Suppose that on each play of a game, a gambler either wins 1 with probability p or loses 1 with probability 1–p (or q). The gambler keeps betting until she or he is either up a total of n or down a total of m. What is the probability the gambler will quit an overall winner? You must consider both cases when p = 0.5 and when p ≠ 0.5

Answer:

Point Q

Step-by-step explanation:

Point Q corresponds to Point V, because if you turn the green triangle around, it matches almost exactly the same.

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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The value of the angle x in the parallel lines is 20.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles,  same interior angles, same exterior angles etc.

Therefore, a and b are the parallel lines. The parallel lines are cut by a transversal.

Same-side exterior angles are supplementary.

Hence,

5x + 10 + 4x - 10 = 180

5x + 4x  = 180

9x = 180

divide both sides by 9

x = 180 / 9

x = 20

Therefore,

x = 20

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Answer: $13, don't just copy that answer actually try to understand it. ⬇️

Step-by-step explanation: Think of it as a number line.

$12-$12.10-$12.20-$12.30-$12.40-$12.50-$12.60-$12.70-$12.80-$12.90$13

the $12.50 is directly in the middle of $12 and $13. Lets say it $12.51 now its not directly in the middle, but more over to the $13, so then we would go up to 13$ which is the nearest dollar. If it were $12.49 then it would be closer to the $12, so we would go down to $12.

I hope this helps!

Both equations are linear, so I'll use the integrating factor method.

The first ODE

\(xy' + (x+1)y = 0 \implies y' + \dfrac{x+1}x y = 0\)

has integrating factor

\(\exp\left(\displaystyle \int\frac{x+1}x \, dx\right) =\exp\left(x+\ln(x)\right) = xe^x\)

In the original equation, multiply both sides by eˣ :

\(xe^x y' + (x+1) e^x y = 0\)

Observe that

d/dx [xeˣ] = eˣ + xeˣ = (x + 1) eˣ

so that the left side is the derivative of a product, namely

\(\left(xe^xy\right)' = 0\)

Integrate both sides with respect to x :

\(\displaystyle \int \left(xe^xy\right)' \, dx = \int 0 \, dx\)

\(xe^xy = C\)

Solve for y :

\(y = \dfrac{C}{xe^x}\)

Use the given initial condition to solve for C. When x = 1, y = 2, so

\(2 = \dfrac{C}{1\cdot e^1} \implies C = 2e\)

Then the particular solution is

\(\boxed{y = \dfrac{2e}{xe^x} = \dfrac{2e^{1-x}}x}\)

The second ODE

\((1+x^2)y' - 2xy = 0 \implies y' - \dfrac{2x}{1+x^2} y = 0\)

has integrating factor

\(\exp\left(\displaystyle \int -\frac{2x}{1+x^2} \, dx\right) = \exp\left(-\ln(1+x^2)\right) = \dfrac1{1+x^2}\)

Multiply both sides of the equation by 1/(1 + x²) :

\(\dfrac1{1+x^2} y' - \dfrac{2x}{(1+x^2)^2} y = 0\)

and observe that

d/dx[1/(1 + x²)] = -2x/(1 + x²)²

Then

\(\left(\dfrac1{1+x^2}y\right)' = 0\)

\(\dfrac1{1+x^2}y = C\)

\(y = C(1 + x^2)\)

When x = 0, y = 3, so

\(3 = C(1+0^2) \implies C=3\)

\(\implies \boxed{y = 3(1 + x^2) = 3 + 3x^2}\)

For the coordinates and their weights, the weight average is 5

The given parameters are:

Coordinate 3 has a weight of 1

Coordinate 6 has a weight of 2

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

Substitute the known values in the above equation

So, we have the following equation

Weight average = (3 * 1 + 6 * 2)/(1 + 2)

Evaluate the product in the above equation

So, we have the following equation

Weight average = (3 + 12)/(1 + 2)

Evaluate the sum in the above equation

So, we have the following equation

Weight average = (15)/(3)

Evaluate the quotient in the above equation

So, we have the following equation

Weight average = 5

Hence, the weight average of the coordinates is 5

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Complete question

The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .

Find the weighted average.

The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

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Answer:

16

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

6(y-2) would be 6y-12

Step-by-step explanation:

Answer:

Team A has 16 points

Team B has 4 points

Step-by-step explanation:

let A = 12 + B

also, let A = 4B

therefore, since A = A we can say that 12 + B = 4B

12 + B = 4B

12 = 3B

B = 4

A = 12 + 4 or 16

Answer:

15/56

Step-by-step explanation:

3/7 x 5/8

=> 15/56

Since 15/56 cannot be simplified, 15/56 is our simplified form.

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Answer: A

Step-by-step explanation: c shifts the graph up or down.

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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Answer:

Step-by-step explanation:

we know the sum in an triangle will be 180-(47+39)=94

The step to solve the system of equations using is

Step 1 : A-Since the second equation is solved for x, substitute 6y + 1 for x in the first equation.

Step 2: C-Solve the resulting equation for y

Step 3: B-Substitute the value for y into either equation to find x.

Step 4: D- Write the solution as an ordered pair, and check the solution.

From the question, we are to match each step to show how to solve the system of equations.

The given system of equations is

7x - 2y = -1

x = 6y + 1

Step 1: Since the second equation is solved for x, substitute 6y + 1 for x in the first equation

7(6y + 1) - 2y = -1

Step 2: Solve the resulting equation for y

7(6y + 1) - 2y = -1

42y + 7 - 2y = -1

42y - 2y = -1 - 7

40y = -8

Divide both sides by 40

y = -8/40

y = -1/5

Step 3: Substitute the value for y into either equation to find x

x = 6y + 1

x = 6(-1/5) + 1

x = -6/5 + 1

x = -1/5

Step 4: Write the solution as an ordered pair, and check the solution

7x - 2y = -1

7(-1/5) - 2(-1/5) = -1

-7/5 + 2/5 = -1

-1 = -1

True

x = 6y + 1

-1/5 = 6(-1/5) + 1

-1/5 = -6/5 + 1

-1/5 = -1/5

True

Hence, the steps to solve the system of equations using is

Step 1: A

Step 2: C

Step 3: B

Step 4: D

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Answer:

Step-by-step explanation:

The constant of the expression represents the  installation charge, and the coefficient of x represents the number of computer.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an equation that the total cost of the computers, including an installation charge for all the computers:

y = $115x+$100

y is the total cost.

Here the constant of the expression $100 represents the installation charge and the coefficient of x represents the number of computer,

For 1 computer, the total cost be:

y = $215

For 2 computers the total cost be:

y = $330

Hence, the constant of the expression represents the  installation charge, and the coefficient of x represents the number of computer.

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The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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The associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

Now, The p-value for a one-tailed t-test with a sample size of 18 and a test statistic of 1.9,

Hence, we need to look up the t-distribution table.

So, Using a one-tailed test with,

df = n - 1

= 18 - 1 = 17 degrees of freedom

We find that the area to the left of 1.9 under the curve is 0.0359.

This means that there is a 3.59% probability of observing a t-statistic less than or equal to 1.9 if the null hypothesis is true.

Therefore, the associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

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Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

I think is D

Step-by-step explanation:

because

R:622 and Y:410

Answer:

A. has a right angle

thats one

Answer:

I think it is A and D. Not 100% sure tho.

Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

\(\sqrt{(x-1)^{2} +(y-1)^{2} }\) = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

\(x^{2}\) - 2x + \(y^{2}\) - 4y + 20 = 0

Completing the square for x and y, we get:

\((x-1)^{2}\)  + \((y-1)^{2}\)  = \(6^{2}\)

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer:

18.86

Step-by-step explanation:

5 ⟌94.3

90 ÷ 5 = 18

   18

5 ⟌94.3

    -90

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

      4.3

cant divide by 4 so add a decimal

5 × 0.8 = 4

   18.8

5 ⟌4.3

   - 4.0

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

     0.3

5 × 0.06 = 0.3

  18.86

5 ⟌0.3

  - 0.3

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

     0

I hope this helps!

I will let you decide what counts as a second step, I'm going to write out all the steps.

starting from original equation

49n+986=-43

49n=-1029

n=-21

:D

Answer:

The second step is subtracting 986 from both sides

Step-by-step explanation:

The reason is because you want to isolate the variable. You can't solve it if there are numbers along with the variable in an equation.

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

Option D is the correct answer.

We have,

We need to isolate the absolute value |x + 2| on one side of the inequality.

We subtract 7 from both sides.

|x + 2| > 3

Next, we can split this inequality into two separate inequalities, one for when the expression inside the absolute value is positive, and one for when it is negative:

x + 2 > 3

or

- (x + 2) > 3

Solving for x in the first inequality.

x > 1

Solving for x in the second inequality.

-x - 2 > 3

Adding 2 to both sides and multiplying by -1.

x < -5

So the solution set for the inequality |x + 2| + 7 > 10 is the set of all x-values that satisfy either x > 1 or x < -5.

Using interval notation.

(-∞, -5) U (1, ∞)

Thus,

The solution set includes all real numbers less than -5, and all real numbers greater than 1, but does not include -5 or 1 themselves.

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