5
The edge of a cube-shaped box measures 1 foot long. Three students each
made an observation about the box.
• Grace said that the perimeter of each face is 48 inches long.
• Maddy said that the area of each face is 144 square inches.
• Elena said that the volume of the box is 3 cubic feet.
Whose observations are correct?
A Grace, Maddy, and Elena
B Elena and Grace
C Grace and Maddy
D Elena and Maddy

After 6 fluid ounces , Naya uses 4 glasses as a result.

A unit of weight is an ounce. There are various kinds of ounces, including avoirdupois, troy, and fluid ounces. One sixteenth of a pound is equivalent to one avoirdupois ounce .  A troy ounce, often known as an apothecaries' measure, is equivalent to 480 grains or one-twelfth of a pound. A volume unit is a fluid ounce. 1/8 of a cup, 2 tablespoons, or 6 teaspoons make to one fluid ounce

In Naya's pitcher, there are three glasses of salted lassi.

She fills each glass with six fluid ounces of lassi.

By translating cups to fluid ounces and dividing the entire amount of lassi by the amount put into each glass, we can determine how many glasses Naya uses if she consumes all of the lassi.

8 fluid ounces make constitute a cup.

Consequently, 3 cups equal 24 fluid ounces (3 x 8).

24 divided by 6 results in:

4 glasses are equal to 24/6.

Naya uses four glasses as a result.

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the solution to the equation  is x = -10.use the distributive property of multiplication over addition to simplify the left-hand side of the equation

what is distributive property ?

The distributive property is a mathematical property that is used to simplify expressions that involve multiplication and addition or subtraction. It states that when you multiply a number (or variable) by a sum or difference,

In the given question,

To solve the equation 3(x+6) = x + 8 + x, you can use the distributive property of multiplication over addition to simplify the left-hand side of the equation, and then combine like terms on both sides of the equation.

Here are the steps:

Distribute the 3 on the left-hand side of the equation:

3(x+6) = 3x + 18

Combine the two x terms on the right-hand side of the equation:

3x + 18 = 2x + 8

Subtract 2x from both sides of the equation:

3x - 2x + 18 = 2x - 2x + 8

Simplifying this expression gives:

x + 18 = 8

Finally, subtract 18 from both sides of the equation:

x + 18 - 18 = 8 - 18

Simplifying this expression gives:

x = -10

Therefore, the solution to the equation 3(x+6) = x + 8 + x is x = -10.

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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According to the factor form of the quadratic equation 4 · x² - 484, x = - 11 and x = 11 are the lesser x and the greater x of the expression.

Herein we find a quadratic equation of the form a² · x² - b², whose factor form is introduced below by means of algebra properties:

a² · x² - b² = a² · (x² - b² / a²) = a² · (x - b / a) · (x + b / a)

Where - b /a is the lesser x and + b / a is the greater x.

If we know that a² = 4 and b² = 484, then the roots of the quadratic equation are:

4 · x² - 484 = 4 · (x - 11) · (x + 11)

The lesser x and the greater x are - 11 and 11, respectively.

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Answer: it’s 8.25

Step-by-step explanation: because it’s in between 8 and 8.5. Thank god

Answer: 5 * 5 = 20

20 divided by 1 = 20

If there are 5 apples with an apple:orange ratio of 1:4, there are 20 oranges.

Answer:

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

Step-by-step explanation:

To find the rate of growth of the yeast population, we can use the exponential growth formula:

P(t) = P₀ * e^(kt)

where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.

In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.

Plugging in the values, we get:

160 = 5 * e^(5k)

Divide by 5:

32 = e^(5k)

Now, take the natural logarithm (ln) of both sides to isolate k:

ln(32) = ln(e^(5k))

Using the property that ln(a^b) = b * ln(a):

ln(32) = 5k * ln(e)

Since ln(e) = 1:

ln(32) = 5k

Now, divide by 5:

k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)

So, the growth rate constant k is approximately 0.4641 per hour.

To express the rate of growth as a percentage, multiply the growth rate constant by 100:

0.4641 * 100 ≈ 46.41%

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

The rate of growth of the yeast cells is 31 cells per hour.

The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.

In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.

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The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.

Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.

We are to find the coordinates of the vertices of the image.

We know that

if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :

(a, b)   ⇒    (-a, -b).

So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes

A(-3, 0)   ⇒  (3, 0)

B(-2, 3)   ⇒   (2, -3)

C(-1, 1)    ⇒   (1, -1).

Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).

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Therefore, 65% of all nurses have a starting salary of more than $71,725.31.

Random variable: X, the starting salary of a randomly selected nurse.

b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)

Using the Z-score formula:

z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≥ 1.03) ≈ 0.1492

Therefore, P (X ≥ 78371.8) ≈ 0.1492.

c) P (X ≤ 91407.1)

Using the Z-score formula:

z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probability in the standard normal table or using a calculator, we get:

P(Z ≤ 2.30) ≈ 0.9893

Therefore, P (X ≤ 91407.1) ≈ 0.9893.

d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)

Using the Z-score formula:

z1 = (78371.8 - 67694) / 10333 ≈ 1.03

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probabilities in the standard normal table or using a calculator, we get:

P(Z < 1.03) ≈ 0.8498

P(Z < 2.30) ≈ 0.9893

Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.

e) P (X ≤ 41861.5)

Using the Z-score formula:

z = (41861.5 - 67694) / 10333 ≈ -2.50

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≤ -2.50) ≈ 0.0062

Therefore, P (X ≤ 41861.5) ≈ 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.

g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.

Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.

Using the Z-score formula:

z = (X - μ) / σ

Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:

0.3853 = (X - 67694) / 10333

Solving for X, we get:

X = 10333(0.3853) + 67694 ≈ 71725.31

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Before we begin we must know:

An equation is an algebraic equality in which letters (unknowns) with unknown value appear. The degree of an equation is given by the largest exponent of the unknown. To solve an equation is to determine the value or values of the unknowns that transform the equation into an identity.

Solving the equation, we will first add what is in the first, I mean:

Now we must convert to a fraction, first we will put the greater number on top and the smaller number below.

Now the last thing we should do is divide both numbers by nine (9), and we will have the following:

∴ The result of our equation is y = 9

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Answer: Amaterasu

Step-by-step explanation: The sun goddess Amaterasu is considered the most important of the Shinto gods because she is believed to be the ancestor of the Japanese imperial family, and therefore the protector of the Japanese people. She is also associated with agriculture, which was a vital part of Japanese society.

Answer:

1. Using the kinematic equation h(t) = -16t^2 + v0t + h0, where h0 is the initial height, v0 is the initial velocity, and t is time, we have:

h(t) = -16t^2 + 72t + 4

To find the maximum height, we need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 72:

t = -b/2a = -72/(2(-16)) = 2.25 seconds

To find the maximum height, we substitute t = 2.25 seconds into the equation for h(t):

h(2.25) = -16(2.25)^2 + 72(2.25) + 4 = 82 feet

The range of the function h(t) is [4, 82], since the T-shirt starts at a height of 4 feet and reaches a maximum height of 82 feet before falling back to the ground.

2. Using the same kinematic equation as before, we have:

h(t) = -16t^2 + 80t + 3

To find the maximum height, we again need to find the vertex of the parabolic function h(t). The t-coordinate of the vertex is given by t = -b/2a, where a = -16 and b = 80:

t = -b/2a = -80/(2(-16)) = 2.5 seconds

To find the maximum height, we substitute t = 2.5 seconds into the equation for h(t):

h(2.5) = -16(2.5)^2 + 80(2.5) + 3 = 80 feet

The range of the function h(t) is [3, 80], since the T-shirt starts at a height of 3 feet and reaches a maximum height of 80 feet before falling back to the ground.

Step-by-step explanation:

The similes in the story are:

A simile is a figure of speech that compares two things using the words "like" or "as." It is a type of metaphor that helps to create a vivid and engaging image in the reader or listener's mind.

Similes are often used in literature, poetry, and everyday language to make a comparison more relatable and understandable. For example, "He is as brave as a lion" or "She sings like an angel." These similes help to convey a certain quality or trait by comparing it to something else that is well-known or familiar.

Note: It seems there may be a typo in the last sentence of the story, where the word "e" appears instead of "elephant" or another word that would make sense in context.

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The empty set (also known as the null set) is a subset of every set because it does not contain any elements that are not in the set. In other words, if A is any set, then every element of the empty set is also an element of A, since the empty set contains no elements. This satisfies the definition of a subset, which states that for any two sets A and B, A is a subset of B if every element of A is also an element of B. Therefore, the empty set is a subset of every set.

~~~Harsha~~~

The list of intervals on which the function is constant is:

A(-4,-3) and B(3,6).

A constant function is a function that returns the same value regardless of the input. In other words, for every value of x, the output of the function is the same constant value. For example, the function f(x) = 2 is a constant function because no matter what value of x is plugged into the function, the output will always be 2. Constant functions are often represented by horizontal lines on a graph.

A list of intervals in a graph typically indicates the range of values or intervals on a given axis. For example, on the x-axis of a graph, a list of intervals might represent the range of values from a lower bound to an upper bound, with each interval indicating a range of values that falls between two specific points on the axis. On the y-axis, the intervals might represent the range of possible values for the dependent variable or data being plotted. In general, the intervals on a graph provide a visual representation of the range of values being considered or plotted.

The given function in the graph on intervals A(-4,-3) and B(3.6) is a horizontal line which means there is no change in output. So the function is constant.

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The probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

What is fraction?

A fraction is a method of representing a part of a whole or a ratio of two numbers. It is a number that is written in the form of one integer (the numerator) over another integer (the denominator), separated by a line or slash.

The probability of selecting the 3 oldest people in a group of 10 people depends on the assumption that all 10 people are distinct individuals and that the selection process is truly random.

The total number of ways to select 3 people from a group of 10 people is given by the combination formula:

C(10, 3) = 10! / (3! * 7!) = 120

This means that there are 120 possible ways to select a group of 3 people from a group of 10 people.

Since we are interested in selecting the 3 oldest people, we assume that the 3 oldest people are identified and we only need to select them from the group of 10 people. There is only 1 way to select the 3 oldest people out of the group of 10 people.

Therefore, the probability of selecting the 3 oldest people in a group of 10 people is:

P = Number of ways to select the 3 oldest people / Total number of ways to select 3 people from a group of 10 people

P = 1 / 120

P = 0.0083

So, the probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.

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Answer:

the mass of the solid glass cylinder is approximately 350.67 grams.

Step-by-step explanation:

The diameter of the cylinder is 3 centimeters, which means that its radius is 1.5 centimeters (half the diameter). The area of the base of the cylinder is the area of a circle, calculated as pi (π) multiplied by the radius squared:

Base area = π x radius^2

Base area = π x (1.5 cm)^2

Base area = 7.07 cm^2 (approximately)

The volume of the cylinder is calculated by multiplying the area of the base by the height:

Cylinder Volume = Base Area x Height

Cylinder volume = 7.07 cm^2 x 31 cm

Cylinder volume = 219.17 cm^3 (approximately)

Now that we know the volume of the cylinder, we can calculate its mass using the density of the glass:

Mass = Density x Volume

Mass = 1.6 g/cm^3 x 219.17 cm^3

Mass = 350.67 grams (approximately)

Answer:          To answer these questions using the simple interest formula, we need to know the values of P (the principal or initial investment), r (the interest rate), and t (the time period in years).

In this case, P = $325, r = 0.08 (8% expressed as a decimal), and t = 15.

Using the simple interest formula, I = P ∙ r ∙ t, we can calculate:

I = $325 ∙ 0.08 ∙ 15 = $390

Therefore, Charlie's initial investment will earn $390 in interest over the 15-year period.

To calculate how much money Charlie will have after the 15 years, we need to add the interest earned to the initial investment.

The total amount of money that Charlie will have after the 15 years is:

Total amount = Initial investment + Interest earned

Total amount = $325 + $390

Total amount = $715

Therefore, Charlie will have $715 after 15 years.

Step-by-step explanation:

The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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Answer: a.     c(n) = 15 + 0.75(n - 10)

b.   15 + 0.75(n - 10) = 2.50(n - 10)=

Simplifying and solving for n, we get:

n = 50

c.  n > 50

Step-by-step explanation:

a. The cost c of the credit union account in terms of the number of checks written n can be expressed as:

c(n) = 15 + 0.75(n - 10)

The first term, 15, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

The cost c of the bank account in terms of the number of checks written n can be expressed as:

c(n) = 2.50(n - 10)

The first term, 0, represents the monthly cost of the account, and the second term represents the additional cost per check beyond the first 10 free checks.

b. We want to find the number of checks for which the bank account is more expensive than the credit union account. Let x be the number of checks that makes the cost of the two accounts equal. Then we have:

15 + 0.75(n - 10) = 2.50(n - 10)

Simplifying and solving for n, we get:

n = 50

So if the number of checks written in a month is greater than 50, the bank account will be more expensive than the credit union account.

c. The solution to the inequality is:

n > 50

This means that the number of checks written in a month must be greater than 50 for the bank account to be more expensive than the credit union account.

Answer:

29i

Step-by-step explanation:

While multiplying complex numbers we should remember that i^2=−1.

As p=2 and q=5i,

(2−5i)(p+q)i

= (2−5i)(2+5i)i

= (2×2+2×5i−5i×2−5i×5i)×i

= (4+10i−10i−25×i2)×i

= (4+10i−10i−25×(−1))×i

= (4+25)×i

=29i

The next entry on the long division would be 0.054, and 0.0054

Long division is a method of dividing two numbers using a step-by-step process. Here's how to perform long division:

Step 1: Write the dividend (the number being divided) and the divisor (the number you're dividing by) in the long division format, with the dividend inside the division symbol and the divisor outside.

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For the given equation we have horizontal length of 5 and vertical width of 4 units. The graph that depicts this hyperbola is: Option B.

A hyperbola is a particular kind of conic section in mathematics, which is a curve created by the intersection of a cone and a plane. The collection of all points in a plane that have a constant difference between them and two fixed points, known as the foci, is referred to as a hyperbola. The distance between the foci is referred to as this consistent difference and is represented by the symbol 2a.

Two separate branches that are mirror reflections of one another make up a hyperbola. The vertices are the two locations where the two branches of a hyperbola are joined.

For the given equation of the parabola, the value of a and b = 5 and 4.

Thus, we have horizontal length of 5 and vertical width of 4 units

The graph that depicts this hyperbola is: Option B.

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The complete question is:

Therefore, the surface area of the prism is approximately 557.2 square feet when rounded to the nearest tenth.

The surface area of a prism is the total area of all its faces, including the bases. The formula for finding the surface area of a prism depends on the shape of its base. For a right prism, the surface area can be found by adding the area of the two bases to the lateral area, which is the sum of the areas of all the rectangular faces of the prism.

Here,

To find the surface area of the prism, we need to find the area of each of the six rectangular faces that make up the prism, and then add them together. The two triangular faces are congruent, so we can find the area of one and double it to get the total area of the two.

The area of a triangle is given by:

Area = (1/2) x base x height

For the given triangles, the base is 9 ft and the height is 8 ft (for one triangle) and 10 ft (for the other triangle), so the areas are:

Area1 = (1/2) x 9 ft x 8 ft

= 36 ft²

Area2 = (1/2) x 9 ft x 10 ft

= 45 ft²

The total area of the two triangles is:

TotalArea = 2 x (Area1 + Area2)

= 2 x (36 ft² + 45 ft²)

= 162 ft²

Now, we need to find the area of the four rectangular faces. Each face is a rectangle with a length of 13 ft and a height of 7.6 ft, so the area of each face is:

AreaRect = length x height

= 13 ft x 7.6 ft

= 98.8 ft²

The total area of the four rectangular faces is:

TotalRectArea = 4 x AreaRect

= 4 x 98.8 ft²

= 395.2 ft²

To find the total surface area of the prism, we add the area of the two triangles to the area of the four rectangular faces:

TotalSA = TotalRectArea + TotalArea

= 395.2 ft² + 162 ft²

= 557.2 ft²

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C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.

A parabola is a symmetry U-shaped plane curve. This graph represents a quadratic function using the formula y = ax2 + bx + c. The parabola's direction and shape are determined by the nonzero integers a and b in this equation, whereas the parabola's location on the x-axis is affected by the linear coefficient b and the constant coefficient c. A parabola has a vertex, or the location where the curve changes direction, and it can open upward or downward.

given

We can start by noting that since the vertex of a parabola always lies in the centre of the two x-intercepts for a quadratic function, the parabola's vertex must be at the coordinates (0, 3).

The equation can be expressed in the vertex form of a quadratic function as follows:

[tex]C(t) = a(t-h)^2 + k[/tex]

where "a" is the vertical stretch or compression factor and (h, k) is the vertex. Using the values from the table as inputs, we obtain:

[tex]C(t) = a(t - 0)^2 + 3[/tex]

We still need to determine what "a" is worth. To do this, we can utilise a different table row, for instance (1, 4):

[tex]4 = a(1 - 0)^2 + 3[/tex]

1 = a

C(t equation )'s is thus: [tex]C(t) = (t - 0)^2 + 3[/tex] or condensed, [tex]C(t) = t^2 + 3[/tex] as the vertical stretch or compression factor and (h, k) is the vertex.

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There are 13,800 different recital programs possible.

What is permutation?

In mathematics, a permutation is an arrangement of objects in a specific order. In other words, a permutation is a way of selecting a certain number of objects from a larger set and arranging them in a particular order.

The pianist has 25 choices for the first piece, then 24 choices for the second piece (since one piece has already been played), and 23 choices for the third piece (since two pieces have already been played). Therefore, the number of different recital programs possible is:

25 x 24 x 23 = 13,800

There are 13,800 different recital programs possible.

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a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

Explain probability

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.

According to the given information

a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.

We want to find P(Y < 2070). Standardizing Y, we get:

Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31

Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.

b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².

We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:

Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)

To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.

Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6

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