suppose x and y are events in a sample space such that p(x|y) = 1 3 and p(y) = 1 6 . what is p(x ∩ y)?

Its not must that 3x have to be the one to be subtracted. You could take 8x as well.

But always subtract from the smaller one (in this case 3x) because its easier.

If you are subtracting 3x-3x and 8x-3x, the equation would be like

4 = 5x - 16

5x = 4+16

5x = 20

x = 4

The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Answer:

24 inches

Step-by-step explanation:

We can find different sides of a right angle triangle using Pythagorean theorem: \(c^2 = a^2+b^2\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other sides.

Therefore, we can re-arrange the equation for one of the other sides.

\(c^2-b^2=a^2\).

Since we know these two sides all we have to do is put them into the equation:

\((30)^2-(18)^2=a^2\)

\(a^2 = 576\\a= 24\)

Therefore, the missing side is 24 inches.

The statement that explains how to find the quotient is "write -3 ¹/₃ as -10/3, and find the reciprocal of 4/9 as 9/4.

option B.

To divide a mixed number by a fraction, follow these steps:

Step 1: Convert the mixed number to an improper fraction.

In this case, -3 ¹/₃ can be converted to an improper fraction as follows:

-3 ¹/₃ = (-3 x 3 + 1) / 2 = -10/3

Step 2: Invert the divisor fraction.

The divisor fraction is 4/9, so its reciprocal (inverted form) is 9/4.

Step 3: Multiply the dividend (improper fraction) by the reciprocal of the divisor (inverted form).

-10/3 ÷ 9/4 = -10/3 x 9/4

Step 4: Simplify the result, if possible.

Multiply the numerators and denominators:

-10/3 x 9/4 = -90/12 = - -7¹/₂

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Answer:

\(\frac{dy}{dx} = \frac{sin(y) + ycos(x)}{sin(x) - xcos(y)}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Step-by-step explanation:

Step 1: Define

\(ysin(x) = xsin(y)\)

Step 2: Differentiate

Implicit Differentiation

if I did it right then it's $32.38.

Simplify the given expression as follows:

The missing numbers are - 5 and - 4.

Answer:

258.3 sq inches

Step-by-step explanation:

Use the sphere surface area formula, SA = 4\(\pi\)r²

The diameter is 9.07 inches, so the radius is 4.535 inches.

Plug in 3.14 as pi and 4.535 as r, and solve:

SA = 4\(\pi\)r²

SA = 4(3.14)(4.535)²

SA = 258.3

So, the surface area is approximately 258.3 sq inches

Answer:

  (-1, -5)

Step-by-step explanation:

Each point on a graph is the ordered pair (x, f(x)). Then the point M(-1 -3) is the ordered pair (-1, f(-1)) where f(-1) = -3.

A point on the shifted graph will be ...

  (x, f(x) -2)

Then for x = -1, the point is ...

  (-1, f(-1) -2) = (-1, -3 -2) = (-1, -5)

The minimum on the shifted curve is M'(-1, -5).

_____

Additional comment

f(x) is the y-coordinate of a point on a graph. Then f(x) -2 is the y-coordinate shifted down 2 units.

The inequality that determine the the number of 120-kilogram crates that can be loaded into the shipping container is 27500 ≤ 14300 + 120x.

The solution of the inequality is 110 ≤ x.

A shipping container will be used to transport several 120-kilogram crates across the country by rail.

The greatest weight that can be loaded into the container is 27500 kilograms.  Other shipments weighing 14300 kilograms have already been loaded into the container.

The inequality to determine x, the number of 120-kilogram crates that can be loaded into the shipping container can be represented as follows:

Therefore,

x = the number of 120-kilogram crates that can be loaded into the shipping container

27500 ≤ 14300 + 120x

Let's solve for x

27500 ≤ 14300 + 120x

27500 - 14300 ≤ 120x

13200 ≤ 120x

divide both sides by 120

13200 ≤ 120x

13200 / 120 ≤ x

110 ≤ x

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We have a continuous random variable over -2 < x < 5 so p(x = 1) = 0 because the probability at any given point for any continuous random variable is always 0.

Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.

Probability at any given position is always zero for any continuous random variable. This is because the probability of a single value occurring for a continuous random variable is always 0 because the range of values for the random variable is infinite and therefore the probability of a single value occurring is 0.

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Answer:

The answer is 5x - 13

Step-by-step explanation:

All we do is add the x's and the other numbers.

2 + 3 = 5 and 10 + 3 = 13

So, the equation is 5x - 13

Hope this helps! :)

T41 - T41 OR a42 - a41 = (405 from the arithmetic part) - (approximately 5 * 2^40 from the geometric part)

To calculate T41 or a42 - a41 in the given sequence, we first need to identify the pattern for both the arithmetic and geometric parts of the sequence.

Arithmetic part: The common difference between consecutive terms in the arithmetic part is 10.

Geometric part: The common ratio between consecutive terms in the geometric part is 2.

Now, let's calculate T41 or a42 - a41:

The first term of the sequence is 5.

Arithmetic part:

The 41st term of the arithmetic part can be calculated using the formula:

T(n) = a + (n - 1) * d

where T(n) is the nth term, a is the first term, n is the term number, and d is the common difference.

Using the formula, we can calculate T41 of the arithmetic part:

T(41) = 5 + (41 - 1) * 10

T(41) = 5 + 40 * 10

T(41) = 405

Geometric part:

The 41st term of the geometric part can be calculated using the formula:

T(n) = a * r^(n - 1)

where T(n) is the nth term, a is the first term, n is the term number, and r is the common ratio.

Using the formula, we can calculate T41 of the geometric part:

T(41) = 5 * 2^(41 - 1)

T(41) = 5 * 2^40

T(41) = 5 * 2^40 (approximately)

Finally, we can calculate T41 or a42 - a41 by summing the results from the arithmetic and geometric parts:

T41 - T41 OR a42 - a41 = (405 from the arithmetic part) - (approximately 5 * 2^40 from the geometric part)

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The parametric equations (x, y) = (t - 1, t^2 - 1) describe a curve that is a polynomial of degree 2, which corresponds to option B.

In the given parametric equations, the x-coordinate is defined as x = t - 1, and the y-coordinate is defined as y = t^2 - 1. These equations show that both x and y are expressed as functions of t. When we eliminate the parameter t, we can rewrite the equations in terms of x and y only.

Rearranging the first equation, we have t = x + 1. Substituting this expression for t into the second equation, we get y = (x + 1)^2 - 1. Expanding and simplifying, we have y = x^2 + 2x.

The resulting equation, y = x^2 + 2x, represents a polynomial of degree 2, also known as a quadratic equation. The graph of this equation is a parabola. Thus, the given parametric equations describe a curve that is a polynomial of degree 2, which corresponds to option B.

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The limit of \(\lim_{x \to \infty} \frac{lnx}{x}\)  using L'Hospital rule is 0.

According to the given question.

We have to find the limit of ln(x)/x when x approaches to infinity.

If we let x = ∞, we get an indeterminate form \(\frac{\infty}{\infty}\) ie. \(\frac{ln(x)}{x} = \frac{\infty}{\infty}\).

And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.

Therefore, defferentiating numerator ln(x) and x with respect to x.

\(\implies \frac{d(ln(x))}{dx} = \frac{1}{x}\) and \(\frac{d(x)}{dx} =1\)

So,

\(\lim_{x\to \infty}\frac{\frac{1}{x} }{1}\)

\(= \lim_{x \to \infty} \frac{1}{x}\)

As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.

Therefore,

\(\lim_{x \to \infty} \frac{1}{x} = 0\)

Hence, the limit of \(\lim_{x \to \infty} \frac{lnx}{x}\) is 0.

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Answer:

x = 4.

Step-by-step explanation:

64 = x^3

x^3 = 64

\(\sqrt[3]{x^3} = \sqrt[3]{64}\)

\(\sqrt[3]{x^3} = \sqrt[3]{4 * 4 * 4}\)

\(\sqrt[3]{x^3} = \sqrt[3]{4^3}\)

x = 4.

Hope this helps!

Answer:

x = 3

The cube root of 64 is 4 because 4 x 4 x 4 = 64.

Cube roots have 3 identical factors, while square roots have 2 identical factors.

Hope this helps you!

The overlapping area between the line y = x - 6 and the curve y = 6/x and evaluating the integer coordinates within this region, we find that there are 13 lattice points contained in R.

The region defined by the simultaneous conditions x - y < 6, xy < 6, and x > 0 can be determined by graphing the inequalities.

However, since the question asks for the number of lattice points in the region, we can solve it algebraically.

First, let's consider the condition x - y < 6. If we rearrange this inequality, we get y > x - 6. This represents a region above the line y = x - 6 on the coordinate plane.

Next, let's analyze the condition xy < 6. We can rewrite this inequality as y < 6/x.

This represents a region below the curve y = 6/x.

To find the region that satisfies both conditions, we need to identify the overlapping area between the line y = x - 6 and the curve y = 6/x. This overlapping area is our region of interest, denoted as R.

To determine the lattice points within R, we need to find the integer coordinates (x, y) that satisfy both inequalities.

Since x > 0, we can start by evaluating the integer values of x from 1 to 5. For each x-value, we can calculate the corresponding y-value using the equation y = x - 6. If this y-value is less than 6/x, it satisfies both conditions and is considered a lattice point within R.

For example, when x = 1, y = 1 - 6 = -5, which is less than 6/1. So the lattice point (1, -5) is within R.

By repeating this process for x = 2, 3, 4, and 5, we can determine the other lattice points within R.

After evaluating all possible integer values of x, we find that R contains a total of 13 lattice points.

Therefore, the answer to the question is that the region R contains 13 lattice points.

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Answer:

$39.77

Step-by-step explanation:

The revenue earned is

R=$5804.45. Option D

This is further explained below.

Generally, Revenue is the entire amount of money earned through the sale of products and services connected to the principal activities of the firm. In accounting, revenue refers to the total amount of income generated.

The term "commercial income" is synonymous with "sales" and "turnover" in the business world. Interest, royalties, and many other fees may all be sources of income for certain businesses.

In conclusion, the equation for Revenue is  mathematically given as

R=Profit + expenses

R=4135+((61*6.45)+1276)

R=$5804.45

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Answer:

50%

Step-by-step explanation:

There are two sides on a penny and there have a 50% chance each

The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

To show that each function is O(x^2) using the Definitional proof, we need to find a constant c and a positive number k such that |f(x)| ≤ c|x^2| for all values of x greater than some value k.

(a) For function f(x) = x:

We need to find a constant c and k such that |x| ≤ c|x^2| for all x > k.

Let's choose c = 1 and k = 1.

|f(x)| = |x| ≤ 1 * |x^2| for all x > 1.

Therefore, f(x) = x is O(x^2).

(b) For function f(x) = 9x + 5:

We need to find a constant c and k such that |9x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 14 and k = 1.

|f(x)| = |9x + 5| ≤ 14 * |x^2| for all x > 1.

Therefore, f(x) = 9x + 5 is O(x^2).

(c) For function f(x) = 2x^2 + x + 5:

We need to find a constant c and k such that |2x^2 + x + 5| ≤ c|x^2| for all x > k.

Let's choose c = 8 and k = 1.

|f(x)| = |2x^2 + x + 5| ≤ 8 * |x^2| for all x > 1.

Therefore, f(x) = 2x^2 + x + 5 is O(x^2).

(d) For function f(x) = 10x^2 + log(x):

We need to find a constant c and k such that |10x^2 + log(x)| ≤ c|x^2| for all x > k.

Let's choose c = 11 and k = 1.

|f(x)| = |10x^2 + log(x)| ≤ 11 * |x^2| for all x > 1.

Therefore, f(x) = 10x^2 + log(x) is O(x^2).

In each case, we have found a constant c and a value k such that the inequality |f(x)| ≤ c|x^2| holds for all x greater than k. This satisfies the definition of f(x) being O(x^2).

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Answer:

8

Step-by-step explanation:

Take away the monthly price, since that's going to be included in the total price

20.55 - 4.95 = 15.60

Now, divide the remaining money by the cost per DVD

15.60 / 1.95 = 8

They have bought 8 DVDs

Hope this helps

Answer:

DBE=50 degrees

ABD=140 degrees

Step-by-step explanation:

CA is a line which means that it equals 180 degrees total. Subtract the other angle measurements to find that DBE is 50 degrees. Then add the angles DBE, EBF, and FBA. Hope this helps!

APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100

The formula for APR (annual percentage rate) is given as;

APR = ((F / P) x 12) x 100

Where;

The annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;

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Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!