A class has seven students. What is the probability that exactly five of the students were born on a weekend?

A Pentagon on a coordinate plane would be neither a relation nor a function.

This is because it does not have a unique output for every input, which is a requirement for a function. This is because a function must have a unique output for each input, while a pentagon may have multiple points (outputs) for a given x-coordinate (input) due to its shape. Additionally, it does not satisfy the vertical line test, which is a requirement for a relation. Therefore, it is not a relation or a function.

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The type of fee that will be charged depends on the specific service provided by the broker to the client. Non-transaction fees are typically charged for account maintenance or access to investment tools, while transaction fees are charged for specific trades or transactions.

To determine the type of fee that will be charged in each situation, we need to consider the specific services that were provided by the broker to the client.

For Joanne, her brokerage firm charged her a fee for providing investment information to help her make informed choices. This type of fee is a non-transaction fee, as it is not related to a specific transaction or trade.

Pete, who hasn't bought or sold any stock this year, was charged an inactivity fee of $75 for the year by his broker. This fee is also a non-transaction fee, as it is not related to a specific trade but rather to the inactivity of the account.

John's broker provided him with stock trading software to manage his trading. This type of service is typically included in a brokerage firm's platform fee, which is a non-transaction fee that covers the cost of maintaining the software and other tools that clients can use to manage their investments.

Lisa sold 50 shares of stock A on a given day and her broker charged her $12 for this trade. This type of fee is a transaction fee, which is charged for each specific trade or transaction that a client makes.

Finally, Reggie's broker charged him a front-end load of 2.75% when he purchased a fund. This fee is a type of sales charge or commission that is applied to the initial investment and is considered a transaction fee.

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About $786 billion will be spent at restaurants in 2017 if the trend continues.

We can use the formula for compound interest:

A = P(1 + r)^n

where:

A is the final amount

P is the initial amount

r is the annual interest rate

n is the number of years

In this instance, we're looking to determine how much will be spent at restaurants in 2017, which is 12 years from now, in 2005. The initial amount was $410 billion in 2005, and the yearly interest rate is 6%. We thus have:

A = 410(1 + 0.06)^12

A ≈ 786.34

Therefore, about $786 billion will be spent at restaurants in 2017 if the trend continues.

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We define [tex]9^{\frac{1}{2} }[/tex] to be the square root of nine. This means that [tex](9^{\frac{1}{2} })^{2}[/tex] must be equal to nine.

By using the properties of exponents to explain why [tex]8^{\frac{1}{3} }=2[/tex];

Statement                           Reasons_____________________

[tex]8^{\frac{1}{3} }=2[/tex]                                  Given

[tex](8^{\frac{1}{3} })^3=2^3[/tex]                        Exponent property of equality.

[tex]8^{\frac{1}{3} \times 3}=2^3[/tex]                        Exponent property of a power.

8 = 8                                simplify

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

the variables b and n are numerical values (numbers) or an algebraic expression.

n is referred to as a superscript or power.

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

[tex]9^{\frac{1}{2} }[/tex] = √9 (square root of nine)

[tex](9^{\frac{1}{2} })^{2}=(9^{\frac{1}{2} \times 2})=9^1 = 9[/tex]  

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The perimeter of the triangle is 6 + 4√13

Let's denote the length of the congruent sides of the isosceles triangle as x.

The formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height.

So, we have

A = (1/2)bh

12 = (1/2)(6)(h)

h = 4

Now, using the Pythagorean theorem, we can solve for the length of the congruent sides:

x^2 = 6^2 + 4^2

x^2 = 52

x = √52

The perimeter of the triangle is the sum of the lengths of its sides:

P = 6 + √52 + √52

P = 6 + 2√52

So, we have

P = 6 + 4√13

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80 shoppers in the dairy section at random is a biased sample (d).

To estimate the number of people who buy milk in a grocery store, we need an unbiased sample that represents the entire population. The options provided are 70 shoppers at random as they leave the store, 8 shoppers as they enter the store, 60 women with children at random, and 80 shoppers in the dairy section at random.

The most unbiased sample is selecting 80 shoppers in the dairy section at random because the dairy section is where people are most likely to buy milk, and selecting a random sample of shoppers in that section ensures that we are not introducing any biases.

The other options may introduce biases since they are not necessarily representative of the entire population of shoppers in the store. Therefore, selecting 80 shoppers in the dairy section at random provides the most unbiased estimate of the number of people who buy milk in the grocery store. So d is correct option.

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product rule, chain rule, and sum rule are utilized to assess a subordinate of y = sin(x)cos(x), a subsidiary of y = sin(cos(x)), a subordinate of y = sin(-x), a subsidiary of y = sin(x) + cos(x).

a) subordinate of y = sin(x)cos(x) can be assessed by utilizing the product rule.

[tex]y' = (cos(x))(cos(x)) + (sin(x))(-sin(x)) = cos^2(x) - sin^2(x)[/tex]

b) chain rule is used  to find the derivative of y = sin(cos(x)):

y' = (cos(x))(cos(cos(x)))

c) chain rule is used  to find the derivative of y = sin(-x):

y' = -cos(-x) = -cos(x)

d) derivative of y = sin(x) + cos(x)  can be evaluated by using sum rule

y' = cos(x) - sin(x)

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1. The radius of the cylinder is  7. 05 cm

2. The length of the cylinder is  15, 384 meters

3. The radius of the big cylinder is 5. 64 cm

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that;

1. We have that volume = 2500 cm³

Height = 16cm

Substitute the values, we have;

2500 = π × r² × 16

Divide both sides by 16

r² = 49. 76

Find the square root

r = 7. 05 cm

2. Volume = 20000 cm³/100 = 200 meters

Radius = diameter/2 = 13/2 = 6.5cm = 0. 065 m

Substitute the values

200/0. 013 = h

Divide the values

h = 15, 384 meters

3. Volume = πr²h

Volume = 3.14 × 3.5² × 13

Volume = 500. 045 cm²

Then, substitute the values

500. 045 = 3.14 × r² × 5

r² = 31. 85

find the square root

r = 5. 64 cm

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The prices of the four movies that Sally has already seen will not change after she sees the next movie.

The ticket prices of the four movies that Sally has already seen are fixed and do not depend on whether she sees another movie or not. Therefore, these prices will remain the same even after she sees the next movie. The price of the next movie that Sally plans to see is $34, which is independent of the ticket prices of the previous movies.

Thus, the cost of the previous movies that Sally has seen will not change after she sees the next movie. In other words, the previous expenses are sunk costs and are irrelevant to future decisions.

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The total of oranges left by the taylor is about 10 3/4 pounds

To solve this problem, we will start by using adding the weights of the navel oranges and temple oranges to discover the total weight of oranges Taylor has, that's:

Next, we are able to subtract the weight of the navel oranges she uses from the total weight of navel oranges to discover how a lot she has left, which is:

In the end, we can add the weight of the navel oranges left to the weight of the temple oranges to find the overall weight of oranges Taylor has left, which is:

Therefore, the total of oranges left by the taylor is about 10 3/4 pounds

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The height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches. The z-score associated with the 96th percentile is 1.75.

To find the z-score associated with the 96th percentile, we can use the following steps:

1. Locate the percentile in a standard normal distribution table or use a calculator that can compute percentiles (e.g., a graphing calculator or an online calculator).

2. For the 96th percentile, we find the corresponding z-score. Using a standard normal distribution table or an online calculator, the z-score is approximately 1.75.

So, the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the following formula:

Height = mean + (z-score × standard deviation)

Here, the mean height is 68.3 inches, the z-score is 1.75, and the standard deviation is 2.9 inches. Plugging these values into the formula:

Height = 68.3 + (1.75 × 2.9) ≈ 68.3 + 5.075 ≈ 73.375 inches

So, the height of a 16-year-old boy in the 96th percentile is approximately 73.375 inches.

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The amount of cup of flour for 1 cup of milk is 1/3 cup

Proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 4 girls you could write the ratio as: 1 : 4 (for every one boy there are 4 girls).

Another example is if 5 mangoes cost $250, the price of mango will 250 × 1/5 = $50

Similarly, 3/12 cups of flour is for every 3/4 cups of milk

therefore,

1 cup of milk will need 3/12 × 4/3

= 12/36

= 1/3

therefore for 1 cup of milk 1/3 of flour will be needed.

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Using metric system, we can find that Miss Marge's fish tank holds 100 litres of water.

Everything around us has a quantitative value, from the amount of sugar you put in a cake to the size of a football pitch. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced. The collection of standard units designed to measure length, weight, area, and capacity is known as the metric system of measurement in mathematics. As it uses numbers in powers of 10, it is based on the decimal system.

A litre (L) and millilitres (mL) are two units for measuring capacity in the metric system. A bottle of water holds 1 Liter of water. A millilitre is about 20 drops of water.

So, 100 litres of water will be the correct answer.

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The binomial conditions are not met as the cards are not being replaced, so the independence condition is not met. So, the correct answer is D).

The conditions for a binomial setting are

there are a fixed number of trials,

the trials are independent,

there are only two possible outcomes (success or failure),

the probability of success is constant for each trial.

In this scenario, the first two conditions are met as Lan is turning over the first four cards and they are independent events. The third condition is also met as the success is defined as observing an ace and the failure is observing any other card.

However, the fourth condition is not met as the probability of success changes for each trial. After the first card is turned over, the probability of observing an ace changes for the second trial. Therefore, the scenario does not meet all the conditions for a binomial setting. So, the correct option is D).

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Answer:

Step-by-step explanation:

you multiply 5 by 50 and that would equal 250

5 x 50 = 250

The equation D = 2zv when solved for v is D/2z = v

To solve D = 2zv for v, we need to isolate the variable v on one side of the equation. We can do this by dividing both sides of the equation by 2z:

D = 2zv

So, we have

D/2z = v

So the solution for v is v = D/2z.

This equation tells us that v is equal to the ratio of D divided by 2z. In other words, v is proportional to D, and inversely proportional to 2z.

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Each equation should be matched to the situation it represents as follows;

"Leilah has not yet studied 600 of her 2400 flashcards. She studies 40 new cards each day." ⇒ 2400 - 40x = 600

"Stetson rents studio space for $600 a month for music lessons. He charges his students $40 per hour and earned a profit of $2400 this month." ⇒ 40x - 600 = 2400

"A kit contains 600 letter tiles and 40 number tiles. Each tile has the same mass, and the kit has a total mass of 2400 g." ⇒ (600 + 40)x = 2400.

In this scenario and exercise, the independent variable (domain or input value) would be represented by the variable x, and then each of the situations described by the word sentence (problem) would be translated into an algebraic equation or linear function as follows;

Since Leilah studies 40 new cards per day, but hasn't studied 600 of her 2400 flashcards yet, a linear function to model or represent this situation is given by;

2400 - 40x = 600

The rent for Stetson's studio space is $600 per month and he charges his students $40 each hour while earning a profit of $2400 this month, a linear function to model or represent this situation is given by;

40x - 600 = 2400

Since this kit with a total mass of 2400rams contains 600 letter tiles and 40 number tiles, and each of the tiles have the same mass, the required linear function is given by;

(600 + 40)x = 2400.

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The velocity of the velociraptor is 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S] and  the speed of the velociraptor is 2 m/s.

To calculate the speed of the velociraptor, we need to divide the total distance traveled by the total time taken:

Total distance = 5m + 10m + 3m + 2m = 20m

Total time = 10 seconds

Speed = Total distance / Total time

     = 20m / 10s

     = 2m/s

To calculate the velocity of the velociraptor, we need to consider both the magnitude of its speed and its direction. We can calculate the displacement by subtracting the final position from the initial position:

Displacement = (5m [E] + 10m [W] + 3m [S] + 2m [W])

           = (5m [E] - 8m [W] + 3m [S])

           = 5m [E] - 8m [W] + 3m [S]

Note that we have used negative sign for the distance traveled towards the west.

The time taken is 10 seconds.

Velocity = Displacement / Time taken

        = (5m [E] - 8m [W] + 3m [S]) / 10s

        = 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S]

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The number that best describes the average number of employees' votes each day is 68.

To find the average number of employees' votes each day, we need to find the total number of votes cast and divide it by the number of days:

Total votes cast = 86 + 95 + 38 + 47 + 73 + 68 = 407

Number of days = 6

Average number of employees' votes each day = Total votes cast / Number of days

= 407 / 6

≈ 67.8

Rounding this to the nearest whole number gives us an average of 68 employees' votes each day.

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The standard deviation of X to be approximately 0.4852. The correct answer is option (A).

To calculate the standard deviation of X, we need to first calculate the probability of drawing a red marble on the first draw, which is 11/29. The probability of not drawing a red marble on the first draw is 18/29. The probability of drawing a red marble on the second draw, given that we did not draw a red marble on the first draw, is 11/29. Using the formula for the geometric distribution, which models the number of trials until the first success, we can calculate the expected value of X, which is 1/p, where p is the probability of success (11/29 in this case).

Therefore, the expected value of X is 29/11. To calculate the standard deviation of X, we use the formula sqrt(q/p^2), where q is the probability of failure (18/29) and p is the probability of success (11/29). Plugging in these values, we get the standard deviation of X to be approximately 0.4852.  Therefore, the correct answer is option A, 0.4852.

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Kearney's retirement savings when he retired at age 68, assuming monthly compounding of interest, was $429,336.69.

To calculate Kearney's retirement savings at age 68, we need to use the formula for the future value of an annuity due, which is:

FV = PMT x [((1 + r/n[tex])^(n*t)[/tex] - 1) / (r/n)] x (1 + r/n)

Where:

Plugging in the numbers, we get:

FV = 200 x [((1 + 0.055/12[tex])^(12*38)[/tex] - 1) / (0.055/12)] x (1 + 0.055/12)

FV = $429,336.69

Therefore, Kearney's retirement savings at age 68 would be approximately $429,336.69, assuming he invested $200 per month in securities with an average annual return of 5.5% and monthly compounding of interest. It's important to note that this calculation assumes that Kearney did not withdraw any money from his retirement savings during the 38-year period. Additionally, the actual value of his retirement savings could be different based on fluctuations in the market and any fees or taxes associated with his investments.

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The baker bought approximately 17.5 pounds of flour.

Let's use algebra to solve the problem. Let x be the number of pounds of flour that the baker bought. We know that the cost of the flour is $15.05 and the price per pound is $0.86. So we can set up the equation:

$15.05 = $0.86 x

To solve for x, we can divide both sides by $0.86:

x = $15.05 ÷ $0.86

x ≈ 17.5

Therefore, the baker bought approximately 17.5 pounds of flour.

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The measure of each arc in the circle is given by: 360 degrees / n

where n= number of spokes

If the spokes on a bicycle wheel divide the wheel into congruent sections, then each section is an equal angle at the center of the circle. Since there are "n" spokes on the wheel, the circle will be divided into "n" congruent sections.

Therefore, the measure of each arc in the circle is given by:

= 360 degrees / n

For example, if there are 18 spokes on the wheel, then each arc will have a measure of:

360 degrees / 18 = 20 degrees

So each arc would measure 20 degrees.

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After evaluating the integral ∫√(x-x²)dx, we get:

∫√u (1 - 2x) du, with the limits of integration 0 to 1/4

To evaluate the integral ∫√(x-x²)dx using the indicated table of integrals, you should look for an entry in the table that matches the given integral's form. Unfortunately, I do not have access to the specific table you are referring to. However, I can guide you on how to approach this problem.

First, you should make a substitution:

let u = x - x², then du = (1 - 2x)dx. To proceed with this substitution, you'll need to rewrite the integral in terms of 'u' and 'du'. Notice that when x = 1/2, u = 1/4.

Therefore, you can change the limits of integration as well: x = 0 corresponds to u = 0, and x = 1 corresponds to u = 0.

Now,
∫√(x-x²)dx = (1/2) ∫(1-4x+4x²-3)⁽¹/²⁾ dx

Now, we can look up the integral in the table of integrals, which indicates that:

∫(1-4x+4x²-3)⁽¹/²⁾ dx = (1/2) [ (x-1)√(1-4x+4x²) + 2arcsin(2x-1) ] + C

Therefore, substituting this result back into the original integral, we get:

∫√(x-x²)dx = (1/2) [ (x-1)√(1-4x+4x²) + 2arcsin(2x-1) ] + C

where C is the constant of integration.

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Answer: So the second model is 0.2667 feet longer than the first.

Step-by-step explanation: 8 inches * (1/12 feet per inch) * (1/2.5) = 0.1333 feet

So the length of the first model is 0.1333 feet.

The length of the second model is also at a scale of 1/2.5 feet, so its length can be found directly by multiplying the length of the actual building by the scale factor:

Length of second model = 1/2.5 * 1 foot = 0.4 feet

to make next step we can use difference between these numbers by their lengths: Length of second model - Length of first model = 0.4 feet - 0.1333 feet = 0.2667 feet

To find the maximum height of the soccer ball, we need to determine the vertex of the quadratic function. The vertex is given by the formula:

t = -b/2a

where a = -16 and b = 27 from the given equation:

H = -16t^2 + 27t + 3

Substituting these values into the formula, we get:

t = -27/(2(-16)) = 0.84375

Now that we have the value of t at the vertex, we can find the maximum height by substituting it back into the original equation:

H = -16(0.84375)^2 + 27(0.84375) + 3 = 12.65625

Therefore, the maximum height of the soccer ball is approximately 12.65625 units.

h = -16t^2 + 27t + 3 = -(4t - 27/8)^2 + 921/64

With every number t, h [tex]\leq[/tex] 921/64.

Therefore, the maximum height of the soccer ball is 921/64, or aprroximately 14.4(units)

"=" when 4t = 27/8, or t = 27/32.

13. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

14. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

15.  They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

 16.They're  unfit to be a right triangle's side  measures. The forecourt of the longest side( 62 =  36) can not be calculated by adding the places of the two  lower sides( 22 42 =  20).

17. They can, in fact, be the lengths of a right triangle's sides. A Pythagorean  triadic is formed by them.

18. They're  unfit to be a right triangle's side  measures.

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A bag contains five red socks and eight blue socks. Lucky reaches into the bag and randomly selects two socks without replacement, the probability that Lucky will get different colored socks is 10/39.

We can divide the issue into two distinct possibilities and multiply them together to find a solution.

Let's start by thinking about the likelihood of choosing a red sock during the initial draw.

The likelihood of choosing a red sock on the first draw is 5/13 due to the fact that there are only five red socks among the total of thirteen socks (five red plus eight blue).

There are now twelve socks left in the bag after the first one is drawn, with four red and eight blue.

On the second draw, there is an 8/12 chance of choosing a blue sock, which is a different colour.

We add the probabilities together to determine the likelihood that both events (drawing a red sock first and a blue sock second) will occur:

(5/13) * (8/12) = 40/156 = 10/39

Therefore, the probability that Lucky will get different colored socks is 10/39.

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Yes, The given table is an example of a linear function.

Since, The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

To check the following data an example of a linear function.

Now, We can check the slope of given tables as;

⇒ Slope = (3 - (- 2)) / (0 - (- 7))

             = (5 / 7)

⇒ Slope = (8 - 3) / (7 - 0)

             = (5 / 7)

Thus, This table represent the an example of a linear function.

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