PLEASE HELP THIS IS ONE OF MY OVERDUE ASSIGNMENTS AND I NEED HELP!!!

Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).

In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.

Two disjoint events are independent if and only if at least one of them has zero probability.

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Given the function `f(x) = x + 4/x` and `y = f(x) = x`, we can equate both the equations to get the value of `x`. We get;`y = f(x) = x + 4/x = x`Subtracting `x` from both the sides, we get:`4/x = 0`Multiplying both sides with `x`, we get:`4 = 0`There is no solution to this equation as it is not true for any value of `x`.So, we cannot find any solution when `y = f(x) = x`.

Now, let's find the value of `x` for which `y = f(x) = x + 4/x`.We can write the equation as:`x^2 - xy + 4 = 0`Solving the above quadratic equation using the formula;`

x = [-b ± √(b^2 - 4ac)]/2a`We get;

`x = [y ± √(y^2 - 16)]/2`The given function is a one-to-one function, which means it has an inverse function. So, we can interchange `x` and `y` to get the inverse function, which is;

`x = y + 4/y`Solving for `y`, we get;`y^2 - xy + 4 = 0`Solving the above quadratic equation using the formula;`

y = [x ± √(x^2 - 16)]/2`Since the domain of the function `f(x)` is `[2,∞)`, the value of `x^2 - 16` is always non-negative. Therefore, we only need to consider the positive root.`y = [x + √(x^2 - 16)]/2`The x and y coordinates for the intersection are given by the equation:`(x, y) = (x, [x + √(x^2 - 16)]/2)`The value of `x` at the intersection point can be found by equating `y = x` and solving for `x`.We get:`

x = [x + √(x^2 - 16)]/2`Multiplying both sides by `2`, we get:`

2x = x + √(x^2 - 16)`Squaring both sides, we get:`

3x^2 - 16 = 0`Solving for `x`, we get:`x = ±√(16/3)`We need to consider only the positive root, since the domain of the function `f(x)` is `[2,∞)`.So, `x = √(16/3)` and `y = [√(16/3) + √(16/3 - 16)]/2`.The value of `y` can be simplified as follows;`y = [√(16/3) + √(16/3 - 16)]/2``y = [√(16/3) - √(32/3)]/2``y = (√3 - √6)/2`Therefore, the exact x and y coordinates of the intersection point are `(√(16/3), (√3 - √6)/2)`.

We know that the slope of the normal at `x = a` is given by the formula:`-1/f'(a)`So, we need to find the first derivative of the function `f(x)` and evaluate it at

`x = 4`.`f(x) = x + 4/x`Differentiating `f(x)` with respect to `x`, we get;`f'(x) = 1 - 4/x^2`At `x = 4`, we get:`f'(4) = 1 - 4/16``f'(4) = 3/4`Therefore, the slope of the normal at `x = 4` is `-1/f'(4) = -4/3`.The equation of the normal at `x = 4` can be written as:`y - f(4) = m(x - 4)`Where `m` is the slope of the normal at `x = 4`.Substituting `m = -4/3` and `f(4) = 5`, we get;`y - 5 = (-4/3)(x - 4)`Multiplying both sides by `-3`, we get;`-3y + 15 = 4(x - 4)`Expanding, we get;`4x - 3y - 1 = 0`Therefore, the equation of the normal at `x = 4` is `4x - 3y - 1 = 0`.

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Answer:

this is your ans

Step-by-step explanation:

mark brainliest please

Answer:

3 x 15 x 8 = 360

so, if there were 3 cone sizes, 25 flavors of ice cream, and 8 toppings, there would be about 360 different operations

r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.

r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)

The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.

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On Tuesday there was a loss of $13.6.

Loss is described as holding something or someone leaves or be taken away from you, a feeling of grief when something exists gone, or a decline in money. An example of loss exists when your parent dies. An example of loss stands when you are removed from your job.

A profit exists as an amount of money that accumulates when you exist paid more for something than it cost you to create, get, or do it.

Assume that the loss on Tuesday be x.

given that A certain stock showed a loss of 3.2 points per share, or $3.20 per share, on Monday.

Tuesday each share of that stock lost four and a quarter times Monday's loss.

as per given the loss on Tuesday is

\(x = (4.25) \times 3.2 \\ x = 13.6\)

Therefore the loss on Tuesday is $13.6.

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The tangent line at the given point (x, y) = (2, -1) has the parametric equations x(t) = 2t + 1 and y(t) = -3t²

x'(t) = 2t and y'(t) = -3t²

To find the parametric equations for the tangent line at t = 1, we need to calculate the derivatives x'(t) and y'(t) and evaluate them at t = 1.

Taking the derivatives of x(t) and y(t), we have x'(t) = 2t and y'(t) = -3t².

Evaluating x'(t) and y'(t) at t = 1, we get x'(1) = 2 and y'(1) = -3.

At t = 1, the particle's position is given by x(1) = 2 and y(1) = -1.

Therefore, the tangent line at the given point (x, y) = (2, -1) has the parametric equations x(t) = 2t + 1 and y(t) = -3t².


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Step-by-step explanation:

(a)

First:

Get AE using Pythagoras

\( {ae}^{2} = {6}^{2} + {8}^{2} \)

\( {ae}^{2} = 100\)

AE =10

Connect OM to form Traingle AOM.

AM=5cm (AE is 10 and AM=ME meaning that they are divided into two equal parts)

AM^2=OM^2+AO^2

5^2=OM^2+4^2

OM^2=5^2-4^2

OM=3

(B) OM is parallel to BE because of midpoint theorem

The Theorem states that The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

(C) AOM is a right angled triangle at O because angle AOM is 90°. Because OM is a perpendicular Line that bisects the chord of AB

9514 1404 393

Answer:

Step-by-step explanation:

Let q represent the number of quarters. Then the number of nickels is 68-q, and the number of cents in the jar is ...

  25q +5(68 -q) = 800

  20q +340 = 800 . . . . simplify

  20q = 460 . . . . . . . . subtract 340

  q = 23 . . . . . . . . . . . divide by 20; this is the number of quarters

  68-q = 45 . . . . . . . find the number of nickels

The jar contains 23 quarters and 45 nickels.

Answer:

P’(-5,2)

J’(0,3)

M’(1,2)

Y’(-4,0)

Step-by-step explanation:

when we rotate 90 degrees clockwise, we have that;

(x,y) becomes (-y,x)

Let us get the coordinates before rotation

P (2,5)

J( 3,0)

M ( 2,-1)

Y (0,4)

After the rotation, we have;

P’(-5,2)

J’(0,3)

M’(1,2)

Y’(-4,0)

Answer:

P’(-5,2)

J’(0,3)

M’(1,2)

Y’(-4,0)

Step-by-step explanation:

Answer:

(6,2)

Step-by-step explanation:

The period of y = -2sin (2/3 x -4) is 3π. These three-digit groups are called periods. 893,450,243, for instance, has three periods with three digits each, as is demonstrated below.

length of

\($\sin \left(\frac{2 x}{3}\right) \rightarrow \frac{(3)(2 \pi)}{2}=3 \pi$\)

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Answer:

outcome, sample space.AND EVENT

Answer:

{-9.5, 1,7}

Step-by-step explanation:

For y =f(x)

domain is list of all values of x and range is list of all values of y

Given

ƒ(x) = 3x – 5

domain = {–1.5, 2, 4}.

thus,

range will be value of f(x)

when x = -1.5

x = 2 and x = 4

Thus,

for x = -1.5

ƒ(x) = 3*-1.5 – 5 = -4.5 - 5 = -9.5

\

for x = 2

ƒ(x) = 3*2– 5 = 6 - 5 = 1

for x = 4

ƒ(x) = 3*4– 5 = 12 - 5 = 7

thus,

range of ƒ(x) = 3x – 5 is {-9.5, 1,7}

Jeremy has 45 nickels and Robin has 55 - 45 = 10 nickels.

What is the algebraic equations?

An algebraic equation is a mathematical statement that shows the equality between two expressions, typically with one or more variables.

Let x be the number of nickels Jeremy has. Then, the number of nickels that Robin has is 55 - x.

The total number of nickels they have together is 100, so we can write:

x + (55 - x) = 100

Simplifying the expression, we get:

55 = 100 - x

x = 45

Hence, Jeremy has 45 nickels and Robin has 55 - 45 = 10 nickels.

The equation to describe this situation is:

n = 45

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Step-by-step explanation:

the slope-intercept form of a line (= linear function) is

y = ax + b

"a" is the slope of the line and represents the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.

"b" is the y-intercept (the y value when x = 0; in other words, the y value where the line intercepts the y axis).

so, for the slope, let's compare 2 points. and let's pick just the first 2.

(1, 8) to (2, 11).

x changes by +1 (from 1 to 2).

y changes by +3 (from 8 to 11).

so, the slope is +3/+1 = 3/1 = 3

and our equation looks like

y = 3x + b

to get b, we use one point. I pick the first one for the smallest numbers :

8 = 3×1 + b = 3 + b

5 = b

the full line equation is therefore

y = 3x + 5

Answer:

In short, they are all solutions to your equation.

Step-by-step explanation:

I have attached the work to your problem.

Please see the attachment below. I clarified as much as possible and included all explanations/work.

I hope this helps.

Answer:

Polly do you know the formula for law of Cosines?  

find it if  you don't

Step-by-step explanation:

a = sqrt( b^2 +c^2 - 2bcCos(A) )

a = sqrt( 100 + 62.41 -34.197)

a = sqrt(128.213)

a = 11.323

a = 11.3  ( to the nearest tenth )

If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The mean of the normal distribution = 4

Standard deviation of the normal distribution = 1.5

The value of x = 5.5

The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution

Substitute the values in the equation

The z-score of the normal distribution  = (5.5 - 4) / 1.5

Substract the terms

= 1.5 / 1.5

= 1

Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The complete question is:

suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

The correct option is;

x + y = 1000

Step-by-step explanation:

The data from the table can be presented as follows

Adults (x)            \({}\)                              Children (y)

500                         \({}\)                              500

450                         \({}\)                              550

400                          \({}\)                             600

350                         \({}\)                              650

Therefore, we have the rate of change of the children, y to the adults, x, which is also the slope of the graph of the data given as follows;

The slope, m = dy/dx = (650 - 500)/(350 - 500) = 150/(-150) = -1

m = -1

The function of the graph in point and slope form, using the first point, becomes;

y - 500 = -1 × (x - 500) = -x + 500

∴ y - 500 = -x + 500

y + x = 500 + 500 = 1,000

Which gives

y + x = 1,000

y + x = x + y = 1,000

Answer:

Five less than the number than....... 8/n - 5 +7

Eight more than the product........ 8 +7n - 2

Five times the sum..... 5(n+7)

Twice the difference.... 2 (8-n)

Answer:

Blue:

\( \frac{8}{n} - 5 + 7\)

Green:

\(8 + 7n - 2\)

Orange:

\(5(n + 7)\)

Purple:

\(2(8 - n)\)

Answer:

they are opposite degrees so we can say that 4x=2y-x

Step-by-step explanation:

5x=2y and we complete 4x+(2y+x)=180. and then 5x+2y=180. put 2y from 5x. 4y=180 y= 45 and x= 18°

Now,

(2y + x)° + (2y - x)° = 180° ( straight angle )

or, 2y + x + 2y - x = 180°

or, 4y = 180°

◆ y = 45°

Then,

4x = 2y - x ( vertically opposite angle )

or, 4x = 2*45° - x

or, 5x = 90°

or, x = 90°/5

◆ x = 18 °

I hope it's help you...

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The function will have a value of 0 at x = 1. In that case, the variable "k" will have a value of 2.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Given f(x) = 3x³ + kx – 5, and the factor of the given function is (x – 1).

If the factor (x – 1) is zero. Then the value of the function will be zero.

x – 1 = 0

x = 1

At x = 1, the value of the function will be zero. Then the value of the variable 'k' will be calculated as,

f(1) = 3(1)³ + k(1) – 5

0 = 3 + k – 5

k = 5 – 3

k = 2

The function's value will be 0 at x = 1. The variable "k" will then have a value of 2.

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Answer:

Shark

Step-by-step explanation:

They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.

======================================================

Further explanation:

Answer:

Ashley is 22 years old.

Step-by-step explanation:

When Ashley was born, her mother was 22. That means that when Ashley turns 22, her mother will be 44(twice the age of Ashley). You can check by subtracting 15 from 22. The answer that yields is 7, 37 + 7 = 44, 44 is 2 times 22.

The age of ashley is 22 years.

To find the age of ashley.

What is age?

The amount of time during which someone or something has lived or existed. The length of time that a person has lived or a thing has existed.

Given that:

When Ashley was born, her mother was 22. That means that when Ashley turns 22, her mother will be 44(twice the age of Ashley). To check by subtracting 15 from 22. The answer that yields is 7,

37 + 7 = 44,

44 is 2 times 22.

So, the age of ashley is 22 years.

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For a factorable trinomial x² + bx + c, the absolute value of b can be less than, equal to, or greater than the absolute value of c, depending on the specific values of b and c.

The quadratic trinomial formula in one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero.

For any factorable trinomial of the form x² + bx + c, the absolute value of b can sometimes be less than, equal to, or greater than the absolute value of c. The relationship between the absolute values of b and c depends on the specific values of b and c.

Let's consider a few cases:

1. If both b and c are positive or both negative: In this case, the absolute value of b can be less than, equal to, or greater than the absolute value of c. For example:

  - In the trinomial x² + 2x + 3, the absolute value of b (|2|) is less than the absolute value of c (|3|).

  - In the trinomial x² + 4x + 3, the absolute value of b (|4|) is greater than the absolute value of c (|3|).

  - In the trinomial x² + 3x + 3, the absolute value of b (|3|) is equal to the absolute value of c (|3|).

2. If b and c have opposite signs: In this case, the absolute value of b can also be less than, equal to, or greater than the absolute value of c. For example:

  - In the trinomial x² - 4x + 3, the absolute value of b (|4|) is greater than the absolute value of c (|3|).

  - In the trinomial x² - 2x + 3, the absolute value of b (|2|) is less than the absolute value of c (|3|).

  - In the trinomial x² - 3x + 3, the absolute value of b (|3|) is equal to the absolute value of c (|3|).

Therefore, for a factorable trinomial x² + bx + c, the absolute value of b can be less than, equal to, or greater than the absolute value of c, depending on the specific values of b and c.

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The value of the test statistic is approximately -3.02. this value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.

The test statistic can be calculated using the formula: t = (X - μ) / (s / √n)

where X is the sample mean (4.0 psi), μ is the hypothesized population mean (4.1 psi), s is the population standard deviation (0.7 psi), and n is the sample size (150). Plugging in the values, we get: t = (4.0 - 4.1) / (0.7 / √150) ≈ -3.02

Therefore, the value of the test statistic is approximately -3.02. This value represents how far the sample mean is from the hypothesized population mean in terms of the standard error of the mean.

A negative value indicates that the sample mean is lower than the hypothesized population mean. A value of -3.02 is quite far from zero, suggesting that the engineer's claim that the valve performs to specifications may be false.

The next step would be to determine the corresponding p-value and compare it to the level of significance to make a decision about rejecting or failing to reject the null hypothesis.

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