Conditional probability. Please solve 60 points! :)

On the number line ranging from negative 1 fourth to positive 3 fourths, labeled in increments of 1 fourth, three points are labeled: A, B, and C.

Points A and B are positioned between 0 fourths and 1 fourth, while point C falls between 1 fourth and 2 fourths.

The corresponding labels for each point are as follows: Point A corresponds to the number negative 1 fourth, Point B corresponds to the number zero, and Point C corresponds to the number positive 1 fourth.

To match the points on the number line with their respective labels, we examine their positions relative to the increments of 1 fourth on the number line.

Since point A is between 0 fourths and 1 fourth, it is positioned to the left of zero. Therefore, the corresponding number for Point A is negative 1 fourth.

Point B is between 0 fourths and 1 fourth, suggesting it is positioned directly on zero. Thus, the number for Point B is zero.

Point C is positioned between 1 fourth and 2 fourths, which implies it is located to the right of zero. Hence, the corresponding number for Point C is positive 1 fourth.

Therefore, the correct matching of points A, B, and C with their respective numbers on the number line is as follows: Point A corresponds to negative 1 fourth, Point B corresponds to zero, and Point C corresponds to positive 1 fourth.

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The expressions that represent a 20% discount off the price of an item that originally costs d dollars are A. 0.8d and C. d-0.2d.

A 20% discount off the original price means that the discounted price is equal to 80% (100% - 20%) of the original price. Therefore, we can calculate the discounted price by multiplying the original price (d) by 0.8 (representing 80%).

Expression A (0.8d) represents the discounted price as 80% of the original price (d), so it is correct. Expression C, d-0.2d" represents a 20% discount off the price of an item that originally costs d dollars.

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Full question is:

Select all the expressions below which represent a 20% discount off the price of an item that originally costs d dollars.

A. 0.8d

B. d-0.2

C. d-0.2d

D. 1-0.2d​​

The correct system of equations that represents the cost relationships for the two cell phone plans is option(a) Megacell: y = 0.1x + 14.8 and Fun Fone: y = 0.08x + 18.5.

Let's break down the given information for the two cell phone plans:

Megacell charges $14.80 per month plus 10 cents per minute for every minute over 200. This means that the cost (y) for using x minutes over 200 can be represented by the equation y = 0.1x + 14.8. The $14.80 represents the fixed monthly charge, and the 10 cents per minute over 200 is added to the total cost.

Fun Fone charges $18.50 per month plus 8 cents per minute for every minute over 200. This means that the cost (y) for using x minutes over 200 can be represented by the equation y = 0.08x + 18.5. The $18.50 represents the fixed monthly charge, and the 8 cents per minute over 200 is added to the total cost.

Therefore, the correct system of equations that represents these cost relationships is Megacell: y = 0.1x + 14.8 and Fun Fone: y = 0.08x + 18.5, which corresponds to option A.

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Answer:

I believe it's A

Step-by-step explanation:

Answer:

  27

Step-by-step explanation:

You want to know the ACT composite test score for the 87.49th percentile, given the ACT scores have a mean of 21.0 and a standard deviation of 5.2.

The Z-table in the first attachment shows you the Z-value of the 87.49th percentile is 1.10+0.05 = 1.15.

The corresponding score is ...

  X = μ +σZ

  X = 21.0 +5.2·1.15 ≈ 27

A learner must earn a score of 27 to be at the 87.49th percentile on the ACT composite test.

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The expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

To find the perimeter of the quadrilateral, we need to add up the lengths of all its sides.

The given polynomial expressions represent the lengths of the sides of the quadrilateral:

Side 1: 3x + 5

Side 2: 4x^2 - 7x

Side 3: 5x + 1

Side 4: 2x^2 + 13x

To find the perimeter, we add these side lengths together:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

= (3x + 5) + (4x^2 - 7x) + (5x + 1) + (2x^2 + 13x)

To simplify, we combine like terms:

Perimeter = 3x + 5 + 4x^2 - 7x + 5x + 1 + 2x^2 + 13x

= (4x^2 + 2x^2) + (3x - 7x + 5x + 13x) + (5 + 1)

= 6x^2 + 14x + 6

Therefore, the expression for the perimeter of the quadrilateral is 6x^2 + 14x + 6.

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the total number of magazines they receive is 4

Let's assume the number of letters received by the Brady family is 'L'.

According to the given information:

- The number of magazines is the same as the number of letters, so the number of magazines is also M = L.

- The number of ads be A

- The number of ads is three more than the number of letters, so the number of ads is 'L + 3' = A.

- The number of bills is five more than the number of ads, so the number of bills is B = 'A + 5' = L + 3 + 5 = L + 8

Now, we can set up an equation to represent the total number of pieces of mail received:

L + M + A + B = 27

L + L + (L + 3) + (L + 8) = 27

4L + 11 = 27

4L = 16

L = 4

M = 4

Since the number of magazines is the same as the number of letters (L), the total number of magazines is also 4

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The points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1) are x = 2 + (√585)/2 and x = 2 - (√585)/2.



To find the points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1), we need to consider the coordinates of the points on the x-axis.

Since we are dealing with the x-axis, the y and z coordinates of the points will be zero. Let's assume the coordinates of the points on the x-axis as (x, 0, 0).

The distance between two points can be calculated using the distance formula:Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

In this case, the coordinates of point P are (2, -3, -1) and the distance is given as 25‾√. Plugging these values into the distance formula, we get:

25‾√ = √((x - 2)^2 + (-3 - 0)^2 + (-1 - 0)^2)

Simplifying further:

625/4 = (x - 2)^2 + 9 + 1

625/4 = (x - 2)^2 + 10

Solving for x:

(x - 2)^2 = 625/4 - 10

(x - 2)^2 = 625/4 - 40/4

(x - 2)^2 = 585/4

Taking the square root of both sides:

x - 2 = ±√(585/4)

x = 2 ± (√585)/2

Therefore, the points on the x-axis that are at a distance of 25‾√ from point P(2, -3, -1) are x = 2 + (√585)/2 and x = 2 - (√585)/2.

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The distance formula can be used to calculate the distance from Francesca's house to the beach by considering the coordinates of the two locations and applying the formula, which involves finding the difference between the x-coordinates and the y-coordinates, and then using the Pythagorean theorem.

To find the distance from Francesca's house to the beach using the distance formula, we need to consider the coordinates of both locations. Let's assume Francesca's house has coordinates (x1, y1) and the beach has coordinates (x2, y2). The distance formula is derived from the Pythagorean theorem and states that the distance between two points in a coordinate plane is given by √((x2 - x1)² + (y2 - y1)²).

To apply the distance formula, we substitute the coordinates of Francesca's house and the beach into the formula.

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The given options are 1.7 cm, 71, 21, 1.7 cm, 2.2 cm, 4.3 cm, 53, 377, 2.1 cm, 42, 3.2 cm, 3.8 cm, 3.6 cm, 2.9 cm, 2.5 cm, 34, and 8 cm.

The summary of the answer is that the length of the side is 2.2 cm.

In trigonometry, it is common to use the concept of a right triangle to relate the lengths of its sides with the trigonometric functions. However, without additional context or information about the triangle or the specific problem, it is not possible to determine the length of the side accurately.

Among the given options, the length of the side closest to 2.2 cm is 2.2 cm itself. Therefore, based on the options provided, we can conclude that the length of the side is 2.2 cm. However, it is important to note that without further information or context, this is an assumption based solely on the given options and may not be the correct answer in a different context or problem.

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Based on the information provided, the statement that is true about the samples is: Eldrick can use both of these samples to find the mean frequency of each duck.

The table shows two samples of duck populations at a migratory site, with Sample 1 and Sample 2. Each sample contains data on the number of ducks from different species: Mallard, Wood Duck, Green Wing Teal, and American Widgeon.

Since Eldrick has data from both Sample 1 and Sample 2, he can combine the information to calculate the mean frequency of each duck species. By averaging the frequencies of each species across the two samples, he can obtain a more accurate representation of the duck populations at the migratory site.

The other statements are not supported by the given information. There is no indication of excessive variability or the need for an additional sample. Using both samples allows for a more comprehensive analysis and a better estimation of the mean frequency of each duck species.

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Devika poured out 4.2 ounces of water, which is approximately 35% of the water in the full bottle.

To find out how much water was in the full bottle, we can set up a proportion.

Let x represent the amount of water in the full bottle (in ounces). We know that 4.2 ounces is 35% of x.

We can set up the proportion:

4.2 / x = 35 / 100

To solve for x, we can cross-multiply:

4.2 * 100 = 35 * x

420 = 35x

Dividing both sides of the equation by 35:

420 / 35 = x

12 = x

Therefore, there were approximately 12 ounces of water in the full bottle.

So, Devika estimated that she poured out about 35% of the water in the full bottle, which corresponds to approximately 4.2 ounces.

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The number of pages read in 72 minutes is 144 pages.

When given a table of values, the relationship between the values ​​is often expressed as a rule or an equation. A formula that links the number of pages in a book to the number of minutes it takes to read it is often used in book reviews or book reports.  

Rule relating to the minutes, x, to the number of pages, y

Let us assume that reading x minutes corresponds to y pages. In other words, we want to identify an equation or formula that links the two variables.

The number of pages read in one minute is calculated by dividing the total number of pages by the total time it takes to read them.

y / x = k, where k is the constant of variation, or the number of pages that can be read in one minute. If the number of pages is directly proportional to the number of minutes, then the k value remains constant.

If we solve for y, we get the following:

y = kx

When the minutes equal 72, we will find the number of pages.

We know that k is a constant, so we may use any of the given (x, y) pairs.

The given minute value is x, and we want to find the corresponding page value, y.

Let us assume that 120 pages can be read in 60 minutes.

We may solve for k using this information:120 / 60 = k2 = k

Now that we know k, we may use the equation to determine the number of pages that can be read in 72 minutes:

y = kx

y = 2 * 72y = 144

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To calculate a 15% tip for a restaurant bill of $42.40, we multiply the bill amount by 0.15 to find the tip amount. The result will provide the tip amount, which can be added to the bill to get the total amount to pay. Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To calculate a 15% tip, we take 15% of the bill amount. The tip amount is found by multiplying the bill amount by the decimal equivalent of 15%, which is 0.15.

Given the restaurant bill of $42.40, we can find the tip amount by performing the calculation: $42.40 * 0.15 = $6.36.

Therefore, a 15% tip for a restaurant bill of $42.40 is $6.36.

To check if the answer is reasonable, we can consider the percentage amount and the total bill. A 15% tip is generally considered an average or moderate tip amount. Given the bill of $42.40, a tip of $6.36 seems reasonable in relation to the bill total.

However, tipping customs may vary in different regions or based on personal preferences. It is always advisable to consider the overall service quality and local tipping practices when determining an appropriate tip amount.

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Given, Brad's dinner bill, including a 16% tip, is $10.44. We need to find the amount of the bill before the tip.Let the amount of the bill before the tip be x.So, the bill amount including the tip of 16% will be x + (16/100)x or (116/100)x.

This is because, if x is the bill amount, the tip is 16% of x, which is (16/100)x, then the total bill amount will be x + (16/100)x or (116/100)x.

We know that the bill amount including the tip is $10.44. So,(116/100)x = 10.44=> x = (10.44 × 100)/116= $9 (approx) Therefore, the amount of the bill before the tip is $9. Answer: $9.

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Average seawater salinity = 3.5%100g of salt has been left after seawater has evaporatedThe mass of salt dissolved in 100g of seawater will be 3.5g (since salinity is 3.5%)Let x be the mass of seawater that needs to be evaporated to leave 100g of salt.

According to the law of conservation of mass,Mass of salt in the solution before = Mass of salt in the solution afterTherefore, 100g of salt that has been left after evaporation was originally dissolved in x grams of seawater.

Therefore, the mass of salt in that seawater would have been 3.5% of x.Using the above information, we can write an equation as follows:0.035x = 100g Therefore, about 2857.14 g or 2.85714 kg of seawater needs to have evaporated to leave 100 g of salt.

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The line of best fit is a straight line that best fits the scattered data points on a scatterplot. It is represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In this particular case, the equation of the line of best fit is y = -6x + 97, where x represents the number of absences and y represents the final grade.

This means that for every additional absence a student has, their final grade is expected to decrease by 6 points. The y-intercept of 97 means that if a student had zero absences, their predicted final grade would be 97.

It is important to note that the line of best fit is a prediction, and not a definitive statement about the relationship between the variables. While it can provide some insight into the relationship between the number of absences and final grade, there may be other factors that are not taken into account by the model.

Additionally, the equation of the line of best fit is only valid within the range of the data used to create the model. Extrapolating beyond this range may not produce accurate predictions.

Overall, the line of best fit is a useful tool for analyzing relationships between variables, but it should be used with caution and in conjunction with other analyses to get a complete understanding of the relationship between variables.

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The equation will have all three terms (ax^2+bx+c) if the quadratic equation (x−r)(x+r) is expanded.

When we expand (x−r)(x+r), we get x^2 - r^2. This means that the resulting quadratic equation will have a quadratic term (x^2) and a constant term (-r^2).

However, to have opposite solutions, the constant term (-r^2) should be equal to zero. This implies that r = 0, making the constant term zero.

Therefore, the quadratic equation with opposite solutions, obtained by multiplying (x−r)(x+r), will have a quadratic term (ax^2), a linear term (bx), and a constant term (c) where c = 0.

Hence, the correct answer is option 3: a quadratic term and a linear term only (ax^2+bx).

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Given the information provided, we need to determine the length of the bridge (a) and the distance between the two people.

The person at point Q is 30 meters away from the bridge, and the angle between the bridge and the line of sight from P to Q is 70.9 degrees.

To solve this problem, we can use trigonometry. We can consider the triangle formed by the bridge, point P, and point Q. The angle at point P is 70.9 degrees, and the side opposite to this angle is the length of the bridge (a). The side adjacent to this angle is the distance between the two people.

Using trigonometric functions, we can set up the following equation:

tan(70.9 degrees) = a / 30 meters

By rearranging the equation, we can solve for a:

a = 30 meters * tan(70.9 degrees)

This gives us the length of the bridge.

To find the distance between the two people, we can use the Pythagorean theorem. The distance between the two people is the hypotenuse of the triangle formed by the bridge, point P, and point Q. Using the length of the bridge (a) and the distance from point Q to the bridge (30 meters), we can calculate the distance between the two people using the equation:

Distance = sqrt(a^2 + 30^2)

By substituting the value of a, we can calculate the final answer for the distance between the two people, rounding to two decimal places if necessary.

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Pencils of Brand B is better to buy .

Given,

Brand A = 28 pencils for $4. 19

Brand B = 72 pencils for$9.12

Now,

Firstly for Brand A,

Total pack = 28 pencils

Price = $4.19

Hence ,

Price of one pencil = $4.19/28

Price of one pencil  = $0.14

Secondly for Brand B,

Total pack = 72 pencils

Price = $9.12

Hence ,

Price of one pencil = $9.12/72

Price of one pencil  = $0.126

Thus charlie should buy pencils from brand B.

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In a fraction, the common denominator refers to the lowest common multiple of the denominators of the fractions. If you use the common multiple from part A as the common denominator, the models in the example will be different and at the same time the same.

A common multiple is the product of two or more factors that are common. In other words, it is a number that is a multiple of two or more integers.

Let's take an example of finding the common multiple of 6 and 8:

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ...

The multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

Therefore, the common multiples of 6 and 8 are: 24, 48, 72, 96, 120, 144, ...

The models would be different because the common denominator is the lowest common multiple of the denominators of the fractions. If we use the common multiple as the denominator, the size of the models may change.

Let's take an example:

Suppose we have two fractions, 1/2 and 2/3. The denominators are 2 and 3. The common multiple is 6.

If we use 6 as the common denominator, the fractions become:

1/2 = 3/6 (we multiplied the numerator and denominator by 3)

2/3 = 4/6 (we multiplied the numerator and denominator by 2)

The models would be different because the sizes are based on the denominators of the fractions. If we change the denominator, the size of the model may also change.

The models would be the same because they represent the same fractions.

Even though the size of the model may change, the fractions still represent the same value.

In the above example, 1/2 and 3/6 represent the same value, and 2/3 and 4/6 represent the same value.

Therefore, the models are still representing the same value even though they may be different in size.

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It is not valid to use the Multiplication Rule to estimate the probability of both siblings having blue eyes because it assumes independence between the occurrences, which does not hold true when considering eye color in siblings.

Using the Multiplication Rule in this case is not appropriate because it assumes that the occurrence of blue eyes in siblings is independent. However, in reality, the occurrence of eye color in siblings is influenced by genetic factors, which means that the probability of having blue eyes is not entirely independent for each sibling.

The Multiplication Rule is commonly used when dealing with independent events, where the outcome of one event does not affect the outcome of another. For example, flipping two coins is an independent event, as the outcome of the first coin flip does not impact the outcome of the second flip.

However, when considering eye color in siblings, the occurrence of blue eyes is influenced by shared genetic factors. The probability of having blue eyes is affected by the eye color genes inherited from parents, making it a dependent event. Siblings share a portion of their genetic makeup, increasing the likelihood of having similar eye colors.

To calculate the probability of both siblings having blue eyes, it would be more appropriate to consider conditional probability, taking into account the family's eye color history and genetic factors.

Therefore, in this case, it is not valid to use the Multiplication Rule to estimate the probability of both siblings having blue eyes because it assumes independence between the occurrences, which does not hold true when considering eye color in siblings.

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Answer:

[tex] \frac{100}{360} = \frac{l}{25.2\pi} [/tex]

[tex]l = \frac{5}{18} (25.2\pi) = 7\pi[/tex]

The exact length of the arc is 7π cm.

a) The radian measure is 5π radians.

b) The radian measure is (3πr)/2 radians.

To determine the radian measure corresponding to a certain number of orbits in a circular orbit, we need to know the circumference of the orbit.

The circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius.

Let's assume the radius of the circular orbit is denoted by "r."

(a) To find the radian measure for 2.5 orbits:

The total angle covered in 2.5 orbits is equivalent to 2.5 times the full circumference of the orbit.

Angle = 2.5 * (2πr) = 5πr

Therefore, the radian measure corresponding to 2.5 orbits is 5π radians.

(b) To find the radian measure for 3/2 orbit:

The total angle covered in 3/2 of an orbit is equivalent to (3/2) times the full circumference of the orbit.

Angle = (3/2) * (2πr) = 3πr/2

Therefore, the radian measure corresponding to 3/2 of an orbit is (3πr)/2 radians.

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According to given information, the sales tax on the stuffed elephant is $0.79.

To calculate the sales tax of a stuffed elephant, which Alexis sells for $14.95, and the sales tax is 5% of the sale price, you need to calculate the sale price. The sale price will give us an idea of how much sales tax will be charged.

Using the given information; The price of the stuffed elephant is $14.95.The sales tax is 5% of the sale price, which is unknown.

Now, we need to calculate the sale price. The sale price includes the price of the stuffed elephant plus the sales tax. We can represent the sale price as: X = Price of the stuffed elephant + Sales tax where, Price of the stuffed elephant = $14.95 and Sales tax = 5% of the sale price. To calculate the sale price, we need to use the formula: X = Price of the stuffed elephant + Sales tax.

Substituting the values: X = $14.95 + 0.05X. To solve for X, we will need to simplify and isolate the variable on one side of the equation. X - 0.05X = $14.950.95X = $14.95X = $15.74. Therefore, the sale price of the stuffed elephant is $15.74. Now, let's calculate the sales tax, which is 5% of the sale price. Sales tax = 5% of $15.74. Sales tax = (5/100) × $15.74. Sales tax = $0.79.

Therefore, the sales tax on the stuffed elephant is $0.79.

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The sales tax on the stuffed elephant is approximately $0.75.

A sales tax is a consumption tax imposed by the government on the sale of goods and services. A conventional sales tax is levied at the point of sale, collected by the retailer, and passed on to the government.

A business may be liable for sales taxes in a given jurisdiction if it has a presence there, which can be a brick-and-mortar location, an employee, or an affiliate, depending on the laws in that jurisdiction.

Alexis sells a stuffed elephant for $14.95, and the sales tax is 5% of the sale price. About how much is the sales tax on the elephant?

The given price of the stuffed elephant is $14.95.

5% of the price of the stuffed elephant is the sales tax.

To calculate the sales tax, use the formula:

Sales tax = (5/100) x price of the stuffed elephant

Sales tax= (5/100) x $14.95

Sales tax= 0.05 x $14.95

Sales tax= $0.7475

Sales tax≈ $0.75

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To find the average number of spots per beetle, we need to calculate the total number of spots and divide it by the total number of beetles.

In the given sample:

50 beetles had 4 spots each.

The remaining beetles had 6 spots each.

Let's calculate the total number of spots:

For the 50 beetles with 4 spots each:

50 beetles * 4 spots/beetle = 200 spots

Now, let's calculate the number of remaining beetles:

Total beetles - Beetles with 4 spots = 8 beetles - 50 beetles = -42 beetles

Since we cannot have a negative number of beetles, it seems there might be an error in the given information. If we assume that all the remaining beetles had 6 spots each, we can proceed with the calculations.

For the remaining beetles with 6 spots each:

-42 beetles * 6 spots/beetle = -252 spots

Now, let's calculate the total number of spots by adding the spots from the first group and the spots from the second group:

200 spots + (-252 spots) = -52 spots

Again, we encounter a negative number, which does not make sense in this context. It seems there is an inconsistency or error in the given information. Please double-check the data to provide accurate values for the number of beetles and the number of spots in each group.

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An engineer is designing a storage compartment in an aircraft. The compartment's volume is 72 cubic meters. The width is 2 meters longer than the length. The height is 1 meter less than the length. the dimensions of the compartment are 4m × 6m × 3m.

Find the dimensions of the compartment. Solution:The volume of a rectangular prism is given by;[tex]`V= l × w × h`[/tex] Given that the compartment's volume is 72 cubic meters, let's substitute[tex]`V = 72`[/tex]

cubic meters;[tex]`l × w × h = 72`[/tex]

We also know that;[tex]w = l + 2h = l - 1[/tex]

Substituting w and h in terms of l, we get;[tex]`l(l+2)(l-1) = 72`[/tex]Expanding,

we get;[tex]`l(l²-1) + 2(l²-1) = 72`[/tex]

Simplifying, we get;[tex]`l³ + l² - 2l - 74 = 0`[/tex]

We will use trial and error method to find one of the roots,`l= 4`.

By substitution, we get;[tex]w = 4 + 2 = 6m h = 4 - 1 = 3m[/tex]

Thus, the compartment dimensions are 4m × 6m × 3m. The width is 6 meters, the length is 4 meters, and the height is 3 meters.

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The missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

Based on the given information, we can determine the missing values as follows:

Original price (OP): Let's assume the original price is represented by "x".

Rate of discount (RD): We know that the amount of discount (AD) is Php60.00, and we can calculate the rate of discount as follows:

AD = OP * RD

60 = x * RD

Sale Price (SP): The sale price is calculated by subtracting the amount of discount from the original price:

SP = OP - AD

240 = x - 60

To find the missing values, we need to solve the system of equations formed by the two equations above:

Equation 1: 60 = x * RD

Equation 2: 240 = x - 60

From Equation 2, we can rearrange it to solve for x:

x = 240 + 60

x = 300

Substituting x = 300 into Equation 1, we can solve for the rate of discount:

60 = 300 * RD

RD = 60 / 300

RD = 0.2

Therefore, the missing values are:

Original price (OP): Php300.00

Rate of discount (RD): 0.2 or 20%

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The inequality that represents the given condition is d ≠ 28, meaning that the number of days of sunshine, represented by d, is not equal to 28.

The inequality d ≠ 28 represents a comparison between the number of days of sunshine, denoted by d, and the value 28. In this case, it signifies that the number of days of sunshine is not equal to 28. The "≠" symbol denotes inequality, indicating that d and 28 are not the same. If d were equal to 28, the inequality would not hold true. However, any value other than 28 would satisfy this inequality, whether it is greater than or less than 28.

This inequality allows for flexibility in the value of d, as long as it is not exactly 28. For example, if d = 25, the inequality holds true because 25 is not equal to 28. Similarly, if d = 30, the inequality still holds true because 30 is also not equal to 28. Thus, the inequality d ≠ 28 encompasses all possible values for the number of days of sunshine except for 28, capturing the idea that the value of d cannot be exactly 28 in this context.  

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The approximate wavelength of the light is 353 nm.

The diffraction angle, θ, can be determined using the formula θ = mλ/d, where m is the order of the bright band, λ is the wavelength of light, and d is the spacing between the grating lines.

In this case, we are given the diffraction angle (θ = 45.0°), the order (m = 1), and the spacing between the grating lines (d = 1/500 mm = 2 μm).

To find the wavelength, we rearrange the formula to solve for λ:

λ = d * sin(θ) / m.

Substituting the given values:

λ = (2 μm) * sin(45.0°) / 1,

λ = 2 μm * 0.7071,

λ ≈ 1.414 μm.

To convert micrometers to nanometers, we multiply by 1000:

λ ≈ 1414 nm.

Therefore, the approximate wavelength of the light is 1414 nm, which corresponds to the closest option provided, 943 nm.

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