suppose that a box contains 6 cameras and that 3 of them are defective. a sample of 2 cameras is selected at random with replacement. define the random variable

The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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The set of integers is a Pythagorean triple are option (A) 10, 24, 25 and (D) 6, 8, 10

A Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right triangle.

Let's check each set of integers

A. 10^2 + 24^2 = 100 + 576 = 676 = 25^2. Therefore, (10, 24, 25) is a Pythagorean triple.

B. 9^2 + 12^2 = 81 + 144 = 225 = 15^2. Therefore, (9, 12, 15) is a Pythagorean triple. However, the set given is (9, 12, 21), which is not a Pythagorean triple.

C. 8^2 + 15^2 = 64 + 225 = 289 = 17^2. Therefore, (8, 15, 17) is a Pythagorean triple. However, the set given is (8, 15, 23), which is not a Pythagorean triple.

D. 6^2 + 8^2 = 36 + 64 = 100 = 10^2. Therefore, the set of integers (6, 8, 10) is a Pythagorean triple.

Therefore, the correct options are (A) 10, 24, 25 and (D) 6, 8, 10

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The given question is incomplete, the complete question is:

Which set of integers is a Pythagorean triple?

A.

10, 24, 25

B.

9, 12, 21

C.

8, 15, 23

D.

6, 8, 10

The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].

In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Generally speaking, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^n[/tex]

Where

Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:

Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])

Scientific notation = 0.46 × [tex]10^{8-5}[/tex]

Scientific notation = 0.46 × [tex]10^{3}[/tex].

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Answer:

16 represents the hours available to sew gloves.

2 represents the cost of producing gloves for a small pair.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

all you have to do to find difference is subtract the small number from the bigger number, 18 - 4 = 14

Answer:

14

Step-by-step explanation:

The difference of 18 and 4

18 - 4

14

I think it equals 18 tens

Answer:

3 x 60 x 30 = 5400

Step-by-step explanation:

Answer:

13 - The first option

11 - (x+1)

16 - first option

Step-by-step explanation:

The ticket price that maximizes profit is $2.90.

What is profit and how is it related to revenue and cost?

In business and economics, profit is the amount of money earned after all expenses and costs have been deducted from revenue. Profit is a key metric used to measure the financial success of a company or enterprise. It is calculated as follows:

Profit = Revenue - Cost

Revenue is the total income earned from the sale of goods or services, while cost is the total expense incurred to produce and sell those goods or services. Profit is an important measure of financial performance because it reflects how efficiently a company is using its resources to generate income.

Finding the price that maximizes profit:

We need to find the value of x that corresponds to the maximum value of the revenue function R(x). The price of the tickets can then be determined by adding the value of x to the initial price of $2.

Using the revenue function [tex]R(x)=-30(x-6)^2+320[/tex], we can find the value of x that maximizes the revenue as follows:

Take the derivative of R(x) with respect to x:

[tex]R'(x) = -60(x-6)[/tex]

Set the derivative equal to zero and solve for x:

[tex]R'(x) = 0[/tex]

[tex]-60(x-6) = 0[/tex]

[tex]x = 6[/tex]

Determine the second derivative of R(x) to check that x = 6 corresponds to a maximum:

[tex]R''(x) = -60[/tex]

Since R''(x) is negative, this confirms that x = 6 corresponds to a maximum.

Calculate the corresponding revenue at x = 6:

[tex]R(6) = -30(6-6)^2 + 320[/tex]

[tex]R(6) = 320[/tex]

Determine the ticket price by adding the value of x to the initial price of $2:

Ticket price = $2 + $0.15(x)

Ticket price = $2 + $0.15(6)

Ticket price = $2.90

Therefore, the ticket price that maximizes profit is $2.90.

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Answer:

68.2 degrees

Step-by-step explanation:

[tex]1.19\frac{180}{\pi }[/tex]

[tex]68.2[/tex] degrees

P(strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1

The probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is the same and is equal to 50%. This is because there are an equal number of strawberry chews (10) and cherry chews (10) in the bag of candy. Therefore, the probability of her selecting one of either is 1/2 = 0.5 = 50%.
The word or phrase that describes the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".Explanation:The candy bag of Kadeesha contains 10 strawberry chews and 10 cherry chews. This means there are two flavors of candies in the bag. The probability that she picks a strawberry chew at random without looking will be 10/20, which can be simplified to 1/2. Similarly, the probability of picking a cherry chew at random without looking will be 10/20, which can also be simplified to 1/2. When considering either of the probabilities, it implies that the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is the sum of the probability of picking a strawberry chew and the probability of picking a cherry chew.i.e. P (strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1Therefore, the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is 1, which implies that it is a sure event. Hence, the word or phrase that describes the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".

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The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

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An operations manager has carefully examined the 1500 parts produced in his factory and classified them into 30 families with geometric similarities using codes that contain design attributes. This is an example of: group technology.

Group technology is a manufacturing philosophy that seeks to improve efficiency and productivity by grouping similar parts together and standardizing their production processes.

By grouping similar parts together, manufacturing processes can be standardized and streamlined, reducing the time and cost associated with producing each part. This approach is particularly effective in high-volume manufacturing operations where a large number of parts are produced repeatedly.

In this case, the operations manager has identified 30 families of parts with geometric similarities and used codes that contain design attributes to classify them. By doing so, the manager has created a basis for grouping similar parts together and standardizing their production processes. This can lead to a more efficient and cost-effective manufacturing operation.

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A) 35. 8 million; thirty-five million eight hundred thousand, or thirty-five million eight hundred thousand dollars ,(b)115. 2 thousand; one hundred and fifteen thousand two hundred.(c) 97.8 million eight hundred thousand; 97.8 million eight hundred thousand. or 978 million.

What significance do numbers have?

We need good numeracy skills as parents to assist our children to develop, as patients to grasp healthcare information, and so as politicians to make sense of numbers and economic news. Selections in life were frequently based upon numerical data; in order to arrive at optimal decisions, we must be good at maths.

How are numbers used in everyday life?

Numbers are utilized in a variety of mathematical operations such as summation, subtraction, multiplication, division, percentage, and so on, that we employ in the everyday companies and exchanges. Quantities are numerical symbols representing integers that may be used for numbering, estimating, and doing other arithmetic operations.

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354 Valencia student tickets and 133 non-student tickets were sold.

Let's use algebra to solve the problem. Let

x be the number of Valencia student tickets sold

y be the number of non-student tickets sold

We know that

x + y = 487 (the total number of tickets sold is 487)

14x + 25y = 8391 (the total receipts from ticket sales is $8391)

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y

y = 487 - x

Here we have to use the substitution method, we can then substitute this expression for y into the second equation

14x + 25(487 - x) = 8391

Simplifying and solving for x

14x + 12275 - 25x = 8391

-11x = -3884

x = 354

So, 354 Valencia student tickets were sold. We can use the first equation to find y

x + y = 487

354 + y = 487

y = 133

So, 133 non-student tickets were sold.

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A ship sets out to sail to a point 176 km due north. an unexpected storm blows the ship to a point 112 km due east of its starting point.The ship has to sail approximately 208.7 km to reach its original destination.

To calculate the distance to reach the original destination, you need to use the Pythagorean Theorem. Pythagorean Theorem states that a² + b² = c².

Here, c is the hypotenuse, and a and b are the other two sides of the right triangle.

The given information helps us to identify the legs of the triangle. The hypotenuse is the distance the ship has to sail to reach its original destination.

Therefore, to calculate the distance the ship must sail now to reach its original destination using the Pythagorean Theorem:

a² + b² = c²

where a = 112 km (East) and b = 176 km (North).

Let us substitute these values in the equation to get the value of

c. (112)² + (176)² = c² ⇒ 12,544 + 30,976 = c² ⇒ 43,520 = c²

Take the square root of both sides to get c: c = √43,520 ≈ 208.7 km

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The LCD of 2/5, 1/2, and 3/4 is equal to 20.

In Mathematics, LCD is an abbreviation for least common denominator or lowest common denominator and it can be defined as the smallest number that can act as a common denominator for a given set of fractions.

Next, we would determine the factors of the denominators for the given fraction 5, 2, and 4 as follows;

5 = 5 × 1

2 = 2 × 1

4 = 2 × 2 × 1

Therefore, the least common denominator (LCD) would be calculated as follows:

Least common denominator (LCD) = 5 × 2 × 2 × 1

Least common denominator (LCD) = 20.

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The triange abd is congruent to triangle bcd becasue of bcd were to be rotated 180 degrees clocke wise the two haves would line up exactly.

The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex],  so the value of a+b is given as 107.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Let x be the probability that it rains on Sunday given that it doesn't rain on Saturday then we have,

3/5x + 2/5(2x) = 3/10

7/5x = 3/10

x = 3/14.

Therefore, the probability that it doesn't rain on either day is,

[tex]$\left(1-\dfrac{3}{14}\right)\left(\dfrac{3}{5}\right)=\dfrac{33}{70}$[/tex]

Therefore, the probability that rains on at least one of the days is

[tex]$1-\dfrac{33}{70}=\dfrac{37}{70}$[/tex],

so adding up the 2 numbers, we have,

37 + 70 = 107.

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Complete question;

There is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex], where a and b are relatively prime positive integers. Find a+b.

Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.

The interest rate that is adjusted to the projected cash flows of either an investment to determine its present value is referred to as the discount rate. The expected rate of return on investment that businesses or investors anticipate. The viability of an investment can be determined by computing the net present value via discounting.

Cost price =  $4.50

Percentage increase = 250%.

Marked price = 4.50 + 2.5*4.50

Marked price = $15.75

Discount = 30%

Discounted price = 15.75 - 0.30*15.75

Discounted price = $11.025

Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.

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22.8 units make up the perimeter of ΔSTR (rounded to one decimal place).  

Given that ΔHIJ is similar to ΔSTR and we know the lengths of the corresponding sides, we can find the scale factor between the two triangles as follows:

HI / ST = 5 / 10 = 1/2

IJ / SR = 4 / 12 = 1/3

JH / TR = 6 / 8 = 3/4

The scale factor between the two triangles is 1/2 (the smallest of the three ratios).

To find the perimeter of ΔSTR, we need to know the lengths of its corresponding sides.

We can use the scale factor to find these lengths:

ST = 10, so SR = ST × (IJ / HI) = 10 × (4 / 5) = 8

TR = 8, so TR = TR × (JH / HI) = 8 × (3 / 5) = 24/5

RS = 12, so ST = RS × (IJ / JH) = 12 × (4 / 6) = 8

Now we can add up the lengths of the sides of ΔSTR to find its perimeter:

Perimeter of ΔSTR = ST + SR + TR = 10 + 8 + 24/5 = 50/5 + 40/5 + 24/5 = 114/5

Therefore, the perimeter of ΔSTR is 22.8 units (rounded to one decimal place).

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Correct question:

ΔHIJ is similar to ΔSTR. What is the perimeter of ΔSTR? If ST=10, TR=8, RS=12 and HI=5 IJ=4 JH=6.

Answer:

The formula you are referring to is the quadratic formula, which is used to solve quadratic equations of the form ax^2 + bx + c = 0. The formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are coefficients of the quadratic equation.

The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.

The study of random events or phenomena is the focus of the mathematical field of probability. It is a way to gauge how likely something is to happen. It is represented by a number between 0 and 1, where 0 denotes the event's impossibility and 1 denotes its certainty. There are numerous ways to calculate probabilities, including utilizing theoretical or mathematical models, empirical data, and experimental data.

given

A statistical analysis would be useful to evaluate the effectiveness of the novel technique to the standard procedure based on the study's design.

The recovery periods of the two patient groups might be compared using statistical techniques like hypothesis testing and confidence intervals to assess the efficacy of the new therapy.

Researchers can establish whether the new approach is statistically significantly superior than the usual procedure in terms of minimizing recovery time by comparing the recovery times of the two groups.

The outcomes of the statistical analysis can give medical professionals and patients important knowledge regarding the possible advantages of the new procedure.

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The associative property works with expressions that use a property of addition and multiplication that states that the way the terms are grouped in an expression does not affect the final result.

In associative property, when you add or multiply several numbers together, you can regroup them in any way you like, and the sum or product will be the same.

For example, suppose we have the expression (2 + 3) + 4. By the associative property of addition, we can regroup the terms as 2 + (3 + 4) and the result will be the same, which is 9.

The associative property also works with more elaborate expressions, such as those involving variables, exponents, and parentheses. For instance, the expression 2a(bc) can be regrouped as (2ab)c or a(2bc), and the result will be the same. Similarly, the expression (3x)^2 y can be written as 9x^2 y, or as 3x (3xy), and the result will still be the same.

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ANSWER: dA/dt=0.17A A(0)=950

The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.

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, Doug Bernard would profit $4,014.97 from this arbitrage opportunity.

Explanation:

Yes, Doug Bernard has an arbitrage opportunity based on these quotes. To make an arbitrage profit, he can follow these steps:

1. Convert $1,000,000 to Swiss francs using the Swiss franc/dollar rate: $1,000,000 * (SFr1.5995/$) = SFr1,599,500.
2. Convert the Swiss francs to Australian dollars using the Australian dollar/Swiss franc rate: SFr1,599,500 * (A$1.1458/SFr) = A$1,831,604.90.
3. Convert the Australian dollars back to U.S. dollars using the Australian dollar/U.S. dollar rate: A$1,831,604.90 / (A$1.8242/$) = $1,004,014.97.

The arbitrage profit would be the difference between the initial amount and the final amount

: $1,004,014.97 - $1,000,000 = $4,014.97.

Therefore, Doug Bernard would profit $4,014.97 from this arbitrage opportunity

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The length οf the hypοtenuse AC is 10 units.

In mathematics, a graph is a visual representatiοn οf data οr infοrmatiοn that cοnsists οf pοints, called vertices οr nοdes, and lines, called edges οr arcs, that cοnnect them.

Graphs are οften used tο represent relatiοnships between οbjects, events, οr quantities.

They can be used tο mοdel and sοlve prοblems in variοus fields, such as cοmputer science, engineering, ecοnοmics, and sοcial sciences. There are many types οf graphs, including bar graphs, line graphs, scatter plοts, pie charts, and netwοrk graphs, amοng οthers. Each type οf graph is suited fοr visualizing different types οf data οr relatiοnships.

Based οn the given diagram, we can use the Pythagοrean theοrem tο find the length οf the hypοtenuse AC οf the right triangle ABC:

[tex]AC^2 = AB^2 + BC^2[/tex]

Substituting the given side lengths, we get:

[tex]AC^2 = 6^2 + 8^2[/tex]

[tex]AC^2 = 36 + 64[/tex]

[tex]AC^2 = 100[/tex]

Taking the square rοοt οf bοth sides, we get:

AC = 10

Therefοre, the length οf the hypοtenuse AC is 10 units.

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Sum the first 26 terms of the series is needed  to get an approximation of its sum with an error of less than 0.01.

The question asks about the series 1 - 1/3 1/5 - 1/7 and the number of terms required to approximate its sum with an error of less than 0.01.

We will use the formula for the nth partial sum of an alternating series with terms that decrease in magnitude as n increases. The formula for the nth partial sum of such a series is :Sn = a1 - a2 + a3 - ... + (-1)^(n+1)an where a1, a2, a3, ... are the terms of the series.

If we can find the smallest value of n for which the absolute value of the (n+1)th term is less than 0.01, then the sum of the first n terms will be within 0.01 of the actual sum. We can use the formula for the nth term of the series to find such a value of n.

We have a series of the form:a1 - a2 + a3 - ... + (-1)^(n+1)an where a1 = 1, a2 = 1/3, a3 = 1/5, and so on. The nth term of this series is:an = (-1)^(n+1)/(2n - 1).Therefore, we want to find the smallest value of n for which : |an+1| < 0.01, where an+1 = (-1)^(n+2)/(2(n+1) - 1)

Simplifying this inequality, we get:|(-1)^(n+2)/(2(n+1) - 1)| < 0.01, Multiplying both sides by 2(n+1) - 1 and simplifying, we get:1/(2(n+1) - 1) < 0.01.

Taking the reciprocal of both sides and simplifying, we get:2(n+1) - 1 > 100. Therefore, we want to find the smallest integer value of n such that:2(n+1) > 101n+1 > 50.5n > 49.5n > 50. The smallest integer value of n that satisfies this inequality is n = 26. Therefore, we need to sum the first 26 terms of the series to get an approximation of its sum with an error of less than 0.01.

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The tank contains 1050 milliliters of water when full or 1.05 liters.

To calculate the volume of the tank in milliliters, we multiply the length (15 cm), width (7 cm), and height (10 cm) together:

15 cm x 7 cm x 10 cm = 1050 cm³

Since 1 milliliter equals 1 cubic centimeter (cm^3), we know that the tank can hold 1050 milliliters of water.

To convert milliliters to liters, we can divide the volume in milliliters by 1000:

1050 mL ÷ 1000 = 1.05 L

Therefore, when full, the tank can hold 1050 milliliters of water or 1.05 liters.

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The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of  Permutation and Combination.

If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.

To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.

To get the total number of ways, we can multiply these numbers:

495 x 1,365 = 7,425.

To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.

To get the total number of ways, we can add these numbers:

495 x 5,005 + 2,190 x 3,003 = 58,275.

To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.

To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.

Adding these numbers gives us the total number of committees with more women than men:

15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700

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