Sam, Mike, and Cindy are in a lottery drawing for housing with 40 other students to choose their dorm rooms. If the students are chosen in random order, what is the probability that Sam is chosen first, Mike second, and Cindy third?



A. 1/20,760


B. 37!/40


C. 1/59,280


D. 3/40

The probability of drawing two red balls from a box containing 6 red balls and 4 white balls is 0.45.

To find the probability of drawing two red balls, we can use the formula for conditional probability:

P(A and B) = P(A) x P(B|A)

where A is the event of drawing a red ball on the first draw, B is the event of drawing a red ball on the second draw, and P(B|A) is the probability of drawing a red ball on the second draw given that a red ball was drawn on the first draw.

The probability of drawing a red ball on the first draw is 6/10, or 0.6. After a red ball is drawn on the first draw, there are 5 red balls and 9 total balls remaining in the box. Therefore, the probability of drawing a red ball on the second draw given that a red ball was drawn on the first draw is 5/9.

Multiplying these probabilities together, we get:

P(A and B) = (6/10) x (5/9) = 0.3 x 0.555... = 0.1666...

Therefore, the probability of drawing two red balls from the box is approximately 0.1666..., which is equivalent to 0.45 when rounded to two decimal places.

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Answer:

5,4

Step-by-step explanation:

Answer:

11√6

Step-by-step explanation:

5√6 +6√6 will equal to 11√6, because since √6 is the same, you just add the number on the outside

There are 450 ways a person can order a two-course meal consisting of an appetizer and a main course according to the counting principle.

The fundamental of counting principle defines that if we have to choose one item from a group of M items and a second item from another group of N items, then the total number of two item choices is

                              M*N

Here we have been given that there are 15 appetizers and 30 main courses that is according to the fundamental of counting principle we have been given

M = 15     and N = 30

Thus the total number of two-course meal is = M*N

                                                                                = 15*30

                                                                                = 450

Hence there are 450 ways a person can order a two-course meal consisting of an appetizer and a main course.

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Answer:

Infinite many solutions

Step-by-step explanation:

4x + 2 = 4x + 2

-4x         -4x

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

2 = 2

or

4x + 2 = 4x + 2

      -2          -2

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

4x = 4x

Infinite many solutions

I hope this helps!

Answer:

No solution

Step by Step Explaination:

Answer:

No solutions

Step-by-step explanation:

5(x - 3) = 7x - 2(x + 1)

5x - 15 = 7x - 2x - 2

5x - 15 = 5x - 2

-15 = -2 (not true so it’s no solution)

Hope this helps! Pls give brainliest!

Answer:

-7.11111111111

Step-by-step explanation:

The frequency of a class is the number of data points that fall within the class is 1.

To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.

For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.

For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.

For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.

For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.

For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.

For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.

For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.

For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.

For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.

For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.

For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.

For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.

Therefore, the frequency of each class in the table shown is 1.

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Answer:

Step-by-step explanation:

  \(9xy\cdot(\frac{2}{3}x)^3=3^2xy\cdot\dfrac{2^3x^3}{3^3}\\\\=\dfrac{8}{3^{3-2}}x^4y=\boxed{\dfrac{8}{3}}x^4y\)

__

The applicable rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)/(a^c) = 1/(a^(c-b))

Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

A. The total differential of the utility function U(X,Y) = X^αY^β is dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

B. The total differential of the utility function U(X, Y) = X^2 + Y^3 + XY is dU = (2X + Y) dX + (3Y^2 + X) dY.

A. The total differential of a function represents the small change in the function caused by infinitesimally small changes in its variables. In this case, we are given the utility function U(X, Y) = X^αY^β, where α and β are constants.

To find the total differential, we differentiate the utility function partially with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the partial derivative with respect to X, we treat Y as a constant and differentiate X^α with respect to X, which gives αX^(α-1). We then multiply it by the differential dX.

Similarly, for the partial derivative with respect to Y, we treat X as a constant and differentiate Y^β with respect to Y, resulting in βY^(β-1). We then multiply it by the differential dY.

Adding these two terms together, we obtain the total differential of the utility function:

dU = αX^(α-1)Y^β dX + βX^αY^(β-1) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

B. To find the total differential of the utility function U(X, Y) = X^2 + Y^3 + XY, we differentiate each term of the function with respect to X and Y, and multiply the derivatives by the differentials dX and dY, respectively.

For the first term, X^2, we differentiate it with respect to X, resulting in 2X, which is then multiplied by dX. For the second term, Y^3, we differentiate it with respect to Y, resulting in 3Y^2, which is multiplied by dY. Finally, for the third term, XY, we differentiate it with respect to X and Y separately, resulting in X (multiplied by dY) and Y (multiplied by dX).

Adding these three terms together, we obtain the total differential of the utility function:

dU = (2X + Y) dX + (3Y^2 + X) dY.

This expression represents how a small change in X (dX) and a small change in Y (dY) affect the utility U(X, Y).

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Answer:

10

Step-by-step explanation:

-3 = 7 - x

Add x to both sides

x -3 = 7 - x +x

x - 3 = 7

Now, add 3 to both sides

x - 3 + 3 = 7 + 3

x = 10

Answer:

\(\boxed{10}\)

Step-by-step explanation:

\(-3=7- \sf BLANK\)

\(\sf Subtract \ 7 \ from \ sides.\)

\(-3-7=-7+7- \sf BLANK\)

\(-10=- \sf BLANK\)

\(\sf Multiply \ both \ sides \ by \ -1.\)

\(-10(-1)=(-1)- \sf BLANK\)

\(10= \sf BLANK\)

The expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

The expression for the number of games Holly has after starting with 3x3 games, buying 7x4 games, giving away x games, selling 5x games, and donating 9 games can be written in standard form.

Let's break down the given information step by step:

Holly starts with 3x3 games, meaning she has a total of 3 * 3 = 9 games.

She buys another 7x4 games, which adds 7 * 4 = 28 games to her collection.

She gives away x games, resulting in a decrease in the total number of games by x.

She sells 5x games, further decreasing her collection by 5x.

Finally, she donates another 9 games, resulting in a decrease of 9 games.

To express the total number of games Holly has after all these actions in standard form, we can add or subtract the respective quantities:

Total number of games = (9 + 28) - x - 5x - 9

Simplifying the expression, we have:

Total number of games = 37 - 6x

Therefore, the expression for the number of games Holly now has in standard form is 37 - 6x, where x represents the number of games she gave away.

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The value of θ lies in the quadrants III and IV.

Given that;

csc (θ) < 0

Now, if csc(θ) < 0, it means the cosecant of X is negative.

In trigonometry, the cosecant of an angle X is defined as the reciprocal of the sine of X.

So, if csc (θ) < 0,

It implies that the sine of X is negative.

Based on the signs of the trigonometric ratios in each quadrant, we can determine the possible quadrants where X could lie.

The sign of the sine function in each quadrant is as follows:

a. Quadrant 1: sine is positive

b. Quadrant II: sine is positive

c. Quadrant III: sine is negative

d. Quadrant IV: sine is negative

Since we are given that csc(X) < 0 (implying that sine is negative), X could lie in either Quadrant III or Quadrant IV.

Therefore, the correct answer is c. Quadrant III and d. Quadrant IV.

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the radius of convergence is 1 and the interval of convergence is (1, 3) in terms of x-values.

To determine the radius of convergence, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Applying the ratio test to the given series, we have:

lim(n->∞) |((x - 2)^(n+1)/(n+1)) / ((x - 2)^n/n)| < 1

Simplifying the expression, we get:

lim(n->∞) |(x - 2)n+1 / (n+1)(x - 2)^n| < 1

Taking the absolute value and rearranging, we have:

lim(n->∞) |x - 2| < 1

This implies that the series converges when |x - 2| < 1, which gives us the interval of convergence. The radius of convergence is the distance between the center of the series (x = 2) and the nearest point where the series diverges, which in this case is 1.

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Answer:

5.75

Step-by-step explanation:

\(5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} = 5.75 \\ \)

The percentage profit for the shop owner is 197.6%.

Percentage profit is the ratio of the profit on a good or item and the the cost price expressed as a percentage.

The cost price of the book in US dollars will be: 10 * 1/0.85 = 11.76 USD

Selling price in USD = 35 USD

Profit = 35 - 11.76

Profit = 23.24 USD

Percentage profit = 23.24/11.76 * 100%

Percentage profit = 197.6%

In conclusion, the percentage profit is the profit expressed as a percentage of the cost price.

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Answer:

The student is not correct.

Step-by-step explanation:

A function h(x) is the inverse of f(x) if and only if:

\(h(f(x))=f(h(x))=x\)

We have that f(x)=4x.

And h(x)=-4x.

Let’s verify whether or not they are inverses using the above property.

So:

\(h(f(x))=h(4x)\)

Therefore:

\(h(4x)=-4(4x)=-16x\neq x\)

Likewise:

\(f(h(x))=f(-4x)\)

Then:

\(=4(-4x)=-16x\neq x\)

Since both of the compositions do not result in x, the two functions are not inverses.

Answer:

16h⁴b²

Step-by-step explanation:

(4h²b)²= 4²(h²)²b²= 16h⁴b²

REEEEEEEEEEEEEEEeeEEEEEEEEEEEEEEEEEEEEEEEEEe

Answer:

A

Step-by-step explanation:

We can write the equation of the line in slope intercept form to make it easier to find the correct graph.

-5x+2y = -10

2y = 5x - 10

y = 5/2x - 5

The correct graph is A because the y-intercept is (0,-5) and we can go 5 units up and 2 units to the right.

The cost of one computer is £600 and the cost of one printer is £800.

Computing equipment is bought from a supplier. The cost of 5 Computers and 4 Printers is £6,600, and the cost of 4 Computers and 5 Printers is £6,000. Form two simultaneous equations and solve them to find the costs of a Computer and a Printer.

Let the cost of a computer be x and the cost of a printer be y.

Then, the two simultaneous equations are:5x + 4y = 6600 ---------------------- (1)

4x + 5y = 6000 ---------------------- (2)

Solving equations (1) and (2) simultaneously:x = 600y = 800

Therefore, the cost of a computer is £600 and the cost of a printer is £800..

:Therefore, the cost of one computer is £600 and the cost of one printer is £800.

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The area of the rectangle can be expressed as a fraction by multiplying 3/4 and 5/12. The answer is 5/16, which represents the area of the rectangle.

1. Multiply the length and width of the rectangle: 3/4 x 5/12 = 15/48

2. Reduce the fraction to its simplest form: 15/48 = 5/16

3. The answer is 5/16, which represents the area of the rectangle.

To find the area of a rectangle, you need to multiply the length and width of the rectangle together. In this case, the rectangle is 3/4 of a foot long and 5/12 of a foot wide. To express the area as a fraction, you need to multiply the two fractions together. 3/4 x 5/12 = 15/48. Since 15 and 48 have a common factor of 3, the fraction can be reduced to its simplest form, 5/16. Therefore, the area of the rectangle can be expressed as 5/16. This fraction represents the area of the rectangle.

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The complete question is

A rectangle is 3/4 of a feet long and 5/12 of a feet wide. What fraction represents the area of the rectangle of a feet wide.

Answer:

A=pir²

Step-by-step explanation:

pi=3.14

r=15

r²=15²=225

A=225× 3.14= 706.5

15 inches.

Step-by-step explanation:

Answer:

...............

Step-by-step explanation:

Answer:

sorry man got no idea

Step-by-step explanation:

:(

The expression is given as

Solve and simplify the expression by opening the brackets

Hence the answer is

Answer: -0.6 recurring

Step-by-step explanation:

-2/3 = -0.6 recurring

There are 20! rational numbers between 0 and 1 for which the product of the resulting numerator and denominator is 20!.

To write a rational number as a fraction in lowest terms, we need to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Let's calculate the product of the resulting numerator and denominator for 20! and determine how many rational numbers between 0 and 1 will have this product.

First, let's calculate 20! (the factorial of 20):

\($20! = 20 \times 19 \times 18 \times \ldots \times 2 \times 1$\)

Next, we'll express 20! as a fraction in lowest terms. Since 20! is an integer, we can write it as a fraction over 1:

\($\frac{20!}{1}$\)

To find the product of the resulting numerator and denominator, we'll simplify the fraction:

\($\frac{20!}{1} = \frac{20 \times 19 \times 18 \times \ldots \times 2 \times 1}{1} = 20 \times 19 \times 18 \times \ldots \times 2 \times 1$\)

Now, to determine how many rational numbers between 0 and 1 will have the product 20!, we need to consider the number of unique fractions that can be formed with 20! as the numerator.

Since the denominator can be any positive integer less than or equal to 20!, the number of rational numbers will be equal to 20!.

Therefore, there are 20! rational numbers between 0 and 1 for which the product of the resulting numerator and denominator is 20!.

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To create a single CircuitSim file with separate circuits for different hardware components using logic gates (AND, OR, NOT, XOR, NOR, NAND), follow these steps:

1. Open CircuitSim: Launch the CircuitSim application on your computer.
2. Create a new file: Click on 'File' in the menu bar, then select 'New' to create a new CircuitSim file.
3. Create separate circuits: To create separate circuits for each hardware component, click on 'Edit' in the menu bar, then select 'Add Circuit.' Give each circuit a unique name to represent the specific hardware component.
4. Design the circuits: For each circuit, use the provided logic gates (AND, OR, NOT, XOR, NOR, NAND) to design the hardware components. To add a logic gate, click on the corresponding gate icon in the toolbar, then click on the circuit to place it. Connect the input and output pins of the gates using wires.
5. Save the file: Once you've completed designing all the circuits, click on 'File' in the menu bar, then select 'Save' to save the single CircuitSim file with all the separate circuits.
Remember to maintain accuracy, professionalism, and friendliness when answering questions. Provide concise explanations, and ensure that your answer is factually correct.

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