A person draws balls twice, with replacement, from a urn which contains only one red ball and one black ball. (a) (5 pt) Using the notations R and B to denote the red balls and black balls, respectively, list all the elements of the sample space S. (b) (5 pt) Which elements are in the event A that the person draws one red ball and one black? (c) (5 pt) What is P(A)?

Answer:

It's blank

Step-by-step explanation:

Answer:

Combine like terms

Step-by-step explanation:

Answer:

5^x - 5^-x

Step-by-step explanation:

g(x) = 5^-x

h(x) = 5^x

We want h(x) - g(x)

h(x) - g(x) = 5^x - 5^-x

This cannot be simplified

Given:

Find-: what does point (10,67873) represent.

Sol:

Where,

At point.

Point (10, 67873) represents after the 10-year value of the random tractor is 67873.

Check value for x = 10 year.

The rate at which the gas powered pump deliver water is 160.9 litres per seconds

The gas powered water pump delivers 42.50 gallons of water per minute.

Therefore,

1 gallon = 3.78541 litres

42.50 gallons = ?

cross multiply

volume = 42.50 × 3.78541 = 160.879925 litres

Hence,

60 seconds = 1 minutes

1 second = ?

time = 1 / 60 = 0.01666666666 seconds

Hence,

rate = 160.9 litres per second

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Answer:

By eating plants or other animals that contain nitrogen

Answer:

Use the formula r = d/t. Your rate is 24 miles divided by 2 hours, so: r = 24 miles ÷ 2 hours = 12 miles per hour. Now let's say you rode your bike at a rate of 10 miles per hour for 4 hours.

Answer:

13.23

Step-by-step explanation:

Answer: When we use the order of operations to solve this expression we get the Answer 13.23 Hope this helps

Step-by-step explanation:

If we change the scale of the model to 1 inch = 5 feet, the new model dolphin would be 2 inches long.

The size of the actual dolphin in feet is equal to the size of the model dolphin in inches, multiplied by the scale of the model. Since the scale of the model is 1 inch = 2.5 feet, the size of the actual dolphin in feet is equal to 4 inches * 2.5 feet/inch = 10 feet.

If we change the scale of the model to 1 inch = 5 feet, the size of the new model dolphin in inches is equal to the size of the actual dolphin in feet, divided by the new scale. Thus, the size of the new model dolphin in inches is equal to 10 feet / (5 feet/inch) = 2 inches.

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Step-by-step explanation:

that means we divide 2/3 by 4.

2/3 / 4 = 2/3 / 4/1 = 2/3 × 1/4 = 2/12 = 1/6

so each quarter of the remaining 2/3 pizza is actually 1/6 of the complete pizza.

Answer:

x = 3

Step-by-step explanation:

 (3 • (5x - 15)) -  15 • (x - 3)  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  5x - 15  =   5 • (x - 3)  

Equation at the end of step

3

:

 15 • (x - 3) -  15 • (x - 3)  = 0  

STEP

4

:

Pulling out like terms

4.1      Pull out     15  

Pulling out like terms :

4.2      Pull out     x-3  

After pulling out, we are left with :

     15 • x-3 • ( 1  *  1 +( (-1)  *  (-1) ))

Equation at the end of step

4

:

 30 • (x - 3)  = 0  

STEP

5

:

Equations which are never true

5.1      Solve :    30   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

One solution was found :

x = 3

The required value of a for which the solution of the inequality is all real numbers is a > 4.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

a(x + 3) < 5x + 15 - x

or, a(x + 3) < 4x + 15

Now let us solve for x first,

⇒ ax + 3a  < 4x + 15

Subtract 3a from both sides we get,

ax < 4x + 15 - 3a

Subtract 4x from both sides we get,

ax - 4x < 15 - 3a

or, (a - 4)x < 15 - 3a

Dividing both the side by (a - 4) we get,

x < (15 - 3a) / (a - 4)

Now for solutions to be real numbers,

a - 4 > 0

subtracting 4 both the side we get,

⇒ a > 4

this is the required value of a for which the solution of the inequality is all real numbers

Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.

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The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.

Answer:

b > 15

Step-by-step explanation:

25 1/2 - 1 1/2b < 3

25 1/2 = 51/2 = 25.5

1 1/2 = 3/2 = 1.5

25.5 - 1.5b < 3

-1.5b < -22.5

b > 15

Answer:

Each interior angle measures 108 degrees. All of the angles are congruent. The sum of the measures of the interior angles is 180(5 – 2)°.

The probability of the spinner landing on 9 or 11 is 2/10 or 1/5. This is because there are a total of 10 sections on the spinner and only 2 of them are labeled 9 or 11.

As for the coin, the probability of getting tails is 1/2, since there are only two possible outcomes - heads or tails. To find the probability of both events happening, we need to multiply the probabilities together. So the probability of the spinner landing on 9 or 11 and getting tails on the coin is (1/5) x (1/2) = 1/10 or 0.1. In other words, there is a 10% chance of both events happening together. It is important to note that the outcome of the spinner and the coin flip are independent events, which means that the outcome of one does not affect the outcome of the other.

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Step-by-step explanation:

6x² - 6x - 72 = 0

Using. Completing the squares method.

6x²/6 - 6x/6 = 72/6

x² - x = 12

Take the coefficient of x, halve and square and add to both sides.

(1/2)² = 1/4

( x + 1/4)² = 12 + 1/4

(x + 1/4)² = 48 + 1 /4

(x + 1/4)² = 49/4

x + 1/2 = 7/2

x = 7/2 ±1/2

x = 4 or x = 3

A graph of the image of the given triangle, reflected across the y-axis is shown in the image attached below.

In Geometry, a reflection over the y-axis is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of the pre-image of the triangle include the following:

(x, y)                               →              (-x, y)

Coordinate A = (-5, 3)   →  Coordinate A' = (-(-5), 3) = (5, 3).

Coordinate B = (-2, -8)   →  Coordinate B' = (-(-2), -8) = (2, -8).

Coordinate C = (3, -2)   →  Coordinate C' = (-(3), -2) = (-3, -2).

In conclusion, we would use an online graphing calculator to plot the resulting data points as shown in the image attached below.

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Answer:

\(x = \sqrt{3 \frac{ - 1}{3} } \)

Answer:

x = -7

Step-by-step explanation:

So we are asked to find what x is equal to in the equation:

\(\frac{x}{7}-4=-5\)

In other words, we are asked to solve for x.

\(\frac{x}{7}-4=-5\)

Add 4 to both sides of the equation.

\(\frac{x}{7}=-1\)

Multiply both sides by 7.

x = -7

So we have solve the equation for x and have found that x = -7.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

b) second place is your anser

Answer:

B) 2nd place

Step-by-step explanation:

Answer:

the annswer is 4155 because its in formal information

Step-by-step explanation:

the annswer is 4155 because its in formal information

The graph of linear equation y = -5x + 10 has negative slope

The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points. The graph of all linear equations are straight line

In the linear equation given;

y = -5x + 10

Kindly find attached below the graph of y = -5x + 10

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when The line tangent to y = f(x) at x = 3 is y = 4x the line tangent to y = g(x) at x = 5 is y = 6x - 27

To summarize:

f(3) = 12

f'(3) = 4

g(5) = 3

g'(5) = 6

From the given information, we can determine the values of f(3), f'(3), g(5), and g'(5).

For the function f(x), the line tangent to y = f(x) at x = 3 is y = 4x. This tells us that the slope of the tangent line is equal to the derivative of f(x) at x = 3.

we have:

f'(3) = slope of the tangent line = 4

Now, let's find the value of f(3). Since the tangent line passes through the point (3, f(3)), we can substitute x = 3 into the equation of the tangent line:

y = 4x

f(3) = 4(3)

f(3) = 12

So, we have:

f(3) = 12

f'(3) = 4

Now, let's consider the function g(x). The line tangent to y = g(x) at x = 5 is y = 6x - 27. This tells us that the slope of the tangent line is equal to the derivative of g(x) at x = 5.

Therefore, we have:

g'(5) = slope of the tangent line = 6

Now, let's find the value of g(5). Since the tangent line passes through the point (5, g(5)), we can substitute x = 5 into the equation of the tangent line:

y = 6x - 27

g(5) = 6(5) - 27

g(5) = 30 - 27

g(5) = 3

So, we have:

g(5) = 3

g'(5) = 6

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The profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.

a) Find the profit-maximizing level of output (Q)To determine the profit-maximizing level of output, we must calculate the marginal cost and marginal revenue of the firm.MC= dTC/dQ= -6Q^2-100+68Q=2(17Q^2-34Q-50)So, the marginal cost of the firm is MC= 2(17Q^2-34Q-50)To find the marginal revenue (MR) we must differentiate the revenue function with respect to Q.MR= dTR/dQ= P + Q(dP/dQ)= 20-4QHence, the marginal revenue is MR= 20-4QAt the point of maximum profit, marginal cost (MC) equals marginal revenue (MR).Therefore, 2(17Q^2-34Q-50)=20-4Q34Q^2-68Q-100=0Solving the above equation gives Q=1.91Therefore, the profit-maximizing output is 1.91 units.b) What price should you charge for your product?The price the firm should charge for its product is given by the demand function, P=20-2Q.Substituting Q=1.91 into the demand function,P= 20-2(1.91) = $16.18c) Based on your answers in the previous two questions, how much profit is this firm making at the profit-maximizing level of output?The total profit of the firm is given by the difference between the revenue and the total cost.TR= P x Q = 16.18 x 1.91 = $30.92TC= 100-2(1.91)^3-100(1.91)+34(1.91)^2 = $60.34Profit = TR- TC= $30.92-$60.34= -$29.42At the profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.

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the value of u is:u = ±√[2/5 e^5u + 7t + 1250 - 2/5 e^25]

Given differential equation is du/dt = e^5u + 7tGiven initial condition is u(0) = 5.

To solve this differential equation, we need to follow the below steps:

Separate the variables and integrate them. Integrate both sides with respect to t. Solve for u after integrating. Applying the initial condition, find the value of u.

Substituting the given values in the differential equation, we get:

u du/dt = e^5u + 7t

Multiplying by dt on both sides, we get:

u du = e^5u dt + 7t dt

Integrating both sides:∫u du = ∫e^5u dt + ∫7t dtu²/2 = 1/5 e^5u + (7/2) t + C

Where C is the constant of integration.

Now we need to apply the initial condition u(0) = 5.u(0) = 5, therefore5²/2 = 1/5 e^5(5) + (7/2) (0) + C625/2 = 1/5 e^25 + C

Therefore, C = 625/2 - 1/5 e^25

Now we can substitute this value of C in the previous equation.

u²/2 = 1/5 e^5u + (7/2) t + 625/2 - 1/5 e^25

Multiply by 2:u² = 2/5 e^5u + 7t + 1250 - 2/5 e^25

Therefore, the value of u is:u = ±√[2/5 e^5u + 7t + 1250 - 2/5 e^25]

Answer: u = ±√[2/5 e^5u + 7t + 1250 - 2/5 e^25]

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a. 2.0405 x 10^7

b. 2.0202 x 10^-2

c. 3.450 x 10^-1

d. 1.1111 x 10^-5

e. 1.0101 x 10^2

f. 9.0650 x 10^-2

a. To convert 20405000 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 2.0405, and since we moved the decimal point 7 places to the left, we multiply by 10^7. Therefore, 20405000 can be expressed as 2.0405 x 10^7.

b. To convert 0.0202020 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 2.0202, and since we moved the decimal point 2 places to the right, we multiply by 10^-2. Therefore, 0.0202020 can be expressed as 2.0202 x 10^-2.

c. To convert 0.3450 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 3.450, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.3450 can be expressed as 3.450 x 10^-1.

d. To convert 0.000011111 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 1.1111, and since we moved the decimal point 5 places to the right, we multiply by 10^-5. Therefore, 0.000011111 can be expressed as 1.1111 x 10^-5.

e. To convert 101010 to scientific notation, we move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.01010, and since we moved the decimal point 2 places to the left, we multiply by 10^2. Therefore, 101010 can be expressed as 1.0101 x 10^2.

f. To convert 0.090650 to scientific notation, we move the decimal point to the right until there is one non-zero digit to the left of the decimal point. This gives us 9.0650, and since we moved the decimal point 1 place to the right, we multiply by 10^-1. Therefore, 0.090650 can be expressed as 9.0650 x 10^-2.

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The height in feet of the tree is 111.5 ft.

The height of a house is 52 ft.

A tree beside the house is 7.5 ft more than twice as tall.

The height of the tree is as follows:

let

x = height of the house

Therefore,

The height of the house = x = 52 ft

Hence,

height of the tree = 7.5 + 2x

height of the tree = 7.5 + 2(52)

height of the tree = 7.5 + 104

height of the tree = 111.5

height of the tree = 111.5 ft

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The surface integral of the vector function (x, y, z) over the given parallelogram S, with parametric equations x = u v, y = u - v, z = 1/2u v, where 0 ≤ u ≤ 3 and 0 ≤ v ≤ 1, evaluates to 0.

To evaluate the surface integral, we need to calculate the dot product between the vector function (x, y, z) = (u v, u - v, 1/2u v) and the surface normal vector. The surface normal vector can be found by taking the cross product of the partial derivatives of the parametric equations with respect to u and v. The resulting surface normal vector is (v, -v, 1).

Since the dot product of (x, y, z) and the surface normal vector is (u v * v) + ((u - v) * -v) + ((1/2u v) * 1) = 0, the surface integral evaluates to 0. This means that the vector function is orthogonal (perpendicular) to the surface S, and there is no net flow of the vector field across the surface.

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