Aiden is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury Knee pain Ankle pain 2 4 a 0-12 years old 13-19 years old 1 4 What is the probability that a randomly selected patient suffers from ankle pain given that the patient is 13-19 years old? Simplify any fractions.

The domain is all the values that X can have

While the range is all th values that Y can ahave

What are the values for Y in the graph?

From 9 to 0 (including 9 nd 0, because it is a shaded dot)

So, the correct option would be B

The answer is C. A fraction is basically another way of writing division, and  six divided by three is two.

Step-by-step explanation:

Vertical angles are equal   r = 70 degrees

Answer:

rsgsadfg

Step-by-step explanation:

d dhrtyeyerte

Answer: 388.1ft2

Step-by-step explanation: 10 x 8.9

Answer:

A ,  C , E

Step-by-step explanation:

a = 180 - 128 = 52° (correct)  (supplementary angle)

b = 128° (correspondent angle)

f = 128° (Correct)  (vertical angle)

g = 52° (vertical angle of a)

h = 128° (correct) (vertical angle of b)

Answer:

\((1 + i)^{2n} = \frac{4}{(-1 \± \sqrt{5})^2}\)

Step-by-step explanation:

Using Present Value formula, we have that:

The present value at end of n period is

\(PV_1 = \frac{1}{(1 + i)^n}\)

The present value at end of 2n period is

\(PV_2 = \frac{1}{(1 + i)^{2n}}\)

\(Sum = PV_1 + PV_2\)

And

\(Sum = 1\)

So, we have:

\(PV_1 + PV_2 = 1\)

Substitute values for PV1 and PV2

\(\frac{1}{(1 + i)^n} + \frac{1}{(1 + i)^{2n}}= 1\)

Solving for:

\((1 + i)^{2n\)

\(\frac{1}{(1 + i)^n} + \frac{1}{(1 + i)^{2n}}= 1\)

This can be expressed as

\(\frac{1}{(1 + i)^n} + (\frac{1}{(1 + i)^{n}})^2= 1\)

Let

\(a = \frac{1}{(1 + i)^n}\)

So, we have:

\(a + a^2 = 1\)

Equate to 0

\(a + a^2 - 1= 0\)

\(a^2 + a - 1= 0\)

Using quadratic formula:

\(a = \frac{-B \± \sqrt{B^2 -4AC}}{2A}\)

Where A=1; B =1 and C = -1

\(a = \frac{-1 \± \sqrt{1^2 -4 * 1 * -1}}{2 * 1}\)

\(a = \frac{-1 \± \sqrt{1 +4}}{2 }\)

\(a = \frac{-1 \± \sqrt{5}}{2 }\)

Recall that:

\(a = \frac{1}{(1 + i)^n}\)

So, we have:

\(\frac{1}{(1 + i)^n} = \frac{-1 \± \sqrt{5}}{2 }\)

Invert both sides

\((1 + i)^n = \frac{2}{-1 \± \sqrt{5}}\)

Square both sides

\(((1 + i)^n)^2 = (\frac{2}{-1 \± \sqrt{5}})^2\)

\((1 + i)^{2n} = (\frac{2}{-1 \± \sqrt{5}})^2\)

\((1 + i)^{2n} = \frac{4}{(-1 \± \sqrt{5})^2}\)

Answer:

Step-by-step explanation:

$211000 are 100% - 58% = 42% of the (former) income.

Therefore, 1% is 42 times less: 211000/42 = 5023.81,

and the (former) income was 100 times this value, i.e. GHC 502381.

By taking x as subject the formula becomes x = (v² - u²)/2a.

An equation is a mathematical statement with an 'equal to=' symbol between two expressions that have equal values.

Here given equation:

      v² = u² + 2ax

     2ax = v² - u²

      x = (v² - u²)/2a

Thus, by taking x as subject the formula becomes x = (v² - u²)/2a.

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Answer:

    Positive correlation    

Step-by-step explanation:

A positive correlation is a relationship between two variables in which both variables move in the same direction. Ex:  Higher levels of one variable are associated with higher levels of the other.

A relationship in which higher levels of one variable are associated with higher levels of another is best described as Positive correlation.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

A positive correlation is a relationship between two variables that move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

Hence, A relationship in which higher levels of one variable are associated with higher levels of another is best described as Positive correlation.

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The total ounces she needs to make her recipes is 22 ounces

From the question, we are to determine how many total ounces Marni needs to make her recipe

From the given information,

Marni has 24 ounces of walnuts

Also,

She needs 14 ounces for one recipe

and

1/2 pounds for another

First, we will convert 1/2 pounds to ounces

NOTE: 1 pound = 16 ounces

∴ 1/2 pound = 8 ounces

Then, we can rewrite that

She needs 14 ounces for one recipe

and

8 ounces for another

The total ounces she needs to make her recipes = 14 ounces + 8 ounces

The total ounces she needs to make her recipes = 22 ounces

Hence, the total ounces she needs to make her recipes is 22 ounces

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Answer: -28y^4 - 7y^3 + 62y^2 + 5y - 30

Step-by-step explanation: Just trust me, it's correct

Answer:

$40.00 is the answer

Step-by-step explanation:

also can you mark me as a brainlist if you get a chance

Answer: $40.00

Step-by-step explanation:

12 is 30% of 40

Answer:

Liquid

Step-by-step explanation:

solids :have definite shape and definite volume.

Liquids :have definite volume and shape of the container.(or no definite shape)

Gas: has no definite volume and no definite shape.

Answer:

whats the awnser

Step-by-step explanation:

Answer:

Raphael sells paintings for $200 each at a market, but has to pay $100 to reserve a table. :)

Step-by-step explanation:

Answer:

hypotenuse aka the longest line on a right angle

B

Step-by-step explanation:

Hypotenuse is right I'm pretty sure

1.67. Roll a fair die repeatedly and let \(\mathbf{Y_1, Y_2...}\) be the resulting numbers. Let \(\mathbf{X_n = |\{Y_1, Y_2,...,Y_n\}|}\) be the number of values we have seen in the first n rolls for n ≥ 1 and set X₀ = 0. Xₙ is a Markov chain. (a) The transition probability is:

\(\mathbf{P = \left[\begin{array}{ccccc}\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3} \\ \\\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \end{array}}\right]\)

E(T) = E(Time until absorption) is expressed as:

\(\mathbf{E(T) =\ \left[\begin{array}{c}1 \\ \\ 1 \\ \\ 1 \\ \\ 1 \end{array}}\right] } \\ \\\)

The transition probability is the likelihood of a system transitioning from one phase to another.  If a Markov chain seems to be in state a, the transition probability \(\mathbf{p_{ab}}\) , is the likelihood of transitioning to state b at the next time interval.

From the information given:

\(\mathbf{P = \left[\begin{array}{ccccc}\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3} \\ \\\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \end{array}}\right]\)

B.

Let take state 6 to turn into an absorbing state, then the transition probability matrix can take the form:

\(\mathbf{\implies \left[\begin{array}{ccccc}\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3} \\ \\\ 1&0&0&0&0 \end{array}}\right]\)

\(\mathbf{Q = \left[\begin{array}{cccc}\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\ \dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6} \\ \\ \dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3} \\ \end{array}}\right]\)

As such F = (I-Q)⁻¹

\(\mathbf{F \implies \left[\begin{array}{cccc}1&0&0&0\\ \\ 0&1&0&0 \\ \\0&0&1&0 \\ \\ 0&0&0&1\end{array}\right] - \left[\begin{array}{cccc}\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6}&\dfrac{1}{6} \\ \\ \dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3}&\dfrac{1}{6} \\ \\ \dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{6}&\dfrac{1}{3} \\ \end{array}}\right] } \\ \\\)

\(\mathbf{F \implies \ \left[\begin{array}{cccc}\dfrac{2}{3}&-\dfrac{1}{6}&-\dfrac{1}{6}&-\dfrac{1}{6} \\ \\-\dfrac{1}{6}&\dfrac{2}{3}&-\dfrac{1}{6}&-\dfrac{1}{6} \\ \\ -\dfrac{1}{6}&-\dfrac{1}{6}&\dfrac{2}{3}&-\dfrac{1}{6} \\ \\ -\dfrac{1}{6}&-\dfrac{1}{6}&-\dfrac{1}{6}&\dfrac{2}{3} \\ \end{array}}\right] } \\ \\\)

∴

E(T) = E(Time until absorption) is expressed as:

\(\mathbf{E(T) =\ \left[\begin{array}{c}1 \\ \\ 1 \\ \\ 1 \\ \\ 1 \end{array}}\right] } \\ \\\)

Therefore, from the above explanation, we have clearly understood the transition probability and the E(Time until absorption).

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Answer:

false

Step-by-step explanation:

false

Step-by-step explanation:

This is of the form

(x-h)^2 + ( y-k)^2 = r^2        so r^2 = 16  means r = 4   units

Answer:

Step-by-step explanation:

positive factors are:

1, a, b, a², ab, a²b

Three ways to label a base (b) and corresponding height (h) are:

1. Base as the bottom side, height as a perpendicular line segment.

2. Base as a side, height as a perpendicular line segment.

3. Base as the hypotenuse, height as a perpendicular line segment.

To label a base (b) and corresponding height (h), three possible ways can be demonstrated using the triangles below:

1. Triangle 1:

  - Base (b) is labeled as the bottom side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

2. Triangle 2:

  - Base (b) is labeled as the side of the triangle.

  - Height (h) is labeled as a vertical line segment perpendicular to the base, connecting the opposite vertex to the base.

3. Triangle 3:

  - Base (b) is labeled as the hypotenuse (the longest side) of the triangle.

  - Height (h) is labeled as a vertical line segment drawn from one of the vertices of the base, perpendicular to the base.

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When f is  (x² + 7x + 12) and g is (x² - 9) we use composite function to find (f • g)(x) = x⁴ + 7x³ + 3x² - 63x - 108.

(b) (f/g)(x) = (x + 4) / (x - 3)

a) To find (f • g)(x), we need to multiply f(x) and g(x) together:

f(x) = x² + 7x + 12

g(x) = x² - 9

(f . g)(x) = f(x) * g(x)

Here we perform the operation of function composition.

        = (x² + 7x + 12) x (x² - 9)

        = x⁴ + 7x³ + 12x² - 9x² - 63x - 108

        = x⁴ + 7x³ + 3x² - 63x - 108

Therefore, (f • g)(x) = x⁴ + 7x³ + 3x² - 63x - 108.

b) To find (f/g)(x), we need to divide f(x) by g(x):

f(x) = x² + 7x + 12

g(x) = x² - 9

(f/g)(x) = f(x) / g(x)

        = (x² + 7x + 12) / (x² - 9)

To simplify the formula, we must factor both the numerator and the denominator:

f(x) = x² + 7x + 12 = (x + 4)(x + 3)

g(x) = x² - 9 = (x + 3)(x - 3)

(f/g)(x) = [(x + 4)(x + 3)] / [(x + 3)(x - 3)]

We may simplify the formula by removing the common factor of (x + 3):

(f/g)(x) = (x + 4) / (x - 3)

Therefore, (f/g)(x) = (x + 4) / (x - 3)

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Answer:

Step-by-step explanation:

Section 1

1: 2x + 20

2. 8x - 49
3: 7x + 21

4.8x - 4

5. 15x + 5

6. 12x + 15

7. 20x - 50

8. 21x + 14

9. 24x - 6

10. 45x - 18

11. 18x - 8

12. 30x + 9

13. 24x + 36

14. 25x - 20

15. 14x - 63

16. 32x + 20

17. 24x - 10

18. 42x - 18

19. 24x - 80

20. 48x - 32

9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

Answer:

45 cups

Step-by-step explanation:

The answer of the given question based on the relation is R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}.

Set listing notation is a way to represent a set by listing all of its elements between curly braces { }. If a set has a large or infinite number of elements, it may not be practical to list all the elements. In such cases, we can use set-builder notation to describe the set using a condition or a rule.

The "has the same parity as" relation on set A means that any two elements in A are related if they have the same parity (either both even or both odd).

So, we can write the relation R as a set of ordered pairs where each pair consists of two elements that have the same parity.

R = {(1,1), (3,3), (5,5), (2,2), (4,4), (6,6), (7,7), (1,3), (3,1), (1,5), (5,1), (1,7), (7,1), (2,4), (4,2), (2,6), (6,2), (3,5), (5,3), (3,7), (7,3), (4,6), (6,4), (5,7), (7,5)}

In this set, the ordered pair (x, y) indicates that x and y have the same parity. For example, (1, 3) is in R because 1 and 3 are both odd. Similarly, (2, 4) is in R because 2 and 4 are both even.

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