The probability of event a is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true ?

__A P(BlA) = y

__B P(Al B) =y

__C P(BlA = x

__D P( and B) = x + y

Answer:

\(B)~ 3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\)

Step-by-step explanation:

\(3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\\\\\\= 3\sqrt{\dfrac 75} + i\sqrt{\dfrac 95 }\\\\\text{It is now in the standard form of a complex number (a+bi).}\)

Answer:

Step-by-step explanation:

\(d^2=(x_2-x_1)^2+(y_2-y_1)^2\\ \\ d^2=(-2-1)^2+(5-9)^2\\ \\ d^2=9+16\\ \\ d^2=25\\ \\ d=\sqrt{25}\\ \\ d=5\)

Answer:

PQ = 5

Step-by-step explanation:

Distance Formula

d = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }\)

d = \(\sqrt{{(1} - -2)^2 + (9 - 5)^2 }\)

d = \(\sqrt{3^2+4^2}\)

d = \(\sqrt{9+16}\)

d =\(\sqrt{25}\)

d=5

PQ = 5

By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Answer:

40

Step-by-step explanation

Answer:

40

Step-by-step explanation:

got it right on edge

The vector whose magnitude is 3 and whose components I. the I and j direction are equal is; <3√2/2i, 3√2/2j>.

It follows that the magnitude of a vector in terms of its components in the i and j direction is;

M = √(x² + y²).

On this note, since the i and j components are equal; x = y and hence, we have;

3 = √(x² + x²).

3² = 2x²

x² = 9/2

x = 3/√2

x = 3√2/2

On this note, the required vector which is as described is; <3√2/2i, 3√2/2j>.

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Step-by-step explanation:

thanks for the free points!

have a great day!

Answer:

wym free points do you get points for answering?

Step-by-step explanation:

Answer:

I do this program too, do you have any apps/websites that help with this program??

Step-by-step explanation:

Answer:

150 kg

Step-by-step explanation:

30% of 500 kg

\(=0.30*500\)

\(=150\)

150 kg

The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

7. D) 61in

8. A) 57in

9. A) 47in

Step-by-step explanation:

The perimeter is the distance around the area of a 2-dimensional figure. it can be found by adding up all of the sides of the figure. One can use this to solve for the value of the parameter (x). Then substitute the value back in to find the value of the side.

7.

AB + BC + AC = 145

Substitute,

2x + 2x + 5 + x = 145

Simplify,

5x + 5 = 145

Inverse operations,

5x + 5 = 145

-5

5x = 140

/5

x = 28

Substitute,

AC = 2x + 5= 2(28) + 5 = 61

8.

AB + BC + AC = 135

Substitute,

2x + 2x + 5 + x = 135

Simplify,

5x + 5 = 135

Inverse operations,

5x + 5 = 135

-5

5x = 130

/5

x = 26

Substitute,

AC = 2x + 5 = 2(26) + 5 = 57

9.

AB + BC + AC = 122

Substitute,

x + 22 + 2x + x = 122

Simplify,

4x + 22 = 122

Inverse operations,

4x + 22 = 122

-22

4x = 100

/4

x = 25

Substitute,

AB = x + 22 = 25 + 22 = 47

Answer:

-5.25>-5 3/10

Step-by-step explanation:

let's convert -5 3/10 into a decimal

which is

-5.3 or -5.30

-5.25 and -5.30

because it's negative, the lowest number is the greatest number so

-5.25 is greater than -5.30

Answer: Do you mean this:  -1 1/2 + 1/8=?

If so, the answer is \(-\frac{11}{8} = -1.375\)

Step-by-step explanation:

Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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Savannah walks 8/9 of a mile to school. Wendy walks 2/3 of a mile to school. who walks a further distance?

Answer:

Savannah

Answer:

Savannah walks a further distance

Step-by-step explanation:

8/9 is a larger fraction than 2/3. This might be easier to see if we make these fractions have the same denominator.

\(\frac{8}{9} and \frac{6}{9}\)

Therefore, savannah walked a further distance than Wendy.

The equation of the function in the form y = mx + b, would be y = 5x + 15.

We can start by using the two data points to find the slope of the linear equation:

When x = 5, y = 40

When x = 12, y = 75

Using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (75 - 40) / (12 - 5) = 35 / 7 = 5

To find the y-intercept (b), we can plug in one of the data points:

y = mx + b

40 = 5(5) + b

b = 15

So the y-intercept is 15.

Therefore, the equation of the function in the form y = mx + b is:

y = 5x + 15

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Answer:

$43,260

Step-by-step explanation:

You have the 3% annual income, which you can convert to a decimal. This gives:

42000 * 1.03

42000 represents Blair's initial income, and 0.03 represents the 3% increase.

I chose 1.03 because I don't have to subtract 97% and add it to 42000.

Answer: To find the probability that a person chosen at random has a median lifetime income between 1 to 2 standard deviations below the mean, we need to calculate the area under the normal distribution curve within that range.

First, let's define the variables:

μ = Mean lifetime income = $25800

σ = Standard deviation = $14000

We want to find the probability of having a median lifetime income between 1 to 2 standard deviations below the mean.

1 standard deviation below the mean would be μ - σ, and 2 standard deviations below the mean would be μ - 2σ.

μ - σ = $25800 - $14000 = $11800

μ - 2σ = $25800 - 2 * $14000 = $-2200

Next, we need to find the z-scores for these values. The z-score represents the number of standard deviations a given value is from the mean in a standard normal distribution.

For μ - σ:

z1 = (11800 - μ) / σ = (11800 - 25800) / 14000 ≈ -1.5714

For μ - 2σ:

z2 = (-2200 - μ) / σ = (-2200 - 25800) / 14000 ≈ -2.2857

Using a standard normal distribution table or a statistical software, we can find the corresponding probabilities associated with these z-scores.

The probability of having a median lifetime income between 1 to 2 standard deviations below the mean is the difference between the probabilities corresponding to z1 and z2.

P(1 to 2 standard deviations below the mean) = P(z1 < Z < z2)

You can refer to a standard normal distribution table or use statistical software (such as Excel, R, or Python) to calculate the probabilities. The exact values may vary depending on the specific table or software used.

Answer:

30 FEET TALL

Step-by-step explanation:

Answer: 30 ft

Step-by-step explanation:

Set up a proportional equation to solve for how tall the oak tree will be.

\(\frac{20}{8} = \frac{x}{12}\)    cross product

8x = 240

x= 30

Answer: 3

Distribute

Subtract the numbers

Simplify

Answer:

$300

Step-by-step explanation:

(5000)(2)(3/100)

=300

9514 1404 393

Answer:

Step-by-step explanation:

The number of filled bags will be 35 for each hour (x) that Jackson works, in addition to those already filled. So, the total number filled after x hours is ...

  35x + 20

We want that number to be at least (greater than or equal to) 1000, so the relation is ...

  35x +20 ≥ 1000

__

To solve this, we first subtract 20:

  35x ≥ 980

Now, we can divide by the coefficient of x.

  x ≥ 980/35

  x ≥ 28 . . . . .  the solution

Answer:

~

Step-by-step explanation:

To make it easier to graph using a translation, we can rewrite the given equation as:

y - 5 = √√4x + 16

This is obtained by subtracting 5 from both sides of the equation.

The graph of the original equation y = √√4x+16 +5 can be obtained by taking the graph of y = √√4x + 16 and shifting it upwards by 5 units. The graph of y = √√4x + 16 is a square root function that has a vertical stretch of 2, a horizontal compression of 4, and a vertical translation of 16 units upwards. So the graph of the given equation y = √√4x+16 +5 will be the same as the graph of y = √√4x + 16, but shifted upwards by 5 units.

The product of the two linear functions is:

(fg)(x) =  8x^2 + 10x  - 3

A general linear funuction can be written as:

f(x)= a*x  +b

Let's say that our functions are:

f(x) = ax + b

g(x) = cx + d

The sum is:

(f + g)(x) = ax + b + cx + d = (a + c)x + (b + d)

(f - g)(x) = ax + b - cx - d  =(a - c)x + (b - d)

And we know that:

(f+g)(x)=-6x-2 and (f-g)(x)=-2x+4.

Then we can write:

(a + c)x + (b + d) = -6x - 2

(a - c)x + (b - d) = -2x + 4

Then we have 4 equations:

a + c = -6

b + d = -2

a  - c= -2

b - d = 4

Solving these we can get:

a = -4

c = -2

b = 1

d = -3

(you can check these values)

The two linear functions are:

f(x) = -4x + 1

g(x) = -2x - 3

The product is:

(fg)(x) = (-4x + 1)*(-2x - 3) = 8x^2 + 12x - 2x - 3

                                       = 8x^2 + 10x  - 3

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Option C

f^1(x) = (4x + 3)/(x-1)

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

¿que? no tiene sentido

Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

Answer:

x = 0 ((No Solution))