vector field is conservative, we have to check if it is the gradient of a scalar function.

The gradient of the function f(x, y) is given by

∇f(x, y) = (∂f/∂x, ∂f/∂y)

If a vector field F(x, y) is the gradient of a scalar function f(x, y), then the following conditions must be satisfied:

F(x, y) = ∇f(x, y)

Whether a given vector field satisfies this condition can be checked by taking the partial derivative with respect to x and y.

∂F/∂x = ∂(6x + 5y)/∂x = 6

∂F/∂y = ∂(5x + 4y)/∂y = 4

The partial derivative of a given vector field is the constant, the gradient of the scalar function. So vector fields are conservative and we can find a potential function f(x, y) such that F(x, y) = ∇f(x, y).

To find the potential function, we can integrate the partial derivative of F(x, y) with respect to x and y.

f(x, y) = ∫∂F/∂xdx + ∫∂F/∂ydy

= ∫6dx + ∫4dy

= 3x + 2y + C

where C is the constant of integration. So the potential function for a given vector field is

f(x, y) = 3x + 2y + C

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Answer:

Step-by-step explanation:

The decimal form of the given rational number 2/9 is 0.2

A rational number is a number which is defined in p/q form where q is not equals to 0 and p and q are real numbers or integers.

A decimal number is a standard system to represent the integers and non-integer numbers.

Now convert the given rational number 2/9 into decimal form by dividing the numerator, that is, 2 with the denominator, that is 9.

After division we will get the decimal form of the given rational number

2/9 = 0.222222

When we round off it to nearest thousand it will be written as 0.2

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The probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.

The first power of the transition matrix A is simply the matrix itself:

A1 = [ 0.3 0.1 0.6 ]

[ 0.5 0.2 0.3 ]

The second power of the transition matrix is obtained by multiplying A by itself:

A2 = A1 * A1 = [ 0.30.3+0.10.5 0.30.1+0.10.2 0.30.6+0.10.3 ]

[ 0.50.3+0.20.5 0.50.1+0.20.2 0.50.6+0.20.3 ]

= [ 0.19 0.06 0.33 ]

[ 0.29 0.08 0.33 ]

The third power of the transition matrix is obtained by multiplying A2 by A:

A3 = A2 * A = [ 0.190.3+0.060.5 0.190.1+0.060.2 0.190.6+0.060.3 ]

[ 0.290.3+0.080.5 0.290.1+0.080.2 0.290.6+0.080.3 ]

= [ 0.161 0.052 0.327 ]

[ 0.247 0.068 0.327 ]

To find the probability that state 1 changes to state 2 after three repetitions of the experiment, we need to look at the second element of the first row of A3. This element is 0.052, so the probability that state 1 changes to state 2 after three repetitions of the experiment is 0.052.

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The sample mean is -2.0, the sample variance is 11.67, and the sample standard deviation is 3.42.

The sample mean is the average of a given set of numbers. To find the sample mean of the set of numbers {-8, -4, -3, 0, 1, 2}, you add up all of the numbers and divide by the number of numbers in the set, which is 6. So, the sample mean is -2.0. The sample variance measures the variability of the data, or how spread out the data is. To calculate the sample variance, you first subtract the mean from each number and square the result of each. Then, you add up all of the squares and divide by the number of numbers in the set. In this case, the sample variance is 11.67. The sample standard deviation is the square root of the sample variance and is a measure of how far on average each number is from the mean. To calculate the sample standard deviation, you simply take the square root of the sample variance, which is 3.42.

Sample mean: -2.0 = (-8 + -4 + -3 + 0 + 1 + 2) / 6

Sample variance: 11.67 = (64 + 16 + 9 + 0 + 1 + 4) / 6

Sample standard deviation: 3.42 = √11.67

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G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. preconditions: x

x(x + 1)/2 = O(x^2)

The pseudocode segment given has two nested for loops. The outer loop is iterating over the variable x, while the inner loop is iterating over variable i. G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. Each loop iteration is increasing the variable z by 1. In total, this will result in x*(x+1) / 2 operations being performed. This is equal to O(x^2), which is the worst-case number of operations.

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Step-by-step explanation:

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

Answer: This question is most likely assuming a poisson distribution; it is impossible to compute without some distribution clarified, as otherwise we don't have applicable information.

Poison distribution is:

(λke-k) / k!

Where k is the number of outcomes you are looking for, and λ is the accepted average number of outcomes. So, λ is 6 for this example, and we are looking for values of k to use.

Solving problem b is simply substituting the value.

Prob of 5 parts: (65e-5) / 5!, using a calculator and working it out, this approximates to 0.437.

Solving problem a can be used for c; to get a, do the above equation 5 times for k = 0, 1, 2, 3 and 4, and add them all together. Though somewhat tedious, this would lead to the solution. To get part c, you would use the property of complements:

The cumulative probability here would be 1 - (total prob of all scenarios with k = 0, 1, 2, 3, 4, 5). You can get that total probability by adding the answers to part a and b together.

Finally, regarding part d, the above work can be redone with a new formula, now (λke-k) / k! would have λ as 5. This would reduce the answer for a, but increase it for b and c, which you can verify by running the calculations.

Step-by-step explanation:

On solving the provided question, the differential equations  we obtained are as follows -  [tex]\frac{d^3y}{dx^3} - 3\frac{d^2y}{dx^2} + 3\frac{dy}{dx} -y = 0[/tex] And [tex]\frac{d^3y}{dx^3} +\frac{dy}{dx} -10y = 0[/tex]

An equation comprising one or more functions and their derivatives is known as a differential equation in mathematics. A function's derivative expresses the rate of change of the function at a specific moment. It is mostly employed in the sciences of physics, engineering, and biology.

Since there are 3 basic function, the order of the differential equation is 3. Since the basic finction e^{x} is repeating thrice, the characteristic roots are 1,1,1,(i.e the characteristic root is 1 with multiplicity 3). Hence the characteristic equation is (D-1)^{3} = 0.

[tex]\frac{d^3y}{dx^3} - 3\frac{d^2y}{dx^2} + 3\frac{dy}{dx} -y = 0[/tex]

Since there are 3 basic function, the order of the differential equation is According to the basic finctions, the characteristic roots are [tex]2,-1[/tex]±[tex]2i.[/tex] Hence the characteristic equation is (D-2)(D^{2}+2D+5) = 0. which means D^{3}+D-10 = 0.

[tex]\frac{d^3y}{dx^3} +\frac{dy}{dx} -10y = 0[/tex]

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The coefficient of the given term is 2208

The binomial formula is used for binomial expansion and is given by:   [tex](x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}[/tex]

Given here (2u-s)²⁴

The 22nd term will be given by ;

T₂₂ = ²⁴C₂₂× (2u)²× (-s)²²

     = 552×4× (u)²× (s)²²

     = 2208 (u)²(s)²²

Hence, the coefficient of the given term is 2208

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Answer:

Step-by-step explanation:

No because if the inequality sign had a line under it, it would mean that it could be equal to, but because it doesn't have a line under the inequality sign it isn't a solution.

Answer:

No

Step-by-step explanation:

12 is not a solution to this inequality >12 means all values greater than 12. Since 12 is not greater than 12, the answer is no.

Answer:

1st, 3rd

Step-by-step explanation:

1st: 8-10-12=-14

2nd:10-8-12=-10, so no

3rd:yes, because it just removed the brackets

4th:8-6-12+4=-6, so no

Hope this helps u

All the expressions that are equivalent to (8 - 12 - (6 + 4)) would be,

1) 8 - (6 + 4) - 12

3) 8 - 12 - 6 - 4

Given that,

The expression is,

8 - 12 - (6 + 4)

Now, Used the concpet to simplify the expression by using operations addition, subtraction, etc.

Here, The expression is,

8 - 12 - (6 + 4)

8 - 12 - 10

8 - 22

- 14

For the equivalent expressions we can simplify all the equations,

Option 1,

8 - (6 + 4) - 12

8 - 10 - 12

8 - 22

- 14

So, It is equivalent to a given expression.

Option 2,

(6 + 4) - 8 - 12

10 - 8 - 12

10 - 20

- 10

So, It is not equivalent to a given expression.

Option 3,

8 - 12 - 6 - 4

8 - 12 - 10

8 - 22

- 14

So, It is equivalent to a given expression.

Option 4,

8 - 6 - 12 + 4

8 - 18 + 4

12 - 18

- 6

So, It is not equivalent to a given expression.

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