What is the unit price for a piece of cheese if 1. 24 pounds costs $11. 25

If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.

Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.

Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800

Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.

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100 mph going there, 50 coming back

Answer:-48

(6)2-4×7×3

36-89

-48

The expected profit in the long run can be determined by calculating the expected value of the total revenue from selling the lobsters. The expected total revenue is the sum of the expected revenue from selling the lobsters to the restaurant and the from selling the lobsters to the grocery store.

The expected value of the revenue from selling the lobsters to the restaurant can be calculated by multiplying the expected price per pound from the restaurant by the expected amount of lobsters caught in a day. The expected price per pound from the restaurant follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

The expected value of the revenue from selling the lobsters to the grocery store can be calculated by multiplying the expected price per pound from the grocery store by the expected amount of lobsters caught in a day. The expected price per pound from the grocery store is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

Given the expected values of the total revenue from selling the lobsters to the restaurant and the grocery store, Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can run several simulations with different percentages of lobsters to be sold to the restaurant and compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can calculate the expected value of the total revenue from selling the lobsters to the restaurant and the grocery store, and then run several simulations with different percentages of lobsters to be sold to the restaurant to compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

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The valid reasons to use a sample instead of evaluating a much larger population are contacting the whole population would be only marginally more accurate than a sample. A sample can be chosen to validate a specific idea about the population.

Contacting the entire population would be time consuming.
1. Contacting the whole population would be only marginally more accurate than a sample: This is a valid reason because a well-designed sample can often provide an accurate estimate of the population, while using significantly fewer resources.
2. Sampling is a random process, and therefore more accurate than measuring the whole population: This statement is incorrect. A random sample can provide an unbiased estimate, but it is not necessarily more accurate than measuring the entire population.
3. A sample can be chosen to validate a specific idea about the population: This is a valid reason because sampling can be used to test hypotheses or ideas about the population without having to evaluate every member of the population.
4. Contacting the entire population would be time-consuming: This is a valid reason because sampling can save time and resources compared to attempting to gather data from every individual in a population.

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Answer:

r = \(\sqrt{11}\)

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use \((\frac{b}{2} )^{2}\) to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get \((\frac{2}{2} )^{2} =(1)^{2} =1\)

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get \((\frac{4}{2} )^{2}=(2)^{2} =4\)

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides \(\sqrt{r^{2}} =\sqrt{11}\) to get r = \(\sqrt{11}\)

Answer:

The answer is 3.

Step-by-step explanation:

The length of midsegment of the trapizoid with bases 35 and 71 is 53.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional shape that has both a perimeter and an area. The bases of the trapezoid are the two sides of the form that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the smallest distance between two parallel sides. Calculating a trapezoid's area is easy since its opposite sides are parallel to one another.

A trapezoid differs from other quadrilaterals in that it has the following characteristics:

The length of midsegment is sum of bases divided by 2

therefore midsegment = (35 + 71)/2 = 53.

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a 21.8 g sample of osmium would occupy a volume of approximately 0.9646 cm³.

To calculate the volume occupied by a sample of osmium, we can use the formula:

Volume = Mass / Density

Given:

Mass = 21.8 g

Density = 22.6 g/cm³

Substituting these values into the formula:

Volume = 21.8 g / 22.6 g/cm³

Simplifying:

Volume = 0.9646 cm³

what is volume?

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It quantifies the extent or capacity of an object or substance in terms of how much space it occupies.

In mathematical terms, volume is typically measured in cubic units (such as cubic meters, cubic centimeters, or cubic inches). It is calculated by multiplying together the three dimensions of the object (length, width, and height) or by using specific formulas depending on the shape of the object.

For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height. The volume of a cylinder can be calculated using the formula πr²h, where r is the radius of the base and h is the height.

Volume is an essential measurement in various fields such as physics, engineering, chemistry, and everyday life. It helps determine capacities, quantities, displacements, and the amount of space occupied by objects or substances.

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Using the conversion factor, Joselyn bought 2700 grams of chocolate candy

A conversion factor is a numerical ratio used to convert a measurement from one unit to another. It is a mathematical expression that is used to convert a quantity expressed in one unit of measure into an equivalent quantity expressed in another unit of measure.

To convert 2.7 kg to grams, Joselyn would use a conversion factor between kilograms and grams. The conversion factor is 1000 grams per 1 kilogram, which means there are 1000 grams in one kilogram.

So, to convert 2.7 kg to grams, Joselyn would multiply 2.7 kg by the conversion factor

2.7 kg x 1000 g/kg = 2700 g

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Answer:

3

Step-by-step explanation:

Since it's at the same time of the day, the ratio between the height of the person and the shadow they cast will stay the same. So the man's height to shadow ratio is 6:8 = 3:4. The son's height to shadow ratio would be the same so x:4 = 3:4 therefore his height is 3 feet.

Answer:

Option (A)

Step-by-step explanation:

By the property of a parallelogram,

Opposite sides of a parallelogram are equal and parallel to each other.

AD = BC and DC = AB

9x - 40 = 8x - 34

9x - 8x = 40 - 34

x = 6

4y + 20 = 6x - 4

4y - 6x = -24

2y - 3x = -12

Now we will substitute the value of x,

2y = 3x - 12

2y = 3(6) - 12

2y = 6

y = 3

Therefore, Option (A) will be the correct option.

The value of x is 6 and y is 3.

Given that,

ABCD is a parallelogram in which sides of parallelogram are,

AB = 8x- 34, BC = 6x- 4

CD = 9x-40, AD = 4y+20

We have to find,

The value of x and y in a quadrilateral ABCD ?

According to the question,

By the property of a parallelogram,

The opposite sides of a parallelogram are equal and parallel to each other.

AD = BC

CD = AB

Substitute the values of AD and BC and solve for the value of x and y,

\(\rm 4y +20 = 6x -4 \\\\4y - 6x = -4 -20\\\\4y -6x = -24\\\\ Divide \ by \ 2 \ on \ both \ the \ sides\\\\ 2y - 3x = -12\)

And

\(CD = AB \\\\9x-40=8x-34\\\\9x-8x = 40-34\\\\x = 6\)

Substitute the value of x in equation 1,

\(2y-3x = -12\\\\2y - 3(6) = -12\\\\2y = -18=-12\\\\2y = -12+18\\\\2y = 6\\\\y = \dfrac{6}{2}\\\\y = 3\)

Hence, The value of x is 6 and y is 3.

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Range is about subtracting the lowest number from the highest number!

The lowest number is 54.

The highest number is 65.

65 - 54 = 11

Answer:

11

Step-by-step explanation:

Subtract the highest and lowest values 65-54, and you get 11

Answer:

The \(y\)-intercept is \(\boxed{3}\)

Step-by-step explanation:

The \(y\)-intercept of line is just the point where the \(y\)-axis and the line. From the given line, we can see that the \(y\)-axis and the line that models the temperature on a certain winter day since sunrise \((0,3)\). Also, the question just asked us for the \(y\)-coordinate of the \(y\)-intercept so \(3\)

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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The expression to represent the amount of money Dion spent on fruit is 3x + 2y.

The amount of money Dion spent is $6.15

Expression are numbers, symbols and operators grouped together that show the value of something.

Dion bought 3 pounds of oranges and 2 pounds of grapefruit.

The expression to represents the amount of money Dion spent on fruit is as follows:

let

x = cost of each pounds of oranges

y = cost of each pounds of grapefruit

Therefore,

total cost = 3x + 2y

Let's evaluate the expression

total cost = 3(0.99) + 2(1.59)

total cost = 2.97 + 3.18

total cost = 6.15 dollars

Therefore, Dion spent $6.15

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Answer:

y = -2x + 9

Step-by-step explanation:

(1-3)/(-2--3) = -2/1 = -2 = m

y = mx + b

1 = -2(4) + b

9 = b

y = -2x + 9

Answer:
3(x - 8) < 15

Step-by-step explanation:

3(x - 8) < 15

3x - 24 < 15

3x < 39

x < 13

The constant of proportionality of the equation y = 0.25x is k = 0.25.

Direct proportionality means that the dependence between the two variable x and y in this case, is such that the quotient of those two variable is constant.

We have a direct variation in the form of y = kx

where k is the constant of proportionality.

compare y = kx and y = 0.25x we get,

k = 0.25(constant of proportionality)

y/x = 0.25 .quotient of x and y is constant so we can say that x and y are directly proportional.

Therefore the constant of proportionality of the equation y = 0.25x is k = 0.25.

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Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Answer:

25

Step-by-step explanation:

a/5+3=8

a/5=8-3

a/5=5

cross multiply

a=5×5

a=25

The probability that a sample of 1,000 voters would yield a sample proportion in favor of the candidate within 4 percentage points of the actual proportion is  98.6%.

We are given that the population proportion, p, is 0.6, and we want to find the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of p. Let's first find the standard error of the sample proportion:

SE = √(p*(1-p) / n)

where p is the population proportion, 1-p is the proportion of voters who do not support the candidate, and n is the sample size.

Substituting the given values, we get:

SE = √(0.6 * 0.4 / 1000) = 0.01549193338

To find the probability that the sample proportion is within 0.04 of p, we can use the normal distribution and the z-score formula:

z = (sample proportion - p) / SE

where the sample proportion follows a normal distribution with mean p and standard deviation SE.

Substituting the values, we get:

z = (0.64 - 0.6) / 0.01549193338 = 2.590020246

z = (0.56 - 0.6) / 0.01549193338 = -2.590020246

Using a standard normal distribution table or calculator, we can find the area under the curve between z = -2.590020246 and z = 2.590020246 to be approximately 0.986.

Therefore, the probability that a sample of 1000 voters would yield a sample proportion within 0.04 of the actual proportion is approximately 0.986 or 98.6%.

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The best estimate of the product is b) 1 times 10.

The expression (7/8)8(1/10) can be simplified by canceling out the factor of 8 in the numerator and denominator. This yields the expression 7/10. Therefore, the best estimate of this expression would be 1 times 10, since 7/10 is closest to 1 when rounded to the nearest whole number, and 10 is the closest whole number to the denominator of 7/10.

Thus, the answer is option b, 1 times 10. It is important to note that when estimating products or other mathematical expressions, it is important to consider the context and choose an estimate that is reasonable and makes sense in the given situation.

Correct Question :

Which expression is the best estimate of the product of (7/8)8(1/10)?

a) 0 times 8

b) 1 times 10

c) 7 times 8

d) 1 times 8

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The right alternative to replace the question mark (?) is nik.

The given series is wfb, tgd, qhg. To find the right alternative to replace the question mark (?), we need to identify the pattern in the series.

Looking at the series, we can observe that the first letter in each term is moving back two steps in alphabetical order, while the second letter is moving forward one step, and the third letter is moving forward one step and then moving forward two steps which means that it is moving forward with "n+1" steps where n = 0, 1, 2, 3,...

Applying this, we can determine the next term in the series:

w → t → q → n

f → g → h → i

b → d → g → k

So, the next term comes to be "nik"

Therefore, the right alternative to replace the question mark (?) is "nik".

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The given function, y = 3sin(2x - 4) + 1, can be written in the form y = 3sin(2(x - 2)) + 1, with an amplitude of 3, period of π, horizontal shift of 2 units to the right, and vertical shift of 1 unit up.

The given function is y=3sin(2x-4)+1. To write it in the form of y=a sin b(x-h)+k, we will use the following formula of a sinusoidal function:y=a sin b(x-h)+kwhere a = amplitude, b = period (in radians), h = horizontal shift, and k = vertical shift.

According to this formula, we have to obtain the amplitude, period, horizontal shift, and vertical shift of the given function. Here is the solution: Given function: y = 3sin(2x - 4) + 1

We can see that the given function contains an expression of the form sin(bx) where b = 2. To find the period of the function, we use the formula: T = 2π/b, where T is the period of the function. Substitute the value of b in the formula,T = 2π/2 = π

Thus, the period of the function is π. To obtain the amplitude of the function, we need to find the maximum and minimum values of the function. The maximum value of sinθ is 1 and the minimum value is -1.

Therefore, the maximum value of the function is: 3sin(2x - 4) + 1 ≤ 3(1) + 1 = 4 and the minimum value of the function is:3sin(2x - 4) + 1 ≥ 3(-1) + 1 = -2

Thus, the amplitude of the function is (4 - (-2))/2 = 3. We can see that the function is of the form y = a sin(bx - c). Thus, we can factor out the 2 from the argument of the sin function to get:y = 3sin(2(x - 2) + 1). Now, we have obtained the function in the required form. Therefore, the answer isy = 3sin(2(x - 2) + 1).

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The likelihood of the journey being completed in under 30 hours or exceeding 60 hours is zero.

The PDF for a continuous random variable denotes the likelihood that the variable will assume a given value.

The time duration of the trip represents the stochastic variable in this scenario, with possible values ranging from 30 to 60 hours.

The PDF is given by:

\(f(t) = \frac{1}{21} \quad \text{for} \quad 30 \le t \le 60\)

This implies that all timeframes between the range of 30 to 60 hours have an equal chance of occurring during the trip. The probability of the trip's duration is certain to be 1. Thus, there is an impossibility of the journey taking either under 30 hours or over 60 hours with a probability of 0.

The probability of the trip lasting for any duration adds up to 100%.

The reason for this is that the PDF represents a probability distribution, which necessitates a complete probability of 1.

The likelihood of the journey being completed in under 30 hours or exceeding 60 hours is zero.

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Answer:

A. You bring $40 to the carnival. You need to keep at least $5 for the bus ride home. how many $3 dollar rides can you go on

Step-by-step explanation:

Answer:

ummmmmmmmmm m?mmm?mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Answer:

The difference in the areas of the cross section is 32 m²

Step-by-step explanation:

The given parameters are;

The height of the rectangular pyramid = 8 meters

The length of the base of the pyramid = 7 meters

The width of the base of the pyramid = 15 meters

Whereby triangular cross sections are formed through the vertex and perpendicular to the base, and to each other, we have;

The sides of the two triangles consists of the following;

1) Two slant height of the pyramid each

2) The two perpendicular lines joining the midpoints of the opposite sides of the base of the pyramid with length equal to the length of the adjacent side to the sides from which they are drawn which are 15 meters and 7 meters

3) The two lines and the corresponding slant height form triangles cross section which are perpendicular to each other.

the slant height, \(h_l\), is given as follows;

\(h_l\) = √(8² + (15/2)²) ≈ 10.966

For the triangular cross section with base = 15 m

The area of the cross section = 1/2 × Base₁₅ × Height = 1/2 × 15 m × 8 m = 60 m²

For the triangular cross section with base = 7 m

The area of the cross section = 1/2 × Base₇ × Height = 1/2 × 7 m × 8 m = 28 m²

The difference in the areas of the cross section = 60 m² - 28 m² = 32 m².

Answer:

Step-by-step explanation:

if Charles bought the sneakers for 6.30 and wants to re-sell them with 40% more,

first lets see how much is 40% of 6.30

(6.30*40)/100=2.52

he will resell the shoes with

6.30+2.52=8.82

Answer:

$\(8.82\)

Step-by-step explanation:

\(6.30 + 0.4\times6.30 = 8.82\)

\(\therefore\) Charles will sell the sneakers at a price of $\(8.82\)

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